Differences in $dE/dX$ for $\mu+$ and $\mu-$ and its Effect on the Underground Charge Ratio

TL;DR

This paper discusses how a small theoretical difference in energy loss between positive and negative muons at high energies leads to a measurable charge ratio asymmetry underground, influenced by ionization effects similar to the Barkas effect.

Contribution

It provides a theoretical analysis of the muon charge ratio asymmetry underground caused by differences in energy loss mechanisms.

Findings

Small fractional difference (~0.15%) in $dE/dX$ for $mbda^+$ and $mbda^-$ at high energies.

Amplification of charge asymmetry to about 0.6% underground due to steep energy spectrum.

Theoretical prediction of charge ratio asymmetry influenced by ionization effects.

Abstract

Theoretical calculations predict a small fractional difference in energy loss for $\mu^+$ and $\mu^-$ of the order of $0.15 %$ at high energies. This is predominantly due to a $z^3$ term in an extended ionization $dE/dX$ relation, in analogy to the Barkas effect at low energies around the Bethe-Bloch maximum. The atmospheric muon energy spectrum is steeply falling off with approximately $E^{-3.7}$ and thus the small difference in $dE/dX$ between $\mu^+$ and $\mu^-$ at high energies results in an amplified charge asymmetry of about $0.6 %$ many thousand meters water equivalent deep underground.