MSW Oscillations - LMA and Subdominant Effects

New physics near the TeV scale could modify neutrino-matter interactions or generate a relatively large neutrino magnetic (transition) moment. Both types of effects have been discussed since the 1970’s as alternatives to mass-induced neutrino flavor oscillations. Nowadays, the availability of high-statistics data makes it possible to turn the idea around and ask: How well do the simple mass-induced oscillations describe solar neutrinos? At what level are the above-mentioned nonstandard effects excluded? Can we use solar neutrinos to constrain physics beyond the Standard Model? These notes review the sensitivity of the present-day solar neutrino experiments to the nonstandard neutrino interactions and transition moment and outline progress that may be expected in the near future. Based on a talk given at the Neutrino 2006 conference [1]. Preprint: LA-UR-06-6774 1. Standard LMA solution: basic features The most basic experimental fact about the neutrinos from the Sun is that the electron neutrino survival probability, P std ee ≡ P (νe → νe), is measured to vary as a function of the neutrino energy. At the high end of the spectrum (Eν & 6− 7 MeV) the SNO [2] and Super-Kamiokande [3] experiments have established that P std ee is about ∼ 34 ± 3%. The gallium experiments [4], however, which are sensitive to both highand low-energy neutrinos, see a higher survival probability: the measured rate is 74 ± 7 SNU, whereas the standard solar model prediction [5] (before oscillations) is 131 −10 . This simple fact has highly non-trivial implications. Indeed, this behavior is not “generic” for mass-induced oscillations, even when they combine with the MSW [6, 7] matter effect. A priori, one might have expected solar neutrinos to be in one of these regimes: • matter dominates at the production point, on the way out of the Sun neutrino flavor evolves adiabatically → constant suppression (regime 1); • matter dominates at the production point, on the way out of the Sun neutrino flavor evolves non-adiabatically → vacuum oscillations – vacuum oscillation length ≪ 1 a.u. (astronomical unit) → oscillations average out → constant observed suppression (regime 2); – vacuum oscillation length ≫ 1 a.u. (astronomical unit) → no time to oscillate → no suppression (regime 3); • vacuum oscillations dominate everywhere, matter effects negligible even in the center of the Sun → oscillations average out → constant observed suppression (regime 4). The observed energy-dependent P std ee then implies that solar neutrinos are in one of the several “special regimes”: the transition between regimes 1 and 4 (Large Mixing Angle – LMA – solution); the transition between regimes 2 and 3 (vacuum/quasi-vacuum [8] oscillation solution); the transition between regimes 1 and 2 (Small Mixing Angle – SMA – solution); the regime where the density in the Earth is close to resonant, so that the flavor regeneration in the Earth is large (the LOW solution). These solutions were known for many years, in particular all four were allowed as recently as 2000, see, e.g., [9]. We now of course know that only the LMA solution survives. Let us consider the survival probability P std ee under the (a posteriori justified) assumption that the oscillations take place between just two eigenstates. One easily obtains that during the day time P std, 2ν ee = cos 2 θ⊙ cos 2 θ + sin θ⊙ sin 2 θ. (1) The probability of finding the neutrino in eigenstate 1(2) is cos θ⊙(sin 2 θ⊙), where θ⊙ is the mixing angle at the production point; in turn, the probability of detecting the neutrino already in eigenstate 1(2) as νe is cos 2 θ(sin θ). The key physical ideas here are that the evolution is adiabatic (no level jumping) and incoherent (interferences between 1 and 2 disappear upon integration over energies for ∆m & 10 − 10 eV [10, 8] and over the production region). The angle θ⊙ is determined from the oscillation Hamiltonian Htot = Hvac +Hmat, where Hvac = ( −∆cos 2θ ∆sin 2θ ∆sin 2θ ∆cos 2θ ) , Hmat = ( √ 2GFne 0 0 0 )