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Monte Carlo model for pp, pA and AA collisions at high energy: parameters turning and results
Vladimir Kovalenko
Saint Petersburg State University

The XXI International Workshop High Energy Physics and Quantum Field Theory June 23 ­ June 30, 2013
Saint Petersburg Area, Russia


2
MC model description

Outline





Parameters and fixing procedure


Results for pp and p-Pb collisions



Results for Pb-Pb collisions Conclusions




3
x
1

Color dipoles inside a nucleon

x

3

p
x'
2

x'

6

x

2

x

4

p
x'
1

x'
x'
4

5

z

N

x'

3

N

x i
i

i

p= p

x i=1

x i
i

i

' p= p

x i ' =1


4


p-p interaction: parton distributions

Inclusive momentum distributions are taken from [1,2]:

At n>1 the sea quarks and antiquarks have the same distribution as the valence quarks. Poisson distribution for the number of quark-antiquark (diquark) pairs (n) is assumed with some parameter


[1] A.B. Kaidalov, O.I.Piskunova. Zeitschrift fur Physik C 30(1):145-150, 1986 [2] G.H. Arakelyan, A.Capella, A.B.Kaidalov, and Yu.M.Shabelski. Eur.Phys.J (C), 26(1):81-90, 2002


5


p-p interaction: parton distributions

Corresponding exlusive distribution of the momentum fractions:

Valence quark is labelled by N-1, the diquark by N, and the other refers to sea quarks and antiquarks. N=2*n



6

p-p interaction: parton distributions

Corresponding exlusive distribution of the momentum frations:

Valene quark is labelled by N-1, the diquark by N, and the other refers to sea quarks and antiquarks. N=2*n


7
q

Monte Carlo model: Color dipoles
r1
x
1

x'

2

qq ( q )

r '
x'
1

2

z

r2
x'

x

r '
q

1

2

qq ( ) q
2

qq (q )

qx

1

x'

z
1

q

x

2

Interaction probability amplitude [4, 5]: 2 r - r ' r 2 -r 2 ' (1) f = s ln 2 1 1 2 r 1- r 2 ' r 2- r 1 '

qq ( q )

Two dipoles interact more probably, if the ends are close to each other, and (others equal) if they are wide.

[4] G. Gustafson, Acta Phys. Polon. B40, 1981 (2009) [5] C. Flensburg, G. Gustafson, and L. Lonnblad, Eur. Phys. J. (C) 60, 233 (2009)


8


Miscellaneous

With confinement taken into we obtain [4, 5]: 2 1 - 1 ' rr 2 - 2 ' rr 1- 2 ' rr 2 - 1 ' rr s f= K0 +K 0 -K0 - K0 2 r max r max r max r max where K0 is modified Bessel function.


[(

)(

)(
max

)(

)

]

2

(2)

K 0(r /r At r 0 the formula (1).

max

)

- ln ( r / ( 2r

max

) ) and we return back to
ma x



At

r :

K 0(r /r

max

)

and amplitude decrease exponentially.




r 2r

e

-r / r

The total probability of the inelastic interaction of two protons in the eikonal approximation:

[4] G. Gustafson, Acta Phys. Polon. B40, 1981 (2009) [5] C. Flensburg, G. Gustafson, and L. Lonnblad, Eur. Phys. J. (C) 60, 233 (2009)


9


Calculation of multiplicity
Multiplicity is calculated in the framework of colour strings, stretched between colliding partons; xi determine rapidity ends of strings.

y

min

and ymin are calculated supposing that a string fragments into only two particle with masses 0.15 GeV (for pion) and 0.94 GeV for proton and transverse momentum of 0.3 GeV (and higher at LHC) dN/dy from one string is supposed to be constant 0. String fusion effects considered






10

string fusion

The interaction of colour strings in transverse plane is carried out in the framework of local string fusion model [6] with the introduction of the lattice in the impact parameter plane. The finite rapidity length of strings is taken into account [7-9].

