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Centrality classes, shadowing and modeldependence in p-A collisions
Laboratory of Ultra-high Energy Physics,Saint-Petersburg State University
Centrality classes, shadowing and modeldependence in p-A collisions
Drozhzhova Tatiana
Ettore Majorana Erice School of Subnuclear PhysicsSicily, 2014
• Fix nucleus-target collision•Opposite bunches particlescattering
A
Bb
- Number of wounded nucleons- Number of nucleons-spectators
- Total Energy of collision fixed by calorimeters
- Energy of a nucleon
2 methods of fixing centrality:Nucleon-spectatorsMultiplicity
Author: Drozhzhova Tatiana,Scientific adviser: Dr. Feofilov G.A.
Department of High Energy and Elementary Particles Physics, Faculty of Physics, Saint-Petersburg State University
Fluctuations in physical observables in heavy-ioncollisions have been a topic of interest for some yearsas they may provide important signals regarding theformation of quark-gluon plasma (QGP)For studying fluctuation and searching delicate effect itis necessary to determine precisely measurement`sparameters (to fix the centrality classes) when theobservable`s fluctuation will be minimal.
Nucleus is an extendedobject
nuclear collisions could becharacterized by centrality withrespect to impact parameter.
2x
x - the mean value
The relativefluctuation x in anobservable !
Analysis:Influence of the centrality classes width on thefluctuations of observables (Npart)
Why we use Monte-Carlo?Information about
b Impact ParameterNpart Number of wounded nucleons
Distinctions for different classes of centrality are evident
Aim of the analysis :Minimization of trivial fluctuations of observables
Method:Monte-Carlo simulation of nucleus-nucleus collision
Opposite bunchesparticle scattering
- Number of wounded nucleons- Number of nucleons-spectators
- Total Energy of the collisions fixedby left (L), right (R) calorimeters
- Energy of one nucleon
fix the centrality classes methodsin Experiment:
Fix nucleus-targetcollision
Registration ofparticle Multiplicity
Registration ofnucleons-spectators
Glauber model:Pb-Pb collisionthe nuclear density - Woods-Saxon distribution:
for a spherical nucleus with a radius of 6.62 fm and a skin depth of0.545 fmNuclear collisions are modeled by randomly displacingthe two colliding nuclei in the transverse plane.Nucleons from each nucleus are assumed to collide if the transversedistance between them is less than the distance corresponding to theinelastic nucleon-nucleon cross section)
TeVs 76.2
1
0( ) 1 exp Ar Rra
13
0AR R A0 1.07R fm
0.545a fm
mbinel 564
Motivation:
If y(x) is a function of events distribution versusof impact parameter of AA collision.Then F(x) square under the plotPeak value F(x) = F(0)Example:
Centrality classes inALICE experiment
normalization F(x) :
G(0) = 0%G(xmax)=100%G(x) - function compares value of centralityof the collisions (expressed in percentage)to value of the impact parameter.Borders of intervals of the centrality are equalto values of function G (x) in the points limitingthe given interval.
Events distribution on Impact Parameter Conversion for Impact Parameterfrom fm to % G(x)
! "#$%&
! "' %&
( $"( #%&
) $") #%&
*+,-. /+,01&2311-4-3546+57,01&2311-4-354&
! "#$%&
! "' %&
( $"( #%&
) $") #%&
*+,-. /+,01&2311-4-354
For minimal fluctuations it is necessary to take the width ofcentrality interval:
For the most central collisions - equal to 1% or less.For central collision (lower border of centrality interval 5%, 10%, 15%, 20%)
plateau is around 1-2% of the width of centrality interval .For Semi peripheral collisions(lower border of centrality interval - no
less then 3%.For Peripheral collisions (lower border of centrality interval 60-85%) equal to
10%, as the value of is the same for all widths of centrality interval for eachcentrality class.Mean values for number of wounded nucleons in the same
Impact Parameter and Multiplicity centrality classes are equivalent
Distribution of number of woundednucleons in different centrality classes Distribution of number of wounded
nucleons In different Multiplicitycentrality classes
Distribution of number of wounded nucleonsin different Impact Parameter centralityclasses
Events distribution on Multiplicity Conversion for Multiplicity to %
For Impact Parameter For Multiplicity%
G(0) = 100%G(xmax)=0%
6+57,01&2311-4-354&
Multiplicity: collisionpart NfNf )1( 788.0f
- dispersion
Author: Drozhzhova Tatiana,Scientific adviser: Dr. Feofilov G.A.
