It is shown that recent results from the Super-Kamiokande detector constrain
the tau neutrino diagonal magnetic moment to $\mu_{\nu_{\tau}} < 1.3\times
10^{-7} \mu_{B}$ for the case of $\nu_{\mu}\to \nu_{\tau}$ interpretation of
the atmospheric neutrino anomaly. It is pointed out that the large magnetic
moment of the tau neutrino could affect further understanding of the origin of
the anomaly.Comment: 7 pages, LaTex. To appear in Phys.Lett.

Cooper-Sarkar

Domogatskii

Fukuda

Honda

S.N Gninenko

Segura

Physics Letters B

English

arXiv

It is shown that recent results from the Super-Kamiokande detector constrain the tau neutrino diagonal magnetic moment to $\mu_{\nu_{\tau}} < 1.2\times 10^{-7} \mu_{B}$ for the case of $\nu_{\mu}\to \nu_{\tau}$ interpretation of the atmospheric neutrino anomaly. It is pointed out that the large magnetic moment of the tau neutrino could affect further understanding of the origin of the anomaly.It is shown that recent results from the Super-Kamiokande detector constrain the tau neutrino diagonal magnetic moment to $\mu_{\nu_{\tau}} < 1.3\times 10^{-7} \mu_{B}$ for the case of $\nu_{\mu}\to \nu_{\tau}$ interpretation of the atmospheric neutrino anomaly. It is pointed out that the large magnetic moment of the tau neutrino could affect further understanding of the origin of the anomaly.It is shown that recent results from the Super-Kamiokande detector constrain the tau neutrino diagonal magnetic moment to $\mu_{\nu_{\tau}} < 1.3\times 10^{-7} \mu_{B}$ for the case of $\nu_{\mu}\to \nu_{\tau}$ interpretation of the atmospheric neutrino anomaly. It is pointed out that the large magnetic moment of the tau neutrino could affect further understanding of the origin of the anomaly.It is shown that recent results from the Super-Kamiokande detector constrain the tau neutrino diagonal magnetic moment to $\mu_{\nu_{\tau}} < 1.3\times 10^{-7} \mu_{B}$ for the case of $\nu_{\mu}\to \nu_{\tau}$ interpretation of the atmospheric neutrino anomaly. It is pointed out that the large magnetic moment of the tau neutrino could affect further understanding of the origin of the anomaly.It is shown that recent results from the Super-Kamiokande detector constrain the tau neutrino diagonal magnetic moment to $\mu_{\nu_{\tau}} < 1.3\times 10^{-7} \mu_{B}$ for the case of $\nu_{\mu}\to \nu_{\tau}$ interpretation of the atmospheric neutrino anomaly. It is pointed out that the large magnetic moment of the tau neutrino could affect further understanding of the origin of the anomaly.It is shown that recent results from the Super-Kamiokande detector constrain the tau neutrino diagonal magnetic moment to $\mu_{\nu_{\tau}} < 1.3\times 10^{-7} \mu_{B}$ for the case of $\nu_{\mu}\to \nu_{\tau}$ interpretation of the atmospheric neutrino anomaly. It is pointed out that the large magnetic moment of the tau neutrino could affect further understanding of the origin of the anomaly.It is shown that recent results from the Super-Kamiokande detector constrain the tau neutrino diagonal magnetic moment to μ ν τ <1.3×10 −7 μ B for the case of ν μ → ν τ interpretation of the atmospheric neutrino anomaly. It is pointed out that the large magnetic moment of the tau neutrino could affect further understanding of the origin of the anomaly

Gninenko, S.N.

