The Validity of the Weizsacker-Williams Approximation and the Analysis of Beam Dump Experiments: Production of a New Scalar Boson

Beam dump experiments have been used to search for new particles 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 Weizs\"{a}cker-Williams (WW) approximation] or Monte-Carlo simulations. We display methods, using a new scalar boson as an example, to obtain the cross section and the resulting particle production numbers without using approximations or Monte-Carlo simulations. 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. In the event of a discovery, we generate pseudodata (assuming given values of $m_\phi$ and $\epsilon$) in the currently allowed regions of parameter space. The use of approximations to analyze the pseudodata for the future experiments is shown to lead to considerable errors in determining the parameters. Furthermore, a new region of parameter space can be explored without using one of the common approximations, $m_\phi\gg m_e$. Our method can be used as a consistency check for Monte-Carlo simulations.