HOT HADRONIC MATTER. Hampton University and Jefferson Lab

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1 200 Cr oss sect ion (m b) 0 K ptotal 20 5 K pelastic 2 1 K N THE ROLE OF BARYON RESONANCES IN Relativistic Heavy Ion Collider (RHIC) HOT HADRONIC MATTER Au+Au K d Center of mass energy (GeV) Cr oss sect ion (m b) 0 K dtotal 0 A GeV + 0 A GeV K n saa = 40 TeV saa = 3 TeV at LHC PHOBOS K n 20 5 total PHENIX 2 RHIC elastic 1 1 JoseBRAHMS L. Goity Hampton University and Jefferson Lab Laboratory beam energy (GeV/c) 2 STAR Plots of cross sections and related quantiti 7.22: Total and elastic cross sections for K p and K d (total only), and K n collisions as a function of laboratory beam momentum center-of-mass energy. Corresponding computer-readable data files may be found at of the COMPAS Group, IHEP, Protvino, Russia, August 1999.) Au+Au σ and R in e+e Collisions -2 Baseline ω φ p+p J/ψ -3 AGS ψ(2s) -4 ρ ρ Υ Z σ [mb] TANDEMS

2 Outline Missing hyperons The hot Hadron Resonance Gas HRG and LQCD HRG and heavy ion collisions Hyperon effects in the HRG Remarks and conclusions

3 Talks related to this one hot matter: Rene Bellwied Benjamin Doenigus Claudia Ratti Pasi Huovinen Jacquelyn Noronha Enrique Ruiz Arriola Paolo Alba resonances: Fred Myhrer Simon Capstick LQCD: Robert Edwards

4 Missing states in PDG SU(3) PDG #Σ =#Ξ =#N +# 26; 12; 49 #Ω =# 4; 22 #Λ =#N + #singlets 18; 29 All listed SU(3): # Y= 3(# N+ # )+singlets Important aspects of excited hyperon physics Test the existence of complete SU(3) multiplets Study SU(3) breaking effects in excited baryons Test the indications that excited baryons form SU(6)xO(3) multiplets Important source of information to test the 1/Nc expansion of QCD in baryons Possible role of hyperons in high energy heavy ion collisions

5 Present status of hyperons from PDG ' ()*# #$ ## # & % ' ()*# #$ ## # & % $ $ # # # $ % & # $ % & #+ #+ 1/Nc baryon mass formulas ' ()*# # + ' ()*# # + for 56-plets = 0, 2 : 24 excited hyperons # $ % & # $ % & for 70-plet = 1 : 23 excited hyperons #$ #$ ## # ## # ' ()*# & % ' ()*# & % $ $ # # # $ % & # $ % &

6 Hot hadronic matter: Ideal Hadron Resonance Gas -- IHRG dof: meson-, baryon- and antibaryon- stable states and resonances only light quarks here EoS p n (T,µ)= ( 1)1+B(n) d(n) (2π) 3 T d 3 p log 1+( 1) 1+B(n) exp p2 + m 2 n µ T B(n) =Baryon number, d(n) =(2J n + 1)(2I n + 1) In chemical equilibrium: µ s, µ B for all hadrons use the relativistic EoS

7 Meson I S L J P MassGeV nπdecay Π f Η Ω Ρ Ηp f a Φ h b a a f f Η Π a f h Π Η f Ω f a Ρ Η f f2p f f Ρ h Π f Η Ω Ω Π Φ Ρ Ρ a f Η Π f a Φ Η Π Ρ f a f Ρ f f M GeV M GeV Mesons non-strange J Kaons J Number of dof: 469 Meson I S L J P MassGeV nπdecay K K800 K K K K K K K K K K K K K K K K K

8 Baryons: states up to ~2.7 GeV SU(6) O(3) Multiplets [56, = 0] ground state [56, =0, 2, 4] [70, =1, 2, 3] Number of dof: 1946 many missing states: in SU(3) multiplets and also spin-flavor multiplets (QM & LQCD) use a simple mass formulas fitted to known states to provide masses for the missing states

9 mass formulas: neglect spin-orbit splittings M 56,GS (S =1/2, S) =m c HF c S S JLG & N.Matagne M 56,GS (S =3/2, S) =m c HF c S S M 56 (S =1/2, S) =m c HF c S S M 56 (S =1/2, S) =m c HF c S S M 70 (S = I,S) =m c HF 3 S(S + 1) 7 c S S 4 M 70 (S = I 1, S) =m c HF S(S + 2) 3 c S S 4 M 70 (S = I +1, S) =m c HF S 2 7 c S S 4... or use QM talks by Manley, Myhrer, Capstick Λ 1 70 = m c HF + c S M GeV M GeV plets plets

