Crossover, fluctuations and Anderson transition in quark

matter formationBoris Kerbikov,ITEP

The physics of (nuclear matter) (quark matter) transition

QCD phase diagram

T

μ (GeV)

Tc

Triple point(Stephanov)

2SC

Hadron gas CFL

BCS(Son)

0.3 0.6

We are here today

The interplay of three events

• BEC-BCS crossover

• Strong fluctuations

• Anderson transition (?)

The key parameters describing the NM QM transition

• The three parameters are interrelated

Crossover - what is it?

gap

Cooper pairs Fluctuating pairs Gas of tightlyBound pairs

g/g0

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

3 5i ij jq C q

2 4

3

charge conjugation

color symmetry is broken

C

Pairing mechanism: 4-fermion interaction ( NJL, or instantons, or gluon exchange)

Quark matter emerges in the crossover regime rather than in BCS

NM QM transition goes with strong fluctuations

Ginzburg – Levanyuk parameter is a measure of fluctuations

4 442780

28 (3)c cT T

Gi

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

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 pathImpurities – stochastic field configurations (e.g.,instantons) close to the mobility edge

0D =

Along with D the gradient term in GL functional issuppressed

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