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

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.

Contribution to the 30th International Cosmic Ray Conference, Merida Mexico, 2007 (v2: appending DOE contract number)