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

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

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), 034024); Talks on eQCD 2016, QUARKS2016; Scalar meson masses and decays: THIS TALK

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

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

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

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), 034024); Talk at eQCD 2016.

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, 054024 (2010) Chiral chemical potential = time-component of axial field

Mass spectrum mass matrix and chiral condensate

Mass spectrum in vacuum Take Obtain for

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

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

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

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

Decays with chiral imbalance: P-even vertices

Decays with chiral imbalance: P-even vertices

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

Decays with chiral imbalance: P-odd vertices

Our prediction: Scalar resonance enhancement! M. Kawaguchi, M. Harada, S. Matsuzaki, R. Ouyang , PHYS. REV. C 95, 065204 (2017) Our prediction: Scalar resonance enhancement!

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), 034024); 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?)

Effective meson theory in a medium with LPB

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

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.

Backup slides