Validity of the equivalent-photon approximation for the production of massive spin-1 particles

It is pointed out that the equivalent-photon approximation (EPA) for processes with massive spin-1 particles in the final state would have validity in a more restricted kinematic domain than for processes where it is commonly applied, viz., those with spin-1/2 or spin-0 particles in the final state. The criterion for the validity of EPA for the two-photon production of a pair of charged, massive, point-like spin-1 particles V±, each of mass M and with a standard magnetic moment (k=1) is obtained. In a process in which one of the photons is real and the other virtual with four-momentum q, the condition for the validity of EPA is absolute value of q2 << M2, in addition to the usual condition absolute value of q2 << W2, W being the V+V- invariant mass. In a process in which both photons are virtual (with four-momenta q and q'), the condition is absolute value of q2 absolute value of q'2 W4 << 16 M8, in addition to absolute value of q2 << M2, absolute value of q'2 << M2 and absolute value of q2 << W2, absolute value of q'2 << W2. Even when these extra conditions permitting the use of EPA are not fulfilled, convenient approximate expressions may still be obtained assuming merely absolute value of q2 << W2 and absolute value of q'2 << W2. It is also discussed how the extra conditions are altered when the vector bosons are incorporated in a spontaneously broken gauge theory. Examples of W boson production in Weinberg-Salam model are considered for which the condition absolute value of q2 absolute value of q'2 W4 << 16 M8 is shown to be removed. (author)