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Asymptotics in Relativistic Nuclear Physics
AMalakhov
Joint Institute for Nuclear Research DubnaJoint Institute for Nuclear Research Dubna
The 1st CBM-Russia-JINR Collaboration Meeting
Dubna May 19-22 2009
2
AMBaldin and LADidenko Fortschr Phys 38 (1990) 4 261-332
I + II rarr 1 + 2 + 3 + hellip
bik = - (ui ndash uk)2
ui = pi mi
i k = I II 1 2 3 hellip
uk = pk mk
AMBaldin AIMalakhov and ANSissakian Physics of Particles and Nuclei Vol32 Suppl 1 2001 ppS4-S30
3
Classification of relativistic nuclear collisions on bik
bik ~ 10-2
classic nuclear physics
01 bik lt 1
intermediate domain
bik gtgt 1
nuclei should be considered asquark-gluon systems
4
5
e
Emiddotddp3 = Cmiddotexp(-TT0)
p + Cu rarr (1800) + hellip
6
Beam
+ Target
Beam energy(AGeV)
Intensity(1sec)
Target(mgcm2)
Cross-section
(mbsrcm2)
Yield
(1sec)
Number
of events (1day)
JSi + Si 6 109 30 10-10 10-4 10
Ta + Ta 6 109 30 10-7 10-3 100
AGLitvinenko AIMalakhov PIZarubin
JINR Rapid Communications 1-93 p27
7
Correlation Depletion Principle (CDP)CDP was offered by NNBogolyubov in statistical physics as universal property of the probability distributions for particle location in ordinary space-time (r t)
The principle is based on the idea that the correlation between largely spaced parts of a macroscopic system practically vanishes and the distribution is factorized
CDP in Relativistic Nuclear Physics was suggested by AMBaldin in four-velocity space
Due to complementary of rik and bik this principle is quite opposite to the Bogolyubov CDP
The Bogolyubov CDP is valid for |ri - rk|2 rarr while the Baldin CDP is fulfilled for |ri - rk|2 rarr 0 (or bik rarr ) according to the asymptotic freedom
8
W | rarr Wα Wβ bαβ rarr
α = I β = II
I + II rarr 1 + hellip
d2σ dbII 1dx1 rarr FI FII (bII 1 N1)bII 1 = (uII ndash u1)2
N1 ndash cumulative number
9
Vα - middle point of system
ui - four-velocity of particle i in the system
uk - four-velocity of particle k in the system
bαi ltlt bαk
Example of the Isolated system Wα and Wβ (FI and FII)
The important example of the Isolated system rarr JETS
bαi = - (Vα ndash ui)2
bαk = - (Vα ndash uk)2
Isolated system
10
Invariant definition of hadron jetsThe jet is a claster of hadrons with small relative bik
The jet axis (a unit four-vector)
The summation is performed over all the particles belonging to a selected particle group (claster)
It is possible to determine the squared four-velocity with respect to the axis
V = Σ(ui radic(Σui)2
Vo2 ndash V 2 = 1
bk = - (V ndash uk)2
i
11
12
13
14
bull Distribution of π ndash mesons on bk in jets of hadron-hadron and hadron-nucleus collisions at high energies are UNIVERSAL They do not depend either on the colliusion energy or on the type of fragmenting system
bull This universality of properties of four-dimensional hadron jets indicates that the hadronisation of quark systems is defined by the dynamics of interaction of a color charge with QCD vacuum
15
For jets ltbkgt ~ 1
For hadrons ltbkgt ltlt 1
The jet is well allocated if the condition satisfies
bs I gt ltbkgt
bs II gt ltbkgt
16
Automodelity Principle
bik rarr asymptotic regimes rarr decreasing of the probability distributions (cross-sections) W and factorization (DCP)
Asymptotic regimes rarr automodelity distributions W
Automodelity solutions means reduction of number of arguments of researched function due to importance only some combinations of independent variables rarr similarity parameters
17
Automodelity W ie the assumption of existence universal asymptotic in the relativistic nuclear collisions (nuclear intermediate and a quark-gluon) rarr HYPOTHESIS demanding an experimental substantiation
18
П=min[12(uINI +uII NII)
2]
19
20
А М Балдин А А Балдин Physof Element Part and Atomic Nuclei V29 1998
21
22
23
24
I + II rarr 1 + hellip
(NIPI + NIIPII ndash p1)2 = (NIm0 + NIIm0 + Δ)2
Δ is the mass of the particle providing conservation of the barion number strangeness and other quantum numbers
25
Baldin AM Malakhov AI JINR Rapid Communications No1(87)-98 1998 pp5-12
26
PREDICTIONS
27
Asymptotics
s(2mImII) (uIuII) = ch2Y
Пmin= (mT2m0)[1+radic1+(2-m1
2)mT2]
N 0
28
The analytical representation for П leads to the following conclusions
There is the limiting value of П at high energies
The effective number of nucleons involved in the reaction decreases with increasing collision energy
Probability of observation of antinuclei and fragments in the central rapidity region is small
Strange particles yield increases with increasing collision energy
The ratio of particle to antiparticle and nucleus to antinucleus production cross-section goes to the unit while energy rising
29
30
A2 = min [-Σ(Vα ndash uk)2 - Σ(Vβ ndash ui )2 ]
A3 = min [-Σ(Vα ndash uk)2 - Σ(Vβ ndash ui )2 - Σ(Vγ ndash uj )2 ]
helliphelliphelliphelliphelliphelliphellip
etc
K i
K i j
31
Distribution of jet axes is well described QCD as result of the production of quarks and gluons (ie color charges)
In other words rarr studying of jets is studying of deformation of vacuum by a color charge studying of the deconfinment
32
Observability of particles from which can consist quarks
Observability of short-lived particles is based on two necessary criteria
1) The production cross section for really observable products of secondary interaction (decay) can with a sufficient accuracy presented in the form of two factors
σ = σp Wd
Where Wd is interpreted as the decay probability (or secondary interaction probability) a suggested particle σp its production cross section
2) Universality of Wd or similarity of the Wd properties in various reactions
I + II rarr Jetα + Jetβ
σ = σp Wα(bk)Wβ(bk)
33
34
Conclusion
CBM at SIS-100 is a unique opportunity for investigation of asymptotic of nuclear interactions
35
Thank you
2
AMBaldin and LADidenko Fortschr Phys 38 (1990) 4 261-332
I + II rarr 1 + 2 + 3 + hellip
bik = - (ui ndash uk)2
ui = pi mi
i k = I II 1 2 3 hellip
uk = pk mk
AMBaldin AIMalakhov and ANSissakian Physics of Particles and Nuclei Vol32 Suppl 1 2001 ppS4-S30
3
Classification of relativistic nuclear collisions on bik
bik ~ 10-2
classic nuclear physics
01 bik lt 1
intermediate domain
bik gtgt 1
nuclei should be considered asquark-gluon systems
4
5
e
Emiddotddp3 = Cmiddotexp(-TT0)
p + Cu rarr (1800) + hellip
6
Beam
+ Target
Beam energy(AGeV)
Intensity(1sec)
Target(mgcm2)
Cross-section
(mbsrcm2)
Yield
(1sec)
Number
of events (1day)
JSi + Si 6 109 30 10-10 10-4 10
Ta + Ta 6 109 30 10-7 10-3 100
AGLitvinenko AIMalakhov PIZarubin
JINR Rapid Communications 1-93 p27
7
Correlation Depletion Principle (CDP)CDP was offered by NNBogolyubov in statistical physics as universal property of the probability distributions for particle location in ordinary space-time (r t)
The principle is based on the idea that the correlation between largely spaced parts of a macroscopic system practically vanishes and the distribution is factorized
CDP in Relativistic Nuclear Physics was suggested by AMBaldin in four-velocity space
Due to complementary of rik and bik this principle is quite opposite to the Bogolyubov CDP
The Bogolyubov CDP is valid for |ri - rk|2 rarr while the Baldin CDP is fulfilled for |ri - rk|2 rarr 0 (or bik rarr ) according to the asymptotic freedom
8
W | rarr Wα Wβ bαβ rarr
α = I β = II
I + II rarr 1 + hellip
d2σ dbII 1dx1 rarr FI FII (bII 1 N1)bII 1 = (uII ndash u1)2
N1 ndash cumulative number
9
Vα - middle point of system
ui - four-velocity of particle i in the system
uk - four-velocity of particle k in the system
bαi ltlt bαk
Example of the Isolated system Wα and Wβ (FI and FII)
The important example of the Isolated system rarr JETS
bαi = - (Vα ndash ui)2
bαk = - (Vα ndash uk)2
Isolated system
10
Invariant definition of hadron jetsThe jet is a claster of hadrons with small relative bik
The jet axis (a unit four-vector)
The summation is performed over all the particles belonging to a selected particle group (claster)
It is possible to determine the squared four-velocity with respect to the axis
V = Σ(ui radic(Σui)2
Vo2 ndash V 2 = 1
bk = - (V ndash uk)2
i
11
12
13
14
bull Distribution of π ndash mesons on bk in jets of hadron-hadron and hadron-nucleus collisions at high energies are UNIVERSAL They do not depend either on the colliusion energy or on the type of fragmenting system
bull This universality of properties of four-dimensional hadron jets indicates that the hadronisation of quark systems is defined by the dynamics of interaction of a color charge with QCD vacuum
15
For jets ltbkgt ~ 1
For hadrons ltbkgt ltlt 1
The jet is well allocated if the condition satisfies
bs I gt ltbkgt
bs II gt ltbkgt
16
Automodelity Principle
bik rarr asymptotic regimes rarr decreasing of the probability distributions (cross-sections) W and factorization (DCP)
Asymptotic regimes rarr automodelity distributions W
Automodelity solutions means reduction of number of arguments of researched function due to importance only some combinations of independent variables rarr similarity parameters
17
Automodelity W ie the assumption of existence universal asymptotic in the relativistic nuclear collisions (nuclear intermediate and a quark-gluon) rarr HYPOTHESIS demanding an experimental substantiation
18
П=min[12(uINI +uII NII)
2]
19
20
А М Балдин А А Балдин Physof Element Part and Atomic Nuclei V29 1998
21
22
23
24
I + II rarr 1 + hellip
(NIPI + NIIPII ndash p1)2 = (NIm0 + NIIm0 + Δ)2
Δ is the mass of the particle providing conservation of the barion number strangeness and other quantum numbers
25
Baldin AM Malakhov AI JINR Rapid Communications No1(87)-98 1998 pp5-12
26
PREDICTIONS
27
Asymptotics
s(2mImII) (uIuII) = ch2Y
Пmin= (mT2m0)[1+radic1+(2-m1
2)mT2]
N 0
28
The analytical representation for П leads to the following conclusions
There is the limiting value of П at high energies
The effective number of nucleons involved in the reaction decreases with increasing collision energy
Probability of observation of antinuclei and fragments in the central rapidity region is small
Strange particles yield increases with increasing collision energy
The ratio of particle to antiparticle and nucleus to antinucleus production cross-section goes to the unit while energy rising
29
30
A2 = min [-Σ(Vα ndash uk)2 - Σ(Vβ ndash ui )2 ]
A3 = min [-Σ(Vα ndash uk)2 - Σ(Vβ ndash ui )2 - Σ(Vγ ndash uj )2 ]
helliphelliphelliphelliphelliphelliphellip
etc
K i
K i j
31
Distribution of jet axes is well described QCD as result of the production of quarks and gluons (ie color charges)
In other words rarr studying of jets is studying of deformation of vacuum by a color charge studying of the deconfinment
32
Observability of particles from which can consist quarks
Observability of short-lived particles is based on two necessary criteria
1) The production cross section for really observable products of secondary interaction (decay) can with a sufficient accuracy presented in the form of two factors
σ = σp Wd
Where Wd is interpreted as the decay probability (or secondary interaction probability) a suggested particle σp its production cross section
2) Universality of Wd or similarity of the Wd properties in various reactions
I + II rarr Jetα + Jetβ
σ = σp Wα(bk)Wβ(bk)
33
34
Conclusion
CBM at SIS-100 is a unique opportunity for investigation of asymptotic of nuclear interactions
35
Thank you
3
Classification of relativistic nuclear collisions on bik
bik ~ 10-2
classic nuclear physics
01 bik lt 1
intermediate domain
bik gtgt 1
nuclei should be considered asquark-gluon systems
4
5
e
Emiddotddp3 = Cmiddotexp(-TT0)
p + Cu rarr (1800) + hellip
6
Beam
+ Target
Beam energy(AGeV)
Intensity(1sec)
Target(mgcm2)
Cross-section
(mbsrcm2)
Yield
(1sec)
Number
of events (1day)
JSi + Si 6 109 30 10-10 10-4 10
Ta + Ta 6 109 30 10-7 10-3 100
