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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  eective eld theoretical approach to the QCD. In this paper, by using the  skyrmion model which is an eective 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

Pion decay constants in dense skyrmion matter