The strange degrees of freedom in QCD at high temperature. Christian Schmidt

Transcription

1 The strange degrees of freedom in QCD at high temperature Christian Schmidt Christian Schmidt LAT 213 1

2 Abstract We use up to fourth order cumulants of net strangeness fluctuations and their correlations with net baryon number fluctuations to extract information on the strange meson and baryon contribution to the low temperature hadron resonance gas, on the dissolution of strange hadronic states in the crossover region of the QCD transition, on the quasi-particle nature of strange quark contributions to the high temperature quark-gluon plasma phase. T. T c T c. T. 1.3T c T & 1.3T c T c := chiral crossover temperature Christian Schmidt LAT 213 2

3 Outline 1) Introduction Definitions of cumulants and correlations Motivations to study fluctuations of conserved charges 2) The lattice setup and results The HISQ action 4 th order fluctuations and correlations 3) A closer look to strangeness Strangeness in the HRG model Disentangling different strangeness sectors 4) Summary based on BNL-BI: arxiv: BNL-Bielefeld Collaboration: A. Bazavov, H.-T. Ding, P. Hegde, O. Kaczmarek, F. Karsch, E. Laermann, S. Mukherjee, P. Petreczky, C. Schmidt, D. Smith, W. Soeldner, M. Wagner Christian Schmidt LAT 213 3

4 Generalized Susceptibilites / Cumulants Expansion of the pressure: p T 4 = 1X i,j,k= 1 i!j!k! BQS ijk, µb T i µq T j µs T k X = B, Q, S: conserved charges X n, = 1 VT n ln X /T ) n µ X = generalized susceptibilities only at µ X =! Experiment VT 3 X 2 = ( N X ) 2 VT 3 X 4 = ( N X ) 4 3 ( N X ) 2 2 VT 3 X 6 = ( N X ) 6 15 ( N X ) 4 ( N X ) 2 +3 ( N X ) 2 3 cumulants of net-charge fluctuations N X N X hn X i only at freeze-out ( µ f ( p s),t f ( p s) )! ratios of cumulants are volume independent! Christian Schmidt LAT 213 4

5 Motivations 1) Discover a critical point (if exists) Analyze Taylor series/pade resummations of various susceptiblities: find region of large fluctuations Analyze the radius of convergence directly 2) Analyze freeze-out conditions Expected phase diagram of QCD: 154(9) critical end-point QCD quark-gluon-plasma Match various cumulant ratios of measured electric charge fluctuations to (lattice) QCD results: determine freeze-out parameters.! see talk by M. Wagner 3) Identify the relevant degrees of freedom (this talk) Compare (lattice) QCD fluctuations to various hadronic/quasiparticle models: hadron gas nuclear matter neutron stars Christian Schmidt LAT vacuum chemical potential µ B Does deconfinement take place above the chiral crossover temperature?

6 Motivations Does deconfinement take place above the chiral crossover temperature? The chiral crossover line: T c = 154(9) MeV T c (µ B )=T c () 1.66(7)µ 2 B HotQCD, PRD 85 (212) 5453 BNL-BI, PRD 83 (211) 1454 Karsch, CPOD 213, arxiv: T f [MeV] s NN = 2 GeV s NN = 62.5 GeV LQCD: T c (µ B ) STAR + HRG: PRC 79, 3499 (29) STAR charge flucn. (prelim.) + LQCD PHENIX charge flucn. (prelim.) + LQCD STAR proton flucn. (prelim.) + LQCD baryon flucn. µ B f [MeV] freeze-out points are in agreement with the chiral crossover line apparent discrepancies among the freeze-out points that need to be resolved Christian Schmidt LAT 213 6

7 The Lattice Setup Action: highly improved staggered quarks (HISQ) Lattice size: , , Mass: m q = m s /2! m 16 MeV Statistics: O(1 3 ) - O(1 4 ) Observables: traces of combinations of M and ln = 1 Z DU Tr M 1 M e Tr lnm S e G Z = Tr M 1 2 ln 2 = Tr M 1 M Tr M 1 M M 1 + DTr M 1 M 2 E Method: stochastic estimators with Tr [Q] 1 NX i N Q i i=1 N = 15 with random vectors 1 NX i,x N i,y = lim N!1 i=1 x,y Christian Schmidt LAT 213 7

