Validity of the Weizsacker-Williams approximation and the analysis of beam dump experiments: Production of an axion, a dark photon, or a new axial-vector boson

Beam dump experiments have been used to search for new particles,phi(,) with null results interpreted in terms of limits on masses m(phi) and coupling constants epsilon. However these limits have been obtained by using approximations [including the Weizsacker-Williams (WW) approximation] or Monte Carlo simulations. We display methods to obtain the cross section and the resulting particle production rates without using approximations on the phase space integral or Monte Carlo simulations. In our previous work we examined the case of the new scalar boson production; in this paper we explore all possible new spin-0 and spin-1 particles. We show that the approximations cannot be used to obtain accurate values of cross sections. The corresponding exclusion plots differ by substantial amounts when seen on a linear scale. Furthermore, a new region (m(phi) < 2m(e)) of parameter space can be explored without using one of the common approximations, m(phi) >> m(e). We derive new expressions for the three-photon decays of dark photon and four-photon decays of new axial-vector bosons. As a result, the production cross section and exclusion region of different low mass (m(phi) < 2m(e)) bosons are very different. Moreover, our method can be used as a consistency check for Monte Carlo simulations.