The evidences of missing resonances from THERMINATOR. Viktor Begun

Transcription

1 he evidences of missing resonances from HERMINAOR Viktor Begun Faculty of Physics, Warsaw University of echnology, Poland in collaboration with W. Florkowski, M.I. Gorenstein, M. Rybczynski, V. Vovchenko Excited Hyperons in QCD hermodynamics at Freeze-Out November 6-7, 26 homas Jefferson National Accelerator Facility Viktor Begun (WU) he evidences of missing resonances November 7, 26 / 3

2 he LHC Puzzle hermal model gives particle multiplicities and the freeze-out curve he prediction was too high for ratios to pions, especially proton to pion ratio he best fit of the LHC data still gives three standard deviations for protons he low-transverse-momentum pion spectra show up to 5% enhancement compared to hydrodynamic models he fit of the LHC data gives the parameters that fall out to the "wrong" side Possible explanations: ch (GeV).2.5 ALICE..5 RHIC SPS AGS percolation s/ 3 =7 E/N =.8 GeV GSI µ B (GeV) Cleymans et. al., PRC (26); EPJ (25) hadronization and freeze-out in chemical non-equilibrium (Rafelski et al., PRC (23)) hadronic rescattering (not enough for pion spectra?) in the final stage (Becattini, Stock et al., PRL (23); Ryu, Paquet, Shen et al., PRL (25)) incomplete list of hadrons (Noronha-Hostler, Greiner, ; NPA (24)) Reasons for the non-equilibrium: super(over)cooling of the QGP (Shuryak, ; Csorgo, Csernai, PLB (994)) gluon condensation in CGC (Blaizot, Gelis, Liao, McLerran, Venugopalan, NPA (22); Gelis, NPA (24)) Viktor Begun (WU) he evidences of missing resonances November 7, 26 2 / 3

3 HERMINAOR: hadron gas + a freeze-out surface Single-freeze out Monte-Carlo HERMINAOR model (Broniowski, Florkowski, PRL (2), Chojnacki, Kisiel, Florkowski, Broniowski, Comput. Phys. Commun. (22)): he phase-space distribution of the primordial particles has the form: f i = g i d 3 p, where γ i = γ (2π) 3 γ i exp( p 2 + m 2i / ) ± q N i q +Nī q γ Ni s +Nī s s ( ) µb B i + µ S S i exp, and N i q, Ni are the numbers of light (u, d) and strange (s) quarks in the ith hadron. It s includes all well established resonances from the PDG. Resonances decay according to their branching ratios. he spectra are calculated from the Cooper-Frye formula at the freeze-out hyper surface dn = dσ µ p µ f (p u), t 2 = τ 2 + x 2 + y 2 + z 2, x 2 + y 2 r 2 dyd 2 f max p, assuming the Hubble-like flow: u µ = x µ /τ f. here is only one additional parameter in the model, because the product πτ f r 2 max is equal to the volume (per unit rapidity), while the ratio r max /τ f determines the slope of the spectra. Viktor Begun (WU) he evidences of missing resonances November 7, 26 3 / 3

4 Pions, kaons and protons he fits to the ratios of hadron abundances (Rafelski et al., PRC (23)) yield γ q which is close to the critical pion chemical potential: µ π = 2 ln γ q 34 MeV m π MeV d 2 N dp dy [GeV/c] 2 2πp d 2 N dp dy [GeV/c] 2 2πp Pb+Pb snn = 2.76 ev c = % 5% π + + π K + + K p + p chemical non-equilibrium = 38 MeV λq =., λs =. γq =.63, γs = 2.5 τf = 7.68 fm, rmax =.7 fm χ 2 π+k/dof = 2 =.6 76 chemical equilibrium = 65.6 MeV µb =., µs =. τf = 8.5 fm, rmax =. fm χ 2 π+k/dof = 99 = p [GeV/c] [(GeV/c) 2] [(GeV/c) 2] d 2 N dp dy 2πp d 2 N dp dy 2πp Pb+Pb snn = 2.76 ev c = % 5% primordial + secondary pions secondary pions only chemical non-equilibrium chemical equilibrium p (GeV/c) he spectra favor the non-equilibrium model. It may suggest that a substantial part of π mesons form the condensate (V.B., Florkowski, Rybczynski, PRC (24)) Viktor Begun (WU) he evidences of missing resonances November 7, 26 4 / 3

