Crossover, fluctuations and Anderson transition in quark matter formation

1. Crossover, fluctuations and Anderson transition in quark matter formation Boris Kerbikov,ITEP

2. The physics of (nuclear matter)  (quark matter) transition QCD phase diagram We are here today T Triple point (Stephanov) Tc BCS (Son) Hadron gas CFL 2SC μ (GeV) 0.3 0.6

3. The interplay of three events • BEC-BCS crossover • Strong fluctuations • Anderson transition (?)

4. The key parameters describing the NM  QM transition • The three parameters are interrelated

5. Crossover - what is it? gap Fluctuating pairs Cooper pairs Gas of tightly Bound pairs g/g0

6. Crossover for Quarks In 2SC phase u- and d-quarks are paired, s- is out of the game Pairing pattern: scalar, color 3, flavor singlet Pairing mechanism: 4-fermion interaction ( NJL, or instantons, or gluon exchange) Quark matter emerges in the crossover regime rather than in BCS

7. NM  QM transition goes with strong fluctuations Ginzburg – Levanyuk parameter is a measure of fluctuations 

8. Color diamagnetism Fluctuations of the gluon field are more important than fluctuations of quark pairs Two effects: • Lowering of the critical temperature • First order phase transition instead of second – cubic term in Ginzburg-Landau functional

9. Anderson localization in quark matter Anderson localization – dynamical diffusion coefficient turns zero due to random impurities Ioffe-Regel criterion , l is the quark mean free path Impurities – stochastic field configurations (e.g.,instantons) close to the mobility edge D =  0 Along with D the gradient term in GL functional is suppressed

10. CONCLUSIONS • The dynamics of NM  QM transition is ill known • The phenomenology of NM  QM transition includes three main events: 1) Crossover from strong coupling/low density to weak coupling/high density (BCS) 2) Strong fluctuations including color diamagnetism 3) Possible Anderson localization of quarks The three events are interrelated