CERN Document Server

arXiv:hep-ph/9901289v2  18 Feb 1999Bound on the tau neutrino magnetic momentfrom the Super-Kamiokande dataS.N.Gninenko1CERN, CH-1211 Geneva 23, SwitzerlandandInstitute for Nuclear Research, RAS , Moscow 117312, RussiaAbstractIt is shown that recent results from the Super-Kamiokande detectorconstrain the tau neutrino diagonal magnetic moment to µντ < 1.3 ×10−7µB for the case of νµ → ντ interpretation of the atmospheric neutrinoanomaly. It is pointed out that the large magnetic moment of the tauneutrino could affect further understanding of the origin of the anomaly.Recent results from the Super-Kamiokande (S-K) detector give evidence forneutrino oscillations [1] - [4]. One of the favourable interpretations of the atmo-spheric neutrino anomaly suggested by the S-K collaboration is related to theexistence of νµ → ντ neutrino oscillations. This implies that tau neutrinos havenon-zero masses and therefore may also have a non-zero diagonal magnetic mo-ment ( see e.g. ref. [5]). As a consequence, massive tau neutrinos could manifestthemselves in terrestrial experiments through the effect of νµ → ντ neutrino oscil-lations, and, if the magnetic moment value is large enough, through tau neutrinoelectromagnetic interactions.In ref.[6] (see also [7]), it was shown that the combined existence of νµ → ντ(and/or νe → ντ ) oscillations and non-zero magnetic moment of the tau neutrinowould increase the total rate of events in νµ(νe) neutrino- electron scatteringexperiments. It was used to constrain the mixing angles of the tau neutrino withneutrinos of another flavour. In this Letter it is shown that this effect can alsobe used to constrain the magnetic moment of the tau neutrino from the S-Katmospheric neutrino data.Assuming that a muon neutrino beam has a component of tau neutrinos dueto νµ → ντ oscillations, in the case of two-neutrino mixing, neutrino states evolvewith time t as|ν(t) >= a(t)|νµ > +b(t)|ντ , µντ 6= 0 > (1)1 Sergei.Gninenko@cern.ch1where |νµ > and |ντ > denote weak eigenstates of νµ and ντ neutrinos, anda2(t), b2(t) are the probabilities of finding νµ or ντ in the beam at a given momentt, respectively. It is assumed that a2(0) = 1 at t = 0. The probability b2(t) dependson the parameters of νµ − ντ oscillations as [8]:b2(t ≃Lc) = P (νµ → ντ ) = sin22θµτsin2∆m2L4Eν(2)orP (νµ → ντ ) ≈ sin22θµτsin21.27∆m2(eV 2)L(km)Eν(GeV )(3)where sin22θµτ is the mixing angle, ∆m2 =∣∣m23−m22∣∣ is the difference of thesquares of the mass eigenstates in eV 2, Eν is the neutrino energy in GeV, andL is the mean distance between the neutrino source and the detector in km. Inthe above formula it is also assumed that magnetic field B is weak enough notto affect the probability of oscillations P (νµ → ντ ), i.e. [9]:∆m2/2Eν ≫ µντB (4)Then if the magnetic moment of the ντ exists, it will contribute to a non-coherent part of the ντe− scattering cross section via the reaction that changesthe helicity of the tau neutrino (hence right-handed neutrino states should exist).This might result in a contribution to the observed deviations from unity ofthe flavour ratio of the atmospheric neutrino flux, R ≡((Nνµ + Nνµ)/(Nνe +Nνe))data/((Nνµ +Nνµ)/(Nνe +Nνe))MC, in the S-K detector for both data andMonte Carlo (MC) simulation. Here, Nνµ,νµ and Nνe,νe are the number of muon-like (µ-like) and electron-like (e-like) fully-contained events in the S-K detector[1].Indeed, since the electromagnetic cross section is orders of magnitude largerthan the weak cross section, even a small fraction of tau neutrinos with non-zeromagnetic moment in the atmospheric neutrino flux could lead to an observableexcess of isolated electrons in atmospheric neutrino interactions in the S-K detec-tor whose signature is identical to that of e-like events. Note that the magneticmoments of muon or electron neutrino are experimentally proved to be too smallto give a noticeable contribution to the neutrino interaction rate. The produc-tion rate of isolated electrons via ντe− scattering in the detector depends onthe probability P (νµ → ντ ) of finding ντ neutrinos in the atmospheric neutrinoflux. This probability can be calculated from the neutrino survival and transitionprobabilities using Eq.