The QCD phase diagram and fluctuations

1. The QCD phase diagram and fluctuations Krzysztof Redlich University of Wroclaw • Deconfinement in the SU(N) pure gauge theory and Polyakov loop fluctuations • Polyakov loop fluctuations in the presence of dynamical quarks • Chiral transition and O(4) • criticality: charge fluctuations and • their probability distributions Coll. with: BengtFriman, Olaf Kaczmarek, Pok. Man Lo, Kenji Morita & Chihiro Sasaki

2. Polyakov loop on the lattice needs renormalization • Introduce Polyakov loop: • Renormalized ultraviolet divergence • Usually one takes as an order parameter HotQCD Coll.

3. To probe deconfinement : consider fluctuations SU(3) pure gauge: LGT data • Fluctuations of modulus of the Polyakov loop However, the Polyakov loop Thus, one can consider fluctuations of the real and the imaginary part of the Polyakov loop. HotQCD Coll.

4. Fluctuations of the real and imaginary part of the renormalized Polyakov loop • Imaginary part fluctuations • Real part fluctuations Pok Man Lo, B. Friman, O. Kaczmarek, C. Sasaki & K.R. , PRD (2013)

5. Compare different Susceptibilities: • Systematic differences/simi-larities of the Polyakov lopp susceptibilities • Consider their ratios!

6. Ratios of the Polyakov loop fluctuations as an excellent probe for deconfinement Pok Man Lo, B. Friman, O. Kaczmarek, C. Sasaki & K.R. , PRD (2013) • In the deconfined phase Indeed, in the real sector of Z(3) Expand modulus and find: Expand the modulus, get in the leading order thus

7. Ratios of the Polyakov loop fluctuations as an excellent probe for deconfinement Pok Man Lo, B. Friman, O. Kaczmarek, C. Sasaki & K.R. , PRD (2013) • In the confined phase Indeed, in the Z(3) symmetric phase, the probability distribution is Gaussian to the first approximation, with the partition function consequently Expand modulus and find: Thus and In the SU(2) case is in agreement with MC results

8. Ratio Imaginary/Real of Polyakov loop fluctuations Pok Man Lo, B. Friman, O. Kaczmarek, C. Sasaki & K.R. , PRD (2013) • In the confined phase for any symmetry breaking operator its average vanishes, thus and thus • In deconfined phase the ratio of and its value is model dependent

9. Ratio Imaginary/Real of Polyakov loop fluctuations Pok Man Lo, B. Friman, O. Kaczmarek, C. Sasaki & K.R. , PRD (2013) • Due to Z(3) symmetry breaking in confined phase, the fluctuations of transverse Polyakov loop strongly suppressed, • In confined phase Due to Z(3) symmetry breaking in confined phase, the fluctuations of transverse Polyakov loop strongly suppressed,

10. Ratio Imaginary/Real and gluon screening WHOT QCD Coll: • In the deconfined phase • WHOT QCD Coll. (Y. Maezawa et al.) and WHOT-coll. identified as the magnetic and electric mass: Since Phys. Rev. D81 091501 (2010) 2-flavors of improved Wilson quarks

11. String tension from the PL susceptibilities Pok Man Lo, et al. ( in preparation) • Common mass scale for • In confined phase a natural choose for M O. Kaczmarek, et al. 99 string tension

12. Polyakov loop and fluctuations in QCD • Smooth behavior for the Polyakov loop and fluctuations difficult to determine where is “deconfinement” HOT QCD Coll The inflection point at

13. The influence of fermions on the Polyakov loop susceptibility ratio • Z(3) symmetry broken, however ratios still showing deconfinement • Dynamical quarks imply smoothening of the susceptibilities ratio, between the limiting values as in the SU(3) pure gauge theory Pok Man Lo, B. Friman, O. Kaczmarek, C. Sasaki & K.R. • Change of the slope in the narrow temperature range signals color deconfinement this work

14. The influence of fermions on ratios of the Polyakov loop susceptibilities • Z(3) symmetry broken, however ratios still showing the transition • Change of the slopes at fixed T Pok Man Lo, B. Friman, O. Kaczmarek, C. Sasaki & K.R.

15. Probing deconfinement in QCD lattice with p4 fermion action • HRG factorization of pressure: Pok Man Lo, B. Friman, (013) O. Kaczmarek, C. Sasaki & K.R. • Kurtosis measures the squared of the baryon number carried by leading particles in a medium S. Ejiri, F. Karsch & K.R. (06) S. Ejiri, F. Karsch & K.R. (06) S. Ejiri, F. Karsch & K.R. (06)

16. Probing deconfinement in QCD lattice with p4 fermion action Pok Man Lo, B. Friman, (013) O. Kaczmarek, C. Sasaki & K.R. • The change of the slope of the ratio of the Polyakov loop susceptibilities appears at the same T where the kurtosis drops from its HRG asymptotic value • In the presence of quarks there is “remnant” of Z(N) symmetry in the ratio, indicating deconfi- nement of quarks S. Ejiri, F. Karsch & K.R. (06)

17. Probing deconfinement in QCD Pok Man Lo, B. Friman, O. Kaczmarek, C. Sasaki & K.R. Change of the slope of the ratio of the Polyakov loop susceptibilities appears at the same T where the kurtosis drops from its HRG asymptotic value • In the presence of quarks there is “remnant” of Z(N) symmetry in the ratio, indicating deconfi- nement Still the lattice finite size effects need to be studied S. Ejiri, F. Karsch & K.R. (06) Ch. Schmidt This paper 150 200 T[MeV]

18. Polyakov loop susceptibility ratios still away from the continuum limit: • The renormalization of the Polyakov loop susceptibilities is still not well controlled: Still dependence on in the presence of quarks. Ch. Schmidt et al.

19. Conclusions: • Ratios of the Polyakov loop and the Net-charge susceptibilities are excellent probes of deconfinement and/or the O(4) chiral crossover transition in QCD