AGLitvinenko AIMalakhov PIZarubin
JINR Rapid Communications 1-93 p27
7
Correlation Depletion Principle (CDP)CDP was offered by NNBogolyubov in statistical physics as universal property of the probability distributions for particle location in ordinary space-time (r t)
The principle is based on the idea that the correlation between largely spaced parts of a macroscopic system practically vanishes and the distribution is factorized
CDP in Relativistic Nuclear Physics was suggested by AMBaldin in four-velocity space
Due to complementary of rik and bik this principle is quite opposite to the Bogolyubov CDP
The Bogolyubov CDP is valid for |ri - rk|2 rarr while the Baldin CDP is fulfilled for |ri - rk|2 rarr 0 (or bik rarr ) according to the asymptotic freedom
8
W | rarr Wα Wβ bαβ rarr
α = I β = II
I + II rarr 1 + hellip
d2σ dbII 1dx1 rarr FI FII (bII 1 N1)bII 1 = (uII ndash u1)2
N1 ndash cumulative number
9
Vα - middle point of system
ui - four-velocity of particle i in the system
uk - four-velocity of particle k in the system
bαi ltlt bαk
Example of the Isolated system Wα and Wβ (FI and FII)
The important example of the Isolated system rarr JETS
bαi = - (Vα ndash ui)2
bαk = - (Vα ndash uk)2
Isolated system
10
Invariant definition of hadron jetsThe jet is a claster of hadrons with small relative bik
The jet axis (a unit four-vector)
The summation is performed over all the particles belonging to a selected particle group (claster)
It is possible to determine the squared four-velocity with respect to the axis
V = Σ(ui radic(Σui)2
Vo2 ndash V 2 = 1
bk = - (V ndash uk)2
i
11
12
13
14
bull Distribution of π ndash mesons on bk in jets of hadron-hadron and hadron-nucleus collisions at high energies are UNIVERSAL They do not depend either on the colliusion energy or on the type of fragmenting system
bull This universality of properties of four-dimensional hadron jets indicates that the hadronisation of quark systems is defined by the dynamics of interaction of a color charge with QCD vacuum
15
For jets ltbkgt ~ 1
For hadrons ltbkgt ltlt 1
The jet is well allocated if the condition satisfies
bs I gt ltbkgt
bs II gt ltbkgt
16
Automodelity Principle
bik rarr asymptotic regimes rarr decreasing of the probability distributions (cross-sections) W and factorization (DCP)
Asymptotic regimes rarr automodelity distributions W
Automodelity solutions means reduction of number of arguments of researched function due to importance only some combinations of independent variables rarr similarity parameters
17
Automodelity W ie the assumption of existence universal asymptotic in the relativistic nuclear collisions (nuclear intermediate and a quark-gluon) rarr HYPOTHESIS demanding an experimental substantiation
18
П=min[12(uINI +uII NII)
2]
19
20
А М Балдин А А Балдин Physof Element Part and Atomic Nuclei V29 1998
21
22
23
24
I + II rarr 1 + hellip
(NIPI + NIIPII ndash p1)2 = (NIm0 + NIIm0 + Δ)2
Δ is the mass of the particle providing conservation of the barion number strangeness and other quantum numbers
25
Baldin AM Malakhov AI JINR Rapid Communications No1(87)-98 1998 pp5-12
26
PREDICTIONS
27
Asymptotics
s(2mImII) (uIuII) = ch2Y
Пmin= (mT2m0)[1+radic1+(2-m1
2)mT2]
N 0
28
The analytical representation for П leads to the following conclusions
There is the limiting value of П at high energies
The effective number of nucleons involved in the reaction decreases with increasing collision energy
Probability of observation of antinuclei and fragments in the central rapidity region is small
Strange particles yield increases with increasing collision energy
The ratio of particle to antiparticle and nucleus to antinucleus production cross-section goes to the unit while energy rising
29
30
A2 = min [-Σ(Vα ndash uk)2 - Σ(Vβ ndash ui )2 ]
A3 = min [-Σ(Vα ndash uk)2 - Σ(Vβ ndash ui )2 - Σ(Vγ ndash uj )2 ]
helliphelliphelliphelliphelliphelliphellip
etc
K i
K i j
31
Distribution of jet axes is well described QCD as result of the production of quarks and gluons (ie color charges)
In other words rarr studying of jets is studying of deformation of vacuum by a color charge studying of the deconfinment
32
Observability of particles from which can consist quarks
Observability of short-lived particles is based on two necessary criteria
1) The production cross section for really observable products of secondary interaction (decay) can with a sufficient accuracy presented in the form of two factors
σ = σp Wd
Where Wd is interpreted as the decay probability (or secondary interaction probability) a suggested particle σp its production cross section
2) Universality of Wd or similarity of the Wd properties in various reactions
I + II rarr Jetα + Jetβ
σ = σp Wα(bk)Wβ(bk)
33
34
Conclusion
CBM at SIS-100 is a unique opportunity for investigation of asymptotic of nuclear interactions
35
Thank you
4
5
e
Emiddotddp3 = Cmiddotexp(-TT0)
p + Cu rarr (1800) + hellip
6
Beam
+ Target
Beam energy(AGeV)
Intensity(1sec)
Target(mgcm2)
Cross-section
(mbsrcm2)
Yield
(1sec)
Number
of events (1day)
JSi + Si 6 109 30 10-10 10-4 10
Ta + Ta 6 109 30 10-7 10-3 100
AGLitvinenko AIMalakhov PIZarubin
JINR Rapid Communications 1-93 p27
7
Correlation Depletion Principle (CDP)CDP was offered by NNBogolyubov in statistical physics as universal property of the probability distributions for particle location in ordinary space-time (r t)
The principle is based on the idea that the correlation between largely spaced parts of a macroscopic system practically vanishes and the distribution is factorized
CDP in Relativistic Nuclear Physics was suggested by AMBaldin in four-velocity space
Due to complementary of rik and bik this principle is quite opposite to the Bogolyubov CDP
The Bogolyubov CDP is valid for |ri - rk|2 rarr while the Baldin CDP is fulfilled for |ri - rk|2 rarr 0 (or bik rarr ) according to the asymptotic freedom
8
W | rarr Wα Wβ bαβ rarr
α = I β = II
I + II rarr 1 + hellip
d2σ dbII 1dx1 rarr FI FII (bII 1 N1)bII 1 = (uII ndash u1)2
N1 ndash cumulative number
9
Vα - middle point of system
ui - four-velocity of particle i in the system
uk - four-velocity of particle k in the system
bαi ltlt bαk
Example of the Isolated system Wα and Wβ (FI and FII)
The important example of the Isolated system rarr JETS
bαi = - (Vα ndash ui)2
bαk = - (Vα ndash uk)2
Isolated system
10
Invariant definition of hadron jetsThe jet is a claster of hadrons with small relative bik
The jet axis (a unit four-vector)
The summation is performed over all the particles belonging to a selected particle group (claster)
It is possible to determine the squared four-velocity with respect to the axis
V = Σ(ui radic(Σui)2
Vo2 ndash V 2 = 1
bk = - (V ndash uk)2
i
11
12
13
14
bull Distribution of π ndash mesons on bk in jets of hadron-hadron and hadron-nucleus collisions at high energies are UNIVERSAL They do not depend either on the colliusion energy or on the type of fragmenting system
bull This universality of properties of four-dimensional hadron jets indicates that the hadronisation of quark systems is defined by the dynamics of interaction of a color charge with QCD vacuum
15
For jets ltbkgt ~ 1
For hadrons ltbkgt ltlt 1
The jet is well allocated if the condition satisfies
bs I gt ltbkgt
bs II gt ltbkgt
16
Automodelity Principle
bik rarr asymptotic regimes rarr decreasing of the probability distributions (cross-sections) W and factorization (DCP)
Asymptotic regimes rarr automodelity distributions W
Automodelity solutions means reduction of number of arguments of researched function due to importance only some combinations of independent variables rarr similarity parameters
17
Automodelity W ie the assumption of existence universal asymptotic in the relativistic nuclear collisions (nuclear intermediate and a quark-gluon) rarr HYPOTHESIS demanding an experimental substantiation
18
П=min[12(uINI +uII NII)
2]
19
20
А М Балдин А А Балдин Physof Element Part and Atomic Nuclei V29 1998
21
22
23
24
I + II rarr 1 + hellip
(NIPI + NIIPII ndash p1)2 = (NIm0 + NIIm0 + Δ)2
Δ is the mass of the particle providing conservation of the barion number strangeness and other quantum numbers
25
Baldin AM Malakhov AI JINR Rapid Communications No1(87)-98 1998 pp5-12
26
PREDICTIONS
27
Asymptotics
s(2mImII) (uIuII) = ch2Y
Пmin= (mT2m0)[1+radic1+(2-m1
2)mT2]
N 0
28
The analytical representation for П leads to the following conclusions
There is the limiting value of П at high energies
The effective number of nucleons involved in the reaction decreases with increasing collision energy
Probability of observation of antinuclei and fragments in the central rapidity region is small
Strange particles yield increases with increasing collision energy
The ratio of particle to antiparticle and nucleus to antinucleus production cross-section goes to the unit while energy rising
29
30
A2 = min [-Σ(Vα ndash uk)2 - Σ(Vβ ndash ui )2 ]
A3 = min [-Σ(Vα ndash uk)2 - Σ(Vβ ndash ui )2 - Σ(Vγ ndash uj )2 ]
helliphelliphelliphelliphelliphelliphellip
etc
K i
K i j
31
Distribution of jet axes is well described QCD as result of the production of quarks and gluons (ie color charges)
In other words rarr studying of jets is studying of deformation of vacuum by a color charge studying of the deconfinment
32
Observability of particles from which can consist quarks
Observability of short-lived particles is based on two necessary criteria
1) The production cross section for really observable products of secondary interaction (decay) can with a sufficient accuracy presented in the form of two factors
σ = σp Wd
Where Wd is interpreted as the decay probability (or secondary interaction probability) a suggested particle σp its production cross section
2) Universality of Wd or similarity of the Wd properties in various reactions
I + II rarr Jetα + Jetβ
σ = σp Wα(bk)Wβ(bk)
33
34
Conclusion
CBM at SIS-100 is a unique opportunity for investigation of asymptotic of nuclear interactions
35
Thank you
5
e
Emiddotddp3 = Cmiddotexp(-TT0)
p + Cu rarr (1800) + hellip
6
Beam
+ Target
Beam energy(AGeV)
Intensity(1sec)
Target(mgcm2)
Cross-section
(mbsrcm2)
Yield
(1sec)
Number
of events (1day)
JSi + Si 6 109 30 10-10 10-4 10
Ta + Ta 6 109 30 10-7 10-3 100
AGLitvinenko AIMalakhov PIZarubin
JINR Rapid Communications 1-93 p27
7
Correlation Depletion Principle (CDP)CDP was offered by NNBogolyubov in statistical physics as universal property of the probability distributions for particle location in ordinary space-time (r t)
The principle is based on the idea that the correlation between largely spaced parts of a macroscopic system practically vanishes and the distribution is factorized
CDP in Relativistic Nuclear Physics was suggested by AMBaldin in four-velocity space
Due to complementary of rik and bik this principle is quite opposite to the Bogolyubov CDP
The Bogolyubov CDP is valid for |ri - rk|2 rarr while the Baldin CDP is fulfilled for |ri - rk|2 rarr 0 (or bik rarr ) according to the asymptotic freedom
8
W | rarr Wα Wβ bαβ rarr
α = I β = II
I + II rarr 1 + hellip
d2σ dbII 1dx1 rarr FI FII (bII 1 N1)bII 1 = (uII ndash u1)2
N1 ndash cumulative number
9
Vα - middle point of system
ui - four-velocity of particle i in the system
uk - four-velocity of particle k in the system
bαi ltlt bαk
Example of the Isolated system Wα and Wβ (FI and FII)
The important example of the Isolated system rarr JETS
bαi = - (Vα ndash ui)2
bαk = - (Vα ndash uk)2
Isolated system
10
Invariant definition of hadron jetsThe jet is a claster of hadrons with small relative bik
The jet axis (a unit four-vector)
The summation is performed over all the particles belonging to a selected particle group (claster)
It is possible to determine the squared four-velocity with respect to the axis
V = Σ(ui radic(Σui)2
Vo2 ndash V 2 = 1
bk = - (V ndash uk)2
