Weakly coupled QGP? Péter Petreczky

Weakly coupled QGP? Péter Petreczky QGP is expected to be strongly coupled around T c : how does this features manifest itself in terms of different quantities, how do we observe it on lattice? QGP: state of strongly interacting matter for weakly interacting gas of quark and gluons? T QCD,g 1 2 T m D gt g 2 T Nuclear Theory Seminar, Stony Brook, January 18, 217 EFT approach: EQCD Magnetic screening scale: non-perturnative Perturbative series is an expansion is in g and not α s Loop expansion breaks down at some order (weak coupling may still work) Problem : g(µ = 1 2 GeV) = p 4 s (µ = 1 2 GeV) ' 1 g(µ = 1 16 GeV) ' 1/2 In this talk : Fluctuations of conserved charges, color screening, topological susceptibility

Dimensional reduction at high temperatures Appelquist, Pisarski PRD23 (1981) 235 Nadkarni, PRD27 (1983) 917 F µ = D µ A µ D A µ A µ! 1/2 A µ EQCD Braaten, Nieto, PRD 51 (95) 699, PRD 53 (96) 3421 Kajantie et al, NPB 53 (97) 357, PRD 67 (3) 158 s g 2 /(4 m D ) F = F(non-static) + T F 3d Integrate out A 3d YM theory MQCD F 3d ~ g 6 3

Resummed (HTL) perturbation theory Basic idea: ignore the static magnetic sector and assume no hierarhy of scales T and m D Expansion parameter: g 2 /(4 π) but the coefficients are function of m D F (T )= X n n s F n (T,m D ) Karsch, Patkós, PP; Blaizot, Iancu, Rebhan; Andersen, Braaten, Strickland.

QCD thermodynamics at non-zero chemical potential Taylor expansion : S hadronic quark Taylor expansion coefficients give the fluctuations and correlations of conserved charges, e.g. information about carriers of the conserved charges ( hadrons or quarks ) probes of deconfinement

Deconfinement : fluctuations of conserved charges 1.8 B = 1 VT 3 hb2 i hbi 2 Q = 1 VT 3 hq2 i hqi 2 S = 1 VT 3 hs2 i hsi 2 i / i SB baryon number electric charge strangeness Ideal gas of massless quarks :.6.4.2 i=b Q S filled : HISQ, N =6, 8 open : stout continuum SB S =1 conserved charges carried by light quarks 15 2 25 3 35 conserved charges are carried by massive hadrons HotQCD: PRD86 (212) 3459 BW: JHEP 121 (212) 138,

Deconfinement of strangeness Partial pressure of strange hadrons in uncorrelated hadron gas: Strange hadrons are heavy treat them As Boltzmann gas should vanish! v 1 and v 2 do vanish within errors at low T v 1 and v 2 rapidly increase above the transition region, eventually reaching non-interacting quark gas values Bazavov et al, PRL 111 (213) 8231.3.25.2.15.1.5. uncorr. hadrons non-int. quarks χ 2 B -χ4 B 14 18 22 26 3 34 v 1 v 2

Quark number fluctuations at high T At high temperatures quark number fluctuations can be described by weak coupling approach due to asymptotic freedom of QCD.9.85 u 4 / ideal 4 quark number fluctuations -.2 ud 11 quark number correlations.8 -.4.75 1.5 -.6 EQCD u 2 / ideal 2 -.8 N =6.7 1 8.95 -.1 1.65 12 EQCD -.12 cont 4.6 u (cont).9 3-loop HTL.85 -.14 3 5 7 9 25 3 35 4 45 5 55 6 65 7.55 3 35 4 45 5 55 6 65 7 Good agreement between continuum extrapolated lattice results and the weak coupling approach Quark number correlations vanish at any loop order but can be calculated in EQCD and the EQCD calculations agree with the continuum extrapolated lattice results Bazavov et al, PRD88 (213) 9421, Ding et at, PRD92 (215) 7443

