1. QCD with chiral chemical potential: models versus lattice
A.Andrianov, V. Andrianov, D. Espriu,
A. Putilova, A.Yakubovich
SPbSU, Russia & ICCUB, Spain
11th APCTP-BLTP JINR-PNPI NRC-SPbU Joint Workshop
“Modern Problems in Nuclear and Elementary Particle Physics”
24-28 July 2017, Petergof, St.Petersburg

2. Outline of the report In search for local parity breaking
Chiral Imbalance and Axial (chiral) chemical potential
Effective meson theory from QCD inspired meson Lagrangian for SU_f (2)
Mass spectra and parameters of the effective Lagrangian
Effective masses of light scalar mesons in a chiral imbalanced medium
Light meson exotic decays in a chiral medium with local parity breaking.
Résumé

3. In search for local parity breaking
, J.Bjorken
Any mechanism of left and right chiral states separation
based on PCAC + gluon anomaly (see next slides)
DETECTION: vector meson masses depending on their polarizations
A.A., V,A.Andrianov, D.Espriu, X.Planells, Phys. Lett. B 710 (2012) 230,
Phys. Rev. D, 90 (2014), ); Talks on eQCD 2016, QUARKS2016;
Scalar meson masses and decays: THIS TALK

4. Or of less size!? (K.Fukushima, private communication)

5. Induced chiral Imbalance
Neglecting space boundary flows in fireballs! Their metastability condition.

6. Topological vs.Chiral chemical potentials
A.A., V,A.Andrianov, D.Espriu, X.Planells, Phys.Lett. B 710 (2012) 230

7. A.A., D.Espriu, X.Planells, Eur. Phys. J. C73, 2294 (2013)
A.A., V,A.Andrianov, D.Espriu, X.Planells, Phys. Lett. B 710 (2012) 230,
Phys. Rev. D, 90 (2014), ); Talk at eQCD 2016.

8. QCD inspired effective meson lagrangian (SU(2) case)
current quark mass
pions
scalar mesons (isosingles + isotriplets)
D. Parganlija, F. Giacosa, D.H. Rischke, Phys. Rev.D 82, (2010)
Chiral chemical
potential
= time-component
of axial field

9. Mass spectrum
mass matrix
and
chiral condensate

10. Mass spectrum in vacuum
Take
Obtain
for

11. SU(2) effective T = 0 Lagrangian T = 158 MeV
In the above model quark condensate is governed by the decay constant v
SU(2) effective
Lagrangian
this talk
T = 0
NJL model
V.Braguta, A.Kotov.
PRD, 93,105025(2016)
SU(2) QCD
V.Braguta et al
JHEP 06 (2015) 094)
T = 158 MeV

12. Masses with chiral imbalance
When
< 0
but no instability!
“tachyon” in flight

13. Effective masses of scalar and pseudoscalar states states
Massless “pions”
at large chemical potentials

14. Mixing of scalars and pseudoscalars and their decays
( depending on velocity )
k = 0
k = 1000 MeV

15. Decays with chiral imbalance: P-even vertices

16. Decays with chiral imbalance: P-even vertices

17. Wess-Zumino action strong CP violation in chiral-imbalance medium:
polarization effects

18. Decays with chiral imbalance: P-odd vertices

20. Our prediction: Scalar resonance enhancement!
M. Kawaguchi, M. Harada, S. Matsuzaki, R. Ouyang , PHYS. REV. C 95, (2017)
Our prediction:
Scalar resonance
enhancement!

21. Résumé
Strong CP violation is quite a challenging possibilityto be revealed
in heavy-ion collisions both at high energy densities (temperatures) and
when triggering by large baryon densities.
2. However the existing theoretical arguments for arising CP violation
in FINITE volumes are not well enough to calculate the production rate
of CP violating nuclear medium.
3. There are two ways to improve the discovery potential: firstly,
to elaborate the recipes for experimentalists to detect peculiar effects
generated in CP odd background, secondly, to measure the probability
of production of the mass states without a firm CP parity. In both cases
the chiral chemical potential method helps a lot.
4. Earlier we already suggested the vector meson dominance model
with chiral imbalance:
A.A., V,A.Andrianov, D.Espriu, X.Planells, Phys. Lett. B 710 (2012) 230,
Phys. Rev. D, 90 (2014), ); Talk at eQCD 2016.
The spectrum of massive vector mesons splits
into three components with different polarizations and with different
effective masses that can be used to detect local parity breaking.
LET US HOPE TO DETECT SUCH PECULIAR STATES SOON…
(LHC ALICE? RHIC? CBM FAIR? NICA?)

22. Effective meson theory in a medium with LPB

23. More details in
A.A., V.A. Andrianov’s, D. Espriu and X.Planells, Phys. Lett. B 684 (2010) 101; B 710 (2012) 230,…

24. Observables sensitive to P-odd effects
We study the angular distributions for the polarizations in the mentioned reactions when the angle between the two outgoing leptons in the decay of meson constrained with the laboratory frame.
In order to select the transverse polarizations in the spectrum, we will
perform the different cuts for each angle and study the variations of the
\rho (and \omega)- spectral function.

25. Backup slides