5 Centrality dependence for pions, kaons and protons Data / Model d 2 N / ( 2 p dp dy) [(GeV/c)-2 ] Chemical non-equilibrium: V,, γ q, γ s, r max /τ f 5-% -2% 2-3% 4-5% 5-6% 6-7% 7-8% 8-9% chemical non-equilibrium K 8-9% 8-9% 8-9% % x x x x x. x. x. x. x. x. p 8-9% p [GeV/c] Data / Model d 2 N / ( 2 p dp dy) [(GeV/c)-2 ] Chemical equilibrium: V,, r max /τ f chemical equilibrium 5-% -2% 2-3% 4-5% 5-6% 6-7% 7-8% 8-9% K 8-9% 8-9% 8-9% % x x x x x. x. x. x. x. x. p 8-9% p [GeV/c] One can observe a good agreement for pions and kaons, however, protons in central collisions are described only in non-equilibrium. Protons were not fitted! (V.B., Florkowski, Rybczyński, PRC (24) 5492). Viktor Begun (WU) he evidences of missing resonances November 7, 26 5 / 3

6 Strange particles d 2 N / ( dp dy) [(GeV/c)- ] 2 - -% -2% 2-4% 4-6% 6-8% chemical non-equilibrium -2% 2-4% 4-6% 6-8% -2% 2-4% 4-6% 6-8% K S K* (892) (2) p [GeV/c] he fit done initially for π + + π and K + + K only appears also very good for K S, K (892) and φ(2)! (V.B., Florkowski, Rybczyński, PRC (24) 5492) Viktor Begun (WU) he evidences of missing resonances November 7, 26 6 / 3

7 Can the LHC data be explained by the updated sigma? 6 R. Kamiński Figure 2 presents differences in values estimated for the position of the he recent PDG reviews report much lower mass and width of the f (5) or the sigma σ meson pole (real and imaginary parts) before 22 and after. As is seen, the Roy s and GKPY equations led to dramatic changes in these estimations. he lower Following mass of these new σ would results result the in S it s ππ higher amplitudes multiplicity. can be parameterized It decays intowith pions, therefore much it could higheradd precision. some of the missing pions Kaminski, Acta Fig. Phys. 2. Polon. Present Supp. and(25); previous Garcia-Martin, ranges of Kaminski, the real Pelaez, and imaginary Ruiz de Elvira, parts Phys. of Rev. the Lett. σ (2) pole estimated by the Particle Data Group (PDG22 and PDG2 respectively). In the middle of the circle, there are positions of this pole calculated by the Madrid Viktor Begun (WU) he evidences of missing resonances November 7, 26 7 / 3

8 No! Sigma should not be included in thermal models at all K + / π + Λ / π μ b thermal model SAR PHENIX NA49 NA44 E82,E866 E866,E895 E895 E896 NA49 NA57,NA44 SAR thermal model 2 3 s NN (GeV) Andronic, Braun-Munzinger, Stachel, PLB (29) (MeV) μ b (MeV) C o n tr ib u tio n fr o m s [% ] w ith o u t r e p u ls io n π + π - w ith r e p u ls io n 2 3 V.B., Broniowski, Giacosa, PRC (25) L H C s /2 N N [G e V ] he contribution from σ cancels in all isospin-averaged observables (Pelaez et. al., PRD (23), Pelaez, Phys.Rept. (26).) he K /π horn can not be explained by the σ All ratios to pions, and therefore the extracted temperatures are affected. Viktor Begun (WU) he evidences of missing resonances November 7, 26 8 / 3

9 Finite size effects in a quantum gas In the thermodynamic limit, V, the sum over momentum levels is transformed into the integral over momentum p (V /(2π) 3 ) d 3 p: N = g n n p 2 n exp +m2 µ = g exp ( m µ ) + exp g p 2 +m2 µ V p min d 3 p (2π) 3 exp ( g p 2 +m 2 µ ) he momentum at the first excited level p /V /3 and the corresponding number of particles N V 2/3 vanish in the thermodynamic limit. While the zero momentum level grows as fast as the volume and survives (V.B., Gorenstein, PRC (28), V.B. EPJ (25)) N g exp ( m µ d 3 p ) + V (2π) 3 exp ( g p 2 +m 2 µ ) = N cond + N norm, where N cond is the number of particles in Bose condensate and N norm is the number of particles in normal state. For small volumes one should take into account at least the ground state. Viktor Begun (WU) he evidences of missing resonances November 7, 26 9 / 3

