Comparison of various Monte Carlo for response-function studies of a plastic $\beta$-detector used in precise $\beta^+$-branching-ratios experiments

In order to test the Conserved Vector Current hypothesis of the Standard Model, precise determination of the branching ratios for superallowed $\beta$ transitions is needed~[1]. For this purpose, we are using an experimental setup in which one of the main components is a plastic scintillator, and a knowledge of the Response Function (RF) of this scintillator to $\beta$ particles as a function of energy is important. In previous works we compared a Monte Carlo (MC) simulated RF with experiment for $\beta$-particles from standard $\beta$-sources as well as from ``on-line" measurements~[2]. However, we found that various MC programs predict slightly different results. To investigate this, we created the simplified configurations for the MC programs and studied the RF of a plastic disk to monoenergetic positrons with different energies from a point-like source in the air. We concentrated on an intercomparison between the MC results from physics models of various codes: Geant4, Penelope and EGSsrc. For energies between 0.1~MeV to 20~MeV, we see 2\% relative differences in the efficiency calculations from different programs. [1]~J.C.~Hardy and I.S.~Towner. \newblock {\em PRC}, 71(5):055501, 2005. [2]~V.V.~Golovko \textit{et. al.} \newblock {\em BAPS 59}, no~6, p.~DH4 83, 2006; \newblock {\em BAPS 52}, no~3, p.~C16 53, 2007.