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1. FEB1S33
a tt «aj= ii
IC/82/216
INTERNATIONAL CENTRE FORTHEORETICAL PHYSICS
THE LONGITUDINAL PHASE SPACE (LPS) ANALYSIS
OF THE INTERACTION np •* ppir" AT P Q= 3-5 GeV/c
INTERNATIONALATOMIC ENERGY
AGENCY
UNITED NATIONSEDUCATIONAL,
SCIENTIFICAND CULTURALORGANIZATION
Burhan Fatah
Calin Beshliu
and
Gruia Silviu Gruia
1982MIRAMARE-TRIESTE
IC/82/216 Analysis of the experimental data for the reaction
np ppn (1)
International Atomic Energy Agency
and
United Nations Educational Scientific and Cultural Organisation
INTERNATIONAL CENTRE FOR THEORETICAL PHYSICS
THE LONGITUDINAL PHASE SPACE (LP8) ANALYSIS
OF THE INTERACTION np •* ppiT AT P =3-5 GeV/c *n
Burhan Fatah
International Centre for Theoretical Physics, Trieste, Italy,
Calln Beshliu and Gruia Silviu Gruia
Department of Nuclear Physics, University of Bucharest, Romania.
ABSTRACT
The react ion np •+ ppiT i s analyzed at P = 5.10 and 3.83 GeV/c using
longitudinal phase space (LPS) ana lys i s . The d i s t r ibu t ions of u {Van Hove's
angle) along with the hexagonal p lo t s are investigated in d e t a i l . From the
w-distr ibut ions i t i s possible to conclude t h a t , whenever, allowed, the
di f f rac t ive mechanism (Pomeron exchange) dominates the three Trody f ina l s t a t e .
For the f i r s t time the approximate percentage, on the basis of hexagonal
d i s t r i b u t i o n s , of the different processes involved (d i f f rac t ive , per iphera l ,
e t c . ) i s calculated which may very well agree with the expectations at these
energies .
The Invest igat ion has been performed at the Laboratory of High Energies,
Laboratory of Computing Techniques and Automation, JINR., Dubna and Laboratory
of Nuclear Physics, University of Bucharest.
MIRAMARE - TRIESTENovember 1932
To be submitted for publ icat ion.
i s d i f f i cu l t due to the large number of kinematical variables needed for
every event. For example, in the case of n -pa r t i e l e s in the f ina l s t a t e
3n~h independent variables are needed (or 3n-5 var iables when the incident energy
i s f ixed) . Therefore one always looks for different p o s s i b i l i t i e s in order
to minimize t h i s large number of parameters.
One of the most successful methods, in t h i s d i rec t ion , i s Van Hove's
Longitudinal Phase Space {LPS) analysis [ l ] . We r eca l l here b r i e f ly the
or ienta t ion of the three f ina l p a r t i c l e s , In react ion ( i ) , in the hexagonal
d i s t r i bu t ions : de t a i l s of the hexagonal p lots can be found elsewhere [ 2 , 3 ] .
The general scheme of the longitudinal phase space p l o t , along with the
different exchange diagrams, i s presented in F i g . l , where the axis marked
P. refers t o the longitudinal cm . momentum of the f ina l s t a t e p a r t i c l e s .
I f the masses and the t ransverse momenta of the f ina l p a r t i c l e s are small
compared with the t o t a l c m . energy, the experimental events tend t o l i e along
the kinematical border of t h i s plot which at large energies becomes a regular
hexagon. The angle in between the three p a r t i c l e s i s 120 . The signs
marked "+" and " -" refer t o the "forward" and "backward" motions of the final
par t ic les , respectively.
Three exchange diagrams (Feynman graphs) wil l be discussed in detail
throughout th is a r t ic le . The f i rs t diagram refers to the displacement of
particles when P f (Fast Proton) [k] along with Ps (Slow Proton) [h] goes in
the backward direction. The most protable part ic le exchanged trajectory,
between the two vert ices, i s a pomeron.