Sk ­ area, where k strings are overlapping, 0 single string transverse area, 0 and p0 ­ mean multiplicity and transverse momentum from one string
[6 [7 [8 [9 pt ] ] ] ] Braun, M.A. and Pajares, C. Eur. Phys. J. (C),16,349,2000 V. Vechernin and R. Kolevatov, Physics of Atomic Nuclei 70, 1797 (2007) V. Vechernin and R. Kolevatov, Physics of Atomic Nuclei 70, 1809 (2007) Vechernin, V. V. and Kolevatov, R. S., Simple cellular model of long-range multiplicity and correlations in high-energy nuclear collisions 2003 http://arxiv.org/abs/hep-ph/0304295v1


11


Description of a nucleus

We use usual Woods-Saxon form of nuclear distribution:



All partons from each nucleon are considered together A nucleus is participating in the collision if at least one of it's partons collides with other from the proton. Every parton can interact with other one only once ­ this provide energy conservation in the initial state






12

p-p interaction: parameter fixing

Strategy for parameters fixing:
Correspondence of mean number of dipoles and energy is obtained using data on total inelastic cross section


Performed for each parameters set
, mb

tot

inel


13

p-p interaction: parameter fixing

Strategy for parameters fixing:
Mean multiplicity per rapidity from one string 0 is fixed once at intermediate LHC energy (2.36 TeV)


Data on energy dependence of multiplicity in pp collisions is used to constrain the rest of parameters


p-Pb at 5.02 GeV minimum bias: =16.81 ± 0.71 [10]


Look at PbPb collisions

[10] B. Abelev et al (ALICE Collaboration) Phys. Rev. Lett. 110, 032301, 2013


14

p-p interaction: parameter fixing

Initial range of parameters:


r0: 0.4 ­ 0.7 fm r
max



/r0: 0.3 ­ 0.6



S: 0.2 ­ 2.8 rstr: 0 (no fusion); 0.2-0.6 fm Energy range: 53 ­ 7000 GeV






15

parameter fixing: After accounting of pp multiplicity

pp multiplicity in the model


Not sensitive to string fusion r0 arounf 0.5 ­ 0.6 is favoured r
max





and S: no conclusion



0: always about 1.1 ­ 1.2


16

parameter fixing: After accounting of p-Pb multiplicity

p-Pb multiplicity gives us:


Large string radius is disfavoured r0 of 0.4 ­ 0.5 fm is excluded large S excluded





for both rmax and S: less are favoured: higher and lower elementary collision probability




0: is still about 1.1 ­ 1.2


17

Results: PbPb collisions at 2.76 TeV


18

Results: PbPb collisions at 2.76 TeV

[11] [12] [13]

[11] K. Aamodt et al. Phys. Rev. Lett.106:032301, 2011 [12]. S. Chatrchyan et al, JHEP 08 (2011) 141 [13]. G. Aad et al. Phys. Lett. B710 (2012) 363


19

Results: PbPb collisions at 2.76 TeV dN/dy
[14]

[14] E. Abbas, et al. (ALICE Collaboration) arXiv:1304.0347 [nucl-ex], 2013


20

Results: PbPb collisions at 2.76 TeV dN/dy, normalized at y=0


21


Conclusions

The present non-Glauber Monte-Carlo model describes multiplicity yields in wide energy range and for different colliding systems. The results on pp collisions do not fully constrain the model and one have to use other colliding systems


Multiplicity per rapidty from one single string is about 1.0 ­ 1.2

Comparison with experiment of the dependence of multiplicity per participant on the centrality in PbPb collisions at 2.76 TeV shows that good agreement is obtained only when the string fusion effects are present with the radius of string 0.2-0.3 fm.


