Application of the Nonextensive Statistical Approach for High Energy Particle Collisions

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1 Application of the Nonextensive Statistical Approach for High Energy Particle Collisions Gábor Bíró Wigner RCP of the HAS, Heavy Ion Research Group Gergely Gábor Barnaföldi Tamás Sándor Biró Károly Ürmössy M a x E nt 2016 July

2 Content Motivation Non-extensive statistics 2/ Small system, large fluctuations: Tsallis Pareto distribution Fitting hadron spectra Why de we need high energy collisions? CM energy evolution of the parameters Summary

3 Why do we need high energy collisions? 3/

4 Why do we need high energy collisions? 4/

5 Why do we need high energy collisions? 5/

6 Why do we need high energy collisions? Image source: 6/ Image source: arxiv:

edu/ 7/ Quark-gluon plasma (QGP): strongly interacting

7 Why do we need high energy collisions? Image source: 7/ Quark-gluon plasma (QGP): strongly interacting hot, dense matter (and perfect fluid) Temperature: ~1012 K Lifetime: ~fm/c Hadronization is still mystery

8 Why high energy collisions? 8/

9 Why high energy collisions? 9/

10 Why do we need high energy collisions? STAR ALICE 10/ PHENIX

Small system, large fluctuations High energy physics:

collisions can be described by the Tsallis distribution

the multiplicity N Phys.Lett.B701 (2011) 111-116, J.

11 Small system, large fluctuations High energy physics: new particles from collisions Hadron spectra in pp collisions can be described by the Tsallis distribution spectra in pp collisions depends similarly on and on the multiplicity N Phys.Lett.B701 (2011) , J.Phys. G36 (2009) arxiv: , , v2 11/

12 Small system, large fluctuations Spectrum: low pt (soft): Boltzmann Gibbs high pt (hard): power-law tailed (pqcd) the whole range is difficult # of particles in classical atomic matter: # of particles produced in heavy ion collisions: # of particles produced in high energy pp collisions: 12/

13 Small system, large fluctuations Extensive Boltzmann Gibbs statistics: Non-extensivity due to fluctuations generalized entropy Eur. Phys. J. A49 (2013) 110 Physica A 392 (2013) /

14 Small system, large fluctuations Boltzmann Gibbs entropy as q 1 limit: Maximizing the Tsallis entropy: the Tsallis Pareto distribution can be obtained 14/

15 Small system, large fluctuations In high energy collisions: fixed and where The Tsallis-entropy: q: the measure of non-extensivity, if q 1: If q-1 is large, that means that fluctuations due to small size effects are significant 15/ Eur. Phys. J. A49 (2013) 110 Physica A 392 (2013) 3132

16 Small system, large fluctuations Program: Fit spectra of identified hadrons measured in pp, pa and AA collisions Investigate the dependency of the fitted parameters (and other dependencies: mass, strangeness content, centrality, multiplicity...) Verification of the scale evolution Predictions for other collision energies (13-14TeV) and for other quantities (v₂ anizotropic flow...) Eur. Phys. J. A49 (2013) 110 Physica A 392 (2013) /

17 Results

18 Fitted pp PID hadron spectra Data/Fits are good, 13 TeV: coming soon... 18/

19 The evolution of fitted q and T parameters Predictions for 13 TeV (spoiler: quite good ) q is increasing for mesons very similarly, but ~constant for protons (barions) T is increasing, but very differently for mesons/barions T₂ for kaons and pions is similar, but T₁ is not strangeness? 19/

20 T(q-1): 20/ 62 GeV

21 T(q-1): 21/ 200 GeV

22 T(q-1): 22/ 900 GeV

23 T(q-1): 23/ 2760 GeV

24 T(q-1): 24/ 7000 GeV

25 T(q-1), all energies T as effective temperature For AA: can be negative Soft+hard model? Eur. Phys. J. A40, 299 (2009) Phys. Rev. C79, (2009) 25/

26 Scaled T(q-1), all energies Coalescence: Hadron distribution quark distribution For Also shows strong dependency : Phys. Lett. B, Vol 689, (2010) 26/

27 Summary Maximizing Tsallis-entropy: thermodinamical expressions for particle spectra obtained in high energy pp collisions The fluctuation of the number of particles is large Fitted Tsallis Pareto distributions describe the spectra very well The q and T parameters show a strong CM energy dependence Physical picture from the T vs (q-1) function Similar behaviour in electron-positron, proton-nucleus and nucleus-nucleus collisions Soft+hard model, transverse flow, coalescence Thank you! 27/

28 References Non-Extensive Approach to Quark Matter, T.S. Biró, G. Purcsel, K. Ürmössy, Eur.Phys.J. A40 (2009) ; arxiv: v2 Large Transverse Momenta and Tsallis Thermodynamics, J. Cleymans, M.D. Azmi, J.Phys. Conf. Ser. Vol 668 (2016), ; arxiv: v1 Disentangling Soft and Hard Hadron Yields in PbPb Collisions at snn = 2.76 ATeV, K. Ürmössy, T.S. Biró, G.G. Barnaföldi, Z. Xu, arxiv: v2 Abstract composition rule for relativistic kinetic energy in the thermodynamical limit, T.S. Biró, EPL 84 (2008) 56003; arxiv: New Entropy Formula with Fluctuating Reservoir, T.S. Biró, G.G. Barnaföldi, P. Ván, Physica A 417 (2014) ; arxiv: Statistical Power Law due to Reservoir Fluctuations and the Universal Thermostat Independence Principle, T.S. Biró, P. Ván, G.G. Barnaföldi, K. Urmossy, Entropy 16 (2014) ; arxiv: A 'soft+hard' model for Pion, Kaon, and Proton Spectra and v2 measured in PbPb Collisions at $\sqrt{s}$ = 2.76ATeV, G.G. Barnaföldi, K. Ürmössy, G. Bíró, JP: CS, Vol 612 (2015); arxiv: Quark-gluon plasma connected to finite heat bath, T.S. Biró, G.G. Barnaföldi, P. Ván, Eur. Phys. J. A49 (2013) 110; arxiv: /

Investigation of high energy nuclear collisions using Q-entropy

Investigation of high energy nuclear collisions using Q-entropy Gábor Bíró Wigner RCP of the HAS, Heavy Ion Research Group Gergely Gábor Barnaföldi Ta m á s S á n d o r B i r ó Á d á m Ta k á c s International