Bottomonium melting at T >> Tc. Pedro Bicudo CFTP, IST, Lisboa

Transcription

1 Bottomonium melting at T >> Tc Pedro Bicudo CFTP, IST, Lisboa Motivation The finite T string tension The quark mass gap equation with finite T and finite quark mass Chiral symmetry and confinement crossovers with a finite current quark mass Confinement and chiral SB critical points 1

2 Motivation For ++ discussions, I also apply quark-gluon models and Lattice QCD to Temp. =0 chiral symmetry, all sorts of exotics, molecules, excited hadrons and to surf tech Confinement and chiral SB critical points 2

3 Motivation The main motivation is to contribute to understand the QCD phase diagram, for finite T and µ, to be studied at LHC, RHIC and FAIR. But how to address confinement together with chiral symmetry?? - SU(3) lattice QCD, in euclidian space, can t go directly to finite µ... - most QCD models of chiral symmetry, say the Nambu and Jona-Lasinio model have no explicit confinement... so this is a good job for the modern quark model that include not only confinement but also chiral symmetry breaking and quark mass generation, notice we address here light quarks, not as easy as heavy quarks where, mb, mc >> Λ QCD, and mc >> Tc but mu, md, ms ~ Λ QCD ~Tc ~ σ need the finite T propagator, the spontaneous chiral symmetry breaking, the relativisty of quarks and he hadronic coupled channels. Confinement and chiral SB critical points 3

4 Iluustration, thanks to FAIR Motivation SPS see also NA61/SHINE Marcinek s talk Confinement and chiral SB critical points 4

5 NA60 data, thanks to Carlos Lourenço et al Motivation Confinement and chiral SB critical points 5

6 Fits of the finite T string tension from the Lattice QCD energy F1 The confinement, modelled by a string, is dominant at moderate distances Confining string quark antiquark σ is the string tension V(r) ----> π 12 r + Vo + σ r, at finite T log terms also occur At short distances we have the Luscher or Nambu-Gotto Coulomb due to the string vibration + the OGE coulomb, but since the Coulomb is important for UV renormalization but less important for chiral symmetry breaking, PB, PRD 2009 thus we will focus on the linear confinement Confinement and chiral SB critical points 6

7 Fits of the finite T string tension from the Lattice QCD energy F1 Flux Tube picture of confinement Pressure α f With Temperature: q Volume α r q Potential: V(r) = - f d r Free Energy: F 1 (r)= - f d r S d T OK for isotermic Internal Energy: E 1 (r)= - f d r + T d S OK for adiabatic Confinement and chiral SB critical points 7

8 Fits of the finite T string tension from the Lattice QCD energy F1 T x y The Polyakov loop is a gluonic path, closed in the imaginary time t 4 / inverse temperature T direction in QCD discretized in a periodic boundary euclidian Lattice. It measures the free energy F of one or more static quarks P = N Exp[ - F /T ] tr{p(0)p + (r)} = N Exp[ - F /T ] Confinement and chiral SB critical points 8

9 Fits of the finite T string tension from the Lattice QCD energy F1 q If we consider a single solitary lonely quark in the universe, in the confining phase, his string will travel as far as needed to look for a partner antiquark, resulting in an infinite energy F. Thus the 1 quark Polyakov loop P is a frequently used order parameter for deconfinement. P(T) It is a phase transition in pure gauge QCD! Tc T However, since we are interessed in appoaching the deconfinement transition from below Tc, we perefer here to use the string tension σ as the order parameter, computed in the quark-antiquark colour singlet Polyakov loop P. Confinement and chiral SB critical points 9

10 Fits of the finite T string tension from the Lattice QCD energy F1 Lattice QCD data, thanks to Olaf Kaczmarek et al. PRD (2007) Free Energy F1 solid line : T=0 qq potential V Confinement and chiral SB critical points 10

11 Fits of the finite T string tension from the Lattice QCD energy F1 Lattice QCD data, thanks to Olaf Kaczmarek et al. PRD (2007) Free Energy F1 solid line : T=0 qq potential V Confinement and chiral SB critical points 11

12 Fits of the finite T string tension from the Lattice QCD energy F1 Linear fir of the longer distance part of the fee energy F. We cut the short distance in such a way that the fit is cutoff independent. F(r)/Tc._IMG_2118.jpg r σ 1/2 Confinement and chiral SB critical points 12

