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Institute for Nuclear Study University of Tokyo Tanashi, Tokyo 188, Japan And lNS-Rep.-645 INSTITUTE FOR NUCLEAR STUDY . UNIVERSITY OF TOKYO Sept 1987 Tanashi, Tokyo 188 Japan Resonant Spin-Flavor Precession of k Solar and Supernova Neutrinos Chong-Sa Lim and William J. Marciano •3300032376 INS-Rep.-645 Sept. 1987 Resonant Spin-Flavor Precession of Solar and Supernova Neutrinos Chong-Sa Lin Institute for Nuclear Study University of Tokyo Tanashi, Tokyo 188, Japan and William J. Mareiano Brookharen National Laboratory Upton. New Kork 11973, U.S.A. Abstract: The combined effect of natter and aagnetic fields on neutrino spin and flavor precession is examined. We find a potential new kind of resonant solar neutrino conversion \>_ * eL v or vT (for Dirac neutrinos) or «e *• « or vT (for Hajorana R R neutrinos). Such a resonance could help account for the lower than' expected solar neutrino v flux and/or Indications of an antl-oorrelatlon between fluctuations in the v( flux and sunspot activity. Consequences of spin-flavor precession for supernova neutrinos are also briefly discussed. - 1 - There has been a longstanding disagreement between the solar neutrino v_ flux monitored by B. Davis"" and collaborators Average Flux - 2.1 i 0.3 SHU , (1) (1 SNU - 10*' captures/s-atom) 7 37 via the reaction \>e • ' Cl •• «" • Ar and Bahcall'a standard solar model prediction Predicted Flux - 7.9 ± 2.5 SNU <3o errors) . <2) That discrepancy has come to be known as the solar neutrino puzzle. Attempts to resolve It have given rise to many speculative Ideas about unusual properties of neutrinos and/or the solar interior. One rather recently proposed solution, the MSW"-' (Mlkheyev, Snlrnov, Wolfensteln) effect is particularly elegant. It eaploys the changing solar density and the difference between ve and other neutrinos' interactions with matter to bring about an energy level crossing resonance. In that way, v neutrinos propagating fron the core of the sun to Its surface can encounter a resonance region (generally In the radiation zone which extends = from O.OIR^ to 0.7H# where R9 7«1O c«) and be converted to \>H> \>r or some as yet unknown flavor. Part of the MSH solution's appeal is that it naturally provides the required flux depletion (cf. Eqa. (1) and (2)) tor a large range of neutrino mass "~ 2 — differences im^ - m| - ra^ - 10"T - 10 eV2 and mixing angles, 2 rui sin 26>0.001; so, it is not contrived . In fact, the required parameters are very much In keeping with theoretical prejudices and expectations. A more speculative solution to the solar neutrino puzzle originally advocated by Cisneros'' , involves endowing neutrinos with magnetic moments such that spin precession in the strong interior solar magnetic fields can lead to v - \J . The eL eR sterility of v would then lead to an effective depletion in the eR measured flux. That scenario has been recently revived and improved by Okun, Voloshin and Vysotsky (henceforth referred to as OVV). Their motivation cane from the observation that there appears to be an anticorrelation between sunspot activity and variations in the detected solar vg flux ^'' . During times of high sunspot activity (i.e. large magnetic field disturbances in the convection zone > 0.7Ra), the measured flux is smallest. It is, therefore, quite natural to correlate the flux variation with spin precession which would of course be greatest when the magnetic fields are moat intense. The precession scenario has been studied in some detail by OVV'- . They noted that either a magnetic or electric dipole moment could give v - v precession, while flavor transition eL eR moments between different species could result in the combined spin-flavor precession «„ * NJ or « (for 1 component Dirac eL "R 'H «•— o ^ neutrinos) and v •» Z or u (for Majorana neutrinos ). In e u T all cases, however, they concluded that uB, where v is a generic dipole or transition moment and B is the transverse solar magnetic field, must at least be of order IO"l6-1O"15eV to make such a scenario viable. Since they argued that B could be of order io' Gauss ii: the sun's convection zone where precession was envisioned, they required 10 |uj = 0.3-1>10~ e/2ne . (3) That large a moment is consistent with direct experimental boundss1 ^03 10 ( [li:1 |uv | < H.10" e/2me (from v>e data ) , (1) but the upper range is slightly In conflict with astrophysloal arguments which imply 11 |uv | < 8.5-1O" e/2me (astrophysics bound) . (5) In addition, it is generally difficult to generate such a large moment while keeping the neutrino mass very small. For example, the standard SU(2)L»U<1) model with a singlet right-handed neutrino gives rise to "Precession of Majorana neutrinos gives rise (for example) to v. • (u ) with C being the charge conjugation operator. Since (v, ) is right-handed and generally called v , we refer to it that way. - 4 - /1eV)e/2me , (6) which is much too small for a viable solar neutrino precession scenario. Recently, however, a model has been proposed by [11] Fukugita and Yanagida in which a SU(2)L charged scalar singlet can induce at the one loop level a neutrino magnetic moment in the range of Eq.