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We use the recent KamLAND observations to predict the solar antineutrino spectrum at some confidence limits. We find a scaling of the antineutrino probability with respect to the magnetic field profile –in the sense that the same probability function can be reproduced by any profile with a suitable peak field value– which can be utilised to obtain a general shape of the solar antineutrino spectrum. This scaling and the upper bound on the solar antineutrino event rate, that can be derived from the data, lead to: 1) an upper bound on the solar antineutrino flux, 2) the prediction of their energy spectrum. We get φν̄ < 4.9×10−3φ(8B) or φν̄ < 1.3×10−3φ(8B) at 95% CL, assuming Gaussian or Poissonian statistics, respectively. For 90% CL these become φν̄ < 4.4× 10−3φ(8B) and φν̄ < 1.0× 10−3φ(8B). This provides an improvement by a factor of 3-10 with respect to existing bounds. These limits are quite general and independent of the detailed structure of the magnetic field in the solar interior. The recent KamLAND experiment [1] searching for antineutrinos of Eν > 1.8 MeV via νe + p → n+ e (1) has provided strong indications through the observation of reactor antineutrinos that the solution to the solar neutrino problem is dominated by matter oscillations with a large mixing angle (LMA). Before the appearance of KamLAND data, the resonant spin flavour precession (RSFP) [2–4] with Majorana neutrinos based on a transition magnetic moment, provided very good fits to the solar neutrino data [5]. After adding the KamLAND result, it has become clear that SFP solutions, both resonant and non-resonant, may only be accepted at 99.86%C.L. or 99.88%C.L. respectively [6]. Hence SFP cannot be the leading solar neutrino problem solution. It can however be present at a subdominant level. Such a ∗Speaker. †Work done in collaboration with Bhag C. Chauhan (CFIF-IST) and E. Torrente-Lujan (Dep. Fisica, Grupo de Fisica Teorica, Univ. Murcia). a h e p 2 0 0 3 International Workshop on Astroparticle and High Energy Physics Joao Pulido possibility was recently investigated [7], its signature being the appearance of antineutrinos from the Sun [3, 8, 9]. The production of these antineutrinos must predominantly occur as a vacuum oscillation from the Sun to the Earth [7] νeL → ν̄μR → ν̄eR , (2) with the first step in this sequence (SFP) taking place inside the Sun. The amplitude for the νeL → ν̄μR transition was evaluated in perturbation theory for small μB, the product of the neutrino magnetic moment by the solar magnetic field and found to be, assuming the LMA solution to be dominant [7] A(νeL → ν̄μR) = μB(ri) sin 2 θ̃(ri, E) g ′ 2(ri) . (3) In this expression ri denotes the neutrino production point, g ′ 2 is a function of the interaction potentials Ve, Vμ and θ̃(ri, E) is the matter mixing angle. Recently we proposed a more realistic case [10] in which we convolute the neutrino production distribution spectrum with the solar magnetic field profile. In this way, the overall antineutrino production probability is obtained as P (νeL → ν̄eR) = 1 2 sin2θ ∫ |A(νeL → ν̄μR)|fB(ri)dri , (4) where the factor 1/2 comes from averaging over the vacuum oscillations, θ is the vacuum mixing angle [7], fB represents the neutrino production distribution function for Boron neutrinos [11] and the integral extends over the whole production region. The essential point is that the 8B production spectrum is sharply peaked around 0.054 of the solar radius so this probability is almost independent of the shape of the solar field profile. This can be made clear if one considers the limiting case of an infinitely peaked 8B production spectrum P (νe → ν̄eR) = μ2 2 sin2θ ∫ B(ri)sin θ̃(ri, E) g ′2 2 (ri, E) δ(0.054 − ri)dri . (5)

Solar antineutrino bounds and magnetic field: spin flavour precession after KamLAND