Pion decay constants in dense skyrmion matter

According to the QCD, the hadronic matter can have various phases with matter density and temperature. In general, when there is phase transition in a matter, it is known that a symmetry in the matter changes. In case of the hadronic matter, the chiral symmetry in the matter is expected to be restored when the matter density (or temperature) increases. The actual order parameter with respect to the chiral symmetry in the hadronic matter is known as the quark condensate from the QCD, but the pion decay constant, corresponding to the radius of the chiral circle, plays the role of the order parameter in an effective field theoretical approach to the QCD. In this paper, by using the skyrmion model which is an effective theory to the QCD, we construct the skyrmion matter as a model of the hadronic matter (nuclear matter) and calculate the pion decay constant in the matter. Because of presence of the matter, the pion decay constant is split into the two components, the temporal component and the spatial component. We discuss the phase transition in the skyrmion matter and behavior of the two components of the decay constant for massless pion with density of the skyrmion matter