Similarly in the second diagram we consider the movement of f . in the
forward direction while the combination p ir~ goes backward, in cm. Clearlys
a Tr-meson exchange takes place. Lastly an exotic exchange Is expected when
both nucleona appear at the same vertex.
In this paper we are presenting an anlysis of experimental data
obtained by Dubna-Bucharest University Collaboration. The 1-w hydrogen
bubble chamber was irradiated at J.I.S.R, Dubna using, a monochromatical
neutron beam ( — ^ - 3 %, A6<li0.3 m rad) [5] , The reaction channel
np •* PP"" wa identified at four different incident momenta P = 1.73,
2.23, 3.83 and 5.1 GeV/c having a s t a t i s t i c s of 1*623, 2933, 2093 and 892
events, respectively [6].
- 2 -
A3 it w b e «••-. from U-.r- o-ptrii .-.^tal distributions cf th.-: transverse
momenta for Lhe t,.,ree final state p a r t i e s of the reaction under discussion
(see Figs.2,3,4), their valves are sufficiently low anfl constant (the figures
are self-explanatory, the solid line refers ...• ... • : • . . . observation which
allows us to be within the demands of the longitudinal phase space (LPS)
analysis. In such a situation a transverse momentum cut could fce made in
the total incident momenta.
An eventual inclusion of the transverse phase space in the calculations
(along with LPS) may not lead to significant physical informations, moreover,
this has the disadvantage of introducing another parameter, something which
evidently makes the calculations difficult without obtaining an efficiency in
the physical analysis of the experimental data.
Hext we consider the experimental distributions of the longitudinal
momenta, in cm., for reaction ( i ) . If Fig.5 the corresponding distribution
for the TT -meson are given whereas Figs.6,T represent the longitudinal momenta
distributions for the p f and p s , respectively. All the three distributions
are considered at four different incident momenta P = 5.10, 3.83, 2.23 and
1.73 GeV/c. The solid line represents phase space.
As i t was expected before, the longitudinal momenta distributions for
the » -meson are isotropic around zero whereas the "p " and "p " are more
dominant in the "forward" and "backward" directions, in cm. , respectively.
This kind of movement of the particles grows with an increase in the incident
neutron momenta. These experimental distributions indicate, strongly, the
existence of particle exchange Feynman diagrams, for the process under
consideration, which favours the selection of the LPS analysis.
The previous differential applications of the existing data showed
the importance of LPS analysis [ 7 , . . . AT]. A characteristic parameter,
of LPS analysis, is the radial vector p (see Fig.8) which is
presented, for all three possible combinations, at two different incident
momenta FQ = 5.10 and 3.83 GeV/c. According to these distributions the length
of the radial vector is almost constant for all the combinations in the
framework of the same energy considered. The small lengths of the p-distributions
as well as their constant positions, at both of the energies, together with the
transverse momenta representations (also having values practically constant
and Independent of the incident energy) show the grouping of majority of the
events to the boundaries of the hexagon.
In Figs.9,10 two Van Hove plots for the incident momenta P = 5.10,
3.83 GeV/c, respectively, are presented. On the three axes, having an angle
of 120 between them, the longitudinal momenta (P ), in cm., for the three
- 3 -
final particles are shown. These diagrams, based on the phenomenologieal
characteristics, show the grouping of events, in the plots, under the form
of regular hexagon, with the observation that this geometrical form is more
pronounced with the increasing incident energy. Under the circumstances
when p is approximately constant the polar angle u becomes the only decisive
parameter and shall be used in the following discussion very frequently. The
tendency of the events to group around the boundaries of the hexagon corresponds
to the kinematical fact that the transverse momenta, of al l the outgoing
particles, is relatively small.
In Figs.11,12 we present the distributions of the polar angle ID for
the combinations p ir~ and p it", respectively, at P = 5.10 and 3.83 GeV/c
(892 and 2093 events, respectively). The grouping of the events can be
observed very clearly at ID i< 60° and i< 120° for the combinations p• IT" and
p IT , respectively. These distributions are allowed by the phase space,
graphically represented with the solid line. The values which exceed the
phase space curves, in the central regions, refer to the resonance process which
appear in the irN combination. In order to understand more explicitly the
presence of resonances, in the u distributions, we use the double plots
ID vs. M (where co is the Van Hove's polar angle, M stands for an effective
mass distribution).
