Exotic Solutions to the Solar Neutrino Anomaly

263 Brazilian Journal of Physics, vol. 31, no. 2, June, 2001 Exotic Solutions to the Solar Neutrino Anomaly M. M. Guzzo Instituto de F sica Gleb Wataghin Universidade Estadual de Campinas, UNICAMP 13083-970, Campinas, SP, Brazil Received on 19 April, 2001 We analyze the status of the exotic solutions to the solar neutrino problem, i.e., those solutions based on new phenomena which are not the usual neutrino oscillations induced by masses and mixing. These solutions are based on di erent assumptions: a) resonant spin- avor precession induced by non-vanishing neutrino magnetic moment, b) the existence of non-standard avor-changing and non-universal neutrino interactions and c) the violation of the equivalence principle. We investigate the quality of the t provided by each one of these solutions not only to the total rate measured by all solar neutrino experiments but also to the day-night and seasonal variations of the event rate, as well as the recoil electron energy spectrum measured by the SuperKamiokande collaboration. I Introduction Homestake [1], GALLEX/GNO [2], SAGE [3], Kamiokande [4] and SuperKamikande [5] have observed a solar neutrino ux which is smaller than predicted by the standard solar models (SSM) [6, 7, 8, 9, 10]. This discrepancy has been called the solar neutrino problem [11]. Better statistics and calibration of the pioneering experiments, as well as the rst nextgeneration experiment SuperKamiokande, measuring the solar neutrino spectrum and the event rate as a function of the zenith angle with unprecedented precision, have provided a lot of new information about the solar neutrino problem [11]. On the theoretical side several substantial improvements have been made in the SSM which now includes di usion of helium and heavy elements and updated low energy nuclear cross sections relevant to the solar neutrino production [12]. Furthermore, the SSM has received an important independent con rmation by the excellent agreement between its predicted sound speeds and recent helioseismological observations [7]. In order to understand the solar neutrino anomaly it has been suggested that neutrinos are endowed with properties which are not present in the standard electroweak theory [13]. These new properties allow the electron neutrinos to be converted along their way from the center of the sun to the detectors on earth into different neutrino avors, i.e. into muon, tau, or possibly sterile [14] neutrinos. The fact that the terrestrial experiments are less sensitive to these neutrino avors explains the observed lower counting rates. Several mechanisms can provoke the electron neutrino convertion into di erent neutrino avors. Up to our knowledge, the mechanisms that t the solar neutrino data can be classi ed in four essentially di erent types: The most famous solutions to the solar neutrino anomaly assume that neutrinos are massive and there is mixing in the lepton sector. Under this circunstance, neutrino avor oscillations can happen in vacuum [15] as well as in matter where it can be resonantly enhanced [16, 17] (the Mikheyev-Smirnov-Wolfenstein (MSW) e ect). In both scenarios solar electron neutrinos can be converted into neutrino of a di erent avor (muon or tau) and consequently explain the de cit of observed solar neutrino de cit to the predictions of the SSM. These solutions are called the standard solutions to the solar neutrino problem and are very well described in recent references [18], [19] and [20]. In this review, we will not describe the solutions to the solar neutrino anomaly based on mass-induced oscillation phenomenon. We wil concentrate on more exotic solution like those one described below. II Resonant spin- avor phenomenon Assuming a nonvanishing transition magnetic moment of neutrinos, active solar neutrinos interacting with the magnetic eld in the Sun can be spin- avor converted into sterile nonelectron neutrinos [21, 22] (if we are dealing with Dirac particles) or into active nonelectron antineutrinos [23] (if the involved particles are Majorana). In both cases the resulting particles interact with solar neutrino detectors signi cantly less than the original active electron neutrinos in such a way that this phe- 264 M.M. Guzzo i d dt  eL  R  =  ae  B  B
m2 + a 2E  eL  R  ; (1) and where e and  R are active electron2 neutrinos muon antineutrinos, respectively,
m = m2 m2e is their squared mass di erencepand E is the neutrinopenergy, ae = GF (2Ne Nn)= 2 and a = GF Nn= 2, with Ne and Nn being electron and neutron number densities, respectively. In eq. (1) it is assumed that neutrinos are Majorana particles. For the Dirac case, the spin- avor precession involves e $ s , where s is a sterile neutrino and as = 0. In order to obtain the survival probability one should integrate the evolution equations (1) with varying matter density in the Sun [11] for some assumed pro les of the magnetic eld which will be described below. Using the solar neutrino ux in ref. [8], it was computed in Ref. [32] the expected solar neutrino event rate in each experiment, taking into account the relevant absorption cross sections [11] for 71Ga and 37Cl experiments as well as the scattering cross sections for e -e and  -e reactions including also the eÆciency function for the SuperKamiokande experiment in the same way as in ref. [33]. Note that in this analysis it was always adopted the solar model in ref. [8] as a reference SSM. It is obvious from the evolution equations (1) that the RSFP mechanism crucially depends on the solar magnetic eld pro le along the neutrino trajectory. In the analisys of Ref. [32] it was chosen several different pro les which cover in general all the previously [27, 28, 29, 30, 31] analysed magnetic pro les which led to a solution to the solar neutrino anomaly. In Fig. 1, these magnetic elds are presented in their general aspects. The constant magnetic pro le B1(r) was adopted in references [29], while the general aspects of the pro les B3(r) and B4(r) have already appeared in refs. [28, 30, 27], and [31], respectively. Magnetic Field Profiles nomenon can induce a depletion in the detectable solar neutrino ux. Spin- avor precession of neutrinos can be resonantly enhanced in matter [24, 25], in close analogy with the MSW e ect [16, 17]. In this case the precession strongly depends on the neutrino energy and provokes di erent suppressions for each portion of the solar neutrino energy spectrum. Therefore RSFP provides a satisfactory description [26, 27, 28, 29, 30, 31, 32] of the actual experimental panorama [1, 2, 3, 4, 5]: all experiments detect less than the theoretically predicted solar neutrino uxes [9, 10] and di erent suppressions are observed in each experiment, suggesting that the mechanism to conciliate theoretical predictions and observations has to di erentiate the di erent parts of the solar neutrino spectrum. The time evolution of neutrinos interacting with a magnet (...truncated)