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

We point 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-½ or spin-0 particles in the final state. We obtain 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 (κ=1). 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 |q 2|« M 2, in addition to the usual condition |q 2|«W 2,W being the V+ V- invariant mass. In a process in which both photons are virtual (with four-moment aq and q'), our condition is |q 2||q'2|W 4« 16M8, in addition to |q 2| «M2, |q'2| «M 2 and |q 2| «W2, |q'2| «W 2. Even when these extra conditions permitting the use of EPA are not fulfilled, convenient approximate expressions may still be obtained assuming merely |q2| «W 2 and |q'2| «W 2. We also discuss 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 |q2||q'2|W 4 « 16M8 is shown to be removed