In Figs.13,11* we present M _ vs. m _ and M ^- vs. « _ ,M_ « _
respectively, at tile two incident momenta ?n » 5.10, 3.83 GeV/c (statistics
is 892 and 2093 events, respectively). Grouping of the events is quite clear
at m i> 60 and ^ 120 , respectively for Pffl~ and V if . Resonance masses
seem tobelong to the regions from 1-2 GeV/c2. A detailed study is needed in
order to understand the physical structure of these resonances.
These experimental observations allow us to believe the presence of
some dynamics of the type peripherical and diffractive In the reaction channel
( i ) . For a better understanding of the dynamical process involved, in the
reaction under discussion, we think i t useful to have a. phenomenological
discussion of the experimental data from the point of Van Hove's hexagonal plots.
We again go back to Figs.9)10 where the two hexagonal diagrams, for
the three final particles In reaction U ) , are plotted at ?n = 5.10 and 3.83
GeV/c having number of events 892, 2093, respectively. In the region u 1 60
(conform notions from Fig.l) one can observe a preferred movement of Pf and
- l t -
::. s ZWt S
the IT -meson in the forward hemisphere whereas the P continues i t s motion ins
the backward direction. The dominance of these dynamics corresponds to the
region 0° < cu < l£0° having a maxinum of i> 60°. This kind of movement
of the particles, generally speaking, refers to the diffraction dissociation
process (the exchanged particle trajectory between the two vertices being
a pomeron). In the second region 60° < <J) < l8o° one sees a dominance of
the displacement of p^, along with v~, in the 'backward direction while the
p f moves in the opposite hemisphere. This region is dominated by a grouping
of events in about the value of a i> 120 corresponding to a process with the
exchange of a meson.
A special remark must be made for an agglomeration of the events, in
Figs.9,10, in the intermediate region between 60° and 120° which corresponds
to the direction of flight of one of the final protons in the backward direction.
Aa a matter of fact these are the non-resonant events (see Figs.11,12). By
looking at the distribution in the longitudinal momenta (Figs.5,6,T) one can
drav the evident conclusion that p , most probably, appears at the second
vertex. Therefore i t may be said that the majority of the events from the
overlapping, observed in the mentioned area (a bit before), corresponds to
the situation in which Pg and ir~ move together in the backward direction.
Events which are spread around u ^ O°/36o° show the absence of some
anomalies in the direction of flight of the two protons ( i .e . small probability
for both the protons to appear at the some vertex), this fact being only
possible in the allowed limits of phase space. Therefore i t may be concluded
that the data, from the experiment ttnder discussion, shows the absence of some
dibaryonic (PP) resonant states.
In the spirit of the classical ideology of Van Hove, therefore in the
limits of the analysis of experimental material froffl the point of view of
longitudinal phase space, one can, approximately, calculate the contributions
of the dominant process from reaction ( t ) . Calculations were done for the
highest neutron incident energy, at disposal, in the present experiment
Pn = 5.10 GeV/c, stat ist ics being 892 events.
The procedure consists of an analysis of the two intervals, in the
hexagonal representation, of flu = 36°, each having values in between:
and
102" for peripherical process
- 5 -
for diffractive process
By looking at the distributions of the experimental events in these
subdivided regions (see Tables Tl, T2) i t may be remarked, with a good
approximation, that the bias of other types of diagrams is sufficiently
reduced. Weighing these numbers of events to the to ta l number of events
one can get the rough approximate results:
Diffractive processes ^ 50 %
Peripheral processes "» kO %
Other types of processes i< 10 %
In the end some final concluding remarks can be made about the analysis
performed!
The first conclusion, which one can draw, is the satisfactory interpretation
of the experimental data using the longitudinal phase space (LPS) analysis,.