(3) without conflicting with low energy phenomenology. Therefore, in this paper we keep in open mind regarding the magnitude of u. It has also been noted that neutrino interactions with matter can quei.ch spin precession. In the case of v. •> « eL eR precession, the v and u_ interact differently with matter. eL eR The difference in their interactions effectively 3pllts their degeneracy and suppresses precession. To illustrate that point, we consider the evolution equation connecting the chlral components « and v e e R e R 1 - I II n | j7j where B is the transverse magnetic field and av (t) represents the "matter" potential experienced by v. as it propagates through the sun. In the standard model (for an unpolarized medium)' 2 2 a^.(t) - -i [(1-«sin etf)Ne • <1-Hsin eM)Np - Mj . (8) - 5 - 5 2 2 where Gu - 1.16636«io" GeV" , sin ew = 0.23 and Hf is the fermlon number density. (For other neutrino 3pecies (1 «• 2 2 1sin ew)Ne » (-1*'lsin 8M)Ne, while for antineutrinO3, the sign of a(t) is reversed.) For a neutral medium Ne - N and one finds from Eq.(8) S(t)" itf?"3"Nn) • (9! The t (or spatial) dependence comes about because the densities in Eq.(9) vary as the neutrino propagates outward through the solar interior. In addition, B will also vary with t; but it is likely to exhibit a complicated dependence. To get a feel for the matter effect, we can solve Eq.(7) for constant densities and constant B. In that case, the spin precession probability of starting with vg at t-0 and finding v_ at time t is given by eH In a vacuum where a - 0, that expression reduces to a standard 2 2 spin precession formula with frequency uB; but if a* >>(2uB) , precession is suppressed. Of course, to carry out a realistic calculation, one needs a density and magnetic field profile for the solar interior. The densities of electrons and neutrons in the convection zone and upper radiation zone'- ^ is well approximated by - 6 - N,, = 2.'4»1026exp[-r/0.09R ]/em3, 0.2<r/R <1 , (11a) while iri the lower radiation zone the linear approximation 25 25 • -- 6.10 (l - JJ°° f) , Nn = 2<1O (1 - (11b) 0.1 < r/R0 < 0.2 works well. (The relative neutron density increases.) Unfortu- nately, little is known about magnetic fields in the core, radi.at.ion zone or convection zone, except that they may be quite large. We have examined the evolution in Eq.(7) for an average B of 0(10 Gauss) in the convection zone (i.e. for a distance - 2«10 cm) and find for u - 10~ e/2m , one can obtain a v flux depletion consistent with Eqa. (1) and (2). That finding is in keeping with the results of OVV^ •* and a more recent analysis by Barbieri and "lorentini^ . Of course, if that scenario is realized, the \>e flux depletion would be strongly dependent on the magnitude of magnetic flel4. Hence, one could expect a strong correlation between v solar flux and sunspot activity which is a measure of the convection zone magnetic field. We come now to the main focus of our work, the effect of matter on spin-flavor precession. To begin, we note that even If an electromagnetic transition moment between mass eigenstates v. and \>, exists, one expects spin-flavor precession, "w * U2R' ln magnetic fields to be suppressed by the mass difference between v, an,d v-, unless •'''•'•' - 7 - U21B > Am^/aE^ , (12) with u21 the transition moment and Ev the neutrino energy. For 3 u21 = 10"'° e/2me, B = 10 Gauss, and Ey= 10 MeV, that condition requires 4ml, < 10~7 eV2, which is below the MSW solutions but not prohibitively small. (Of course, the condition depends on energy.) Partly because of that mass difference suppression, neutrino spin-flavor precession seems not to have been thoroughly studied. However, here we will show that matter interactions of the distinct neutrino flavors can compensate for the mass difference. In fact, for a mediuia of changing density, such as the sun, a resonance region can exist where neutrino spin-flavor precession may occur unimpeded. The physics of that resonance is quite similar to the HSK resonance"^ as we shall see. To illustrate the resonant spin-flavor precession phenomenon, we first consider the case of 2 generations with 1 component Dirac neutrinos .
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