Confined chirally symmetric dense matter

Transcription

1 Confined chirally symmetric dense matter L. Ya. Glozman, V. Sazonov, R. Wagenbrunn Institut für Physik, FB Theoretische Physik, Universität Graz 28 June 2013 L. Ya. Glozman, V. Sazonov, R. Wagenbrunn (Institut Confinedfür chirally Physik, symmetric FB Theoretische dense matter Physik, Universität Graz) 28 June / 16

2 Overview 1 Basics of QCD 2 Chiral symmetry 3 QCD phase diagram 4 Chirally symmetric model with confinement 5 Chiral symmetry restoration 6 Conclusions L. Ya. Glozman, V. Sazonov, R. Wagenbrunn (Institut Confinedfür chirally Physik, symmetric FB Theoretische dense matter Physik, Universität Graz) 28 June / 16

3 Basics of QCD Quantum chromodynamics (QCD) ˆ is a theory of the strong interactions ˆ is a non-abelian gauge theory ˆ describes the interactions between quarks and gluons which make up hadrons QCD enjoys two peculiar properties: ˆ Confinement - the force between quarks does not diminish as they are separated. ˆ Asymptotic freedom, which means that in very high-energy reactions, quarks and gluons interact very weakly. QCD Lagrangian: L QCD = q i (i(γ µ D µ ) ij m δ ij ) q j 1 4 G a µνg µν a L. Ya. Glozman, V. Sazonov, R. Wagenbrunn (Institut Confinedfür chirally Physik, symmetric FB Theoretische dense matter Physik, Universität Graz) 28 June / 16

4 Standard Model L. Ya. Glozman, V. Sazonov, R. Wagenbrunn (Institut Confinedfür chirally Physik, symmetric FB Theoretische dense matter Physik, Universität Graz) 28 June / 16

5 Hadrons L. Ya. Glozman, V. Sazonov, R. Wagenbrunn (Institut Confinedfür chirally Physik, symmetric FB Theoretische dense matter Physik, Universität Graz) 28 June / 16

6 Chiral symmetry ˆ m u, m d Λ QCD, where Λ QCD is a typical scale of QCD, generated by renormalization. ˆ massless QCD Lagrangian obeys flavor chiral symmetry ˆ U(1) A is broken by quantization ˆ Left and right quarks: SU(2) L SU(2) R U(1) V U(1) A q L = P L q, q R = P R q, P L + P R = 1 transform independently under SU(2) L and SU(2) R respectively L. Ya. Glozman, V. Sazonov, R. Wagenbrunn (Institut Confinedfür chirally Physik, symmetric FB Theoretische dense matter Physik, Universität Graz) 28 June / 16

7 Spontaneous symmetry breaking ˆ the QCD Lagrangian is invariant under SU(2) A SU(2) V U(1) V ˆ quarks and anti-quarks attract each other and form a quark condensate < qq > ˆ because of the quark condensate vacuum (ground state) is not invariant under SU(2) A L. Ya. Glozman, V. Sazonov, R. Wagenbrunn (Institut Confinedfür chirally Physik, symmetric FB Theoretische dense matter Physik, Universität Graz) 28 June / 16

8 QCD phase diagram L. Ya. Glozman, V. Sazonov, R. Wagenbrunn (Institut Confinedfür chirally Physik, symmetric FB Theoretische dense matter Physik, Universität Graz) 28 June / 16

9 QCD phase diagram at N c N c The same gluon dynamics in the vacuum and in the matter because of absence of quark loops in both cases. At large chemical potential a pressure N c. For a pure hadronic gas it must be 1. For a deconfining quark-gluon matter it must be N 2 c. L. Ya. Glozman, V. Sazonov, R. Wagenbrunn (Institut Confinedfür chirally Physik, symmetric FB Theoretische dense matter Physik, Universität Graz) 28 June / 16

10 4-d chirally symmetric model with confinement typical QCD diagram: instantaneous interaction, rainbow - ladder approximation: L. Ya. Glozman, V. Sazonov, R. Wagenbrunn (Institut Confinedfür chirally Physik, symmetric FB Theoretische dense matter Physik, Universität Graz) 28 June / 16

11 Effect of non-zero chemical potentials To include finite chemical potential, all occupied levels below p f has to be removed, because of Pauli blocking. L. Ya. Glozman, V. Sazonov, R. Wagenbrunn (Institut Confinedfür chirally Physik, symmetric FB Theoretische dense matter Physik, Universität Graz) 28 June / 16

12 Chiral symmetry restoration Above the critical Fermi momentum p f > p cr f, chiral symmetry gets restored: < qq >= 0; < qq > p f L. Ya. Glozman, V. Sazonov, R. Wagenbrunn (Institut Confinedfür chirally Physik, symmetric FB Theoretische dense matter Physik, Universität Graz) 28 June / 16

13 Confined but chirally symmetric dense matter L. Ya. Glozman, V. Sazonov, R. Wagenbrunn (Institut Confinedfür chirally Physik, symmetric FB Theoretische dense matter Physik, Universität Graz) 28 June / 16

14 Possible QCD phase diagram L. Ya. Glozman, V. Sazonov, R. Wagenbrunn (Institut Confinedfür chirally Physik, symmetric FB Theoretische dense matter Physik, Universität Graz) 28 June / 16

15 Diffused Fermi surface < qq > = 0 = 0.02 = 0.06 = 0.09 = p f Quark condensate as a function of the Fermi momentum p f, at different fixed values of diffusing. L. Ya. Glozman, V. Sazonov, R. Wagenbrunn (Institut Confinedfür chirally Physik, symmetric FB Theoretische dense matter Physik, Universität Graz) 28 June / 16

16 Conclusions ˆ We have demonstrated that it is possible to have at finite chemical potential a confining but chirally symmetric matter consisting of chirally symmetric hadrons. ˆ Whether this happens in QCD or not is still an open question but it definitely suggests that there are no reasons to believe that deconfinement and chiral restoration necessarily coincide at finite density. ˆ Interacting valence quarks imply the diffused Fermi surface. ˆ A chiral phase transition, previously observed for a rigid quark Fermi surface, survives. ˆ For any reasonable diffusion width there always exists such a Fermi momentum, that the chiral restoration phase transition does take place. L. Ya. Glozman, V. Sazonov, R. Wagenbrunn (Institut Confinedfür chirally Physik, symmetric FB Theoretische dense matter Physik, Universität Graz) 28 June / 16