i
11
12
13
14
bull Distribution of π ndash mesons on bk in jets of hadron-hadron and hadron-nucleus collisions at high energies are UNIVERSAL They do not depend either on the colliusion energy or on the type of fragmenting system
bull This universality of properties of four-dimensional hadron jets indicates that the hadronisation of quark systems is defined by the dynamics of interaction of a color charge with QCD vacuum
15
For jets ltbkgt ~ 1
For hadrons ltbkgt ltlt 1
The jet is well allocated if the condition satisfies
bs I gt ltbkgt
bs II gt ltbkgt
16
Automodelity Principle
bik rarr asymptotic regimes rarr decreasing of the probability distributions (cross-sections) W and factorization (DCP)
Asymptotic regimes rarr automodelity distributions W
Automodelity solutions means reduction of number of arguments of researched function due to importance only some combinations of independent variables rarr similarity parameters
17
Automodelity W ie the assumption of existence universal asymptotic in the relativistic nuclear collisions (nuclear intermediate and a quark-gluon) rarr HYPOTHESIS demanding an experimental substantiation
18
П=min[12(uINI +uII NII)
2]
19
20
А М Балдин А А Балдин Physof Element Part and Atomic Nuclei V29 1998
21
22
23
24
I + II rarr 1 + hellip
(NIPI + NIIPII ndash p1)2 = (NIm0 + NIIm0 + Δ)2
Δ is the mass of the particle providing conservation of the barion number strangeness and other quantum numbers
25
Baldin AM Malakhov AI JINR Rapid Communications No1(87)-98 1998 pp5-12
26
PREDICTIONS
27
Asymptotics
s(2mImII) (uIuII) = ch2Y
Пmin= (mT2m0)[1+radic1+(2-m1
2)mT2]
N 0
28
The analytical representation for П leads to the following conclusions
There is the limiting value of П at high energies
The effective number of nucleons involved in the reaction decreases with increasing collision energy
Probability of observation of antinuclei and fragments in the central rapidity region is small
Strange particles yield increases with increasing collision energy
The ratio of particle to antiparticle and nucleus to antinucleus production cross-section goes to the unit while energy rising
29
30
A2 = min [-Σ(Vα ndash uk)2 - Σ(Vβ ndash ui )2 ]
A3 = min [-Σ(Vα ndash uk)2 - Σ(Vβ ndash ui )2 - Σ(Vγ ndash uj )2 ]
helliphelliphelliphelliphelliphelliphellip
etc
K i
K i j
31
Distribution of jet axes is well described QCD as result of the production of quarks and gluons (ie color charges)
In other words rarr studying of jets is studying of deformation of vacuum by a color charge studying of the deconfinment
32
Observability of particles from which can consist quarks
Observability of short-lived particles is based on two necessary criteria
1) The production cross section for really observable products of secondary interaction (decay) can with a sufficient accuracy presented in the form of two factors
σ = σp Wd
Where Wd is interpreted as the decay probability (or secondary interaction probability) a suggested particle σp its production cross section
2) Universality of Wd or similarity of the Wd properties in various reactions
I + II rarr Jetα + Jetβ
σ = σp Wα(bk)Wβ(bk)
33
34
Conclusion
CBM at SIS-100 is a unique opportunity for investigation of asymptotic of nuclear interactions
35
Thank you
6
Beam
+ Target
Beam energy(AGeV)
Intensity(1sec)
Target(mgcm2)
Cross-section
(mbsrcm2)
Yield
(1sec)
Number
of events (1day)
JSi + Si 6 109 30 10-10 10-4 10
Ta + Ta 6 109 30 10-7 10-3 100
AGLitvinenko AIMalakhov PIZarubin
JINR Rapid Communications 1-93 p27
7
Correlation Depletion Principle (CDP)CDP was offered by NNBogolyubov in statistical physics as universal property of the probability distributions for particle location in ordinary space-time (r t)
The principle is based on the idea that the correlation between largely spaced parts of a macroscopic system practically vanishes and the distribution is factorized
CDP in Relativistic Nuclear Physics was suggested by AMBaldin in four-velocity space
Due to complementary of rik and bik this principle is quite opposite to the Bogolyubov CDP
The Bogolyubov CDP is valid for |ri - rk|2 rarr while the Baldin CDP is fulfilled for |ri - rk|2 rarr 0 (or bik rarr ) according to the asymptotic freedom
8
W | rarr Wα Wβ bαβ rarr
α = I β = II
I + II rarr 1 + hellip
d2σ dbII 1dx1 rarr FI FII (bII 1 N1)bII 1 = (uII ndash u1)2
N1 ndash cumulative number
9
Vα - middle point of system
ui - four-velocity of particle i in the system
uk - four-velocity of particle k in the system
bαi ltlt bαk
Example of the Isolated system Wα and Wβ (FI and FII)
The important example of the Isolated system rarr JETS
bαi = - (Vα ndash ui)2
bαk = - (Vα ndash uk)2
Isolated system
10
Invariant definition of hadron jetsThe jet is a claster of hadrons with small relative bik
The jet axis (a unit four-vector)
The summation is performed over all the particles belonging to a selected particle group (claster)
It is possible to determine the squared four-velocity with respect to the axis
V = Σ(ui radic(Σui)2
Vo2 ndash V 2 = 1
bk = - (V ndash uk)2
i
11
12
13
14
bull Distribution of π ndash mesons on bk in jets of hadron-hadron and hadron-nucleus collisions at high energies are UNIVERSAL They do not depend either on the colliusion energy or on the type of fragmenting system
bull This universality of properties of four-dimensional hadron jets indicates that the hadronisation of quark systems is defined by the dynamics of interaction of a color charge with QCD vacuum
15
For jets ltbkgt ~ 1
For hadrons ltbkgt ltlt 1
The jet is well allocated if the condition satisfies
bs I gt ltbkgt
bs II gt ltbkgt
16
Automodelity Principle
bik rarr asymptotic regimes rarr decreasing of the probability distributions (cross-sections) W and factorization (DCP)
Asymptotic regimes rarr automodelity distributions W
Automodelity solutions means reduction of number of arguments of researched function due to importance only some combinations of independent variables rarr similarity parameters
17
Automodelity W ie the assumption of existence universal asymptotic in the relativistic nuclear collisions (nuclear intermediate and a quark-gluon) rarr HYPOTHESIS demanding an experimental substantiation
18
П=min[12(uINI +uII NII)
2]
19
20
А М Балдин А А Балдин Physof Element Part and Atomic Nuclei V29 1998
21
22
23
24
I + II rarr 1 + hellip
(NIPI + NIIPII ndash p1)2 = (NIm0 + NIIm0 + Δ)2
Δ is the mass of the particle providing conservation of the barion number strangeness and other quantum numbers
25
Baldin AM Malakhov AI JINR Rapid Communications No1(87)-98 1998 pp5-12
26
PREDICTIONS
27
Asymptotics
s(2mImII) (uIuII) = ch2Y
Пmin= (mT2m0)[1+radic1+(2-m1
2)mT2]
N 0
28
The analytical representation for П leads to the following conclusions
There is the limiting value of П at high energies
The effective number of nucleons involved in the reaction decreases with increasing collision energy
Probability of observation of antinuclei and fragments in the central rapidity region is small
Strange particles yield increases with increasing collision energy
The ratio of particle to antiparticle and nucleus to antinucleus production cross-section goes to the unit while energy rising
29
30
A2 = min [-Σ(Vα ndash uk)2 - Σ(Vβ ndash ui )2 ]
A3 = min [-Σ(Vα ndash uk)2 - Σ(Vβ ndash ui )2 - Σ(Vγ ndash uj )2 ]
helliphelliphelliphelliphelliphelliphellip
etc
K i
K i j
31
Distribution of jet axes is well described QCD as result of the production of quarks and gluons (ie color charges)
In other words rarr studying of jets is studying of deformation of vacuum by a color charge studying of the deconfinment
32
Observability of particles from which can consist quarks
Observability of short-lived particles is based on two necessary criteria
1) The production cross section for really observable products of secondary interaction (decay) can with a sufficient accuracy presented in the form of two factors
σ = σp Wd
Where Wd is interpreted as the decay probability (or secondary interaction probability) a suggested particle σp its production cross section
2) Universality of Wd or similarity of the Wd properties in various reactions
I + II rarr Jetα + Jetβ
σ = σp Wα(bk)Wβ(bk)
33
34
Conclusion
CBM at SIS-100 is a unique opportunity for investigation of asymptotic of nuclear interactions
35
Thank you
7
Correlation Depletion Principle (CDP)CDP was offered by NNBogolyubov in statistical physics as universal property of the probability distributions for particle location in ordinary space-time (r t)
The principle is based on the idea that the correlation between largely spaced parts of a macroscopic system practically vanishes and the distribution is factorized
CDP in Relativistic Nuclear Physics was suggested by AMBaldin in four-velocity space
Due to complementary of rik and bik this principle is quite opposite to the Bogolyubov CDP
The Bogolyubov CDP is valid for |ri - rk|2 rarr while the Baldin CDP is fulfilled for |ri - rk|2 rarr 0 (or bik rarr ) according to the asymptotic freedom
8
W | rarr Wα Wβ bαβ rarr
α = I β = II
I + II rarr 1 + hellip
d2σ dbII 1dx1 rarr FI FII (bII 1 N1)bII 1 = (uII ndash u1)2
N1 ndash cumulative number
9
Vα - middle point of system
ui - four-velocity of particle i in the system
uk - four-velocity of particle k in the system
bαi ltlt bαk
Example of the Isolated system Wα and Wβ (FI and FII)
The important example of the Isolated system rarr JETS
bαi = - (Vα ndash ui)2
bαk = - (Vα ndash uk)2
Isolated system
10
Invariant definition of hadron jetsThe jet is a claster of hadrons with small relative bik
The jet axis (a unit four-vector)
The summation is performed over all the particles belonging to a selected particle group (claster)
It is possible to determine the squared four-velocity with respect to the axis
V = Σ(ui radic(Σui)2
Vo2 ndash V 2 = 1
bk = - (V ndash uk)2
i
11
12
13
14
bull Distribution of π ndash mesons on bk in jets of hadron-hadron and hadron-nucleus collisions at high energies are UNIVERSAL They do not depend either on the colliusion energy or on the type of fragmenting system
bull This universality of properties of four-dimensional hadron jets indicates that the hadronisation of quark systems is defined by the dynamics of interaction of a color charge with QCD vacuum
15
For jets ltbkgt ~ 1
For hadrons ltbkgt ltlt 1
The jet is well allocated if the condition satisfies
bs I gt ltbkgt
bs II gt ltbkgt
16
Automodelity Principle
bik rarr asymptotic regimes rarr decreasing of the probability distributions (cross-sections) W and factorization (DCP)
Asymptotic regimes rarr automodelity distributions W
Automodelity solutions means reduction of number of arguments of researched function due to importance only some combinations of independent variables rarr similarity parameters
17
Automodelity W ie the assumption of existence universal asymptotic in the relativistic nuclear collisions (nuclear intermediate and a quark-gluon) rarr HYPOTHESIS demanding an experimental substantiation
18
П=min[12(uINI +uII NII)
2]
19
20
А М Балдин А А Балдин Physof Element Part and Atomic Nuclei V29 1998
21
22
23
24
I + II rarr 1 + hellip
(NIPI + NIIPII ndash p1)2 = (NIm0 + NIIm0 + Δ)2
Δ is the mass of the particle providing conservation of the barion number strangeness and other quantum numbers
25
Baldin AM Malakhov AI JINR Rapid Communications No1(87)-98 1998 pp5-12
26
PREDICTIONS
27
Asymptotics
s(2mImII) (uIuII) = ch2Y
Пmin= (mT2m0)[1+radic1+(2-m1
2)mT2]
N 0
28
The analytical representation for П leads to the following conclusions
There is the limiting value of П at high energies
The effective number of nucleons involved in the reaction decreases with increasing collision energy
Probability of observation of antinuclei and fragments in the central rapidity region is small
Strange particles yield increases with increasing collision energy
