Identical pions femtoscopic studies in Au+Au
collisions at sNN = 27 GeV with STAR at the RHIC
TCHoU Workshop for the Division of Quark Nuclear Matters(Date: 24/03/2022)

Ashutosh Kumar Pandey
Shinichi Esumi
Tomonaga Center for the History of the Universe,
University of Tsukuba

Introduction• Big-Bang theory of the universe predicts that matter existed in QGP form after ~1µs of theuniverse formation• Lattice QCD predicts QGP at ~170 MeV temperature• Very hot and dense QGP like medium formation in heavy-ion collisions due to inelastic
collisions between nuclei and conversion of kinetic energy into heat

• To obtain the equation of state, it is important to know the dimensions of fireball which isimpossible to measure directly due to its very small size

Ashutosh Kumar Pandey

2Introduction (contd.)• Femtoscopy (or HBT technique) provides a direct tool to measure the source size
• Probe space-time characteristics of the source using particle correlations inmomentum space• Main sources of correlations:➡ Quantum statistics (QS)HBT analysis• Identical bosons - Bose-Einstein quantum statistics• Identical fermions - Fermi-Dirac quantum statistics➡Final-state interactions (FSI)• Strong interaction• Coulomb interaction (repulsion/attraction)
QS + FSI→ Femtoscopic analysis
Ashutosh Kumar Pandey

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Two-particle correlation function
paP2 (pa , pb )C2 =P1 (pa )P1 (pb )rarrb

q = p a - pbpb

Koonin-Pratt Equation,
PLB70 (1977) 43,S. Pratt et al., PRC42 (1990) 2646

C(q) =ZSource function

dr| (q, r)|2 S(r)Experimental correlation function

Pair wave function➡ P2(pa,pb) – probability of detection of particles with momenta pa and pb➡ P1(pi) – probability of detection of particle with momentum pi
Ashutosh Kumar Pandey

4Bertsch–Pratt ‘Out-Side-Long’ coordinate system• side is interpreted as geometric size
• out gives info on emission process• long is used for emission time approx.
Longitudinal co-moving system (LCMS):
A rest frame moving along the beam direction such that Pz = 0

Pair rest frame (PRF):

Where MT 2= P02 – Pz2 , PT2 = Px2 + Py2 and Minv2 = P2
Ashutosh Kumar Pandey5Femtoscopic studies w.r.t. Ѱ1
ALICE Collaboration, Phys. Rev. Lett. 111 (2013) 232302

STAR Collaboration, Phys. Rev. C 73 (2006) 34903

ηAu + Au 62.4 GeV, charged particle v1• Directed flow v1 ( = 〈cos(ϕ - Ѱ1)〉 ) is produced due to interaction between spectator andparticipant particles• v1(η) is zero three times at around mid, forward and backward rapidities : possible
signature of phase transition (J. Brachmann et al. Phys. Rev. C 61 (2000) 024909)• v1 can’t be explained by hydrodynamical models unlike v2 or v3Ashutosh Kumar Pandey

6Femtoscopic studies w.r.t. Ѱ1M. A. Lisa et al. New J. Phys. 13 (2011) 065006• v1 signal can be generated from assuming
the “tilted source” initial conditions• Femtoscopic measurements w.r.t. Ѱ1 cangive the information about tilt angle θs• Fit function for identical particles withcross term:C(q) = N [(1) + K(qinv )(1 + G(q))]

2 222222G(q) = exp(−Routqout − Rside
qside− Rlongqlong− Rosqout qside − Rol2 qout qlong − Rsl2 qsideqlong)• Goal: to perform femtoscopic analysis w.r.t. Ѱ1 and extract θs which is expected todecrease with energy

2−4R1sl,1θs = tan−12( R2l,0 − R2s,0 + 2R2s,2 )Fit function

222Rμ,0+ 2Rμ,1cos(ϕ − Ψ1) + 2Rμ,2cos(2(ϕ − Ψ1)), (μ = o, s, l, ol){R + 2R sin(ϕ − Ψ ) + 2R sin(2(ϕ − Ψ )), (μ = os, sl)
2μ,02μ,1

12μ,2Ashutosh Kumar Pandey

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THANK YOU

Ashutosh Kumar Pandey

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