Fluctuation and correlations and deconfinement of charm XY C nml = T m+n+l @n+m+l p(t,µ X,µ Y,µ C )/T 4 @µ n X @µm Y @µl C Bazavov et al, PLB 737 (214) 21 m c T only C =1 sector contributes 3. 2.5 In the hadronic phase all BC-correlations are the same! BC BC 13 / 22 BC BC 11 / 13 N : 8 6 non-int. quarks.5.4.3.2.1 χ uc mn /χc 2 HTLpt EQCD m n: 22 13 31 11 2.. 1.5 1. un-corr. hadrons 14 16 18 2 22 24 26 28 Hadronic description breaks down just above T c open charn deconfines above T c -.1 16 18 2 22 24 26 28 3 32 34 The charm-light quark correlations can understood in terms of weak coupling calculations for T>25 MeV but are much larger than the weak coupling result close to T c

1..8.6 Quasi-particle model for charm degrees of freedom Charm dof are good quasi-particles at all T because M c >>T and Boltzmann approximation holds p C (T,µ B,µ c )=p C q (T ) cosh(ˆµ C +ˆµ B /3) + p C B(T ) cosh(ˆµ C +ˆµ B )+p C M (T ) cosh(ˆµ C ) C 2, BC 13, BC 22 ) p C q (T ),p C M (T ),p C B(T ) Partial meson and baryon pressures described by HRG at T c and dominate the charm pressure then drop gradually, charm quark only dominant dof at T>2 MeV p q C /p C p B C /p C ˆµ X = µ X /T Partial pressures drop because hadronic cxcitations become broad at high temperatures (bound state peaks merge with the continuum).4.2 p M C /p C Mukherjee, PP, Sharma, PRD93 (216) 1452 See Jakovác, PRD88 (213), 6512 Biró, Jakovác, PRD(214)6512. 15 17 19 21 23 25 27 29 31 33.3 Vice versa for quarks

Deconfinement and color screening Onset of color screening is described by Polyakov loop (order parameter in SU(N) gauge theory)! L = P exp ig Z 1/T d A (~x, ) F Q Q(r!1,T)=2F Q (T ) exp( 2+1 flavor QCD, continuum extrapolated (TUMQCD, to be published) F Q Q(r, T )/T )= 1 9 htrl(r)trl ()i.9 L ren (T) T QCD c T PG c free energy of static quark anti-quark pair shows Debye screening SU(N) gauge theory QCD! at high temperatures Similar results with stout action Borsanyi et al, JHEP4(215) 138.8.7.6.5.4.3.2.1 stout, cont. HISQ, cont. SU(3) SU(2) 15 2 25 3 35 4 45 5

The entropy of static quark TUMQCD, PRD 93 (216) 11452 1 9 8 7 6 5 4 3 2 1 S Q T/T c N f =2+1, m =161 MeV N f =3, m =44 MeV N f =2, m =8 MeV N f =.8 1 1.2 1.4 1.6 1.8 2.5.4.3.2.1 S Q (T) S Q = @F Q @T LO NLO, µ=(1-4) T NNLO lattice 1 15 2 25 3 35 4 45 5 At high temperature the static quark only sees the medium within a Debye radius, as T increases the Debye radius decreases and S Q also decreases The onset of screening corresponds to peak is S Q and its position coincides with T c The entropy of the static quark has been calculated at NNLO accuracy Berwein et al, PRD93 (216) 341 Weak coupling (EQCD) calculations work only or T> 15 MeV

The entropy of static quark (cont d) Consider SU(3) gauge theory (no quarks) m D and g 3 2 are know to NNLO.35.3.25.2.15.1.5 S Q (T) LO NLO, µ=(1-6) T NNLO N =4 -.1 -.2 -.3 -.4 -.5 -.6 6 8 1 12 14 16 18 2 22 24 -.7 T/T c F Q stat /(g 4 T) T/T c full EQCD 4-loop 3-loop 2-loop 1-loop 6 8 1 12 14 16 18 2 22 24 FQ stat = C F g 2 @ 2N htra2 i = @m 2 F 3d D Using the result from the 3d pressure the static part of F Q can be evaluated exactly or up to 4-loop order and convergence of the perturbative expansion can be studied Reasonable convergence down to 6 T c => The biggest uncertainty comes from the non-static part which is known up to LO

