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Initial energy density estimation from RHIC Au+Au dataGábor Kasza1,2,3; Tamás Csörgő1,2
1HAS Wigner RCP2Eszterházy Károly University3Eötvös Loránd University
Gábor KaszaWigner RCP, Eszterházy Károly UniversityEmail: [email protected]
Phone: +36-1/392-2512/1939
Contact1. T. Csörgő, G. Kasza, M. Csanád and Z-F. Jiang, Universe no. 4, 69.2. PHENIX Collaboration, Phys. Rev. Lett. 98, 162301.3. G. Kasza and T. Csörgő, arXiv:1811.09990 [nucl-th]. 4. J. D. Bjorken, Phys. Rev. D 27, 140.5. M. I. Gorenstein, Yu. M. Sinyukov and V. I. Zhdanov, Phys. Lett 71B, 199-202.6. PHENIX Collaboration, Phys. Rev. C 69, 034909.7. T. Csörgő, B. Lörstad and J. Zimányi, Z.Phys. C71 (1996) 491-497.8. T. Csörgő and G. Kasza, Proceedings supplement of WPCF 2018, arXiv:1810.00154 [nucl-th].9. T. Csörgő and G. Kasza, Proceedings supplement of WPCF 2018, arXiv:1806.11309 [nucl-th].
References
▪ Original idea: initial energy density of QGP can be measuredfrom dE/dy distributions
▪ Bjorken’s famous estimation for boost-invariant systems [4]:
▪ But Bjorken’s formula ignores the 1st law of thermodynamics!The correct formula for boost-invariant systems was found byGorenstein, Sinyukov and Zhdanov (before Bjorken!) [5]:
▪ Measurments: dN/dη is not flat, thus we need an acceleratingsolution of hydro to reevaluate the initial energy density!
▪ We have developed a novel method to estimate the initialenergy density in three steps. We applied this new method onthree systems: Au+Au at 62.4, 130 and 200 GeV [3]
Motivation
▪ At 130 and 200 GeV: Teff is published by PHENIX▪ At 62.4 GeV: we had to fit the pT (or mT-m0) spectra with the following fit function [6]:
▪ The centrality dependence of the Teff parameter of pions is found to be negligible.▪ In the next steps, we assume pion dominance: we use centrality independent Teff values
The Csörgő-Kasza-Csanád-Jiang (CKCJ) solution
▪ Rapidity density (embedded to 1+3 d space) [1]:
▪ Four fit parameters: κ (or the speed of sound, known from PHENIX meas.), λ, Teff , dN/dy|y=0
▪ The values of Teff are determined from fits to the transverse mass spectra of hadrons▪ The pseudorapidity density distribution is determined as a parametric curve, where the parameter
of the curve is the momentum-space rapidity y:
▪ Fits to PHOBOS data [3]:
2nd step: obtain the acceleration parameter (λ)
▪ For a 1+1 d relativistic, Gaussian source, obtained from the CKCJ solution [7,8]:
▪ Here Δηx is the Gaussian width of the rapidity distribution▪ From fits to dN/dη: λ, Teff are known▪ τf is the only fit parameter▪ Fits to PHENIX and STAR data [3]:
3rd step: obtain the lifetime (τf)
▪ We used a realistic, but average value of speed of sound. It is measured by PHENIX in ref. [2].▪ In 1+1 dimensions, the Rindler coordinates are useful: τ (proper time), ηx (space-time rapidity)▪ The fluid rapidity (Ω) and the four-velocity is the function of only ηx:▪ A finite, accelerating, 1+1 dimensional relativistic solution was recently given by Csörgő, Kasza,
Csanád and Jiang as a family of parametric curves (where the parameter is H) [1]:
▪ Here λ is the acceleration parameter, s=s(τ,H) is the scale variable, and νσ is the scaling function.▪ This solution is limited to a cone around mid-rapidity.
1st step: obtain the effective temperature (Teff)
▪ From the CKCJ solution ε0 is exactly calculated [9]:
▪ Now, the fundamental correction to ε0Bj is known
▪ λ and τf are obtained by fits → τ0 dependence▪ Calculated for Au+Au at 62.4, 130 and 200 GeV, only the
thermalized energy is included [3]
▪ Bjorken’s formula can be applied only for order of magnitudeestimation!
▪ Indication for an increasing initial energy density withdecreasing colliding energy?
▪ The results suggest a non-monotonic behaviour of the initialenergy density with s
▪ At LHC energies, our method predicts greater ε0
▪ At 200 GeV, our results are compared to 1+3 d numerical hydro,with lQCD EoS: surprisingly good agreement
▪ Of course, further investigations are needed: lower collisionenergies, extensions of CKCJ solution (1+3 d, shockwaves, fit todata on the whole η interval)
Initial energy density estimation