The ratio of particle to antiparticle and nucleus to antinucleus production cross-section goes to the unit while energy rising
29
30
A2 = min [-Σ(Vα ndash uk)2 - Σ(Vβ ndash ui )2 ]
A3 = min [-Σ(Vα ndash uk)2 - Σ(Vβ ndash ui )2 - Σ(Vγ ndash uj )2 ]
helliphelliphelliphelliphelliphelliphellip
etc
K i
K i j
31
Distribution of jet axes is well described QCD as result of the production of quarks and gluons (ie color charges)
In other words rarr studying of jets is studying of deformation of vacuum by a color charge studying of the deconfinment
32
Observability of particles from which can consist quarks
Observability of short-lived particles is based on two necessary criteria
1) The production cross section for really observable products of secondary interaction (decay) can with a sufficient accuracy presented in the form of two factors
σ = σp Wd
Where Wd is interpreted as the decay probability (or secondary interaction probability) a suggested particle σp its production cross section
2) Universality of Wd or similarity of the Wd properties in various reactions
I + II rarr Jetα + Jetβ
σ = σp Wα(bk)Wβ(bk)
33
34
Conclusion
CBM at SIS-100 is a unique opportunity for investigation of asymptotic of nuclear interactions
35
Thank you
8
W | rarr Wα Wβ bαβ rarr
α = I β = II
I + II rarr 1 + hellip
d2σ dbII 1dx1 rarr FI FII (bII 1 N1)bII 1 = (uII ndash u1)2
N1 ndash cumulative number
9
Vα - middle point of system
ui - four-velocity of particle i in the system
uk - four-velocity of particle k in the system
bαi ltlt bαk
Example of the Isolated system Wα and Wβ (FI and FII)
The important example of the Isolated system rarr JETS
bαi = - (Vα ndash ui)2
bαk = - (Vα ndash uk)2
Isolated system
10
Invariant definition of hadron jetsThe jet is a claster of hadrons with small relative bik
The jet axis (a unit four-vector)
The summation is performed over all the particles belonging to a selected particle group (claster)
It is possible to determine the squared four-velocity with respect to the axis
V = Σ(ui radic(Σui)2
Vo2 ndash V 2 = 1
bk = - (V ndash uk)2
i
11
12
13
14
bull Distribution of π ndash mesons on bk in jets of hadron-hadron and hadron-nucleus collisions at high energies are UNIVERSAL They do not depend either on the colliusion energy or on the type of fragmenting system
bull This universality of properties of four-dimensional hadron jets indicates that the hadronisation of quark systems is defined by the dynamics of interaction of a color charge with QCD vacuum
15
For jets ltbkgt ~ 1
For hadrons ltbkgt ltlt 1
The jet is well allocated if the condition satisfies
bs I gt ltbkgt
bs II gt ltbkgt
16
Automodelity Principle
bik rarr asymptotic regimes rarr decreasing of the probability distributions (cross-sections) W and factorization (DCP)
Asymptotic regimes rarr automodelity distributions W
Automodelity solutions means reduction of number of arguments of researched function due to importance only some combinations of independent variables rarr similarity parameters
17
Automodelity W ie the assumption of existence universal asymptotic in the relativistic nuclear collisions (nuclear intermediate and a quark-gluon) rarr HYPOTHESIS demanding an experimental substantiation
18
П=min[12(uINI +uII NII)
2]
19
20
А М Балдин А А Балдин Physof Element Part and Atomic Nuclei V29 1998
21
22
23
24
I + II rarr 1 + hellip
(NIPI + NIIPII ndash p1)2 = (NIm0 + NIIm0 + Δ)2
Δ is the mass of the particle providing conservation of the barion number strangeness and other quantum numbers
25
Baldin AM Malakhov AI JINR Rapid Communications No1(87)-98 1998 pp5-12
26
PREDICTIONS
27
Asymptotics
s(2mImII) (uIuII) = ch2Y
Пmin= (mT2m0)[1+radic1+(2-m1
2)mT2]
N 0
28
The analytical representation for П leads to the following conclusions
There is the limiting value of П at high energies
The effective number of nucleons involved in the reaction decreases with increasing collision energy
Probability of observation of antinuclei and fragments in the central rapidity region is small
Strange particles yield increases with increasing collision energy
The ratio of particle to antiparticle and nucleus to antinucleus production cross-section goes to the unit while energy rising
29
30
A2 = min [-Σ(Vα ndash uk)2 - Σ(Vβ ndash ui )2 ]
A3 = min [-Σ(Vα ndash uk)2 - Σ(Vβ ndash ui )2 - Σ(Vγ ndash uj )2 ]
helliphelliphelliphelliphelliphelliphellip
etc
K i
K i j
31
Distribution of jet axes is well described QCD as result of the production of quarks and gluons (ie color charges)
In other words rarr studying of jets is studying of deformation of vacuum by a color charge studying of the deconfinment
32
Observability of particles from which can consist quarks
Observability of short-lived particles is based on two necessary criteria
1) The production cross section for really observable products of secondary interaction (decay) can with a sufficient accuracy presented in the form of two factors
σ = σp Wd
Where Wd is interpreted as the decay probability (or secondary interaction probability) a suggested particle σp its production cross section
2) Universality of Wd or similarity of the Wd properties in various reactions
I + II rarr Jetα + Jetβ
σ = σp Wα(bk)Wβ(bk)
33
34
Conclusion
CBM at SIS-100 is a unique opportunity for investigation of asymptotic of nuclear interactions
35
Thank you
9
Vα - middle point of system
ui - four-velocity of particle i in the system
uk - four-velocity of particle k in the system
bαi ltlt bαk
Example of the Isolated system Wα and Wβ (FI and FII)
The important example of the Isolated system rarr JETS
bαi = - (Vα ndash ui)2
bαk = - (Vα ndash uk)2
Isolated system
10
Invariant definition of hadron jetsThe jet is a claster of hadrons with small relative bik
The jet axis (a unit four-vector)
The summation is performed over all the particles belonging to a selected particle group (claster)
It is possible to determine the squared four-velocity with respect to the axis
V = Σ(ui radic(Σui)2
Vo2 ndash V 2 = 1
bk = - (V ndash uk)2
i
11
12
13
14
bull Distribution of π ndash mesons on bk in jets of hadron-hadron and hadron-nucleus collisions at high energies are UNIVERSAL They do not depend either on the colliusion energy or on the type of fragmenting system
bull This universality of properties of four-dimensional hadron jets indicates that the hadronisation of quark systems is defined by the dynamics of interaction of a color charge with QCD vacuum
15
For jets ltbkgt ~ 1
For hadrons ltbkgt ltlt 1
The jet is well allocated if the condition satisfies
bs I gt ltbkgt
bs II gt ltbkgt
16
Automodelity Principle
bik rarr asymptotic regimes rarr decreasing of the probability distributions (cross-sections) W and factorization (DCP)
Asymptotic regimes rarr automodelity distributions W
Automodelity solutions means reduction of number of arguments of researched function due to importance only some combinations of independent variables rarr similarity parameters
17
Automodelity W ie the assumption of existence universal asymptotic in the relativistic nuclear collisions (nuclear intermediate and a quark-gluon) rarr HYPOTHESIS demanding an experimental substantiation
18
П=min[12(uINI +uII NII)
2]
19
20
А М Балдин А А Балдин Physof Element Part and Atomic Nuclei V29 1998
21
22
23
24
I + II rarr 1 + hellip
(NIPI + NIIPII ndash p1)2 = (NIm0 + NIIm0 + Δ)2
Δ is the mass of the particle providing conservation of the barion number strangeness and other quantum numbers
25
Baldin AM Malakhov AI JINR Rapid Communications No1(87)-98 1998 pp5-12
26
PREDICTIONS
27
Asymptotics
s(2mImII) (uIuII) = ch2Y
Пmin= (mT2m0)[1+radic1+(2-m1
2)mT2]
N 0
28
The analytical representation for П leads to the following conclusions
There is the limiting value of П at high energies
The effective number of nucleons involved in the reaction decreases with increasing collision energy
Probability of observation of antinuclei and fragments in the central rapidity region is small
Strange particles yield increases with increasing collision energy
The ratio of particle to antiparticle and nucleus to antinucleus production cross-section goes to the unit while energy rising
29
30
A2 = min [-Σ(Vα ndash uk)2 - Σ(Vβ ndash ui )2 ]
A3 = min [-Σ(Vα ndash uk)2 - Σ(Vβ ndash ui )2 - Σ(Vγ ndash uj )2 ]
helliphelliphelliphelliphelliphelliphellip
etc
K i
K i j
31
Distribution of jet axes is well described QCD as result of the production of quarks and gluons (ie color charges)
In other words rarr studying of jets is studying of deformation of vacuum by a color charge studying of the deconfinment
32
Observability of particles from which can consist quarks
Observability of short-lived particles is based on two necessary criteria
1) The production cross section for really observable products of secondary interaction (decay) can with a sufficient accuracy presented in the form of two factors
σ = σp Wd
Where Wd is interpreted as the decay probability (or secondary interaction probability) a suggested particle σp its production cross section
2) Universality of Wd or similarity of the Wd properties in various reactions
I + II rarr Jetα + Jetβ
σ = σp Wα(bk)Wβ(bk)
33
34
Conclusion
CBM at SIS-100 is a unique opportunity for investigation of asymptotic of nuclear interactions
35
Thank you
10
Invariant definition of hadron jetsThe jet is a claster of hadrons with small relative bik
The jet axis (a unit four-vector)
The summation is performed over all the particles belonging to a selected particle group (claster)
It is possible to determine the squared four-velocity with respect to the axis
V = Σ(ui radic(Σui)2
Vo2 ndash V 2 = 1
bk = - (V ndash uk)2
i
11
12
13
14
bull Distribution of π ndash mesons on bk in jets of hadron-hadron and hadron-nucleus collisions at high energies are UNIVERSAL They do not depend either on the colliusion energy or on the type of fragmenting system
bull This universality of properties of four-dimensional hadron jets indicates that the hadronisation of quark systems is defined by the dynamics of interaction of a color charge with QCD vacuum
15
For jets ltbkgt ~ 1
For hadrons ltbkgt ltlt 1
The jet is well allocated if the condition satisfies
bs I gt ltbkgt
bs II gt ltbkgt
16
Automodelity Principle
bik rarr asymptotic regimes rarr decreasing of the probability distributions (cross-sections) W and factorization (DCP)
Asymptotic regimes rarr automodelity distributions W
Automodelity solutions means reduction of number of arguments of researched function due to importance only some combinations of independent variables rarr similarity parameters
17
Automodelity W ie the assumption of existence universal asymptotic in the relativistic nuclear collisions (nuclear intermediate and a quark-gluon) rarr HYPOTHESIS demanding an experimental substantiation
18
П=min[12(uINI +uII NII)
2]
19
20
А М Балдин А А Балдин Physof Element Part and Atomic Nuclei V29 1998
21
22
23
24
I + II rarr 1 + hellip
(NIPI + NIIPII ndash p1)2 = (NIm0 + NIIm0 + Δ)2
Δ is the mass of the particle providing conservation of the barion number strangeness and other quantum numbers
25
Baldin AM Malakhov AI JINR Rapid Communications No1(87)-98 1998 pp5-12
26
PREDICTIONS
27
Asymptotics
s(2mImII) (uIuII) = ch2Y
Пmin= (mT2m0)[1+radic1+(2-m1
2)mT2]
N 0
28
The analytical representation for П leads to the following conclusions
There is the limiting value of П at high energies
The effective number of nucleons involved in the reaction decreases with increasing collision energy
Probability of observation of antinuclei and fragments in the central rapidity region is small
Strange particles yield increases with increasing collision energy
The ratio of particle to antiparticle and nucleus to antinucleus production cross-section goes to the unit while energy rising
29
30