(2).The neutrino-electron scattering process via magnetic moment has a crosssection [10]:2dσµdEe=piα2m2eµ2νµ2B( 1Ee−1Eν)(5)where Ee is the electron energy, µν is the neutrino magnetic moment andµB = e/2me is Bohr magneton. For the case of constant Eν the integral crosssection isσµ =piα2m2eµ2νµ2B[ln(EmaxeEmine)−(Emaxe − Emine )Eν]= 2.7× 10−39( µν10−7µB)2[ln(EmaxeEmine)−(Emaxe −Emine )Eν]cm2(6)where Emaxe , Emine are the high and low electron energy cuts, respectively.Note that the integral cross- section σµ depends very weakly on the neutrinoenergy. It rises only logarithmically with the neutrino energy, while the totalneutrino cross section rises linearly with Eν . Thus, it is advantageous to search fora tau neutrino magnetic moment using the low energy (sub-GeV, Evisible < 1.33GeV) S-K data [1].Approximately, all atmospheric neutrino giving rise to the fully contained µ-like events in the S-K detector have energy above 400 MeV, see e.g. Ref. [11](MC studies showed the mean neutrino energy for CC interactions to be about800 MeV for µ-like events [1]). Thus, for the lowest electron energies analysed inthe S-K, from Emine = 100 MeV to Emaxe = 200 MeV (first bin of the histogramin Fig.4(a) corresponding to e-like events, ref. [1]), the cross section of ντ − escattering due to non-zero magnetic moment isσµ = 1.2× 10−39(µν/10−7µB)2 cm2 (7)Here, we assume the tau neutrino energy Eν = 400 MeV, thus the integralcross section is underestimated.The total number ∆Ne of e-like events from ντ−e scattering in the first energyof Fig.4(a) in [1] can be written in the form∆Ne =∫k0 · fν · σµ · ε · dΩ · dEν = k1Nντσµ (8)where k0 is a factor related to the ν-target mass, fν is tau neutrino flux,the cross section σµ is constant, ε is detection efficiency which is practicallyindependent of energy for Ee > 100 MeV [1], k1 is a factor corresponding tothe convolution of detector acceptance, detection efficiency and ν-target mass3and Nντ is the total number of tau-neutrinos crossing fiducial volume of the S-Kdetector.The number of tau-neutrinos is estimated using the number of the initiallyproduced muon atmospheric neutrino:Nντ = (Nνµ +Nνµ)P (νµ → ντ ) (9)The observation of the small value of R = 0.61± 0.03(stat.)± 0.05(syst.) [1]and zenith angle dependent deficit of µ-like events suggests, that in the case oftwo -neutrino oscillation scenario of νµ → ντ more than 30% (90%C.L.) of theinitially produced muon neutrinos arrive at the S-K detector as tau neutrinos[2, 3]. We assume that the average probability of oscillations P (νµ → ντ ) = 0.3.Muon-neutrino quasi-elastic events detected in the S-K detector were used toestimate the expected total number of muon neutrino. Similarly to Eq.(8) onecan writeN q.e.µ = k2(Nνµσνq.e. +Nνµσνq.e.)(1− P (νµ → ντ ))= k2(Nνµ +Nνµ)(1− P (νµ → ντ ))σq.e.(10)where k2 has the same meaning as k1 in Eq.(8), and σνq.e.,σνq.e. are the cross-sections of quasi-elastic scattering of muon neutrino on (bounded) neutrons andanti-muon neutrino on protons in the H20-target, respectively, which were takento be constant and to be equal to its maximal values of σνq.e. = 1.0 × 10−38 cm2and σνq.e. = 0.4 × 10−38 cm2 in the energy region Eν <1.33 GeV, see e.g. [11].The average cross section σq.e. = (σνq.e. + σνq.e.)/2, since according to MC simu-lation used in the experiment the ratio Nνµ/Nνµ = 1 within a few percent forthe neutrino energy range considered [12]. Thus, the total muon neutrino fluxis underestimated. The number of detected quasi-elastic muon-neutrino eventscan be extracted from the number of µ-like events in Table 1 of ref.[1]. Underthe νµ → ντ oscillation hypothesis used the fractions of νeCC, νµCC and NCevents in a detected sample of µ-like events calculated for P (νµ → ντ ) = 0.3should be 0.7%, 94% and 5.3%, respectively, instead of 0.5%, 95.8% and 3.7%given in Table 1 of ref.[1]. Thus, N q.e.µ = 900× .94× 916.9/1166.5 = 665 events.We also assume that the final state signature in water Cherenkov detectors arepractically the same for quasi-elastic νe and ντ − e elastic scattering processes, sodetection efficiencies for these processes are the same. The efficiencies for identi-fying quasi-elastic νe and νµ events were 93% and 95%, respectively [1]. Finally,since detection efficiences for fully-contained e-like (Pe >100 MeV/c) and µ-like(Pµ > 200 MeV/c) events are practically energy independent we neglect thissmall difference in efficiencies and assume that k1 = k2.4Using the above value for N q.e.µ , Eqs.(7-10) and µντ = 5.4 × 10−7µB, whichcorresponds to the BEBC experiment upper limit on diagonal tau neutrino mag-netic moment [13], it is found that in the first bin of histogram in Fig.4(a) [1] theS-K experiment should detect:∆N1e = Nq.e.