Bounds on the Mass and Coupling Constant of Radion in the Randall-Sundrum Theory

Assuming the Goldberger-Wise mechanism, we investigated the effective potential at the one-loop level in the Randall-Sundrum theory. We found the lower and upper bounds of the radion mass m_\phi and the radion-SM coupling constant, 0.8 GeV \lesssim m_\phi \lesssim 260 GeV and 1400 GeV \lesssim \Lambda_\phi \lesssim 1500 GeV for the one-loop level potential. These bounds were determined from two constraints of warp factor = O(M_W/M_{Pl}) and Higgs vev \simeq 246 GeV, which can produce strong bounds of m_\phi and \Lambda_\phi. It is phenomenologically important that the one-loop allowed upper bound of the radion mass is about five times larger than the tree-level one, but the radion is still lighter than the Kaluza-Klein modes.