Magnetic effects on color–flavor-locked quark matter and non-Abelian vortices via Ginzburg–Landau approach

By using a general Ginzburg–Landau approach, we study the effects of external magnetic background on color–flavor-locked quark color-superconducting matter. The rotated magnetic field B˜ is introduced, not only accounting for the unbroken symmetry with the rotated electric charge, but also resulting in new effects for the collective excitations such as the Nambu–Goldstone and Higgs modes. In particular, it is found that the masses of Higgs octet are no longer degenerated and part of them acquire the magnetic-induced contribution. To the leading order in the applied field, we construct an effective Ginzburg–Landau formalism through these B˜-related masses. As the application, we investigate magnetic responses of the non-Abelian vortices arising from color–flavor-locked symmetry breaking pattern. The B˜-field dependence of their spatial configurations and tension energies are calculated for the first time.