We discuss the impact of different solar neutrino data on the
spin-flavor-precession (SFP) mechanism of neutrino conversion. We find that,
although detailed solar rates and spectra allow the SFP solution as a
sub-leading effect, the recent KamLAND constraint on the solar antineutrino
flux places stronger constraints to this mechanism. Moreover, we show that for
the case of random magnetic fields inside the Sun, one obtains a more stringent
constraint on the neutrino magnetic moment down to the level of \mu_\nu \lsim
few \times 10^{-12}\mu_B, similar to bounds obtained from star cooling.Comment: 4 pages, 3 figures. Final version to appear in Phys. Rev. Let

A. I. Rez

A. Kolmogorov

Emilio Torrente-Lujan

F. Moreno-Insertis

J. W. F. Valle

L. D. Landau

M. Stix

O. G. Miranda

Paola Alliani

T. I. Rashba

V. A. Kutvitskii

Ya. B. Zeldovich

English

arXiv

Crossref

Constraining the Neutrino Magnetic Moment with Antineutrinos from the Sun

We discuss the impact of different solar neutrino data on the spin-flavor-precession (SFP) mechanism of neutrino conversion. We find that, although detailed solar rates and spectra allow the SFP solution as a sub-leading effect, the recent KamLAND constraint on the solar antineutrino flux places stronger constraints to this mechanism. Moreover, we show that for the case of random magnetic fields inside the Sun, one obtains a more stringent constraint on the neutrino magnetic moment down to the level of \mu_\nu \lsim few \times 10^{-12}\mu_B, similar to bounds obtained from star cooling

Miranda, O.G.

Rashba, Timur I.

Rez, A. I.