Though energies considered were rather low for an application of this analysis
but s t i l l the results were good. It was further observed that the overall
efficiency of the analysis was Improved with an increase in the incident
neutron energy.
The most important result from this analysis, applied to np •* ppif at
P = 5.10 GeV/c, was the estimation of the different processes dominating
the reaction channel under discussion. Using the hexagonal representation
an approximate percentage of the diffractive aa well as peripheral processes
was calculated which came out to be 50 % and !»0 %, respectively.
The last conclusion is a very general one. The LPS analysis seems to be
an effective tool to explain some of the final state particle properties,
e.g. diffractive behaviour etc. in a fairly nice way. On the other hand,
i t was felt that the LPS analysis is unable to explain some very Important
factors in the experimental hadron physics, e.g. resonance production mechanism,
etc. It was further noticed that at moderate energies *v> 5 GeV the analysis
may not be very effective as the contribution of the transverse momenta, to the
total outgoing momenta, is higher and one may not be in a position to neglect
i t totally. c
ACOOWLEDGMKiraS
We are grateful to A.P. lerusaliwov and Yu,A. Troyan for stimulating
discussions. One of the authors (B.F.) would like to thank Professor Abdus Salam,
the International Atomic Energy Agency and UNESCO for hospitality at the
International Centre for Theoretical Physics, Trieste.
REFERENCES AND FOOTNOTE
[1] L. Van Hove, Nuel. Phys. B9, 331 (1969); Phys. Lett. 28B, 1*29 (1969).
[2] V. Kittel, L. Van Hove and W. Wojlck, CERH (D. Ph.Il) Phys. 70-8.
[3] A. Bialas, A. Eskreys, W. Kittel, S. Pokorskl, J.K. Tuominiemi and
L. Van Hove, Nucl. Pays. Bll, 1*79 (1969)-
[It] In order to make a distinction between the tvo final protons ve assign
each of them a label which is based on their energies. The proton vhich
has more energy Is called fast proton while the other one is called slow-
proton .
[5] Abdlvaliev A. et al., Hucl. Phys. Bg£, ^ ^ 5 ) PAU5.
[6] Abaivaliev A. et al., D1-81-T56 preprint, Dubna (19-81).
[7] L. Van Hove, Proc. of the Colloquium on Multiparticle Dynamics, Helsinki
(19T1).
[8] J. Bartsch et al., Nucl. Phys. B19, 38l (19T0).
[9] G. Bossompierre et al., Hucl Phys. BlU, 1U3 (1969).
[10] W. Kittel, Proc. of the Colloquium on Multiparticle Dynamics, Helsinki
(1971).
[ll] M. Deutschmann, Rapporteur's talk given at the Amsterdam International
Conference on Elementary Particles, Amsterdam (1971).
[12] w. Kittel, S. Ratti and L. Van Hove, Nucl. Phys. B30, 333 (1971).
[13] J.E. Brau, F.T. Dao, M.F. Hodous, I.A. Pless and R.A. Singer, Phys. Rev-
Lett. 27-2, 1U81 (1971).
[Ik] E. De Wolf et al., Nucl. Phys. BU6, 333 (1972).
[15] J. Beaupre et al., Nucl Fhys. B35, 6l (1971).
[16] J. Beaupre et al., "How does am LPS analysis separate production mechanism*
in IT p interaction at 8 and 16 GeV/c" CERN preprint, CERN (D. Ph.II)
Phys. 72-1.
[17] J. Benecke et al., Phys. Rev. 188, 2159 (1969).
-7-
TOTAL EVENTS
CAPTIOUS
S£ 60' 66' 72" 78
(1)
(2)
(3)
15
10
7
t.
U
11
a
*.-
67
53
33
9
53
«
22
7
32
16
11
t,
11
17
10
Table Tl
TOTAL EVENTS
102* Xtf lit 120 126 132*
12
7
J
11
8
5
3
61
50
30
8
53
39
19
5
29
13
8
3
8
7
3
Fig.2
FiR.3
Fig.lt
Fifi.5
F1J;.6
Fig.7
Fig.8
Fig.9
The most probable exchange diagrams from the point of view of Van
Hove's hexagonal representation.