10 Bose-Einstein condensation of pions at the LHC he p distribution is (2 ) - d 2 N / (p dp dy) 5 5 (a) dn dydφ p p dp = N cond V ( ) / 2 ALICE 2.76 ev -% -2% 2-4% 2 3 p [MeV/c] τ 3 f m 2 θ (r max p τ f /m) (V.B., Florkowski, PRC (25)): (2 ) - d 2 N / (p dp dy) (b) ( ) / 2 ALICE 2.76 ev 4-6% 6-8% 2 3 p [MeV/c] Condensate rate and p spectrum for charged pions. he grey area show the % deviation from the best fit. he inclusion of several more levels would lead to finer steps he data on multiplicities and spectra are compatible with 5% of the condensate If not the condensate, then plenty of heavy resonances decaying into low p pions? If there is the condensate, there must be large fluctuations of pions, which should be seen starting from the fourth moment of the multiplicity distribution (V.B., PRC (26), arxiv: ) Viktor Begun (WU) he evidences of missing resonances November 7, 26 / 3

11 An estimate of the amount of missing resonances One can predict the multiplicities of not yet measured particles. HADRON MULIPLICIIES AND CHEMICAL FREEZE-OU... PHYSICAL REVIEW C 93, 6496 (26) ABLE I. he comparison between fitted and measured total 4π multiplicities, and the prediction for the unmeasured yields. he fit is done within the CE formulation of the HRG. Some yields at the lowest energy are omitted from the table, because the energy of the system is not enough for their creation. he mean multiplicities in p+p inelastic interactions are measured by HADES [8]at snn = 3.2 GeV, and by NA6/SHINE [4] at snn = 6.3 GeV and 7.7 GeV. Many decay channels for heavy resonances are unknown. Missing branching ratios lead to the missing charge. For example, the missing charge for the p+p at 58 GeV/c is B/B.5/2 8%, Q/Q./2 6% and S. (V.B., Vovchenko, Gorenstein, ongoing work. hanks to H. Stroebele for fruitful discussion!). snn = 3.2 GeV snn = 6.3 GeV snn = 7.7 GeV Measurement Fit Measurement Fit Measurement Fit π ± ± π ± ± K ± ±.8.3 K ± ±.5.5 p p ± π.39 ± KS.3 ± η.2 ± ω.6 ± K + (2. ±.6) K K K φ (52) Vovchenko, where a =.66 ± V.B.,.2Gorenstein, GeV, b =.39 ± PRC.6(26) GeV, and c =.53 ±.2 GeV 3. he width of the band indicates the corresponding error bars, that were obtained for each (μb) point from the errors of the a, b, and c, usingthe standard methods of propagations of uncertainties. ogether Eq. (3) gives = 57 MeV at μb =, which is close to the latest findings at the LHC [52 54]. he change in the parametrization of the chemical freezeout line (3) and (4) is a combination of two effects: the extension of the list of particles, and the changes in Viktor Begun (WU) he evidences of missing resonances November 7, 26 / 3 the experimentally measured particle set. he HRG fit of

12 Conclusions he non-equilibrium thermal model explains very well the spectra of π, K, p, K S, K (892) and φ(2) particles at the LHC he enhancement of the pion spectra may be interpreted as a signature of the onset of pion condensation at the LHC A similar effect may be produced by many heavy (m > 2.5GeV?) not yet discovered resonances decaying predominantly into low momentum, p < 5 MeV, pions Viktor Begun (WU) he evidences of missing resonances November 7, 26 2 / 3

13 Bose-Einstein condensation Bose statistics discovered Bose-Einstein condensation predicted two experimental groups created BEC 2 - leaders of the groups, Cornell, Wieman, and Ketterle, won the Nobel Prize he density of bosons is calculated from ρ = d 3 p (2π) 3 exp[( p 2 + m 2 µ)/ ] Velocity profile of the first BEC (left to right): > C, < C, C he BEC temperature for /m is C m ρ 2/3. he density depends on the proper particle radius as ρ r 3. hen the ratio of the BEC temperature in the atomic gases, C (A), to that in the pion gas, C (π), in non-relativistic approximation (V.B., Gorenstein, PRC (28)) C (π) C (A) m A m π ( ra r π ) 2 m A m π he BEC of atoms is achieved at temperatures C (A) 8 K he BEC of pions would have 2 higher temperature and very different properties due to different interaction forces, much smaller volumes, and higher densities Viktor Begun (WU) he evidences of missing resonances November 7, 26 3 / 3