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-1/2 or spin-0 particles in the final state. We obtain the criterion for the validity ofEPA for the two-photon production of a pair of charged, massive, point-like spin-1 particlesV±, each of massM 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-momentumq, the condition for the validity ofEPA is |q2|≪M2, in addition to the usual condition |q2|≪W2,W being theV+V− invariant mass. In a process in which both photons are virtual (with four-momentaq andq′), our condition is |q2||q′2|W4 ≪ 16M8, in addition to |q2| ≪M2, |q′2| ≪M2 and |q2| ≪W2, |q′2| ≪W2. Even when these extra conditions permitting the use ofEPA are not fulfilled, convenient approximate expressions may still be obtained assuming merely |q2| ≪W2 and |q′2| ≪W2.
We also discuss how the extra conditions are altered when the vector bosons are incorporated in a spontaneously broken gauge theory. Examples ofW boson production in Weinberg-Salam model are considered for which the condition |q2||q′2|W4 ≪ 16M8 is shown to be removed.
Volume 96, 2022
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