Exploring energy balance in multihadron production:from hadronic to nuclear collisions

A. N. Mishra1,∗ R. Sahoo1, Edward K. G. Sarkisyan2,3, and A. S. Sakharov2,4,51Discipline of Physics, School of Basic Sciences,

Indian Institute of Technology Indore, Indore-452017, India2Department of Physics, CERN, 1211 Geneva 23, Switzerland

3Department of Physics, The University of Texas at Arlington, Arlington, TX 76019, USA4Department of Physics, New York University, New York, NY 10003, USA and

5Physics Department, Manhattan College, New York, NY 10471, USA

Introduction

Study of global observables of multiparticleproduction and their universality in differenttypes of high-energy collisions is one of themost intriguing topics in high-energy interac-tion studies. Recently, the center of mass en-ergy,

√sNN , dependence of the midrapidity

pseudorapidity density and the transverse en-ergy density in the midrapidity of charged par-ticles measured in the head-on nucleus-nucleuscollisions using the effective energy approachbased on pp/pp̄ data and the centrality depen-dence of these two variables within the dissi-pating participant energy approach have beendemonstrated to be well described [? ].

In the present work, the energy andcentrality dependences are studied for thecharged particle mean multiplicity, extendingthe earlier energy-dependence analysis donein Ref. [? ] to LHC energies and adding tothat the centrality dependence study. Withinthe approach, combining the constituentquark picture together with Landau relativis-tic hydrodynamics [? ], one can calculatemultiplicity, Nch, for a given rapidity den-sity ρ(0) at

√sNN , and the rapidity density

ρpp(0) and the multiplicity Nppch at 3

√sNN , as:

2Nch

Npart= Npp

ch

ρ(0)

ρpp(0)

√1− 2 ln 3

ln (4.5√sNN/mp)

(1)

∗Electronic address: Aditya.Nath.Mishra@cern.ch

0

20

40

60

80

100

120

10 102

103

√s−

NN , √s

−

pp/3 , ε

NN [GeV]

2 N

ch /

Np

art

AA central collisions

ALICEPHOBOSNA49

E895

hybrid fit: log2(s) + power-law

power-law fitlog

2(s) fit up to RHIC data

HADES

Effective-energy calculationsfor AA centrality data at ε

NN

ALICE

PHOBOS (with energy balancedlimiting fragmentation scaling)

hybrid fit: log2(s) + power-law

power-law fit

AA energy dissipation calculationswith pp/p

–p data

LHC (using hybrid fit, this work)E735UA5ISRbubble chamber

Predictions for LHC

AA at √s−

NN = 5.52 TeV

AA from energy dissipation for pp at √s

−

pp = 14 TeV

FIG. 1: Charged particle mean multiplicity perparticipant pair as a function of center of massenergy,

√sNN .

We introduce a new scaling, called theenergy balanced limiting fragmentation scal-ing, which leads to the scaling between themeasured pseudorapidity distribution and thedistribution calculated within the dissipat-ing participant energy approach using theeffective-energy concept. Using this scaling, acomplementarity of the multiplicities in head-on nuclear collisions and centrality data is ob-tained.

Proceedings of the DAE-BRNS Symp. on Nucl. Phys. 60 (2015) 750

Available online at www.sympnp.org/proceedings

20

40

60

80

100

120

100 200 300 400

Npart

2 N

ch /

Np

art

ALICE 2.76 TeV x 1.47

ALICE 2.76 TeV

PHOBOS 200 GeV x 2.87

PHOBOS 200 GeV

PHOBOS 130 GeV

PHOBOS 62.4 GeV

Effective-energy dissipation

with energy balanced

limiting fragmentation

Effective-energy dissipation

Energy dissipation, pp-based

Effective-energy dissipation

prediction for √s−

NN = 5.52 TeV

FIG. 2: Charged particle mean multiplicity perparticipant pair as a function of the number ofparticipants, Npart.

Result and DiscussionFigure ?? shows the c.m. energy depen-dence of the multiplicity measured in head-onnucleus-nucleus collisions in the energy rangeof√sNN = 2 GeV to 2.76 TeV. We fit the

head-on data by the “hybrid” function [? ],which shows a good agreement with data. Onecan see that the power-law fit well describesthe data and is almost indistinguishable fromthe hybrid fit upto the LHC data. Some mi-nor deviation between the two fits can be seenin the range from the top RHIC energy to theLHC energy. Meanwhile, the 2nd-order log-plynomial fit lies below at

√sNN > 200 GeV.

This observation supports a possible transi-tion to a new regime in high energy heavy-ioncollisions at

√sNN at about 1 TeV, as also

indicated [? ] in the studies of midrapiditypseudorapidity particle and transverse energydensities. We also show that the mean mul-tiplicity per participant-pair, calculated fromEq. ?? for nucleus-nucleus interactions usingthe pp/pp̄ measurements follow the nuclearmeasurements for the entire available collisionenergy range. The RHIC centrality data, after

removing the energy balanced limiting frag-mentation scaling ingredient, shows energy de-pendent behaviour similar to head-on datameasurements as soon as the centrality dataare considered in terms of the effective energy.Fig. ?? shows charged particle mean multiplic-ity per participant pair, Nch/(Npart/2) as afunction of the number of participants, Npart.The dotted lines represent the effective-energyapproach calculations based on the hybrid fitto the c.m. energy dependence of the midra-pidity density in the most central heavy-ioncollisions shown in Fig. ??. One can seethat the calculations, which are driven by thecentrality-defined effective c.m. energy εNN ,well reproduce the LHC data except slightlyunderestimating a couple of the most periph-eral measurements. However, for the RHICdata, there is a significant difference betweenthe calculations and the measurements. Thisdifference in data and calculation is explainedby a new effective energy calculation includ-ing the energy balanced limiting fragmenta-tion scaling.

Energy balanced limiting fragmentationscaling provides a solution of the RHIC “puz-zle” of the difference between the centralityindependence of the mean multiplicity vs. themonotonic decrease of the midrapidity pseu-dorapidity density with the increase of central-ity (more details can be found in Ref. [? ]).The mean multiplicity is shown to get a frac-tion of additional contribution to account forthe balance between the collision c.m. energyshared by all nucleons and the effective energyof the participants. Meantime, the midrapid-ity pseudorapidity density is fully defined bythe effective energy of colliding participants.

References[1] A. N. Mishra, R. Sahoo, E. K. G. Sark-

isyan, A. S. Sakharov, Eur. Phys. J. C 74,3147 (2014)

[2] E. K. G. Sarkisyan, A. S. Sakharov, Eur.Phys. J. C 70, 533 (2010)

[3] R. Sahoo, A. N. Mishra, Int. J. Mod. Phys.E 23, 1450024 (2014)

[4] E. K. G. Sarkisyan, A. N. Mishra, R.Sahoo, A. S. Sakharov, arXiv:1506.09080(2015)

Proceedings of the DAE-BRNS Symp. on Nucl. Phys. 60 (2015) 751

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