The Pion Decay Constants and the Rho-Meson Mass at Finite Temperature in the Hidden Local Symmetry

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We study the temperature dependence of the pion decay constant and rho-meson mass in the hidden local symmetry model at one loop. Using the standard imaginary time formalism, we include the thermal effect of rho meson as well as that of pion. We show that the pion gives a dominant contribution to the pion decay constant and rho-meson contribution slightly decreases the critical temperature. The rho-meson pole mass increases as T⁴/mρ² at low temperature dominated by the pion-loop effect. At high temperature, although the pion-loop effect decreases the rho-meson mass, the rho-loop contribution overcomes the pion-loop contribution and rho-meson mass increases with temperature. We also show that the conventional parameter a is stable as the temperature increases.