A2 = min [-Σ(Vα ndash uk)2 - Σ(Vβ ndash ui )2 ]
A3 = min [-Σ(Vα ndash uk)2 - Σ(Vβ ndash ui )2 - Σ(Vγ ndash uj )2 ]
helliphelliphelliphelliphelliphelliphellip
etc
K i
K i j
31
Distribution of jet axes is well described QCD as result of the production of quarks and gluons (ie color charges)
In other words rarr studying of jets is studying of deformation of vacuum by a color charge studying of the deconfinment
32
Observability of particles from which can consist quarks
Observability of short-lived particles is based on two necessary criteria
1) The production cross section for really observable products of secondary interaction (decay) can with a sufficient accuracy presented in the form of two factors
σ = σp Wd
Where Wd is interpreted as the decay probability (or secondary interaction probability) a suggested particle σp its production cross section
2) Universality of Wd or similarity of the Wd properties in various reactions
I + II rarr Jetα + Jetβ
σ = σp Wα(bk)Wβ(bk)
33
34
Conclusion
CBM at SIS-100 is a unique opportunity for investigation of asymptotic of nuclear interactions
35
Thank you
11
12
13
14
bull Distribution of π ndash mesons on bk in jets of hadron-hadron and hadron-nucleus collisions at high energies are UNIVERSAL They do not depend either on the colliusion energy or on the type of fragmenting system
bull This universality of properties of four-dimensional hadron jets indicates that the hadronisation of quark systems is defined by the dynamics of interaction of a color charge with QCD vacuum
15
For jets ltbkgt ~ 1
For hadrons ltbkgt ltlt 1
The jet is well allocated if the condition satisfies
bs I gt ltbkgt
bs II gt ltbkgt
16
Automodelity Principle
bik rarr asymptotic regimes rarr decreasing of the probability distributions (cross-sections) W and factorization (DCP)
Asymptotic regimes rarr automodelity distributions W
Automodelity solutions means reduction of number of arguments of researched function due to importance only some combinations of independent variables rarr similarity parameters
17
Automodelity W ie the assumption of existence universal asymptotic in the relativistic nuclear collisions (nuclear intermediate and a quark-gluon) rarr HYPOTHESIS demanding an experimental substantiation
18
П=min[12(uINI +uII NII)
2]
19
20
А М Балдин А А Балдин Physof Element Part and Atomic Nuclei V29 1998
21
22
23
24
I + II rarr 1 + hellip
(NIPI + NIIPII ndash p1)2 = (NIm0 + NIIm0 + Δ)2
Δ is the mass of the particle providing conservation of the barion number strangeness and other quantum numbers
25
Baldin AM Malakhov AI JINR Rapid Communications No1(87)-98 1998 pp5-12
26
PREDICTIONS
27
Asymptotics
s(2mImII) (uIuII) = ch2Y
Пmin= (mT2m0)[1+radic1+(2-m1
2)mT2]
N 0
28
The analytical representation for П leads to the following conclusions
There is the limiting value of П at high energies
The effective number of nucleons involved in the reaction decreases with increasing collision energy
Probability of observation of antinuclei and fragments in the central rapidity region is small
Strange particles yield increases with increasing collision energy
The ratio of particle to antiparticle and nucleus to antinucleus production cross-section goes to the unit while energy rising
29
30
A2 = min [-Σ(Vα ndash uk)2 - Σ(Vβ ndash ui )2 ]
A3 = min [-Σ(Vα ndash uk)2 - Σ(Vβ ndash ui )2 - Σ(Vγ ndash uj )2 ]
helliphelliphelliphelliphelliphelliphellip
etc
K i
K i j
31
Distribution of jet axes is well described QCD as result of the production of quarks and gluons (ie color charges)
In other words rarr studying of jets is studying of deformation of vacuum by a color charge studying of the deconfinment
32
Observability of particles from which can consist quarks
Observability of short-lived particles is based on two necessary criteria
1) The production cross section for really observable products of secondary interaction (decay) can with a sufficient accuracy presented in the form of two factors
σ = σp Wd
Where Wd is interpreted as the decay probability (or secondary interaction probability) a suggested particle σp its production cross section
2) Universality of Wd or similarity of the Wd properties in various reactions
I + II rarr Jetα + Jetβ
σ = σp Wα(bk)Wβ(bk)
33
34
Conclusion
CBM at SIS-100 is a unique opportunity for investigation of asymptotic of nuclear interactions
35
Thank you
12
13
14
bull Distribution of π ndash mesons on bk in jets of hadron-hadron and hadron-nucleus collisions at high energies are UNIVERSAL They do not depend either on the colliusion energy or on the type of fragmenting system
bull This universality of properties of four-dimensional hadron jets indicates that the hadronisation of quark systems is defined by the dynamics of interaction of a color charge with QCD vacuum
15
For jets ltbkgt ~ 1
For hadrons ltbkgt ltlt 1
The jet is well allocated if the condition satisfies
bs I gt ltbkgt
bs II gt ltbkgt
16
Automodelity Principle
bik rarr asymptotic regimes rarr decreasing of the probability distributions (cross-sections) W and factorization (DCP)
Asymptotic regimes rarr automodelity distributions W
Automodelity solutions means reduction of number of arguments of researched function due to importance only some combinations of independent variables rarr similarity parameters
17
Automodelity W ie the assumption of existence universal asymptotic in the relativistic nuclear collisions (nuclear intermediate and a quark-gluon) rarr HYPOTHESIS demanding an experimental substantiation
18
П=min[12(uINI +uII NII)
2]
19
20
А М Балдин А А Балдин Physof Element Part and Atomic Nuclei V29 1998
21
22
23
24
I + II rarr 1 + hellip
(NIPI + NIIPII ndash p1)2 = (NIm0 + NIIm0 + Δ)2
Δ is the mass of the particle providing conservation of the barion number strangeness and other quantum numbers
25
Baldin AM Malakhov AI JINR Rapid Communications No1(87)-98 1998 pp5-12
26
PREDICTIONS
27
Asymptotics
s(2mImII) (uIuII) = ch2Y
Пmin= (mT2m0)[1+radic1+(2-m1
2)mT2]
N 0
28
The analytical representation for П leads to the following conclusions
There is the limiting value of П at high energies
The effective number of nucleons involved in the reaction decreases with increasing collision energy
Probability of observation of antinuclei and fragments in the central rapidity region is small
Strange particles yield increases with increasing collision energy
The ratio of particle to antiparticle and nucleus to antinucleus production cross-section goes to the unit while energy rising
29
30
A2 = min [-Σ(Vα ndash uk)2 - Σ(Vβ ndash ui )2 ]
A3 = min [-Σ(Vα ndash uk)2 - Σ(Vβ ndash ui )2 - Σ(Vγ ndash uj )2 ]
helliphelliphelliphelliphelliphelliphellip
etc
K i
K i j
31
Distribution of jet axes is well described QCD as result of the production of quarks and gluons (ie color charges)
In other words rarr studying of jets is studying of deformation of vacuum by a color charge studying of the deconfinment
32
Observability of particles from which can consist quarks
Observability of short-lived particles is based on two necessary criteria
1) The production cross section for really observable products of secondary interaction (decay) can with a sufficient accuracy presented in the form of two factors
σ = σp Wd
Where Wd is interpreted as the decay probability (or secondary interaction probability) a suggested particle σp its production cross section
2) Universality of Wd or similarity of the Wd properties in various reactions
I + II rarr Jetα + Jetβ
σ = σp Wα(bk)Wβ(bk)
33
34
Conclusion
CBM at SIS-100 is a unique opportunity for investigation of asymptotic of nuclear interactions
35
Thank you
13
14
bull Distribution of π ndash mesons on bk in jets of hadron-hadron and hadron-nucleus collisions at high energies are UNIVERSAL They do not depend either on the colliusion energy or on the type of fragmenting system
bull This universality of properties of four-dimensional hadron jets indicates that the hadronisation of quark systems is defined by the dynamics of interaction of a color charge with QCD vacuum
15
For jets ltbkgt ~ 1
For hadrons ltbkgt ltlt 1
The jet is well allocated if the condition satisfies
bs I gt ltbkgt
bs II gt ltbkgt
16
Automodelity Principle
bik rarr asymptotic regimes rarr decreasing of the probability distributions (cross-sections) W and factorization (DCP)
Asymptotic regimes rarr automodelity distributions W
Automodelity solutions means reduction of number of arguments of researched function due to importance only some combinations of independent variables rarr similarity parameters
17
Automodelity W ie the assumption of existence universal asymptotic in the relativistic nuclear collisions (nuclear intermediate and a quark-gluon) rarr HYPOTHESIS demanding an experimental substantiation
18
П=min[12(uINI +uII NII)
2]
19
20
А М Балдин А А Балдин Physof Element Part and Atomic Nuclei V29 1998
21
22
23
24
I + II rarr 1 + hellip
(NIPI + NIIPII ndash p1)2 = (NIm0 + NIIm0 + Δ)2
Δ is the mass of the particle providing conservation of the barion number strangeness and other quantum numbers
25
Baldin AM Malakhov AI JINR Rapid Communications No1(87)-98 1998 pp5-12
26
PREDICTIONS
27
Asymptotics
s(2mImII) (uIuII) = ch2Y
Пmin= (mT2m0)[1+radic1+(2-m1
2)mT2]
N 0
28
The analytical representation for П leads to the following conclusions
There is the limiting value of П at high energies
The effective number of nucleons involved in the reaction decreases with increasing collision energy
Probability of observation of antinuclei and fragments in the central rapidity region is small
Strange particles yield increases with increasing collision energy
The ratio of particle to antiparticle and nucleus to antinucleus production cross-section goes to the unit while energy rising
29
30
A2 = min [-Σ(Vα ndash uk)2 - Σ(Vβ ndash ui )2 ]
A3 = min [-Σ(Vα ndash uk)2 - Σ(Vβ ndash ui )2 - Σ(Vγ ndash uj )2 ]
helliphelliphelliphelliphelliphelliphellip
etc
K i
K i j
31
Distribution of jet axes is well described QCD as result of the production of quarks and gluons (ie color charges)
In other words rarr studying of jets is studying of deformation of vacuum by a color charge studying of the deconfinment
32
Observability of particles from which can consist quarks
Observability of short-lived particles is based on two necessary criteria
1) The production cross section for really observable products of secondary interaction (decay) can with a sufficient accuracy presented in the form of two factors
σ = σp Wd
Where Wd is interpreted as the decay probability (or secondary interaction probability) a suggested particle σp its production cross section
2) Universality of Wd or similarity of the Wd properties in various reactions
I + II rarr Jetα + Jetβ
σ = σp Wα(bk)Wβ(bk)
33
34
Conclusion
CBM at SIS-100 is a unique opportunity for investigation of asymptotic of nuclear interactions
35
Thank you
14
bull Distribution of π ndash mesons on bk in jets of hadron-hadron and hadron-nucleus collisions at high energies are UNIVERSAL They do not depend either on the colliusion energy or on the type of fragmenting system
bull This universality of properties of four-dimensional hadron jets indicates that the hadronisation of quark systems is defined by the dynamics of interaction of a color charge with QCD vacuum
15
For jets ltbkgt ~ 1
For hadrons ltbkgt ltlt 1
The jet is well allocated if the condition satisfies
bs I gt ltbkgt
bs II gt ltbkgt
16
Automodelity Principle
bik rarr asymptotic regimes rarr decreasing of the probability distributions (cross-sections) W and factorization (DCP)
Asymptotic regimes rarr automodelity distributions W
Automodelity solutions means reduction of number of arguments of researched function due to importance only some combinations of independent variables rarr similarity parameters
17