Furtado Valle, José Wagner

Repositori d'Objectes Digitals per a l'Ensenyament la Recerca i la Cultura

arXiv:hep-ph/0311014v2  6 Jun 2004IFIC/03-49Constraining the neutrino magnetic moment with anti-neutrinos from the SunO. G. Miranda∗Departamento de F´ısica, Centro de Investigacio´n y de Estudios Avanzados del IPNApdo. Postal 14-740 07000 Mexico, DF, MexicoT. I. Rashba,† A. I. Rez,‡ and J. W. F. Valle§Instituto de F´ısica Corpuscular – C.S.I.C., Universitat de Vale`nciaEdificio Institutos, Apt. 22085, E–46071 Vale`ncia, Spain(Dated: December 24, 2013)We discuss the impact of different solar neutrino data on the spin-flavor-precession (SFP) mech-anism of neutrino conversion. We find that, although detailed solar rates and spectra allow theSFP solution as a sub-leading effect, the recent KamLAND constraint on the solar antineutrinoflux places stronger constraints to this mechanism. Moreover, we show that for the case of randommagnetic fields inside the Sun, one obtains a more stringent constraint on the neutrino magneticmoment down to the level of µν <∼ few × 10−12µB, similar to bounds obtained from star cooling.PACS numbers: 26.65.+t Solar neutrinos 96.60.Jw Solar interior 13.15.+g Neutrino interactions 14.60.PqNeutrino mass and mixingThe latest KamLAND result [1] greatly improves theexpected sensitivity limit on a possible antineutrino com-ponent in the solar flux from 0.1 % [2] of the solar boronνe flux to 2.8× 10−2 % at the 90 % C.L., about 30 timesbetter than the recent Super-K limit [3].The presence of anti-neutrinos in the solar flux maysignal the existence of SFP conversions induced by non-vanishing neutrino transition magnetic moments [4, 5]or, alternatively, neutrino decays in models with sponta-neous violation of lepton number [6]. Here we focus onthe more likely case of anti-neutrinos produced by SFPconversions. Several solar magnetic field models are pos-sible, characterized by different assumptions pertainingto their magnitude, location and typical scales [7, 8, 9].Previous to the latest KamLAND limit on the solaranti-neutrino flux, the first KamLAND evidence of re-actor anti-neutrino disappearance [10] had already ex-cluded SFP scenarios as solutions to the solar neutrinoproblem [11]. However, even with the recent SNO saltresults [12] which confirm the simplest three-neutrino os-cillation picture [13], a neutrino magnetic moment couldstill play a role as a sub-leading effect. In order to illus-trate this, we have performed a χ2 analysis taking into ac-count all the solar experimental data plus the KamLANDdisappearance data for the same self-consistent profile forthe magnetic field in the convective zone used in previ-ous analyses [14]. The results are shown in fig. 1, werewe have taken different values for the product µνB (neu-trino magnetic moment in units of 10−11µB and maxi-∗Electronic address: Omar.Miranda@fis.cinvestav.mx†On leave from Institute of Terrestrial Magnetism, Ionosphereand Radio Wave Propagation of the Russian Academy of Sciences(IZMIRAN), 142190, Troitsk, Moscow, Russia‡Electronic address: rez@ific.uv.es; On leave from IZMIRAN§Electronic address: valle@ific.uv.es;URL: http://www.ific.uv.es/~ahep/mum magnetic field value in convective zone in units ofMG) and plotted the allowed regions at 90 %, 95 % and99 % C. L.One can see how the allowed LMA-MSW region ofoscillation parameters (upper left panel) is modified inthe presence of SFP conversions (upper right panels) inFig. 1. The lower panels in this figure give the ∆χ2 pro-files with respect to ∆m2soland sin2 θsol, from where onecan determine the corresponding allowed ranges. Giventhe current laboratory best limit on the neutrino mag-netic moment µν¯e < 1.0× 10−10µB [15, 16], and the factthat magnetic field amplitude inside the convective zoneshould not exceed 0.1-0.3 MG [17] one can see that, al-though limited, there is room left for sub-dominant SFPconversions.We now turn to the recent KamLAND result on theν¯e ’s from the Sun. The Collaboration has reported thatthe antineutrino flux Φν¯e is less than 3.7×102 cm −2 s −1at 90 % C. L. which corresponds to a 0.028 % of the so-lar 8 B νe flux (in the energy window between 8.3 MeVand 14.8 MeV). It is this last result that will substan-tially limit the possibility of subleading SFP componentin the neutrino conversion mechanism, establishing therobustness of the oscillation hypothesis.Within our generalized picture (LMA-MSW+SFP), af-ter the MSW νe → νµ conversion takes place in the cen-tral region of the Sun, ν¯e’s are produced due to the mag-netic moment conversion νµ → ν¯e. To analyse quantita-tively the restrictions imposed by this result we considerthree models for the solar magnetic field:1. regular magnetic fields, both in the convective(CZ) [7] and radiative (RZ) [9] zones of the Sun2. convective zone random magnetic fields [18]For definiteness we consider the simplest aproximatetwo-neutrino picture, which is justified in view of thestringent limits that follow mainly from reactor neutrino2B = 5 MG0 0.2 0.4 0.6 0.8 1sin2θ10-510-410-3 B = 0 MGµν=10-11µB0 0.2 0.4 0.6 0.8 1sin2θ10-510-410-3 B = 7.5 MG0 0.2 0.4 0.6 0.8 1sin2θ10-510-410-3 024681012140 0.2 0.4 0.6 0.8 1∆ χ2sin2θ3 σ2 σ0246810121410-5 10-4 10-3∆ χ2∆ m2 (eV2)FIG. 1: Solar neutrino oscillation parameters for zero (upper left panel) and non-zero (upper right panels) self-consistent CZmagnetic field used