1 / 22

Charge and isospin fluctuations in a non-ideal pion gas

This study investigates fluctuations in the number of particles and relative isospin composition of a non-ideal pion gas with charge conservation. The effects of quantum statistics and pion interaction on fluctuations are analyzed using a simplified model. The results can be applied to analyze experimental data in heavy-ion collisions.

mtara
Download Presentation

Charge and isospin fluctuations in a non-ideal pion gas

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Charge and isospin fluctuations in a non-ideal pion gas E.E. Kolomeitsev, D.N. Voskresensky and M.E. Borisov Matej Bel University, Banska Bystrica, Slovakia JINR, Dubna, Russia National Research Nuclear University “MEPhI”, Moscow, Russia COST ACTION

  2. BEC in ideal Bose gases Ideal gas of boson with mass m Compton wave length: Critical temperature Tc is given by equation prediction: Bose and Einstein (1924) realization: Cornell, Ketterle, Wieman (1995) Academic interest P.T. Landsberg, Thermodynamics withQuantum Statistical Illustrations (1961) Particle-antiparticle system with charge conservation Haber, Weldon PRL 46 (1981) 1497 Standard model, Higgs J.I. Kapusta, PRD 24 (1981) 426

  3. kinematical separation of heavier baryon component • QGP hadronization meson-resonance-enriched medium • resonance decays pion-enriched medium T m time 0 Pion gas in heavy-ion collisions central (midrapidity) regions in HIC [Goity, Leutwyler PLB 228(89)517] for pion absorption rate (inelastic collision) is smaller than rescattering rate (elastic collisions) equilibration time Can a quantum regime be reached? Possible signals? On some time interval we deal with a pion gas with a approximately constant number of particles

  4. Pion gas in heavy-ion collisions LHC data: Pb+Pb SPS data: O+Au @ 200 GeV/A [Kataja, Ruuskanen, PLB 243(1990)181] [Begun, Florkowski, Rybczynski, PRC90 (2104) 014906] m=134.9 MeV T=167 MeV m=126 MeV Mishustin et al, PLB 276 (1992) 403; PRC 51 (1995) 2099 … effects of quantum statistics could be important

  5. Pion gas in heavy-ion collisions The appearance of a pion BEC and its consequences were discussed by Voskresensky, JETP 78 (1994) 793 pion BEC from resonance decays [Ornik Plumer, Strottman, PLB 314 (1993) 401] fluctuations of particle number and relative isospin composition calculated by Begun, Gorenstein [PLB 653 (2007) 190] for an ideal gas divergent at Tc SVD-2 Collaboration observed an enhancement in variance of #charged pion/#total in events with high pion multiplicity in p+p@ 50 GeV [Ryadovikov et al PAN75 (2012)]

  6. SPS data: O+Au @ 200 GeV/A T=167 MeV, m=126 MeV LHC data: Pb+Pb T=138 MeV, m=134.9 MeV pion interaction is to be included We will use a simplified lf4 model -- pion gas with dynamically fixed number of particles -- general properties of pion spectra -- mixed variances of pion species -- gas with small isospin imbalance … study influence of a pion interaction on fluctuations …

  7. Lagrangian for a system with dynamical fixed number of pions Weinberg’s chiral Lagrangian Introduce charged and neutral pion fields Introduce creation and annihilation operators Write the Lagrangian in terms of and keep terms with equal number of c.o. and a.o

  8. (3 complex fields) keeps the number of each pion species fixed equilibration among pion species (fast reactions) only 2 chemical potentials in equilibrium The system is described by 2 numbers: total number of pions N and total charge Q We drop (slow reactions) collision term in kinetic equation (gain, loss terms)

  9. Pion spectrum in Hartree approximation (only tadpole term) replacement: Divergent vacuum parts are small after renormalization effective mass The partial densities of pions are determined as

  10. Isospin symmetric pion gas p+,p-, p0 • pion effective mass increases with a temperature decrease • at “induced” Bose condensation a pole in momentum distribution function • for pion chemical potential Lagrangian of a condensate 1st order p.t.?

  11. Susceptibilities and fluctuations pressure normalized variance of the total particle number Divergent! Higher order susceptibilities will diverge even stronger Well known result of the grand canonical description (GCE).[D. ter Haar, Proc. R. Soc. Lond. A 212 (1952) 552] GCE description might be applied for incomplete measurements (momentum/rapidity and acceptance cuts) [Jeon, Koch, hep-ph/0304012]

  12. final expression 3 new functions: All these integrals diverge at Tc! But some combinations are finite Non-perturbative result!

  13. Cross variances of the numbers of pions GCE partition function normalized cross-variances total number of particles charge charged vs. neutral pions

  14. Cross variances of the numbers of pions

  15. This result is similar to that for the free pion gas, all the terms explicitly dependent on l canceled out. means that the stronger the multiplicity of an event deviates from the expected mean value the higher will be the probability that the numbers of positive and negative pions are different in this event. Variances for N, G, and Q increase with a decrease of the temperature, whereby the hierarchy of fluctuation variances is and an increase of l leads to a reduction of the variances. Note that the normalized variance of G is different in its magnitude from that of N. We emphasize that the results for ought to be used in analysis of SVD-2 experimental data

  16. Why Q-variance is divergent? incompressibility of matter with respect to change in The Lagrangian, which we consider, is isospin invariant and If the Coulomb interaction, breaking the isospin symmetry, is taken into account Debye momentum finite!

  17. Properties of the pion gas with small isospin imbalance Consider the system with a small isospin imbalance

  18. Fluctuations in the pion gas with small isospin imbalance Consider a slightly positively charged gas with pion densities The BEC critical temperature is the highest for positively charged pions. We are interested in the behaviour of fluctuations when the temperature approaches Tc+ from above. All finite at Tc

  19. However we recover old relations: “pole”+background terms and regularized Q-fluctuations:

  20. Conclusions • Pion-enriched gas can be created in HIC • The number of pions is approximately fixed on a final stage of collision • collision rate >> absorption rate • At freeze-out the pion gas can be close to a quantum limitmp~mp • Interaction lead to an increase of pion mass and a decrease of Tc • Pion number fluctuation remains finite at Tc if a pion interaction is take into account non-perturbatively • N-variance < G-variance < Q-variance • Dedicated analysis of selected multi-pion events is needed

  21. Creation of a pion BEC? non-equilibrium overcooling effects [Voskresensky, JETP 78 (1994) 793] non-equilib. pions from resonance decays [Ornik et al., PLB 314 (1993) 401] decomposition of a “blurred phase" of hot baryonless matter [Voskresensky NPA 744 (2004) 378] sudden hadronization of supercooled QGP [Csorgo Csernai PLB 333 (1994) 494] decay of gluon BEC preformed at the initial stage of heavy-ion collision [Blaizot NPA 873(2012) 68] [Xu, Zhoum, Zhuang, Greiner, PRL114, 182301][Peshier, Giovannoni, JPCS668 (2016) 012076] glueball condensation [Kochelev, Phys.Part.Nulc.Lett 13 (2016) 149] The critical condition m=mp* cannot be reached in an isentropic expansion [Greiner,Gong, Mueller, PLB316, 226]

  22. BEC from non-equilibrium pion gas Equilibration is much faster than expansion Initial non-equilibrium distribution of pions is characterized byEin and nin After a while the system riches the thermal equilibrium characterized by m and T Bose-enhancement formation time non-eq. distributions [Semikoz, Tkachev PRL74 (1995) 3093] symmetric pion gas

More Related