Department of High Energy and Elementary Particles Physics, Faculty of Physics, Saint-Petersburg State University
Fluctuations in physical observables in heavy-ioncollisions have been a topic of interest for some yearsas they may provide important signals regarding theformation of quark-gluon plasma (QGP)For studying fluctuation and searching delicate effect itis necessary to determine precisely measurement`sparameters (to fix the centrality classes) when theobservable`s fluctuation will be minimal.
Nucleus is an extendedobject
nuclear collisions could becharacterized by centrality withrespect to impact parameter.
2x
x - the mean value
The relativefluctuation x in anobservable !
Analysis:Influence of the centrality classes width on thefluctuations of observables (Npart)
Why we use Monte-Carlo?Information about
b Impact ParameterNpart Number of wounded nucleons
Distinctions for different classes of centrality are evident
Aim of the analysis :Minimization of trivial fluctuations of observables
Method:Monte-Carlo simulation of nucleus-nucleus collision
Opposite bunchesparticle scattering
- Number of wounded nucleons- Number of nucleons-spectators
- Total Energy of the collisions fixedby left (L), right (R) calorimeters
- Energy of one nucleon
fix the centrality classes methodsin Experiment:
Fix nucleus-targetcollision
Registration ofparticle Multiplicity
Registration ofnucleons-spectators
Glauber model:Pb-Pb collisionthe nuclear density - Woods-Saxon distribution:
for a spherical nucleus with a radius of 6.62 fm and a skin depth of0.545 fmNuclear collisions are modeled by randomly displacingthe two colliding nuclei in the transverse plane.Nucleons from each nucleus are assumed to collide if the transversedistance between them is less than the distance corresponding to theinelastic nucleon-nucleon cross section)
TeVs 76.2
1
0( ) 1 exp Ar Rra
13
0AR R A0 1.07R fm
0.545a fm
mbinel 564
Motivation:
If y(x) is a function of events distribution versusof impact parameter of AA collision.Then F(x) square under the plotPeak value F(x) = F(0)Example:
Centrality classes inALICE experiment
normalization F(x) :
G(0) = 0%G(xmax)=100%G(x) - function compares value of centralityof the collisions (expressed in percentage)to value of the impact parameter.Borders of intervals of the centrality are equalto values of function G (x) in the points limitingthe given interval.
Events distribution on Impact Parameter Conversion for Impact Parameterfrom fm to % G(x)
! "#$%&
! "' %&
( $"( #%&
) $") #%&
*+,-. /+,01&2311-4-3546+57,01&2311-4-354&
! "#$%&
! "' %&
( $"( #%&
) $") #%&
*+,-. /+,01&2311-4-354
For minimal fluctuations it is necessary to take the width ofcentrality interval:
For the most central collisions - equal to 1% or less.For central collision (lower border of centrality interval 5%, 10%, 15%, 20%)
plateau is around 1-2% of the width of centrality interval .For Semi peripheral collisions(lower border of centrality interval - no
less then 3%.For Peripheral collisions (lower border of centrality interval 60-85%) equal to
10%, as the value of is the same for all widths of centrality interval for eachcentrality class.Mean values for number of wounded nucleons in the same
Impact Parameter and Multiplicity centrality classes are equivalent
Distribution of number of woundednucleons in different centrality classes Distribution of number of wounded
nucleons In different Multiplicitycentrality classes
Distribution of number of wounded nucleonsin different Impact Parameter centralityclasses
Events distribution on Multiplicity Conversion for Multiplicity to %
For Impact Parameter For Multiplicity%
G(0) = 100%G(xmax)=0%
6+57,01&2311-4-354&
Multiplicity: collisionpart NfNf )1( 788.0f
- dispersion
Centrality in Pb-Pb collisionsat 2.76 TeV
based on Glauber Model
Centrality in Pb-Pb collisionsat 2.76 TeV
based on Glauber Model
MC Glauber, PbPb 2.76TeV
PercentileMultiplicity
Some multiplicity centrality classes Npart distribution in the differentcentrality classes
MC Glauber, PbPb 2.76TeV•With decrease of width of centralitybin the RMS decreases
•Plato (~5-10) is reached at centrality widthFor central events near 3%For peripheral 10% is enough
RM
S of
Npa
rt
See details in T.Drozhzhova poster report ISSP 2014
Centrality in p-Pb collisionsat 5.02 TeV
HIJING 1.38
Centrality in p-Pb collisionsat 5.02 TeV
HIJING 1.38
HIJING [1]• It was based on a two-component geometrical model of minijet
production and soft interaction.• It has incorporated nuclear effects such as nuclear modification of the
parton distribution functions (gluon shadowing)Gluon shadowing [2]
• Without shadowing nucleons interaction will be independent• There are differences between nuclear and proton PDF(parton
distribution function) (observed in experiments).• This leads to decrease of nucleon-nucleon cross section at low x.