in Ref. [7]. Lower panels give ∆χ2 profiles with respect to ∆m2sol and sin2 θsol.experiments [13]. From the resulting 4 × 4 form of theneutrino evolution equation [4, 5], we compute the ex-pected ν¯e yield for each magnetic field model. For thecase of CZ magnetic fields, this 4×4 form of the neutrinoevolution further decouples into LMA-MSW conversionsdeep in the Sun followed by (approximate) vacuum SFPconversions [4] inside the CZ. In contrast, for the RZ casethere is no decoupling of the neutrino evolution, due tothe large strength of the magnetic field [28].In order to obtain a conservative bound on µνB wehave calculated the minimum ν¯e yield as the oscillationparameters vary within the acceptable range (at the 90 %C.L.) in the absence of magnetic field (pure LMA-MSWcase). Such minimum predicted anti-neutrino fluxes forthe case of regular field profiles are shown in the curvesdepicted in Fig. 2, while the recent KamLAND limit isindicated by the lower horizontal lines. For comparison,we present the previous Super-K bound, indicated by theupper horizontal lines. Note that in both cases of regularfield profile we can only constrain the product µνB, asopposed to the intrinsic neutrino magnetic moment [29].[15].A more interesting picture for SFP scenario is obtainedif we consider the case of turbulent random magneticfields inside the Sun. As we will see, the reason forthis is twofold: (i) we will be able to fix, to some ex-tent, the dependence on the magnetic field, in contrastto previous analysis of the random magnetic field pre-sented in Ref. [18, 19], where an extra parameter L0 ap-peared, characterizing the scale of the random magneticfield cells, and (ii) this model leads to more stringentlimits on the neutrino magnetic moment by itself.In the following we give a brief discussion of our newapproach to the problem (a more detailed analysis willbe published elsewhere [20]). The mean magnetic fieldvalue over the solar disc is of the order of 1 G and mag-netic field strength in the solar spots reaches 1 kG. It iscommonly accepted that fields measured at the solar sur-face are substantially weaker than those near the bottomof the convective zone (CZ) where they are supposed tobe generated by a dynamo mechanism [21, 22]. In dy-namo theory, the mean magnetic field is accompanied bya small-scale random magnetic field, which is not directlytraced by sunspots or any other tracers of solar activity.By small scales we denote a typical scale of about thesolar granule size (∼ 1000 km) [23] where the rms mag-netic field amplitudes (generated either as a by-productof a large-scale dynamo mechanism or directly by a small-scale dynamo) in the range of 50-100 kG are reasonable.For LMA oscillations the MSW conversion occurs wellbelow the CZ resulting in a coherent mixture of twoneutrino flavours at the bottom of the convective zone.When neutrinos cross the randomly fluctuating magneticfield of the CZ it is expected that νeL will convert to ν¯µRand νµL will convert to ν¯eR as a result of the CZ magneticfield. For the case of random CZ magnetic fields thesepopulations will tend to equilibrate. However, given thelaboratory upper limits on µν and the finite depth of theCZ, this equilibration is not achieved. The relaxation canbe viewed as a small-amplitude random walk of the neu-trino polarization vector leading to a small appearance ofelectron and muon antineutrinos at the solar surface (cf.[24] for the vacuum case, and also discussion in [18]). Inwhat follows we describe the main features of this calcu-lation and give the main result.Because of the randomness of the underlying magneticfields, the spin flavour evolution looses coherence, i.e., in-stead of evolving neutrino wave functions over the wholeCZ and then obtaining the final probabilities, one hasto compute the probabilities in each correlation cell andafterwards add them. As a result, independently of therandom magnetic field model, the appearance of antineu-trinos is proportional to the relevant Fourier harmonic ofthe transverse two-point magnetic correlation function,with space period equal to the LMA-MSW neutrino os-cillation length (cf. [24] and discussion in [25] for the31 10µ11Bmax [100 kG]0.010.11φ ν_ e/φ ν B [%]SuperKamiokandeKamLANDKamLAND proposalSuperKamiokandeKamLAND proposalKamLAND1 10µ11Bmax [MG]Kutvitsky-Solov’ev Friedland-GruzinovFIG. 2: Bounds on µνB for regular magnetic field models, Kutvitsky-Solov’ev (left) and Friedland Gruzinov (right). Thehorizontal lines indicate the bounds on solar anti-neutrinos from Super-K and KamLAND.MSW matter noise).We will assume for definiteness that random magneticfield evolution is due to the highly developed steady-stateMHD turbulence treated within the Kolmogorov scalingtheory [26, 27]. The magnetic Reynolds number withinthe CZ is very large, Rm ∼ 108 [22], and the correspond-ing inertial range is very wide, ldiss < l < Lmax wherethe outer scale is supposed to be Lmax ≃ 1000 km, aboutthe solar granule size, and ldiss = LmaxR−3/4m ∼ 1 m.The rms magnetic field bl is assumed to scale as bl ∼ l1/3.This implies that, after fixing the maximum field ampli-tude at the outer scale Lmax it is straightforward to ob-tain the rms field at the neutrino oscillation scale, whichis about several hundreds kilometers for LMA-MSW case,well within the inertial range where scaling arguments arevalid [20]. Here we show