8 Generalized Susceptibilites / Cumulants.3 2 B B T c =154(9)MeV N =6 8 BNL-Bielefeld preliminary S S T c =154(9)MeV N =6 8 BNL-Bielefeld preliminary structure consistent with O(4) critical behavior at µ B =, m = Christian Schmidt LAT 213 8

9 BS Correlations 2 nd order 4 th order BS - 11 N = BS - 13 N =6 8 T c =154(9)MeV BS 22 T c =154(9)MeV BNL-Bielefeld preliminary CBS [Koch et al., PRL 95 (25) 18231] BS 11 / S 2 HRG BNL-Bielefeld preliminary Cont N =6 N =8 N =12 free BS Christian Schmidt LAT 213 9

10 Strangeness within the HRG HRG: p HRG T 4 = 1 VT 3 i mesons ln Zm M i (T,V,µ S )+ 1 VT 3 i baryons ln Z B m i (T,V,µ B,µ S ) with ln Z M/B m i = VT3 π 2 d i ( mi T ) 2 k=1 (±1) k+1 K k 2 2 (km i /T )cosh(k(b iˆµ B + S iˆµ S )) here we have set µ Q For baryons and strange particles we can assume Boltzmann approximation: validity of Boltzmann approx. ln Z M/B m i / f(m i,t) cosh(b i ˆµ B + S i ˆµ S ) µ B,µ S -dependence factorizes pressure obtains contributions from different hadronic sectors, defined by all possible (B i,s i )-combinations Christian Schmidt LAT 213 1

11 The pressure obtains contributions from different hadronic sectors: p HRG Strangeness within the HRG = f T 4 (,) (T )+f (,1) (T ) cosh( ˆµ S ) } mesons + f (1,) cosh(ˆµ B )+f (1,1) (T ) cosh(ˆµ B µ S ) } baryons + f (1,2) (T ) cosh(ˆµ B 2ˆµ S )+f (1,3) (T ) cosh(ˆµ B 3ˆµ S ) χ 4 S /χ2 S HRG HRG S=1 BS n,m 6 N τ =6 8 B n B n+2 S for diagonal fluctuations:, whereas (multi-strange hadrons) for correlations: BS n+2,m free at T. 16 MeV we find reasonable agreement with the HRG (within 2%) at T & 16 MeV deviations from HRG become large Christian Schmidt LAT BS BS χ 31 /χ11 n 6 S n+2 HRG N τ =6.2 free

12 Disentangling different strangeness sectors The pressure obtains contributions from 4 different strangeness sectors: p HRG = f T 4 (,) (T )+f (,1) (T ) cosh( ˆµ S ) } mesons + f (1,) cosh(ˆµ B )+f (1,1) (T ) cosh(ˆµ B µ S ) } baryons + f (1,2) (T ) cosh(ˆµ B 2ˆµ S )+f (1,3) (T ) cosh(ˆµ B 3ˆµ S ) ) p HRG T 4! S6= = M 1 + B 1 + B 2 + B 3 ) diagonal fluctuations and correlations are given as linear combinations of the different strangeness sectors S 2 =( 1)2 M 1 +( 1) 2 B 1 +( 2) 2 B 2 +( 3) 2 B 3 S 4 =( 1)4 M 1 +( 1) 4 B 1 +( 2) 4 B 2 +( 3) 4 B 3 BS 11 =( 1)B 1 +( 2)B 2 +( 3)B 3 BS =( 1)2 B 1 +( 2) 2 B 2 +( 3) 2 B 3 invert this relation! Christian Schmidt LAT

