The $\tau$-contamination of the golden muon sample at the Neutrino Factory

TL;DR

This paper investigates how tau neutrino contributions affect muon samples at the Neutrino Factory, identifying systematic errors and proposing a correction method using a migration matrix to improve measurement precision.

Contribution

It introduces a method to correct tau-induced muon contamination using a migration matrix, enhancing the accuracy of neutrino oscillation measurements at the Neutrino Factory.

Findings

Tau contributions can cause significant systematic errors if uncorrected.

Applying the migration matrix effectively removes tau-related systematic errors.

The correction enables precise measurements even for large  values.

Abstract

We study the contribution of $\nu_e \to \nu_\tau \to \tau \to \mu$ transitions to the wrong-sign muon sample of the {\em golden} channel of the Neutrino Factory. Muons from tau decays are not really a background, since they contain information from the oscillation signal, and represent a small fraction of the sample. However, if not properly handled they introduce serious systematic error, in particular if the detector/analysis are sensitive to muons of low energy. This systematic effect is particularly troublesome for large $\theta_{13} \geq 1^\circ$ and prevents the use of the Neutrino Factory as a precision facility for large $\theta_{13}$. Such systematic error disappears if the tau contribution to the golden muon sample is taken into account. The fact that the fluxes of the Neutrino Factory are exactly calculable permits the knowledge of the tau sample due to the $\nu_e \to \nu_\tau$ oscillation. We then compute the contribution to the muon sample arising from this sample {\em in terms of the apparent muon energy}. This requires the computation of a migration matrix $M_{ij}$ which describes the contributions of the tau neutrinos of a given energy $E_i$, to the muon neutrinos of an apparent energy $E_j$. We demonstrate that applying $M_{ij}$ to the data permits the full correction of the otherwise intolerable systematic error.