Physical Masses and the Vacuum Expectation Value of the Higgs Field

By using the Ward-Takahashi identities in the Landau gauge, we derive exact relations between particle masses and the vacuum expectation value of the Higgs field in the Abelian gauge field theory with a Higgs meson. PACS numbers : 03.70.+k; 11.15-q Despite the pioneering work of ’t Hooft and Veltman on the renormalizability of gauge field theories with a spontaneously broken vacuum symmetry, a number of questions remain open. In particular, the number of renormalized parameters in these theories exceeds that of bare parameters. For such theories to be renormalizable, there must exist relationships among the renormalized parameters involving no infinities. As an example, the bare mass M0 of the gauge field in the Abelian-Higgs theory is related to the bare vacuum expectation value v0 of the Higgs field by M0 = g0v0, (1) where g0 is the bare gauge coupling constant in the theory. We shall show that