Automodelity W ie the assumption of existence universal asymptotic in the relativistic nuclear collisions (nuclear intermediate and a quark-gluon) rarr HYPOTHESIS demanding an experimental substantiation
18
П=min[12(uINI +uII NII)
2]
19
20
А М Балдин А А Балдин Physof Element Part and Atomic Nuclei V29 1998
21
22
23
24
I + II rarr 1 + hellip
(NIPI + NIIPII ndash p1)2 = (NIm0 + NIIm0 + Δ)2
Δ is the mass of the particle providing conservation of the barion number strangeness and other quantum numbers
25
Baldin AM Malakhov AI JINR Rapid Communications No1(87)-98 1998 pp5-12
26
PREDICTIONS
27
Asymptotics
s(2mImII) (uIuII) = ch2Y
Пmin= (mT2m0)[1+radic1+(2-m1
2)mT2]
N 0
28
The analytical representation for П leads to the following conclusions
There is the limiting value of П at high energies
The effective number of nucleons involved in the reaction decreases with increasing collision energy
Probability of observation of antinuclei and fragments in the central rapidity region is small
Strange particles yield increases with increasing collision energy
The ratio of particle to antiparticle and nucleus to antinucleus production cross-section goes to the unit while energy rising
29
30
A2 = min [-Σ(Vα ndash uk)2 - Σ(Vβ ndash ui )2 ]
A3 = min [-Σ(Vα ndash uk)2 - Σ(Vβ ndash ui )2 - Σ(Vγ ndash uj )2 ]
helliphelliphelliphelliphelliphelliphellip
etc
K i
K i j
31
Distribution of jet axes is well described QCD as result of the production of quarks and gluons (ie color charges)
In other words rarr studying of jets is studying of deformation of vacuum by a color charge studying of the deconfinment
32
Observability of particles from which can consist quarks
Observability of short-lived particles is based on two necessary criteria
1) The production cross section for really observable products of secondary interaction (decay) can with a sufficient accuracy presented in the form of two factors
σ = σp Wd
Where Wd is interpreted as the decay probability (or secondary interaction probability) a suggested particle σp its production cross section
2) Universality of Wd or similarity of the Wd properties in various reactions
I + II rarr Jetα + Jetβ
σ = σp Wα(bk)Wβ(bk)
33
34
Conclusion
CBM at SIS-100 is a unique opportunity for investigation of asymptotic of nuclear interactions
35
Thank you
15
For jets ltbkgt ~ 1
For hadrons ltbkgt ltlt 1
The jet is well allocated if the condition satisfies
bs I gt ltbkgt
bs II gt ltbkgt
16
Automodelity Principle
bik rarr asymptotic regimes rarr decreasing of the probability distributions (cross-sections) W and factorization (DCP)
Asymptotic regimes rarr automodelity distributions W
Automodelity solutions means reduction of number of arguments of researched function due to importance only some combinations of independent variables rarr similarity parameters
17
Automodelity W ie the assumption of existence universal asymptotic in the relativistic nuclear collisions (nuclear intermediate and a quark-gluon) rarr HYPOTHESIS demanding an experimental substantiation
18
П=min[12(uINI +uII NII)
2]
19
20
А М Балдин А А Балдин Physof Element Part and Atomic Nuclei V29 1998
21
22
23
24
I + II rarr 1 + hellip
(NIPI + NIIPII ndash p1)2 = (NIm0 + NIIm0 + Δ)2
Δ is the mass of the particle providing conservation of the barion number strangeness and other quantum numbers
25
Baldin AM Malakhov AI JINR Rapid Communications No1(87)-98 1998 pp5-12
26
PREDICTIONS
27
Asymptotics
s(2mImII) (uIuII) = ch2Y
Пmin= (mT2m0)[1+radic1+(2-m1
2)mT2]
N 0
28
The analytical representation for П leads to the following conclusions
There is the limiting value of П at high energies
The effective number of nucleons involved in the reaction decreases with increasing collision energy
Probability of observation of antinuclei and fragments in the central rapidity region is small
Strange particles yield increases with increasing collision energy
The ratio of particle to antiparticle and nucleus to antinucleus production cross-section goes to the unit while energy rising
29
30
A2 = min [-Σ(Vα ndash uk)2 - Σ(Vβ ndash ui )2 ]
A3 = min [-Σ(Vα ndash uk)2 - Σ(Vβ ndash ui )2 - Σ(Vγ ndash uj )2 ]
helliphelliphelliphelliphelliphelliphellip
etc
K i
K i j
31
Distribution of jet axes is well described QCD as result of the production of quarks and gluons (ie color charges)
In other words rarr studying of jets is studying of deformation of vacuum by a color charge studying of the deconfinment
32
Observability of particles from which can consist quarks
Observability of short-lived particles is based on two necessary criteria
1) The production cross section for really observable products of secondary interaction (decay) can with a sufficient accuracy presented in the form of two factors
σ = σp Wd
Where Wd is interpreted as the decay probability (or secondary interaction probability) a suggested particle σp its production cross section
2) Universality of Wd or similarity of the Wd properties in various reactions
I + II rarr Jetα + Jetβ
σ = σp Wα(bk)Wβ(bk)
33
34
Conclusion
CBM at SIS-100 is a unique opportunity for investigation of asymptotic of nuclear interactions
35
Thank you
16
Automodelity Principle
bik rarr asymptotic regimes rarr decreasing of the probability distributions (cross-sections) W and factorization (DCP)
Asymptotic regimes rarr automodelity distributions W
Automodelity solutions means reduction of number of arguments of researched function due to importance only some combinations of independent variables rarr similarity parameters
17
Automodelity W ie the assumption of existence universal asymptotic in the relativistic nuclear collisions (nuclear intermediate and a quark-gluon) rarr HYPOTHESIS demanding an experimental substantiation
18
П=min[12(uINI +uII NII)
2]
19
20
А М Балдин А А Балдин Physof Element Part and Atomic Nuclei V29 1998
21
22
23
24
I + II rarr 1 + hellip
(NIPI + NIIPII ndash p1)2 = (NIm0 + NIIm0 + Δ)2
Δ is the mass of the particle providing conservation of the barion number strangeness and other quantum numbers
25
Baldin AM Malakhov AI JINR Rapid Communications No1(87)-98 1998 pp5-12
26
PREDICTIONS
27
Asymptotics
s(2mImII) (uIuII) = ch2Y
Пmin= (mT2m0)[1+radic1+(2-m1
2)mT2]
N 0
28
The analytical representation for П leads to the following conclusions
There is the limiting value of П at high energies
The effective number of nucleons involved in the reaction decreases with increasing collision energy
Probability of observation of antinuclei and fragments in the central rapidity region is small
Strange particles yield increases with increasing collision energy
The ratio of particle to antiparticle and nucleus to antinucleus production cross-section goes to the unit while energy rising
29
30
A2 = min [-Σ(Vα ndash uk)2 - Σ(Vβ ndash ui )2 ]
A3 = min [-Σ(Vα ndash uk)2 - Σ(Vβ ndash ui )2 - Σ(Vγ ndash uj )2 ]
helliphelliphelliphelliphelliphelliphellip
etc
K i
K i j
31
Distribution of jet axes is well described QCD as result of the production of quarks and gluons (ie color charges)
In other words rarr studying of jets is studying of deformation of vacuum by a color charge studying of the deconfinment
32
Observability of particles from which can consist quarks
Observability of short-lived particles is based on two necessary criteria
1) The production cross section for really observable products of secondary interaction (decay) can with a sufficient accuracy presented in the form of two factors
σ = σp Wd
Where Wd is interpreted as the decay probability (or secondary interaction probability) a suggested particle σp its production cross section
2) Universality of Wd or similarity of the Wd properties in various reactions
I + II rarr Jetα + Jetβ
σ = σp Wα(bk)Wβ(bk)
33
34
Conclusion
CBM at SIS-100 is a unique opportunity for investigation of asymptotic of nuclear interactions
35
Thank you
17
Automodelity W ie the assumption of existence universal asymptotic in the relativistic nuclear collisions (nuclear intermediate and a quark-gluon) rarr HYPOTHESIS demanding an experimental substantiation
18
П=min[12(uINI +uII NII)
2]
19
20
А М Балдин А А Балдин Physof Element Part and Atomic Nuclei V29 1998
21
22
23
24
I + II rarr 1 + hellip
(NIPI + NIIPII ndash p1)2 = (NIm0 + NIIm0 + Δ)2
Δ is the mass of the particle providing conservation of the barion number strangeness and other quantum numbers
25
Baldin AM Malakhov AI JINR Rapid Communications No1(87)-98 1998 pp5-12
26
PREDICTIONS
27
Asymptotics
s(2mImII) (uIuII) = ch2Y
Пmin= (mT2m0)[1+radic1+(2-m1
2)mT2]
N 0
28
The analytical representation for П leads to the following conclusions
There is the limiting value of П at high energies
The effective number of nucleons involved in the reaction decreases with increasing collision energy
Probability of observation of antinuclei and fragments in the central rapidity region is small
Strange particles yield increases with increasing collision energy
The ratio of particle to antiparticle and nucleus to antinucleus production cross-section goes to the unit while energy rising
29
30
A2 = min [-Σ(Vα ndash uk)2 - Σ(Vβ ndash ui )2 ]
A3 = min [-Σ(Vα ndash uk)2 - Σ(Vβ ndash ui )2 - Σ(Vγ ndash uj )2 ]
helliphelliphelliphelliphelliphelliphellip
etc
K i
K i j
31
Distribution of jet axes is well described QCD as result of the production of quarks and gluons (ie color charges)
In other words rarr studying of jets is studying of deformation of vacuum by a color charge studying of the deconfinment
32
Observability of particles from which can consist quarks
Observability of short-lived particles is based on two necessary criteria
1) The production cross section for really observable products of secondary interaction (decay) can with a sufficient accuracy presented in the form of two factors
σ = σp Wd
Where Wd is interpreted as the decay probability (or secondary interaction probability) a suggested particle σp its production cross section
2) Universality of Wd or similarity of the Wd properties in various reactions
I + II rarr Jetα + Jetβ
σ = σp Wα(bk)Wβ(bk)
33
34
Conclusion
CBM at SIS-100 is a unique opportunity for investigation of asymptotic of nuclear interactions
35
Thank you
18
П=min[12(uINI +uII NII)
2]
19
20
А М Балдин А А Балдин Physof Element Part and Atomic Nuclei V29 1998
21
22
23
24
I + II rarr 1 + hellip
(NIPI + NIIPII ndash p1)2 = (NIm0 + NIIm0 + Δ)2
Δ is the mass of the particle providing conservation of the barion number strangeness and other quantum numbers
25
Baldin AM Malakhov AI JINR Rapid Communications No1(87)-98 1998 pp5-12
26
PREDICTIONS
27
Asymptotics
s(2mImII) (uIuII) = ch2Y
Пmin= (mT2m0)[1+radic1+(2-m1
2)mT2]
N 0
28
The analytical representation for П leads to the following conclusions
There is the limiting value of П at high energies
The effective number of nucleons involved in the reaction decreases with increasing collision energy
Probability of observation of antinuclei and fragments in the central rapidity region is small
Strange particles yield increases with increasing collision energy
The ratio of particle to antiparticle and nucleus to antinucleus production cross-section goes to the unit while energy rising
29
30
A2 = min [-Σ(Vα ndash uk)2 - Σ(Vβ ndash ui )2 ]
A3 = min [-Σ(Vα ndash uk)2 - Σ(Vβ ndash ui )2 - Σ(Vγ ndash uj )2 ]
helliphelliphelliphelliphelliphelliphellip
etc
K i
K i j
31
Distribution of jet axes is well described QCD as result of the production of quarks and gluons (ie color charges)
In other words rarr studying of jets is studying of deformation of vacuum by a color charge studying of the deconfinment
32
Observability of particles from which can consist quarks
Observability of short-lived particles is based on two necessary criteria
1) The production cross section for really observable products of secondary interaction (decay) can with a sufficient accuracy presented in the form of two factors
