• DOI:10.1103/PhysRevD.92.025004
• Corpus ID: 117061070

Anisotropic Propagator for the Goldstone Modes in Color-flavor Locked Phase in the Presence of a Magnetic Field

@article{Sen2015AnisotropicPF,
  title={Anisotropic Propagator for the Goldstone Modes in Color-flavor Locked Phase in the Presence of a Magnetic Field},
  author={Srimoyee Sen},
  journal={Physical Review D},
  year={2015},
  volume={92},
  pages={025004}
}

• S. Sen
• Published 11 March 2015
• Physics
• Physical Review D

We consider the phase diagram of QCD at very high baryon density and at zero temperature in the presence of a strong magnetic field. The state of matter at such high densities and low temperatures is believed to be a phase known as the color-flavor locked phase which breaks color and electromagnetic gauge invariance, leaving a linear combination of them, denoted as $U(1{)}_{\stackrel{\texttildelow{}}{em}}$, unbroken. Of the nine quarks (three flavors and three colors), five are neutral under this unbroken generator and four are oppositely charged (two with a charge of $+1$ and two with $\ensuremath{-}1$). In the presence of a magnetic field corresponding to $U(1{)}_{\stackrel{\texttildelow{}}{em}}$, however, the properties of the condensate change and a new phase known as the magnetic color-flavor locked (MCFL) phase is realized. This phase breaks an approximate $SU(3{)}_{C}\ifmmode\times\else\texttimes\fi{}SU(2{)}_{L}\ifmmode\times\else\texttimes\fi{}SU(2{)}_{R}\ifmmode\times\else\texttimes\fi{}U(1{)}_{B}\ifmmode\times\else\texttimes\fi{}U(1{)}_{A}^{\ensuremath{-}}$ symmetry of the Lagrangian to $SU(2{)}_{C+L+R}\ifmmode\times\else\texttimes\fi{}U(1{)}_{\stackrel{\texttildelow{}}{em}}$ giving rise to six Goldstone modes, five of which are pseudo Goldstone modes. These Goldstone modes are composed of excitations that correspond to both neutral quarks and charged quarks. Hence it is natural to expect that the propagators of these Goldstone modes are affected in the presence of a magnetic field, and their speed becomes considerably anisotropic. Although this anisotropy is self-evident from symmetry arguments, it has not been quantified yet. We calculate this anisotropy in the speed of the Goldstone modes using a Nambu--Jona-Lasinio model type of interaction between the quarks and comment on the impact of such anisotropic modes on transport properties of the MCFL phase.