Casimir scaling of the Polyakov loop Instead of fundamental representations consider Polyakov loop P n in arbitrary representation n PP, Schadler, PRD92 (215) 94517 P 3 = L ren Use symanzik flow to renormalized the Polyakov loop and reduce the noise Fodor et al, JHEP 149 (214) 18 Casimir scaling: free energy is proportional to qudratic Casimir operator C n of rep n R n = C n /C 3 P 1/R n n 1.2 1..8.6 32 3 8.4.2. P 3 P 6 P 8 P 1 P 15 P 15 P 24 P 27 1 2 3 4 5 Expected in weak coupling expansion: e.g. at LO F n Q = C n s m D

Casimir scaling of the Polyakov loop (con t) n =1 P 1/R n n /P 3 n. 8. -.1 -.1 -.2 24 3 6 -.2 -.3 -.3 -.4 -.5 6 15 8 24 1 27 15 1 2 3 4 5 6 7 -.4 -.5 N = 6 N = 8 N = 1 N = 12 15 2 25 3 Casimir scaling holds for T>3 MeV color screening like in weakly coupled QGP? Breaking of Casimir scaling first appear at order α s 4 in the weak coupling expansion Berwein et al, PRD93 (216) 341

Free energy and singlet free energy of static quark-antiquark e F Q Q (r,t )/T = 1 9 htrl(r)trl ()i e F S(r,T )/T = 1 3 htrl(r)l ()i e F Q Q (r,t )/T = 1 9 e F S(r,T )/T + 8 9 e F O(r,T )/T 1e-1 _ -9r 2 TF QQ _ (r,t) 421 5814 1e 1e-1 F i (r, T )=F i (r, T ) 2F Q (T ) Coulomb gauge _ -rf S (r,t)/c F 22 333 421 1222 2923 5814 1e-2 1e-2 1e-3 1e-3 rt.2.4.6.8 1 1.2 1e-4.5 1 1.5 2 rt TUMQCD, to be published Lattice results are in reasonable agreement with NLO weak coupling result for rt<.6, at larger distances, non-pertubtative effects (due to chromo-magnetic sector ) become important

Instanton gas at work? The amount of U A (1) breaking at high T is reduced because of the reduced instanton density => dilute instanton gas approximation (DIGA), Gross et al, RMP 53 (1981) 43 Topological susceptibility with HISQ action using Symanzik flow top = 1 V hq2 i hqi 2 top/m 2 l = disc,5 ' disc Schadler, Sharma, PP, PLB 762 (216) 498 1 8 6 4 t 1/4 [MeV] this work Bonati et al., DIGA DIGA is compatible with the lattice results if a K factor ~1.79 is included 2 Similar K factor was found for SU(3) gauge theory, Borsányi et al, PLB 752 (216) 175 1 5 T/T c 1 1.5 2 3 3.5

Summary The deconfinement transition temperature defined in terms of the free energy of static quark agrees with the chiral transition temperature for physical quark mass Deconfinement transition can be studied in terms of fluctuations and correlations of conserved charges, strongly coupled QGP manifest itself as incomplete dominance of quark dof close to T c Charm hadrons can exist above T c and are the dominant dof for T<18 MeV For T > 3 MeV weak coupling expansion works well for quark number susceptibilities For T>3 MeV Casimir scaling for Polyakov loop for higher representations predicted by weak coupling calculations holds. The NLO weak coupling expansion for the r-dependence of the free energy of static quark anti-quark pair agrees with lattice results for T>4 MeV, while the T-dependence of F Q (T) is described by the weak coupling calculations only for T>15 MeV Dilute instanton gas works for T>3 MeV

Back-up:.2.16.12.8.4 -.4.12.8.4 F Q (T)/T g 5, mixed g 5, EQCD g 6, mixed g 6, EQCD lattice EQCD 6 8 1 12 14 16 18 2 22 24 T/T c