The Validity of the Weizsacker-Williams Approximation and the Analysis of Beam Dump Experiments

Yu-Sheng Liu, David McKeen, Gerald A. Miller

Published 2016-09-22Version 1

Beam dump experiments have been aimed at searching for new particles or putting constraint limits on their existence by comparing null results with expectations based on the cross section calculated using the Weizsacker-Williams (WW) and other approximations to simplify the phase space integral and amplitude calculation. We examine the validity of the widely used WW approximation along with other popular assumptions. Using scalar boson production as an example, we perform the complete calculation to obtain the cross section and the resulting number of particles produced without such approximations, apply these results to exclusion plot and data fitting, and examine the error when using these commonly used approximations. We find that there could be more than 100\% errors in cross sections and 20\% errors in exclusion plot boundaries for certain parameters. In the event of a discovery, the mass and coupling of the new boson as determined by the approximate and exact calculations could differ at more than the $2\sigma$ level.