σ = σp Wd
Where Wd is interpreted as the decay probability (or secondary interaction probability) a suggested particle σp its production cross section
2) Universality of Wd or similarity of the Wd properties in various reactions
I + II rarr Jetα + Jetβ
σ = σp Wα(bk)Wβ(bk)
33
34
Conclusion
CBM at SIS-100 is a unique opportunity for investigation of asymptotic of nuclear interactions
35
Thank you
19
20
А М Балдин А А Балдин Physof Element Part and Atomic Nuclei V29 1998
21
22
23
24
I + II rarr 1 + hellip
(NIPI + NIIPII ndash p1)2 = (NIm0 + NIIm0 + Δ)2
Δ is the mass of the particle providing conservation of the barion number strangeness and other quantum numbers
25
Baldin AM Malakhov AI JINR Rapid Communications No1(87)-98 1998 pp5-12
26
PREDICTIONS
27
Asymptotics
s(2mImII) (uIuII) = ch2Y
Пmin= (mT2m0)[1+radic1+(2-m1
2)mT2]
N 0
28
The analytical representation for П leads to the following conclusions
There is the limiting value of П at high energies
The effective number of nucleons involved in the reaction decreases with increasing collision energy
Probability of observation of antinuclei and fragments in the central rapidity region is small
Strange particles yield increases with increasing collision energy
The ratio of particle to antiparticle and nucleus to antinucleus production cross-section goes to the unit while energy rising
29
30
A2 = min [-Σ(Vα ndash uk)2 - Σ(Vβ ndash ui )2 ]
A3 = min [-Σ(Vα ndash uk)2 - Σ(Vβ ndash ui )2 - Σ(Vγ ndash uj )2 ]
helliphelliphelliphelliphelliphelliphellip
etc
K i
K i j
31
Distribution of jet axes is well described QCD as result of the production of quarks and gluons (ie color charges)
In other words rarr studying of jets is studying of deformation of vacuum by a color charge studying of the deconfinment
32
Observability of particles from which can consist quarks
Observability of short-lived particles is based on two necessary criteria
1) The production cross section for really observable products of secondary interaction (decay) can with a sufficient accuracy presented in the form of two factors
σ = σp Wd
Where Wd is interpreted as the decay probability (or secondary interaction probability) a suggested particle σp its production cross section
2) Universality of Wd or similarity of the Wd properties in various reactions
I + II rarr Jetα + Jetβ
σ = σp Wα(bk)Wβ(bk)
33
34
Conclusion
CBM at SIS-100 is a unique opportunity for investigation of asymptotic of nuclear interactions
35
Thank you
20
А М Балдин А А Балдин Physof Element Part and Atomic Nuclei V29 1998
21
22
23
24
I + II rarr 1 + hellip
(NIPI + NIIPII ndash p1)2 = (NIm0 + NIIm0 + Δ)2
Δ is the mass of the particle providing conservation of the barion number strangeness and other quantum numbers
25
Baldin AM Malakhov AI JINR Rapid Communications No1(87)-98 1998 pp5-12
26
PREDICTIONS
27
Asymptotics
s(2mImII) (uIuII) = ch2Y
Пmin= (mT2m0)[1+radic1+(2-m1
2)mT2]
N 0
28
The analytical representation for П leads to the following conclusions
There is the limiting value of П at high energies
The effective number of nucleons involved in the reaction decreases with increasing collision energy
Probability of observation of antinuclei and fragments in the central rapidity region is small
Strange particles yield increases with increasing collision energy
The ratio of particle to antiparticle and nucleus to antinucleus production cross-section goes to the unit while energy rising
29
30
A2 = min [-Σ(Vα ndash uk)2 - Σ(Vβ ndash ui )2 ]
A3 = min [-Σ(Vα ndash uk)2 - Σ(Vβ ndash ui )2 - Σ(Vγ ndash uj )2 ]
helliphelliphelliphelliphelliphelliphellip
etc
K i
K i j
31
Distribution of jet axes is well described QCD as result of the production of quarks and gluons (ie color charges)
In other words rarr studying of jets is studying of deformation of vacuum by a color charge studying of the deconfinment
32
Observability of particles from which can consist quarks
Observability of short-lived particles is based on two necessary criteria
1) The production cross section for really observable products of secondary interaction (decay) can with a sufficient accuracy presented in the form of two factors
σ = σp Wd
Where Wd is interpreted as the decay probability (or secondary interaction probability) a suggested particle σp its production cross section
2) Universality of Wd or similarity of the Wd properties in various reactions
I + II rarr Jetα + Jetβ
σ = σp Wα(bk)Wβ(bk)
33
34
Conclusion
CBM at SIS-100 is a unique opportunity for investigation of asymptotic of nuclear interactions
35
Thank you
21
22
23
24
I + II rarr 1 + hellip
(NIPI + NIIPII ndash p1)2 = (NIm0 + NIIm0 + Δ)2
Δ is the mass of the particle providing conservation of the barion number strangeness and other quantum numbers
25
Baldin AM Malakhov AI JINR Rapid Communications No1(87)-98 1998 pp5-12
26
PREDICTIONS
27
Asymptotics
s(2mImII) (uIuII) = ch2Y
Пmin= (mT2m0)[1+radic1+(2-m1
2)mT2]
N 0
28
The analytical representation for П leads to the following conclusions
There is the limiting value of П at high energies
The effective number of nucleons involved in the reaction decreases with increasing collision energy
Probability of observation of antinuclei and fragments in the central rapidity region is small
Strange particles yield increases with increasing collision energy
The ratio of particle to antiparticle and nucleus to antinucleus production cross-section goes to the unit while energy rising
29
30
A2 = min [-Σ(Vα ndash uk)2 - Σ(Vβ ndash ui )2 ]
A3 = min [-Σ(Vα ndash uk)2 - Σ(Vβ ndash ui )2 - Σ(Vγ ndash uj )2 ]
helliphelliphelliphelliphelliphelliphellip
etc
K i
K i j
31
Distribution of jet axes is well described QCD as result of the production of quarks and gluons (ie color charges)
In other words rarr studying of jets is studying of deformation of vacuum by a color charge studying of the deconfinment
32
Observability of particles from which can consist quarks
Observability of short-lived particles is based on two necessary criteria
1) The production cross section for really observable products of secondary interaction (decay) can with a sufficient accuracy presented in the form of two factors
σ = σp Wd
Where Wd is interpreted as the decay probability (or secondary interaction probability) a suggested particle σp its production cross section
2) Universality of Wd or similarity of the Wd properties in various reactions
I + II rarr Jetα + Jetβ
σ = σp Wα(bk)Wβ(bk)
33
34
Conclusion
CBM at SIS-100 is a unique opportunity for investigation of asymptotic of nuclear interactions
35
Thank you
22
23
24
I + II rarr 1 + hellip
(NIPI + NIIPII ndash p1)2 = (NIm0 + NIIm0 + Δ)2
Δ is the mass of the particle providing conservation of the barion number strangeness and other quantum numbers
25
Baldin AM Malakhov AI JINR Rapid Communications No1(87)-98 1998 pp5-12
26
PREDICTIONS
27
Asymptotics
s(2mImII) (uIuII) = ch2Y
Пmin= (mT2m0)[1+radic1+(2-m1
2)mT2]
N 0
28
The analytical representation for П leads to the following conclusions
There is the limiting value of П at high energies
The effective number of nucleons involved in the reaction decreases with increasing collision energy
Probability of observation of antinuclei and fragments in the central rapidity region is small
Strange particles yield increases with increasing collision energy
The ratio of particle to antiparticle and nucleus to antinucleus production cross-section goes to the unit while energy rising
29
30
A2 = min [-Σ(Vα ndash uk)2 - Σ(Vβ ndash ui )2 ]
A3 = min [-Σ(Vα ndash uk)2 - Σ(Vβ ndash ui )2 - Σ(Vγ ndash uj )2 ]
helliphelliphelliphelliphelliphelliphellip
etc
K i
K i j
31
Distribution of jet axes is well described QCD as result of the production of quarks and gluons (ie color charges)
In other words rarr studying of jets is studying of deformation of vacuum by a color charge studying of the deconfinment
32
Observability of particles from which can consist quarks
Observability of short-lived particles is based on two necessary criteria
1) The production cross section for really observable products of secondary interaction (decay) can with a sufficient accuracy presented in the form of two factors
σ = σp Wd
Where Wd is interpreted as the decay probability (or secondary interaction probability) a suggested particle σp its production cross section
2) Universality of Wd or similarity of the Wd properties in various reactions
I + II rarr Jetα + Jetβ
σ = σp Wα(bk)Wβ(bk)
33
34
Conclusion
CBM at SIS-100 is a unique opportunity for investigation of asymptotic of nuclear interactions
35
Thank you
23
24
I + II rarr 1 + hellip
(NIPI + NIIPII ndash p1)2 = (NIm0 + NIIm0 + Δ)2
Δ is the mass of the particle providing conservation of the barion number strangeness and other quantum numbers
25
Baldin AM Malakhov AI JINR Rapid Communications No1(87)-98 1998 pp5-12
26
PREDICTIONS
27
Asymptotics
s(2mImII) (uIuII) = ch2Y
Пmin= (mT2m0)[1+radic1+(2-m1
2)mT2]
N 0
28
The analytical representation for П leads to the following conclusions
There is the limiting value of П at high energies
The effective number of nucleons involved in the reaction decreases with increasing collision energy
Probability of observation of antinuclei and fragments in the central rapidity region is small
Strange particles yield increases with increasing collision energy
The ratio of particle to antiparticle and nucleus to antinucleus production cross-section goes to the unit while energy rising
29
30
A2 = min [-Σ(Vα ndash uk)2 - Σ(Vβ ndash ui )2 ]
A3 = min [-Σ(Vα ndash uk)2 - Σ(Vβ ndash ui )2 - Σ(Vγ ndash uj )2 ]
helliphelliphelliphelliphelliphelliphellip
etc
K i
K i j
31
Distribution of jet axes is well described QCD as result of the production of quarks and gluons (ie color charges)
In other words rarr studying of jets is studying of deformation of vacuum by a color charge studying of the deconfinment
32
Observability of particles from which can consist quarks
Observability of short-lived particles is based on two necessary criteria
1) The production cross section for really observable products of secondary interaction (decay) can with a sufficient accuracy presented in the form of two factors
σ = σp Wd
Where Wd is interpreted as the decay probability (or secondary interaction probability) a suggested particle σp its production cross section
2) Universality of Wd or similarity of the Wd properties in various reactions
I + II rarr Jetα + Jetβ
σ = σp Wα(bk)Wβ(bk)
33
34
Conclusion
CBM at SIS-100 is a unique opportunity for investigation of asymptotic of nuclear interactions
35
Thank you
24
I + II rarr 1 + hellip
(NIPI + NIIPII ndash p1)2 = (NIm0 + NIIm0 + Δ)2
Δ is the mass of the particle providing conservation of the barion number strangeness and other quantum numbers
25
Baldin AM Malakhov AI JINR Rapid Communications No1(87)-98 1998 pp5-12
26
PREDICTIONS
27
Asymptotics
s(2mImII) (uIuII) = ch2Y
Пmin= (mT2m0)[1+radic1+(2-m1
2)mT2]
N 0
28
The analytical representation for П leads to the following conclusions
There is the limiting value of П at high energies
The effective number of nucleons involved in the reaction decreases with increasing collision energy
Probability of observation of antinuclei and fragments in the central rapidity region is small
Strange particles yield increases with increasing collision energy
The ratio of particle to antiparticle and nucleus to antinucleus production cross-section goes to the unit while energy rising
29
30
A2 = min [-Σ(Vα ndash uk)2 - Σ(Vβ ndash ui )2 ]
A3 = min [-Σ(Vα ndash uk)2 - Σ(Vβ ndash ui )2 - Σ(Vγ ndash uj )2 ]
helliphelliphelliphelliphelliphelliphellip
etc
K i
K i j
31
Distribution of jet axes is well described QCD as result of the production of quarks and gluons (ie color charges)