Transverse momenta of the ir~-meson at P = 5.10, 3.83, 2.23 and 1.73
GeV/c. Solid curve represents corresponding phase space.
Transverse momenta of the "fast" protons (p ) at P = 5.10, 3.83, 2.23and 1.73 GeV/c. Solid curve represents corresponding phase space.
Transverse momenta of the "slow11 protons fp ) at P = 5.10, 3.83, 2.23s n
and 1.73 GeV/c. Solid curve represents corresponding phase space.
Longitudinal momenta of the Tr"-meson, in cm. , at P = 5.10, 3.83, 2.23
and 1/73 GeV/c. Solid curve represents corresponding phase space.
Longitudinal momenta of the "fast" protons ( p J , in cm. , at P = 5.10,
3.83, 2.23 and 1.73 GeV/c, Solid curve represents corresponding
phase space.
Longitudinal momenta of the "slow" protons (u ) , in cm. , at P = 5.10,
3.83, 2.23 and 1.73 GeV/c. Solid curve represents corresponding
phase space.
Experimental distributions of Van Hove's radial vector "p" calculated
for al l the possible final state particles combinations, in cm. , at
PQ = 5.10 and 3.83 GeV/c.
Distribution of the experimental events in Van Hove's hexagonal plotat P = 5.10 GeV/c.
Distribution of the experimental events in Van Hove's hexagonal plot
at P = 3.83 GeV/cnVan Hove's polar angle "«" distributions, calculated for the
combination pfw~ at Pn = 5.10 and 3.83 OeV/c. Solid line represents
the corresponding phase space.
Van Hove's polar angle "u>" distributions, calculated for the
combination p fl~ at P =5.10 and 3.83 GeV/c Solid line represents
the corresponding phase space.
102*<uj<138*
Table T2
-9 -
-10-
Fig. 13 Double p lo t s H v s . to at ? * -,-iu tin a 3.83 GeV/c.P f - '
Fia. lU Double p lo t s M VB' ID - tit P = 5.10 and 3.S3 GeV/c.
Data Tables: Tl , T2.
Pf
P .
n
P .
Pf
Flg. 1- 1 2 -
np
50
5.10 GeV/c
892 ev.
15
tf>
100
50
0
180
90
0400
£ 300
z 200
100
0
750
500
250
np
Pn=5.10 GeV
892 ev.
Pn-3.83GeVc
Pn=2.23G*/c
Pn=1.73GeVc
4623 ev.
- 1 5 -
-15 -10 -0.5 0.0 0.5 10 1.5
Flg.5
-16-
150
100
50
270
«180ztuiuu. 90O
I0
300
200
100
0
500
250
np •—— ppji
P n -510GeV / c
892 ev.
Pn=3.83GeV/c
2093 ev.
Pn= 2.23 GeV
2933 ev.
Pn=173GeV/c
4623 ev.
-15 -10 -05 0.0 O5 10 t5
Fig. 6-17-
150
HI
u.O
np ppjr
Pn = 510GeV/c
892 ev
Pn=3.83GeV/c
2093 ev
2.23 Gev>c
2933 ev
1.73 GeV/c
4623 ev
-15 -1.0 -05 0.0 05 1.0 1.5
Flfl. 7-18-
150
100
LU
50
300 F
200
100
np
15.10
3.83 GeV/c
np —-pprc"
5.10
np
383GeV/c
510GeV/c
5 10 15 2 0 5 1 0 15 205 10 15 20e P f * - e p ^ - epf Ps
Fig. 8-19-
Fig. 9-20-
MA*
\ /*
np
V\ .\ v
0.
• '
/
/
f
\
\
>
.5 1.
/ »
• f t
• • A
\\
\
2093 «v.
\
f
Fig. 10
-21-
200
Ato
Io6
300
np
Pn-5.10GeW/c
892 ev.
Pn-5.10G<*//c
892 «v.
90° 180° 270° 360°
Fig. 11
-22-
300
200
100
en
IIu.O
i 450
300
24
16
1.2
24
Mp./r'
1.6
1,2
np
- I •—I
Pn=51O(3eV/c
892 ev.
