Past exam of the particle physics course of the University of Oxford / 2015 / 4 / c

TODO: a numerical estimate from the missing MINOS spectrum cannot be supplied. On source page 7 the graph is absent: PDF Form /Im3 invokes undefined image /Im1 with no image resources, and the archived bundle has the same defect. In particular, no measured minimum energy survives. For maximal mixing angle, the first minimum of muon neutrino survival obeysA restored spectrum or fitted data are needed to choose $E_{\min }$. This is a relation for the survival minimum; a minimum in the raw event spectrum also depends on flux, cross section and smearing. For context only, accelerator and atmospheric results put the splitting at a few $10^{-3}{\mathrm{eV}}^2$, versus the solar splitting about $7.5\times 10^{-5}{\mathrm{eV}}^2$, roughly thirty times smaller. This known scale is not a reconstruction of the absent graph. ^[ref]

Finite event statistics, hadronic shower energy resolution, the muon scale, near-to-far flux extrapolation, interaction and nuclear modeling, backgrounds and detector calibration limit the precision; the baseline itself is comparatively well known. In a two-flavour vacuum fit the sign of $\Delta m^2$ is inaccessible. Evidence for dominant ${\nu }_{\mu }\to {\nu }_{\tau }$ includes the zenith-angle-dependent atmospheric deficit in Super-Kamiokande, approximately preserved active neutral current rates, small electron-flavour appearance at this scale, atmospheric tau appearance and direct tau appearance in OPERA. The latter had already reported four candidates and $4.2\sigma$ evidence in 2014; a later five-candidate discovery result is not needed for this June 2015 answer. ^[ref] These tests constrain a dominant sterile conversion as well as conversion into electron neutrinos.