1. Chiral Symmetry Restoration and Deconfinement in QCD at Finite Temperature M. Loewe Pontificia Universidad Católica de Chile Montpellier, July 2012.

2. This talk is based on the following article: Chiral symmetry restoration and deconfinement in QCD at finite temperature: C. A. Dominguez, M. Loewe and Y. Zhang. Hep-ph 1205.336. Submitted to Phys. Rev. D I acknowledge support form : FONDECYT 1095217 and Proyecto Anillos ACT119 (CHILE)

3. There are two (at least two) phase transitions that may occur in QCD at finite temperature and/or density: 1)Deconfinement due to color screening 2)Chiral symmetry restoration: Moving from a Nambu-Goldstone to a Wigner-Weyl realization Which are the relevant order parameters in each case? Both transitions seem to occur approximately at the same temperature

4. General Aspects: An order parameter is a quantity that vanishes in a certain phase, being finite in a second one. The relevant physical variables are temperature (T) and baryon chemical potential (μ B ) Normally the Polyakov loop (confinement) and the quark condensate (chiral symmetry restoration) are used as order parameters When μ B = 0 and T ≠ 0 lattice results provide a consistente picture, resulting in a similar T c for both transitions in the range 170 MeV < T c < 200 MeV (finite quark masses) However…..

5. For finite Baryon Chemical Potential, the fermion determinant becomes complex and lattice simulations are not possible. So, perhaps we need a new variable, instead of the Polyakov Loop, for discussing deconfinement. An attractive possibility: the continuum threshold of the hadronic resonance spectral function. Phenomenological order parameter. This discussion can be done in the frame of the extended (finite T and μ B ) QCD Sum Rules program

6. Realistic Spectral Function Im Π s ≡ E 2 s0s0

7. Realistic Spectral Function (T) Im Π s ≡ E 2 S 0 (T)

8. For this purpose we will use QCD Sum Rules. OPERATOR PRODUCT EXPANSION OF CURRENT CORRELATORS AT SHORT DISTANCES ( BEYOND PERTURBATION THEORY) CAUCHY’S THEOREM IN THE COMPLEX ENERGY (SQUARED) S-PLANE

9. CONFINEMENT STRONG MODIFICATION TO QUARK & GLUON PROPAGATORS NEAR THE MASS SHELL INCORPORATE CONFINEMENT THROUGH A PARAMETRIZATION OF PROPAGATOR CORRECTIONS IN TERMS OF QUARK & GLUON VACUUM CONDENSATES

10. We reconsider the light quark axial-vector channel, using the first three FESR, together with an improved spectral function Π 0 (q 2 ) and Π 1 (q 2 ) are free of kinematical singularities

11. Invoking the OPE No evidence for d=2 at T=0. The dimension d=4 is given by The second term is negligible compared with the gluon condensate

12. For d=6 we invoke vacuum saturation Our set of FESR (leading order in PQCD) are given by

13. The normalization of the correlator in PQCD In the hadronic sector we have the pion pole followed by the a 1 (1260) resonance A good fit to the ALEPH data is given by

14. rt M a1 = 1.0891 GeV, Γ a1 = 568.78 MeV, C f a1 = 0.048326. From the first Weinberg Sum Rule we get f a1 = 0.073 → C = 0.662

15. r The pion decay constant is related to the quark Condensate through the GMOR relation The first three sum rules will be used to determine the PQCD threshold S 0, d=4 and d=6 condensates. These magnitudes will be used later to normalize our finite tempe- rature results. To leading order in PQCD we get S 0 = 0.7 GeV 2 from the pion pole. → 1.15 GeV 2 when taking the a 1 into account. For the condensates we get the usual results.

16. Thermal Extension of the QCD Sum Rules There are important differences: 1) The vacuum is populated (a thermal vacuum) 2) A new analytic structure in the complex s-plane appears, due to scattering. This effect turns out to be very important

17. New cut associated to a scattering process with quarks (antiquarks) in the populated vacuum (Bochkarev- Schaposnikov)

18. Finite Temperature Effects 1) Time-like region: ω 2 - │q │ 2 > 0 2) Space-like region: ω2 - │q │2 < 0

19. Evolution of the quark condensate (equivalent to f π ). The solid line (Schwinger-Dyson approach) is chiral limit. Dotted line is for massive quarks (Lattice data) T c = 197 MeV Previous Information uark condensate h¯qqi(T )/h¯qqf2(T )/f2(0) as a function of T/Tc in the chiral limit (mq =M = 0) with Tc = 197 Meuark condensate h¯qqi(T )/h¯qqf2(T )/f2(0) as a function of T/Tc in the chiral limit (mq =M = 0) with Tc = 197 Me

20. We will concentrate on the chiral limit, as we find that the FESR have only solutions up to 0.9 T c where the quark condensate is essentially unique. Gluon Condensate

21. The first three sum rules: 1) 2)

22. 3) From these Sum Rules, we are able to get: S 0 (T); f a1 (T); Γ a1 (T) Assumption: m a1 does not depend on T

23. S 0 (T) / S 0 (0): Solid curve. f π 2 (T) / f π 2 (0): Dotted curve.

24. The width definitely grows with temperature

25. The coupling decreases!!

26. Conclusions: We have confirmed the picture where S 0 (T) moves to the left, being a phenomenological order parameter for deconfinement. The width of the a 1 has a divergent behavior as function of T. The coupling f a1 (T) vanishes at the critical temperature.