Both energy conservation in the initial state and string fusion are important in PbPb collisions for the description of multiplicity


[15] Irais Bautista, Carlos Pajares, JosИ Guilherme Milhano, Jorge Dias de Deus. Phys. Rev. C 86, 034909 (2012) arXiv:1206.6737 [nucl-th]


22

Conclusions
fm


23

Backup


22


References

V.Kovalenko. Modelling of exclusive parton distributions and long-range rapidity correlations for pp collisions at the LHC energy accepted at Phys. Atom. Nucl. Vol. 93, N 10 (2013) arXiv:1211.6209 [hep-ph] V.Kovalenko, V.Vechernin. Model of pp and AA collisions for the description of long-range correlations PoS (Baldin ISHEPP XXI) 077 arXiv:1212.2590 [nucl-th]



25

Backup


27


p-p interaction: color dipoles

The probability amplitude for the ollision of two dipoles with oordinates (r1,r2), (r3,r4) [3,4]:



r

Confienment is taken into account by introduction of some cut off at 0.2 - 0.3fm. It leads: max



The total probability of the inelastic interaction of two protons in the eikonal approximation:

[3] G. Gustafson, Acta Phys. Polon. B40, 1981 (2009) [4] C. Flensburg, G. Gustafson, and L. Lonnblad, Eur. Phys. J. (C) 60, 233 (2009)


28

p-p interaction: string fusion

The interaction of colour strings in transverse plane is carried out in the framework of local string fusion model [5] with the introduction of the lattice in the impact parameter plane. The finite rapidity length of strings is taken into account [6-8].

Sk ­ area, where k strings are overlapping, 0 single string transverse area, 0 and p0 ­ mean multiplicity and transverse momentum from one string
[5 [6 [7 [8 pt ] ] ] ] Braun, M.A. and Pajares, C. Eur. Phys. J. (C),16,349,2000 V. Vechernin and R. Kolevatov, Physics of Atomic Nuclei 70, 1797 (2007) V. Vechernin and R. Kolevatov, Physics of Atomic Nuclei 70, 1809 (2007) Vechernin, V. V. and Kolevatov, R. S., Simple cellular model of long-range multiplicity and correlations in high-energy nuclear collisions 2003 http://arxiv.org/abs/hep-ph/0304295v1


29

string fusion mechanism versions


30


Glauber Model [2, 3]

Nucleus-Nucleus collision is a sequence of nucleons collisions Nucleons are distributed according to Woods-Saxson:



Trajectories of nucleons are linear Each nucleus can collide several times with the same inelastic cross section: corresponding to proton-proton inelastic cross section Energy loss due to particle production is not considered





[2] Bialas A, Bleszynski M, Czy W. Nucl.Phys.B 111:461,1976; Glauber RJ. Nucl. Phys.A 774:3, 2006 [3] M. L. Miller, K. Reygers, S. J. Sanders, P. Steinberg. Ann. Rev. Nucl. Part. Sci., 57:205­243, 2007


31

AA interaction: charged multiplicity PbPb, 2.76TeV

[10]

[10] K. Aamodt et al (ALICE Collaboration).Phys. Rev. Lett.,106, 032301, 2011.


32

AA interactions Compare with Glauber's model

Number of participant, number of binary collisions, their variations and scaled variatons and correlator for inelNN =34mb, calculated in the model of this work:
10 9 8 7 6 5 4 3 2 1 00 00 00 00 00 00 00 00 00 00 0 Np a rtA Np a rtAB N_ C
250 200 150 100 50 0 1 9 Dnp artAB 8 7 DN_ C* 6 5 4 3 2 1 0 10 12 1 4 16 18 DNP artA 0 0 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 0
3,5 3 2,5 2 1,5 1 0,5 0 0 2 4 6 8 10 12 14 16 70 c o rrelator* 60 D /N 50 D _C /N _C 40 30 20 10 0 18

0

2

4

6

8

10 12

14 1 6 1 8

0

2

4

6

8

The same for the Glauber's model (NN =34mb) :
10 9 8 7 6 5 4 3 2 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
250
5000

7 6 5 4 3 2 1 0 0 2 4 6 8 10 12 14

N pa rtA N pa rtAB N _C
200 150 100 50

DNP a rtA Dnp a rtA B DN_ C*

4500 4000 3500 3000 2500 2000 1500 1000 500

70 c orrelator* 60 D /N D _C /N_C 50 40 30 20 10 16 0 18

0

2

4

6

8

10

12

14

16

18

0

0

0

2

4

6

8

10 12 1 4 1 6 18