10 IHRG and LQCD & % $ # crossover stout ( -3p)/T 4 p/t 4 s/4t 3 HISQ T [MeV] # $## $# %## %# &## A. Bazavov et al R. A. Soltz et al. µ S = µ B =0 different contributions to pressure Early Universe at T<T c chemically equilibrated HRG p T #$%&'() #.-)'() $,*-&'() meson dominated HRG 2 #/&,'() *+'() talks by Ratti, Ruiz Arriola

11 Hot hadronic matter in heavy ion collisions off chemical equilibrium τ ch 1 σ ann ρ v th Inelastic collision rates are low and hadron gas is off chemical equilibrium τ ch can be very large > s fm Bebie et al; Shuryak; JLG; Koch et al;... N N nπ is not that slow and should be taken into account stable hadrons develop effective chemical potentials resonances have chemical potentials given by: Rapp & Shuryak µ R = h d h R µ h

12 Chemical potentials for IHRG off chemical equilibrium one assigns chemical potentials to all hadrons ππ ππ πk πk ππ K K ππ ρ etc } detailed balance µ π = µ K = µ η = µ ρ 2 = µ ω 3 = = µ M approximation of SU(3) symmetry MB M B µ N = µ Σ = µ Ξ = = µ B MB B µ B = µ B + µ M assume dominance of 2-body resonance decay as approximation baryon annihilation B B nm µ B = n 2 µ M

13 Effects of chemical potentials $% %# $ ( µ M = µ B =0 all mesons % µ M = 0MeV µ B = 250 MeV p T 4 ' & all baryons $# $ % # # $ $# % )*+ # $ $# % &'( & %# n T 3 ) % ( µ M = 0MeV µ B = 250 MeV Excited hyperons s=0 n T 3 % $# µ M = 0MeV µ B = 250 MeV $ $ # # # #$ #% #& #' $ T [GeV] # $ $# % &'(

14 #( # '( µ B =2.5µ π T = 155MeV no excited hyperons all excited hyperons n B n π ' ( T = 115MeV T = 135MeV ( T = 95MeV ' # $ % & ' '# decreasing number density of Y wrt non-strange baryons as T drops

15 Simple model of fireball expansion for assessing the possible role of hyperon resonances adiabatic expansion several scenarios: Bebie,Gerber,JLG & Leutwyler 1) B B nm in equilibrium n n B + n M = const s 2) B B nm off equilibrium n B s = const, and n M s = const 3) 2) + K K ππ off equilibrium n K s = const, n π = const, etc s I discuss simplest case 1) (real life is more like 3))

16 Freeze out at freeze out all resonances decay and change the chemical potentials of the stable hadrons effective chemical potentials at freeze out µ B [GeV] µ M [GeV] $)- $)#- $)#$ #$%&'( µ B =2.5µ M $)$- onset of pion condensation $)$ $)$$ $)$$ $)$# $)$* $)$+ $)$, $)$.'(#

17 pion and nucleon effective chemical potential at freeze out µ B =2.5 µ M T FO = {90, 0, 1, 120} MeV onset of pion condensation ') '# µ M µ N #$ # '' ' ( #$ # ) #( # '( ' & µ M ( # $ % & ' '% *+,# Y s included # $ % & ' no Y s '% *+,# presence of Y s tend to reduce the effective FO chemical potentials

18 particle yield ratios K π Y π π π K Ȳ Y N Y Y CDEFGH5&,IE&@JK5&LMLNJ@&OLJ@LPQ K π π strangeness freeze out + $, $ # #$% &'( ALICE TeV ) * # #$ #+ #) #* $ &'(# µ K = µ π

19 comparing with data T FO = {90, 0, 1, 120} MeV ALICE Pb-Pb 2.76 TeV & '( % ' #$ # ' + #$ # $ ( # # $ % & ' # $ % & ' '% )*+# '% ()*# % ) ' ' #$ # $ ( # ' #$ # & % $ ' # # $ % & ' # $ % & ' '% *+,# '% ()*# one more indication of early freeze out of strangeness important contribution from the decays for the ratio p π +

20 Remarks Effects of excited Y* s in HRG are not easy to pin down: they make small changes to thermodynamic ratios Small chance to determine the effects of Y*s from LQCD calculations of thermodynamic observables: effects are small in that case, although effects of all resonances together are very important. HRG off chemical equilibrium may be necessary, but effects of Y*s may be smaller than inherent theoretical uncertainties of the models used to describe the evolution and FO of the hadronic fireball. e.g.,: different scenarios of evolution to freeze out; Van der Waals volume corrections to IHRG, which are likely to be significant; hydrodynamics; etc. Early freeze out of strangeness, with expected depletion of Y*s in the HRG through their decay may affect strange particle yields at FO. Ratios of yields seem rather insensitive in the simple model presented. What is (are) the best observable(s) to search for effects due to Y* s?