• Similar effect is also present in Models with energy conservation inelementary nucleon-nucleon collisions (see refs [3-5])
[1] HIJING: A Monte Carlo model for multiple jet production in p p, p A and A A collisions, Xin-Nian Wangand Miklos Gyulassy, Phys.Rev.D 44, 3501 (1991)
[2] J. Jalilian-Marian arXiv:hep-ph/9909507[3] G. Feofilov, A. Ivanov, Number of nucleon-nucleon collisions vs energy in modified Glauber
calculations // Journal of Physics G CS, 5, (2005) 230-237[4] Irais Bautista, Carlos Pajares, Jose Guilherme Milhano, Jorge Dias de Deus. Phys. Rev. C 86 (2012)
034909.[5] V. Kovalenko, Phys. Atom. Nucl. 76, 1189 (2013), arXiv:1211.6209 [hep-ph]; arXiv:1308.1932 [hep-ph],
2013; V. Kovalenko, V. Vechernin. PoS(BaldinISHEPP XXI) 077, 2012, arXiv:1212.2590 [nucl-th]
• It was based on a two-component geometrical model of minijetproduction and soft interaction.
• It has incorporated nuclear effects such as nuclear modification of theparton distribution functions (gluon shadowing)
Gluon shadowing [2]• Without shadowing nucleons interaction will be independent• There are differences between nuclear and proton PDF(parton
distribution function) (observed in experiments).• This leads to decrease of nucleon-nucleon cross section at low x.
• Similar effect is also present in Models with energy conservation inelementary nucleon-nucleon collisions (see refs [3-5])
[1] HIJING: A Monte Carlo model for multiple jet production in p p, p A and A A collisions, Xin-Nian Wangand Miklos Gyulassy, Phys.Rev.D 44, 3501 (1991)
[2] J. Jalilian-Marian arXiv:hep-ph/9909507[3] G. Feofilov, A. Ivanov, Number of nucleon-nucleon collisions vs energy in modified Glauber
calculations // Journal of Physics G CS, 5, (2005) 230-237[4] Irais Bautista, Carlos Pajares, Jose Guilherme Milhano, Jorge Dias de Deus. Phys. Rev. C 86 (2012)
034909.[5] V. Kovalenko, Phys. Atom. Nucl. 76, 1189 (2013), arXiv:1211.6209 [hep-ph]; arXiv:1308.1932 [hep-ph],
2013; V. Kovalenko, V. Vechernin. PoS(BaldinISHEPP XXI) 077, 2012, arXiv:1212.2590 [nucl-th]
Dependence on a shadowing parameter
PRL 110,032301
Experimentaldata is betterdescribed byHIJING withshadowing
sg <Npart> <Mult>0 7.265 99.060.1 6.536 78.10.2 5.454 48.260.3 3.981 30.92
Experimentaldata is betterdescribed byHIJING withshadowing
Centrality from Multiplicity in p-Pb
Centrality from Multiplicity in p-Pb
Normalization of Multiplicity yields
PRL 110,032301
Sg <Npart> <Mult>
<Npart>=7.9±0.6From Glauber model
Sg <Npart> <Mult>0 7.265 99.060.1 6.536 78.10.2 5.454 48.260.28 3.981 30.92
HIJING 1.38Number of participants is depended on models
No straight forward treatment of experimental data on multiplicity,based on normalization to Npart
See details in T. Drozhzhova, G. Feofilov, V. Kovalenko, A. Seryakov. PoS (QFTHEP 2013) 053, 2013
Summary and Conclusions:
• The method of centrality evaluation initiallydeveloped for ion-ion collisions was applied for p+Pb
• Large fluctuations of number of participants inmultiplicity classes make dividing of the events inclasses according to Npart problematically
• Model dependence of Npart makes questionablenormalization of multiplicity yields to Npart
• The method of centrality evaluation initiallydeveloped for ion-ion collisions was applied for p+Pb
• Large fluctuations of number of participants inmultiplicity classes make dividing of the events inclasses according to Npart problematically
• Model dependence of Npart makes questionablenormalization of multiplicity yields to Npart
•Back-up slides
Centrality from impact parameter p-Pb
Centrality from impact parameter p-Pb
AB-collisionPb-PbsNN = 2.76TeV
1
0( ) 1 exp Ar Rr
a
.
13
0AR R A
0 1.07R fm0.545a fm
Woods-Saxon distribution:Nuclear density
Poisson disctribution:
Particle multiplicity is proportional tonumber of produced strings,which is proportional toparticipants’ numberand collisions’ number
Particle multiplicity is proportional tonumber of produced strings,which is proportional toparticipants’ numberand collisions’ number
( )ABN ( )CN
[ 0 ,1]x