only the final result for neutrinomass eigenstate probabilities at the surface of the Sun:|ν1L|2R⊙ = P1(1− η), |ν2R|2R⊙ = P1η , (1)|ν2L|2R⊙ = P2(1− η), |ν1R|2R⊙ = P2η , (2)(note that these obey unitarity) where the common factorη is given byη ≃ 0.3µν2b¯2maxδ2δ · L(δ · Lmax)2/3S2 . (3)Here Pi = PiL = |νiL(r = 0.7R⊙)|2 are the probabili-ties that solar neutrinos reach the bottom of the CZ in agiven mass state, L is the CZ width, δ = ∆m2/4E, andS2 is a rms magnetic field profile shape factorS2 =1L∫ L0dzb¯2(z)b¯2max. (4)Note that S = 1 for constant shape of rms field and ofthe order of unity for other profiles, e.g. S = 0.579 forthe “smooth” profile of [18], and S = 0.577 for a triangleprofile.The different factors in Eq. 3 can be explained ifwe keep in mind that δ is inversely proportional to theneutrino oscillation length, δ = pi/λosc . The ratiob¯2max/(δ ·Lmax)2/3 = b¯2λosc is the squared rms field at thescale l = 1/δ ∼ λosc, and the ratio µ2ν b¯2λosc/δ2 determinesthe fraction of neutrinos which experience (on average)spin-flavour conversion to the antineutrino states in a cor-relation cell of length l ∼ λosc. Finally δ · L ∼ L/λosc isthe number of correlation cells along the neutrino trajec-tory and the factor S2, as already mentioned, accountsfor the specific shape of the rms field profile. (The nu-merical factor 0.3 comes from the integration along thetrajectory).We can rewrite Eq. 3 in normalized units asη ∼ 3× 10−3µ211ε2S2(7× 10−5eV 2∆m2)5/3 (E10MeV)5/3(5)where µ11 is the magnetic moment in units of 10−11µB,and the ratio ε = (b/100 kG)(Lmax/1000 km)1/3.Although the ratio ε is not known precisely, we canobtain a good estimate assuming the equipartition be-tween kinetic energy of hydrodynamic pulsations and therms magnetic energy at the upper (most energetic) scaleLmax [22]ρv¯22∼b¯2max8pi(6)Taking v ∼ 3 × 104cm/s, ρ ∼ 1g/cm3 we obtain bmax ∼100 kG. In what follows we will consider the range bmax ∼50− 100 kG.This specific behaviour implies, on physical grounds,that ε is not allowed to vary substantially, 0.5 < ε < 1,with our assumptions. As mentioned, for different pro-files we found that the parameter S2 lies in the rangebetween 0.5 and 1. With this in mind, we can see thatthe product k = εS lies in the interval 0.25 < k < 1.Since the overall νe → ν¯e conversion probability dependslinearly on η, it follows that, by comparing the resultingν¯e yield to the recent KamLAND bound one can con-strain the value of µν to within a factor 4. More pre-cisely, we have computed the solar anti-neutrino yieldfor this random magnetic field model for all allowed val-ues of neutrino oscillation parameters in the LMA-MSWregion. Our results are shown in fig. 3 as a function of µν ,where the width of the band corresponds to the freedom40.01 0.1 1µ110.010.11φ ν_ e/φ νB [%]KamLANDKamLAND proposalSuperKamiokandeturbulentFIG. 3: Bounds on µν for the turbulent magnetic field modeldescribed in the text. The horizontal lines indicate the boundson solar anti-neutrinos from Super-K and KamLAND.in choosing the parameter k. It is easy to see that, in-deed, the constraint we obtain is better than those thathold for the case of regular magnetic fields. Moreover,from our estimate for the minimum value of k, we canobtain an upper bound for µν which lies in the rangeµν ≤ 1.5× 10−12µB to µν ≤ 5 × 10−12µB. We have ob-tained this result for the Kolmogorov theory. However,it can be easily generalized for arbitrary power-law ex-ponent p (for Kolmogorov theory p = 5/3). We havechecked that our bound on µν is rather robust with re-spect to possible changes of the power-law exponent pwithin the interval from 1 to 2 [20].In short, we have discussed the impact of recent solarneutrino data on the spin-flavor-precession (SFP) mech-anism of neutrino conversion. The recent KamLANDbound on the solar anti-neutrino yield leads to a con-straint on the product of Majorana neutrino transitionmagnetic moment and some magnetic field strength indifferent models for the solar magnetic field. For thecase of random magnetic fields inside the Sun, one canobtain a direct constraint on the intrinsic neutrino mag-netic moment of µν <∼ few× 10−12µB, similar to boundsobtained from star cooling. Comparing these constraintswith Fig. 1 one sees that the robustness of the oscilla-tion interpretation of current solar neutrino data againstpossible magnetic-field-induced transitions is firmly es-tablished.We thank V. B. Semikoz and D. D. Sokoloff for usefuldiscussions. This work was supported by Spanish grantBFM2002-00345, by European RTN network HPRN-CT-2000-00148, by European Science Foundation networkgrant N. 86, by INTAS YSF grant 2001/2-148 and MECDgrant SB2000-0464 (TIR). TIR and AIR were partiallysupported by the Presidium RAS and CSIC-RAS grants.OGM was supported by CONACyT-Mexico and SNI.[1] [KamLAND Collaboration], Phys. Rev. Lett. 92 071301(2004) 071301.[2] [KamLAND Collaboration], Proposal for US participa-tion in KamLAND, 1999.[3] Y. Gando et al. 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Constraining the neutrino magnetic moment with anti-neutrinos from the sun

Constraining the neutrino magnetic moment with anti-neutrinos from the
  Sun

Constraining the neutrino magnetic moment with anti-neutrinos from the Sun

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Repositori d'Objectes Digitals per a l'Ensenyament la Recerca i la Cultura