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 mφ and the radion-SM coupling constant, 0.8 GeV≲mφ≲260 GeV and 1400 GeV≲Λφ≲1500 GeV for the one-loop level potential. These bounds were determined from two constraints of warp factor=O(MW/MPl) and Higgs vev≃246 GeV, which can produce strong bounds of mφ and Λφ. 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.