,/-25»v.
/ / / • /
H ^ 1 h
2093ew./-25ev.
0° 36° 72° 108° 144° 180°270° 360u
Fig. 12
-23-
Fig. 13
-21.-
72° 108'
Fig.14
-25-
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IC/82/113 P. RACZKA, JR. - On the class of simple solutions of SU(2) Yang-MillsINT.REP.* equations.
IC/82/lllt
IC/82/115
IC/82/116
IC/82/117
IC/82/118
lc/82/119INT.REP.*
IC/82/122
IC/82/121*INT.REP.*
IC/82/127INT.REP.*
IC/B2/128INT.REP.*
IC/82/129INT.REP.*
IC/82/130
IC/82/131INT.REP.*
IC/62/132IHT.REP.*
IC/82/133
IC/82/131*INT.REP.*
IC/82/137INT.REP.*
IC/82/138INT.REP.*
IC/S2/l!*0
IC/82/llt2INT.REP.*
IC/82/HI3
IC/82/1M4INTLREF.*
IC/82/llt5
IC/82/1U6
IC/82/1147INT.REP.*
IC/82/lWIMT.REP.*
IC/82/lk9IHT.REP.*
G. LAZARIDES and Q.-SHAFI - Supersymmetric GUTs and cosmology.
B.K. 3HARMA and M. TOMAK - Compton profiles of some 'id transition metals.
M.D. MAIA - Mass splitting induced by gravitation.
PARTHA GHOSE - An approach to gauge hierarchy in the minimal SU(5) modelof grand unification.
PARTHA GHOSE - Scalar loops and the Higgs mass in the Salam-Weinberg-Glashow model.
A. QADIR - The question of an upper bound on entropy.
C.W. LUNG and L.Y. XIONG - The dislocation distribution function in theplastic zone at a crack tip.
EAYANI I. RAMIREZ - A view of bond formation in terms of electron momentumdistributions.
N.N. COHAN and M. WEISMANN - Phasons and amplitudons in one dimensionalincommensurate systems.
M. TOMAK - The electron Ionized donor recombination in semiconductors.
S.P. TEWARI - High temperature superconducting of a Chevrel phase ternarycompound.
LI XINZ HOU, MAUG KELIN and ZHANG JIAMZU - Light spinor monopole.
C.A. MAJID - Thermal analysis of chalcogenides glasses of the system
( A 32 Se3>l-X
K.M. KHANNA and S, CHAUBA SINGH - Radial distribution function and secondvirial coefficient for interacting bosons.
A. QADIR - Massive neutrinos in astrophysics.
H.B. GHASSIB and S. CHATTERJEE - On back flow in tvo and three dimensions.
M.Y.M, HASSAN, A. RABIE and E.H. ISMAIL - Binding energy calculations usingthe molecular orbital wave function.
A. EREZINI - Eigenfunctions in disordered systems near the mobility edge.
Y. FUJIMOTO, K. SHIGEMOTO and ZHAO ZHIYONG - No domain wall problem inSU(ti) grand unified theory.
G.A. CHHISTOS - Trivial solution to the domain wall problem.
S. CHAKRABARTI and A.H. NAYYAR - On stability of soliton solution in HLS-type general field model.
S. CHAKRABARTI - The stability analysis of non-topological solitons ingauge theory and in electrodynamics,
S.N. RAM and C.P. SINGH - Hadronic couplings of open beauty states.
BAYAIJI I. RAMIREZ - Elctron momentum distributions of the first-rowhomonuclear diatomic molecules, A .
A.K. MAJUMDAR - Correlation between magnetoresistance and magnetization inAg Mn and Au Mn spin glasses.
E.A, SAAD, S.A. El WAKIL, M.H. HAGGAG and H.M. MACHALI - Pade approximantfor Chan.drasekhar H function.
G.A. El WAKIL, M.T. ATIA, E.A. SAAD and A. HEBDI - Particle transfer inmultiregion.
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