Quark-antiquark scattering phase shift and meson spectral function in pion superfluid

We study the quark-antiquark scattering phase shift and meson spectral function in the pion superfluid described by the Nambu-Jona-Lasinio model. Meson mixing in the pion superfluid dramatically changes the full scattering phase shift and significantly broadens the spectral function of some collective modes.

Light mesons and phase structures inμB-T-eB andμI-T-eB spaces

Light mesons(σ,π^(0),π^(±))are investigated inμB-T-eB andμI-T-eB spaces using a two-flavor NJL model and used to determine chiral symmetry restoration and the pion superfluid phase transition.InμB-T-eB space,during the chiral symmetry restoration process,the mass of the pseudo-Goldstone modeπ^(0)increases,with sudden jumps.At the critical end point,theπ^(0)meson exhibits a sharp but continuous mass increase,with a sudden mass jump at the Mott transition.In the nearby first order chiral phase transition region,we observe twoπ^(0)mass jumps,one induced by the Mott transition and the other by the quark mass jump.The mass of the Higgs modeσfirst decreases and then increases with chiral symmetry restoration,only showing a jump at the first order chiral phase transition.We plot a chiral phase diagram in terms of the change in quark mass,the Mott transition of the pseudo-Goldstone modeπ^(0),and the minimum mass of the Higgs modeσ.Owing to explicit breaking of chiral symmetry in the physical case,the chiral restoration phase boundaries on theμB-T plane from the order parameter side and meson side are different.Theπ^(0)andσmass jumps will be helpful to the experimental search for the chiral phase diagram and critical end point.On theμI-T plane,the competition between the pion superfluid phase transition and chiral symmetry restoration under magnetic fields is studied in terms of the Goldstone modeπ^(+)and pseudo-Goldstone modeπ^(0).In contrast to the two mass jumps ofπ^(0)in the first order chiral phase transition region,theπ^(+)meson displays several mass jumps in the chiral crossover region.At the critical end point,π^(+)also has sharp but continuous mass change,with a mass jump at the Mott transition.The isospin symmetry is strict,and the pion superfluid phase transition is uniquely determined by the massless Goldstone modeπ^(+).The separation of chiral restoration and the pion superfluid phase boundaries is enhanced by the external magnetic field.