Before its neutral-current measurement, SNO's pure heavy-water phase (2001) measured…

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

Before its neutral-current measurement, SNO's pure heavy-water phase (2001) measured the charged-current flux

\phi_{\rm CC}=1.75

, in units of

10^6\,\mathrm{cm^{-2}s^{-1}}

(sensitive to

\nu_e

only). Super-Kamiokande's water Cherenkov detector had measured the elastic-scattering flux

\phi_{\rm ES}=2.32

in the same units (elastic scattering off electrons, sensitive to all flavours but with muon and tau neutrinos contributing through the neutral current alone, so that

\phi_{\rm ES}=\phi_e+0.156\,\phi_{\mu\tau}

, the factor

0.156

being the ratio of the

\nu_{\mu,\tau}

-electron to

\nu_e

-electron elastic-scattering cross sections at these energies). Combining the quoted statistical and systematic uncertainties on the two rates gives an uncertainty on the derived

\phi_{\mu\tau}

of about

1.1\times10^6\,\mathrm{cm^{-2}s^{-1}}

. ((a)) Using

\phi_{\rm CC}

and the elastic-scattering relation, solve for

\phi_e

and

\phi_{\mu\tau}

. ((b)) Compute

P_{ee}=\phi_e/(\phi_e+\phi_{\mu\tau})

. ((c)) State how many standard deviations

\phi_{\mu\tau}

is from zero, and what that means physically. ((d)) Explain why this derivation of a non-zero

\phi_{\mu\tau}

counts as evidence for flavour conversion that does not rely on the predicted magnitude of the solar neutrino flux, even though it uses no direct neutral-current measurement.

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