In other words rarr studying of jets is studying of deformation of vacuum by a color charge studying of the deconfinment
32
Observability of particles from which can consist quarks
Observability of short-lived particles is based on two necessary criteria
1) The production cross section for really observable products of secondary interaction (decay) can with a sufficient accuracy presented in the form of two factors
σ = σp Wd
Where Wd is interpreted as the decay probability (or secondary interaction probability) a suggested particle σp its production cross section
2) Universality of Wd or similarity of the Wd properties in various reactions
I + II rarr Jetα + Jetβ
σ = σp Wα(bk)Wβ(bk)
33
34
Conclusion
CBM at SIS-100 is a unique opportunity for investigation of asymptotic of nuclear interactions
35
Thank you
25
Baldin AM Malakhov AI JINR Rapid Communications No1(87)-98 1998 pp5-12
26
PREDICTIONS
27
Asymptotics
s(2mImII) (uIuII) = ch2Y
Пmin= (mT2m0)[1+radic1+(2-m1
2)mT2]
N 0
28
The analytical representation for П leads to the following conclusions
There is the limiting value of П at high energies
The effective number of nucleons involved in the reaction decreases with increasing collision energy
Probability of observation of antinuclei and fragments in the central rapidity region is small
Strange particles yield increases with increasing collision energy
The ratio of particle to antiparticle and nucleus to antinucleus production cross-section goes to the unit while energy rising
29
30
A2 = min [-Σ(Vα ndash uk)2 - Σ(Vβ ndash ui )2 ]
A3 = min [-Σ(Vα ndash uk)2 - Σ(Vβ ndash ui )2 - Σ(Vγ ndash uj )2 ]
helliphelliphelliphelliphelliphelliphellip
etc
K i
K i j
31
Distribution of jet axes is well described QCD as result of the production of quarks and gluons (ie color charges)
In other words rarr studying of jets is studying of deformation of vacuum by a color charge studying of the deconfinment
32
Observability of particles from which can consist quarks
Observability of short-lived particles is based on two necessary criteria
1) The production cross section for really observable products of secondary interaction (decay) can with a sufficient accuracy presented in the form of two factors
σ = σp Wd
Where Wd is interpreted as the decay probability (or secondary interaction probability) a suggested particle σp its production cross section
2) Universality of Wd or similarity of the Wd properties in various reactions
I + II rarr Jetα + Jetβ
σ = σp Wα(bk)Wβ(bk)
33
34
Conclusion
CBM at SIS-100 is a unique opportunity for investigation of asymptotic of nuclear interactions
35
Thank you
26
PREDICTIONS
27
Asymptotics
s(2mImII) (uIuII) = ch2Y
Пmin= (mT2m0)[1+radic1+(2-m1
2)mT2]
N 0
28
The analytical representation for П leads to the following conclusions
There is the limiting value of П at high energies
The effective number of nucleons involved in the reaction decreases with increasing collision energy
Probability of observation of antinuclei and fragments in the central rapidity region is small
Strange particles yield increases with increasing collision energy
The ratio of particle to antiparticle and nucleus to antinucleus production cross-section goes to the unit while energy rising
29
30
A2 = min [-Σ(Vα ndash uk)2 - Σ(Vβ ndash ui )2 ]
A3 = min [-Σ(Vα ndash uk)2 - Σ(Vβ ndash ui )2 - Σ(Vγ ndash uj )2 ]
helliphelliphelliphelliphelliphelliphellip
etc
K i
K i j
31
Distribution of jet axes is well described QCD as result of the production of quarks and gluons (ie color charges)
In other words rarr studying of jets is studying of deformation of vacuum by a color charge studying of the deconfinment
32
Observability of particles from which can consist quarks
Observability of short-lived particles is based on two necessary criteria
1) The production cross section for really observable products of secondary interaction (decay) can with a sufficient accuracy presented in the form of two factors
σ = σp Wd
Where Wd is interpreted as the decay probability (or secondary interaction probability) a suggested particle σp its production cross section
2) Universality of Wd or similarity of the Wd properties in various reactions
I + II rarr Jetα + Jetβ
σ = σp Wα(bk)Wβ(bk)
33
34
Conclusion
CBM at SIS-100 is a unique opportunity for investigation of asymptotic of nuclear interactions
35
Thank you
27
Asymptotics
s(2mImII) (uIuII) = ch2Y
Пmin= (mT2m0)[1+radic1+(2-m1
2)mT2]
N 0
28
The analytical representation for П leads to the following conclusions
There is the limiting value of П at high energies
The effective number of nucleons involved in the reaction decreases with increasing collision energy
Probability of observation of antinuclei and fragments in the central rapidity region is small
Strange particles yield increases with increasing collision energy
The ratio of particle to antiparticle and nucleus to antinucleus production cross-section goes to the unit while energy rising
29
30
A2 = min [-Σ(Vα ndash uk)2 - Σ(Vβ ndash ui )2 ]
A3 = min [-Σ(Vα ndash uk)2 - Σ(Vβ ndash ui )2 - Σ(Vγ ndash uj )2 ]
helliphelliphelliphelliphelliphelliphellip
etc
K i
K i j
31
Distribution of jet axes is well described QCD as result of the production of quarks and gluons (ie color charges)
In other words rarr studying of jets is studying of deformation of vacuum by a color charge studying of the deconfinment
32
Observability of particles from which can consist quarks
Observability of short-lived particles is based on two necessary criteria
1) The production cross section for really observable products of secondary interaction (decay) can with a sufficient accuracy presented in the form of two factors
σ = σp Wd
Where Wd is interpreted as the decay probability (or secondary interaction probability) a suggested particle σp its production cross section
2) Universality of Wd or similarity of the Wd properties in various reactions
I + II rarr Jetα + Jetβ
σ = σp Wα(bk)Wβ(bk)
33
34
Conclusion
CBM at SIS-100 is a unique opportunity for investigation of asymptotic of nuclear interactions
35
Thank you
28
The analytical representation for П leads to the following conclusions
There is the limiting value of П at high energies
The effective number of nucleons involved in the reaction decreases with increasing collision energy
Probability of observation of antinuclei and fragments in the central rapidity region is small
Strange particles yield increases with increasing collision energy
The ratio of particle to antiparticle and nucleus to antinucleus production cross-section goes to the unit while energy rising
29
30
A2 = min [-Σ(Vα ndash uk)2 - Σ(Vβ ndash ui )2 ]
A3 = min [-Σ(Vα ndash uk)2 - Σ(Vβ ndash ui )2 - Σ(Vγ ndash uj )2 ]
helliphelliphelliphelliphelliphelliphellip
etc
K i
K i j
31
Distribution of jet axes is well described QCD as result of the production of quarks and gluons (ie color charges)
In other words rarr studying of jets is studying of deformation of vacuum by a color charge studying of the deconfinment
32
Observability of particles from which can consist quarks
Observability of short-lived particles is based on two necessary criteria
1) The production cross section for really observable products of secondary interaction (decay) can with a sufficient accuracy presented in the form of two factors
σ = σp Wd
Where Wd is interpreted as the decay probability (or secondary interaction probability) a suggested particle σp its production cross section
2) Universality of Wd or similarity of the Wd properties in various reactions
I + II rarr Jetα + Jetβ
σ = σp Wα(bk)Wβ(bk)
33
34
Conclusion
CBM at SIS-100 is a unique opportunity for investigation of asymptotic of nuclear interactions
35
Thank you
29
30
A2 = min [-Σ(Vα ndash uk)2 - Σ(Vβ ndash ui )2 ]
A3 = min [-Σ(Vα ndash uk)2 - Σ(Vβ ndash ui )2 - Σ(Vγ ndash uj )2 ]
helliphelliphelliphelliphelliphelliphellip
etc
K i
K i j
31
Distribution of jet axes is well described QCD as result of the production of quarks and gluons (ie color charges)
In other words rarr studying of jets is studying of deformation of vacuum by a color charge studying of the deconfinment
32
Observability of particles from which can consist quarks
Observability of short-lived particles is based on two necessary criteria
1) The production cross section for really observable products of secondary interaction (decay) can with a sufficient accuracy presented in the form of two factors
σ = σp Wd
Where Wd is interpreted as the decay probability (or secondary interaction probability) a suggested particle σp its production cross section
2) Universality of Wd or similarity of the Wd properties in various reactions
I + II rarr Jetα + Jetβ
σ = σp Wα(bk)Wβ(bk)
33
34
Conclusion
CBM at SIS-100 is a unique opportunity for investigation of asymptotic of nuclear interactions
35
Thank you
30
A2 = min [-Σ(Vα ndash uk)2 - Σ(Vβ ndash ui )2 ]
A3 = min [-Σ(Vα ndash uk)2 - Σ(Vβ ndash ui )2 - Σ(Vγ ndash uj )2 ]
helliphelliphelliphelliphelliphelliphellip
etc
K i
K i j
31
Distribution of jet axes is well described QCD as result of the production of quarks and gluons (ie color charges)
In other words rarr studying of jets is studying of deformation of vacuum by a color charge studying of the deconfinment
32
Observability of particles from which can consist quarks
Observability of short-lived particles is based on two necessary criteria
1) The production cross section for really observable products of secondary interaction (decay) can with a sufficient accuracy presented in the form of two factors
σ = σp Wd
Where Wd is interpreted as the decay probability (or secondary interaction probability) a suggested particle σp its production cross section
2) Universality of Wd or similarity of the Wd properties in various reactions
I + II rarr Jetα + Jetβ
σ = σp Wα(bk)Wβ(bk)
33
34
Conclusion
CBM at SIS-100 is a unique opportunity for investigation of asymptotic of nuclear interactions
35
Thank you
31
Distribution of jet axes is well described QCD as result of the production of quarks and gluons (ie color charges)
In other words rarr studying of jets is studying of deformation of vacuum by a color charge studying of the deconfinment
32
Observability of particles from which can consist quarks
Observability of short-lived particles is based on two necessary criteria
1) The production cross section for really observable products of secondary interaction (decay) can with a sufficient accuracy presented in the form of two factors
σ = σp Wd
Where Wd is interpreted as the decay probability (or secondary interaction probability) a suggested particle σp its production cross section
2) Universality of Wd or similarity of the Wd properties in various reactions
I + II rarr Jetα + Jetβ
σ = σp Wα(bk)Wβ(bk)
33
34
Conclusion
CBM at SIS-100 is a unique opportunity for investigation of asymptotic of nuclear interactions
35
Thank you
32
Observability of particles from which can consist quarks
Observability of short-lived particles is based on two necessary criteria
1) The production cross section for really observable products of secondary interaction (decay) can with a sufficient accuracy presented in the form of two factors
σ = σp Wd
Where Wd is interpreted as the decay probability (or secondary interaction probability) a suggested particle σp its production cross section
2) Universality of Wd or similarity of the Wd properties in various reactions
I + II rarr Jetα + Jetβ
σ = σp Wα(bk)Wβ(bk)
33
34
Conclusion
CBM at SIS-100 is a unique opportunity for investigation of asymptotic of nuclear interactions
35
Thank you
33
34
Conclusion
CBM at SIS-100 is a unique opportunity for investigation of asymptotic of nuclear interactions
35
Thank you
34
Conclusion
CBM at SIS-100 is a unique opportunity for investigation of asymptotic of nuclear interactions
35
Thank you
35
Thank you
