A muon-neutrino beam travels through the Earth over a baseline and is detected at energy

PHYSICS · Multi-part · Fermi University Physics · Particle Physics & Quantum Fields · Flavour, neutrinos and CP violation · Flavour, neutrinos and CP violation

Symmetry and Flavour, Ch Neutrino masses, mixing and oscillations

Problem

A muon-neutrino beam travels through the Earth over a baseline L=735 kmL = 735\,\mathrm{km} and is detected at energy E=3 GeVE = 3\,\mathrm{GeV}. Take the two-flavour approximation with Δm2=2.5×10−3 eV2\Delta m^2 = 2.5\times10^{-3}\,\mathrm{eV^2} and maximal mixing, sin⁡22θ=1\sin^22\theta = 1, ignoring matter effects. ((a)) Compute the oscillation phase ϕ=1.267 Δm2[eV2] L[km]/E[GeV]\phi = 1.267\,\Delta m^2[\mathrm{eV^2}]\,L[\mathrm{km}]/E[\mathrm{GeV}]. ((b)) Compute the disappearance probability sin⁡22θsin⁡2ϕ\sin^22\theta\sin^2\phi and hence the survival probability P(νμ→νμ)P(\nu_\mu\to\nu_\mu). ((c)) State whether this baseline sits short of, at, or beyond the first oscillation maximum (ϕ=π/2\phi = \pi/2).

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