13 Disentangling different strangeness sectors Idea: separate strangeness sectors by making use of all diagonal strangeness fluctuations and baryon-strangeness correlations up to the 4 th order x 1 BS 11 + x 2 BS 31 + x 3 S 2 + x 4 BS 22 + x 5 BS 13 + x 6 S 4 = y 1 M 1 + y 2 B 1 + y 3 B 2 + y 4 B 3 solve: A~x =ê i with A = ( ) defined by powers of strangeness charges 1 C A Rank=4 dim (Kernel)=2, spanned by v 1,v 2 v 1 = χ BS 31 χ BS 11 v 2 = 1 3 (χs 2 χ S 4 ) 2χ BS 13 4χ BS 22 2χ BS 31 must vanish if HRG is a valid description! Christian Schmidt LAT

14 Disentangling different strangeness sectors.35.3 v 1 free HTL.35.3 χ 2 B - χ4 B free HTL.25 v N τ =6 (open) N τ =8 (filled) N τ = strange baryons carry baryon number 1 partial pressure from strange particles is hadronic all baryons carry baryon number 1 indicator for the validity of the HRG at at T. 16 MeV T & 16 MeV we find reasonable agreement with the HRG deviations from HRG become large Christian Schmidt LAT

15 Disentangling different strangeness sectors solving the 4 inhomogenous systems A~x =ê i the solutions are translations of the kernel M(c 1,c 2 ) = χ S 2 χbs 22 + c 1v 1 + c 2 v 2 1 ( B 1 (c 1,c 2 ) = χ S 2 4 χ S 2 +5χBS 13 +7χBS 22 B 2 (c 1,c 2 ) = 1 ( χ S 4 4 χ S 2 +4χBS 1 ( B 3 (c 1,c 2 ) = χ S 18 4 χ S 2 +3χBS 13 +4χBS χBS 22 ) + c1 v 1 + c 2 v 2 ) + c1 v 1 + c 2 v 2 ) + c1 v 1 + c 2 v 2 Christian Schmidt LAT

16 Disentangling different strangeness sectors B 1 (,) B 1 (,3/2) B 1 (3,3/2) HRG P S =1,B BNL-BI: arxiv: M(,) M(,-3) M(-6,-3) HRG P S =1,M B 3 (,) B 3 (,1/6) B 3 (1/3,1/6) HRG P S =3,B B 2 (,) B 2 (,-3/4) B 2 (-3/2,-3/4) HRG P S =2,B Christian Schmidt LAT

17 Disentangling different strangeness sectors For T. 155 MeV different strange sectors agree separately with the HRG For higher temperatures the deviations from HRG set in abruptly and rapidly become large modifications of the strange hadron contribution to bulk thermodynamics become apparent in the crossover region and follow the same pattern present also in the light quark sector. Christian Schmidt LAT

18 Strangeness in the QGP We now probe the quasi-particle picture, i.e. to what extent the susceptibilities involving strangeness contributions can be understood in terms of elementary degrees of freedom that carry quantum numbers S = ±1,B = ±1/3,Q = ±1/3 1.8 BQS BQS - χ 211 /χ121 free for a free (uncorrelated) strange quarks we have B 2 Q = BQ 2 =1 lim T!1 BQS 211 / BQS HRG N τ =6 8 for free (uncorrelated) strange hadrons we have contributions from two charge sectors. < 1 BQS 211 / BQS Christian Schmidt LAT

19 Summary We have provided evidence that in QCD the strange hadron sector gets modified strongly in the vicinity of the pseudo-critical temperature determined from the light quark chiral susceptibilities. Deviations from the HRG model start becoming large in the transition region and follow a pattern similar to that known for the light quark sector. There thus is no evidence that deconfinement and the dissolution of hadronic bound states may be shifted to higher temperatures for strange hadrons. We also showed that at temperatures larger than T>1.3Tc a simple quasi-particle model may be sufficient to describe properties of mixed strangeness-baryon number susceptibilities. Closer to Tc the structure of these susceptibilities becomes more complicated. A feature well-known also from bulk thermodynamic quantities like the pressure. Christian Schmidt LAT