µ ·P (νµ → ντ )1− P (νµ → ντ )·σµσq.e.≃ 1420 events (11)This number is much greater than the number of observed events, N1e,data =160 events, or the number of events predicted by MC simulation, N1e,MC = 125events in this energy bin. 2The bound for the tau neutrino magnetic moment can be calculated by usingthe following relation :N q.e.µ ·P (νµ → ντ )1− P (νµ → ντ )·σµσq.e.< (∆N1e )90 (12)where (∆N1e )90 = (N1e,data−N1e,MC)90 (≃ 80 events) is the 90% C.L. upper limitfor the expected number of e-like events from ντ − e scattering in the first energybin of Fig.4(a) (ref.[1]), calculated taken into account the systematic uncertaintyin the absolute normalisation of the MC events of 25% [1] by added the errors inquadrature to the statistical error.This results in a conservative boundµντ < 1.3× 10−7µB (13)The bound is a factor 4 better than the previously published bound obtainedby the BEBC experiment [13] and is obtained on the assumption that νµ → ντoscillations are the origin of the anomaly in atmospheric neutrino data observedby the S-K experiment. It can be improved by a more detailed analysis of theS-K data. Note that Eq.(4) and limit of Eq.(13) are consistent for the region of∆m2 ∼ (10−3−10−2) eV2 suggested by the S-K analysis [4], Eν ≃ O(1 GeV) andfor B equal to the average magnetic field of the earth (B.1 Gauss).In the S-K detector, the oscillation scenario was checked by using pi0 events[1]. For νµ → ντ oscillations the number of neutral -current (NC) events shouldbe unchanged by neutrino oscillations. For νµ → ντ oscillations the numberof νeCC events ( e-like events) should also be unchanged by neutrino oscilla-tions. Therefore, the (pi0/e) ratio of the data should agree with the same ratioof the Monte Carlo without oscillations for νµ → ντ case [4]. It was obtained2 These numbers were read off Fig.4(a) of ref.[1]5(pi0/e)data/(pi0/e)MC = 0.93 ± 0.07(stat) ± 0.19(syst) ( preliminary). The resultis consistent with the νµ → ντ interpretation of the S-K data, however it cannotexclude νµ → νs oscillation hypothesis completely.In a recent publication [14], it was pointed out that a large diagonal and/ortransition magnetic moment of neutrino can contribute to the neutral currenteffects ( by a single pi0 production) used to distinguish the mechanisms of muonneutrino oscillation to tau neutrino or to a sterile neutrino. The effect discussedin the present Letter, as well as the effect discussed in ref. [14], definitely canaffect the interpretation of atmospheric neutrino data.Finally note that helicity flipped states of neutrinos with the large magneticmoment would be trapped in the SN1987a core, so there is no limit on the neutrinomagnetic moment form SN1987a [15]. Others astrophysical constraints on µντare also model dependent and have considerable theoretical and experimentaluncertainties.AcknowledgementsI thank N.V. Krasnikov and V.A. Matveev for useful discussions.6References[1] Y. Fukuda et al., The Super-Kamiokande Collaboration, Phys. Lett. B433(1998) 9.[2] Y. Fukuda et al., The Super-Kamiokande Collaboration, Phys. Rev. Lett.81 (1998) 1562.[3] Y. Fukuda et al., The Super-Kamiokande Collaboration, Phys. Lett. B436(1998) 33.[4] T. Kajita, Talk presented at the Conference NEUTRINO’98, Takayama,Japan, 4-9 June, 1998, Preprint hep-ex/9810001.[5] R.N. Mohapatra and P.B. Pal, in “Massive Neutrinos in Physics and Astro-physics”, World Scientific, Singapore, 1991.[6] S.N. Gninenko, Phys. Lett. B427 (1998) 206;S.N. Gninenko, Mod. Phys. Lett. A13 (1998) 1791.[7] J. Segura, Eur.Phys.J. C5 (1998) 269.[8] See e.g. review: S.M. Bilenky and B. Pontecorvo, Phys. Rep.41 (1978) 225.[9] J.D. Vergados, Nucl. Phys. Proc. Suppl. 22A(1991) 21 .[10] G. Domogatskii and D. Nadezhin, Sov. J. Nucl. Phys. 12(1971)678.[11] T. Kajita, in ”Physics and Astrophysics of Neutrinos”, Eds., M. Fukugitaand A. Suzuki, Springer-Verlag (1994), p. 559.[12] M. Honda et al., Phys. Rev. D52 (1995) 4985.[13] A.M. Cooper - Sarkar et al., Phys. Lett. B280 (1992) 153.[14] S.K. Kang, J.E. Kim, and J.S. Lee, Preprint hep-ph/9812531.[15] S. Pakvasa, Preprint hep-ph/9804426.7

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Bound on the tau neutrino magnetic moment from the Super-Kamiokande data

Bound on the tau neutrino magnetic moment from the Super-Kamiokande data

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