Ⅱ-5. Hadron Physics (Theory)

RIKEN Accel. Prog. Rep. 49 (2016)

Legendre expansion of longitudinal two-particle correlations
A. Monnai∗1 and B. Schenke,∗2cosh(y − yP )sinh(yP − yT )+ (1 − λ)δ(y − yP ), (1)Q(y − yP , yP − yT , y − yP ) = λwhere y is the rapidity and the subscripts T and P
denote target and projectile, respectively. λ is a parameter to be determined experimentally. The entropy
distribution is obtained by depositing entropy between
the last sub-collision pairs. The ﬁnite-density equationof state is constructed by interpolating those of hadronresonance gas and lattice QCD, where the latter is obtained in the Taylor expansion method, at a connecting
temperature near the crossover. Relaxation-type equations derived from the kinetic theory are employed as
the viscous hydrodynamic equations.
We probe the longitudinal properties of the QGP inhydrodynamics by decomposing the two-particle rapidity correlation into Legendre polynomials, which haverecently been measured at the ATLAS Collaboration
at the CERN Large Hadron Collider,3)†∗1∗2Condensed from the articles in Phys. Lett. B 752, 317(2016)RIKEN Nishina Center
Physics Department, Brookhaven National Laboratory, Upton, NY 11973, USA- 116 -0.1(|a(n,m)|)1/2

One of the most remarkable ﬁndings regarding highenergy heavy ion colliders is the ﬂuidity of the quarkgluon plasma (QGP), which is supported by the factthat the anisotropy of azimuthal momentum distribution, characterized by the Fourier coeﬃcients vn , islarge compared with that of the geometrical shape of
the produced medium. Thus far, numerous eﬀorts havebeen made to understand the transverse dynamics of
the QGP by introducing event-by-event ﬂuctuations aswell as oﬀ-equilibrium corrections.
However, the longitudinal dynamics has not been
throughly investigated. The isotropization mechanism
in a heavy-ion system is not fully understood, andno direct experimental evidence for the ﬂuidity of theQCD medium in the longitudinal direction has beenfound yet.
In this study, we extend the (3+1)-dimensional viscous hydrodynamic model Music1) to ﬁnite baryon
density and introduce more realistic setups to study
the forward rapidity dynamics. For longitudinally andtransversely ﬂuctuating initial conditions, the MonteCarlo Glauber model is extended to three dimensions
by introducing a variation of the Lexus model,2) where
the modiﬁcation of the rapidity distribution of the valence quarks after each sub-collision is taken into account to calculate the net baryon distribution. Themodiﬁcation is controlled by the kernel

Pb+Pb 2760 GeV
pT>0.5 GeVATLAS prelim.
initial entropy density
η/s=0, ζ/s=0
η/s=0.12, (ζ/s)(T)
20-25%

0.010.001(1,1)(2,2)(3,3)(4,4)(5,5)(6,6)(1,3)(2,4)(3,5)(4,6)(5,7)

Fig. 1. (Color online) Calculations ofwith experimental data.

an,m =∫√|an,m | compared

CN (η1 , η2 )

Tn (η1 )Tm (η2 ) + Tn (η2 )Tm (η1 ) dη1 dη2, (2)2Y Y√
where Tn (ηp ) = n + 1/2Pn (ηp /Y ) is the scaled Legendre polynomial and CN is the two-particle correlation deﬁned as×C(η1 , η2 ),Cp (η1 )Cp (η2 )∫ Y
1Cp (η1 /2) =C(η1 , η2 )dη2/1 ,2Y −YCN (η1 , η2 ) =(3)(4)

to remove the eﬀects of residual centrality dependence.
Note that a good analogy can be made between thisquantity and the transverse
ﬂow harmonics vn .
√Figure 1 shows |an,m | before and after the hydrodynamic evolution of Pb-Pb collisions at 2.76 TeV for
20-25% centrality. As shown, the hydrodynamic result
is close to the LHC data at n = 1 but has stronger n dependence. The hydrodynamic evolution tends to smearout short range correlations more eﬃciently. Viscouseﬀects are small. The Legendre coeﬃcients of the initial entropy distribution appear to agree with the data,
but the estimations at diﬀerent centralities indicatethat this is a coincidence. This disagreement may be
due to the lack of post-hydrodynamic treatments. Our
recent calculations suggest that they agree with experimental data when short range correlations from resonance decays are considered.4)
References
1) B. Schenke, S. Jeon, C. Gale, Phys. Rev. Lett. 106,042301 (2011).
2) S. Jeon, J. I. Kapusta, Phys. Rev. C 56, 468 (1997).
3) Tech. Rep. ATLAS-CONF-2015-020, CERN, Geneva,2015.
4) G. Denicol et al., in preparation.