13 Fits of the finite T string tension from the Lattice QCD energy F1 Comparing the string tensions at T=0, with the cond mat magnetization curve The magnetization curve of a magnetic material is a text book curve well modelled by the statistics of spin 1/2 systems. Here we show that the same curve also models the σ sting tension and the deconfinement curve! σ/σ 0 our Linear + Coulomb fit our Linear fit Linear + Log fit, Kaczmarek et al PRD (2000) T/Tc Confinement and chiral SB critical points 13

14 Fits of the finite T string tension from the Lattice QCD energy F1 Comparing the string tensions at T=0, with the cond mat magnetization curve σ/σ 0 The magnetization curve of a magnetic material is a text book curve well modelled by the statistics of spin 1/2 systems. Here we show that the same curve also models the σ sting tension and the deconfinement curve! SU(2) Linear + Log fit, Petreczky et al, PRD 2003 SU(3) SU(3) SU(3) T/Tc Confinement and chiral SB critical points 14

15 Fits of the finite T string tension from the Lattice QCD energy F1 Comparing the string tensions at T=0, with the cond mat magnetization curve σ/σ 0 The magnetization curve of a magnetic material is a text book curve well modelled by the statistics of spin 1/2 systems. Here we show that the same curve also models the σ sting tension and the deconfinement curve! solid line : 2nd order phase transition approximation dashed line : 1st order phase transition discontinuity at T= Tc, the entropy S = OO!!! T/Tc Confinement and chiral SB critical points 15

16 The mass gap equation with finite T and finite quark mass Now, the critical point occurs when the phase transition changes to a crossover, and the crossover in QCD is produced by the finite current quark mass m0, since it affects the order parameters P or σ, and m(0) or <qq> order parameter crossover Tc phase transition T Confinement and chiral SB critical points 16

17 The mass gap equation with finite T and finite quark mass The mass gap equation at the ladder/rainbow truncation of Coulomb Gauge QCD in equal time reads, -1 - = At finite T, one may reduce the string tension, σ-> σ * and the mass gap equation is in units of σ*. Confinement and chiral SB critical points 17

18 The mass gap equation with finite T and finite quark mass Solution of the mass gap equation at T=0, in units of σ 2 =0.19 GeV 2 =1 m c = 10.0 m c = 1.00 may be measured in excited hadrons PB et al, PRL 2009 m c = m c = m c = m c = m c = 3.16 m c = 1.00 Confinement and chiral SB critical points 18

19 the mass gap The mass gap equation with finite T and finite quark mass Thus we get for the mass gap m(0) as a function of m 0 / σ this curve. At finite T we just need to use the corresponding σ* m(0) m 0 / σ Confinement and chiral SB critical points 19

20 The quark mass and Chiral symmetry and confinement crossovers Thus at vanishing m 0 we have a chiral symmetry phase transition, and at finite m 0 we have a crossover, that gets weaker and weaker when m 0 increases: m(0) m 0 >> σ m 0 finite Tc m 0 =0 T Confinement and chiral SB critical points 20

21 The quark mass and Chiral symmetry and confinement crossovers In what concerns confinement, the linear confining quark-antiquark potential saturates when it reaches the energy for the creation of a quark-antiquark pair Thus at infinite m 0 we have a confining phase transition, and at finite m 0 we have a crossover, that gets weaker and weaker when m 0 decreases: F T (r) 2m 0 m 0 >> σ m 0 finite saturation at T<Tc 2 m 0 2 m 0 m 0 =0 r Confinement and chiral SB critical points 21

22 The quark mass and Chiral symmetry and confinement crossovers The Polyakov loop, P = N Exp[ - F(OO OO) / T ] then shows a crossover for finite quark mass, with the dependence opposite of the one for the mass gap, m 0 ->0 P(T) m 0 finite m 0 >> σ > OO Tc T Confinement and chiral SB critical points 22

23 Motivation Back to the QCD phase diagram, if the mass m 0 is either small (depicted here), or large the critical points always separate, they will be identical only by coincidence. Deconfinement critical point Chiral Critical Point Confinement and chiral SB critical points 23

24 Conclusion & Outlook on light q with χ symmetry and confinement We remark that the pure gauge finite T string tension σ is well fitted by the condensed matter physics magnetization curve χ. We compute the dynamically generated quark mass m(p), solving the mass gap equation both for finite current quark masses mc and for finite T. We find that the current quark mass changes both the confinement and the and chiral symmetry phase transitions into crossovers. Since the finite current quark mass affects in opposite ways the confinement and the chiral symmetry, we conjecture that: at finite T and µ there will be not one but two critical points, where the crossovers are separated from the phase transitions. In the future we will move on to study light hadrons at finite T and µ. Confinement and chiral SB critical points 24