Elastic ν<Subscript>μ</Subscript><Emphasis Type="Italic">e</Emphasis> scattering as a source for determining the muonic neutrino mass and investigation of its electromagnetic properties

Electroweak (EW) and electromagnetic (EM) contributions to the cross sections of elastic scattering of muonic neutrinos by electron are analyzed. The effect of the neutrino mass and root-mean-square charge radius on the angular and energy distributions of product electrons and the total scattering cross sections is considered. The possibility of measuring the muon neutrino magnetic moment μ_ν by selecting its contribution to the ν_μ e-scattering cross sections is analyzed.     

Limits on neutrino oscillations derived from the ratio of neutral- to charged-current cross sections of neutrinos measured at the CERN SPS NBB

We present an analysis, in terms of neutrino oscillations, of the recent measurements of the ratio R of neutral-current to charged-current neutrino cross sections performed by the CDHS and CHARM Collaborations at the CERN Super Proton Synchroton narrow-band beam. The measurementswere aimed at the determination of sin² θ_w. Our analysis is based on the observation that muon-neutrino oscillations would decrease the number of interactions with a muon in the final state. The effect of oscillations on R can be studied, comparing the actual measurements with the value of R predicted by an independent measurement of sin² θ_w. Limits on ν_μ−ν_e, ν_μ−ν_τ, and ν_μ−ν_x oscillations are presented. They refer to a region of high mass squared difference of the two oscillating neutrinos (Δm² > 3 eV²). For high Δm² the limits on the mixing angle θ are very restrictive. In particular, for the transition ν_μ−ν_x (x≠e, τ) they represent the best available results for large intervals in Δm².     

Probing the violation of equivalence principle at a muon storage ring via neutrino oscillation

We examine the possible tests of violation of the gravitational equivalence principle (VEP) at a muon storage ring via neutrino oscillation experiments. If the gravitational interactions of the neutrinos are not diagonal in the flavour basis and the gravitational interaction eigenstates have different couplings to the gravitational field, this leads to the neutrino oscillation. If one starts with μ⁺ beam then appearance of τ^±, e⁺ and μ⁻ in the final state are the signals for neutrino oscillation. We have estimated the number of μ⁻ events in this scenario in ν_μ–N deep inelastic scattering. Final state lepton energy distribution can be used to distinguish the VEP scenario from the others. A large area of VEP parameter space can be explored at a future muon storage ring facility with moderate beam energy.     

On lepton-pair production in neutrino-nucleus collisions

A calculation of the cross section for the reaction νγ → νμ ⁺ μ ^? which is induced by the neutrino magnetic moment, is described in detail. The expression obtained for this cross section is used to determine the asymptotic behavior of the cross section for the reaction νN → νNμ ⁺ μ ^? by the Weiszäcker-Williams method. It is shown that, upon going over from the nucleus involved to a structureless particle (for example, an electron), the resulting expression is doubled owing to integration with respect to the virtual-photon momentum over the region m _μ?Q?E _ν, where the Weiszäcker-Williams approximation is not applicable. The method developed here makes it possible to obtain straightforwardly the known asymptotic expressions for the cross sections describing the reactions eN → eNμ ⁺ μ ^? and e ⁺ e ^? → W ⁺ W ^? e ⁺ e ^?.     

Effect of the neutrino magnetic moment on the properties of the muon

The effect of the neutrino dipole magnetic moment on the properties of the muon is investigated within the standard model of electroweak interactions and a model based on the SU(2) _L × SU(2) _R × U(1) _B-L gauge group (left-right model). In the case of the Dirac neutrino, muon decay through the channel µ^? → e ^?γ is studied with allowance for the neutrino dipole magnetic moment. It is shown that, both in the standard model supplemented with an SU(2) _L right-handed neutrino singlet and in the standard model featuring two doublets of Higgs fields, radiative muon decay is unobservable. In the left-right model, the contributions of diagrams associated with the neutrino dipole magnetic moment become significant only in the case of a mutual compensation of the contributions of diagrams involving the electromagnetic vertices of charged gauge bosons and singly charged Higgs bosons. At specific values of the parameters of the left-right model, one can then obtain an experimental upper limit on the branching fraction of this reaction. The contributions of the neutrino dipole magnetic moment to the muon anomalous magnetic moment are found for the Dirac and the Majorana neutrino. It is established that, both in the standard model and in the left-right model, values of the neutrino anomalous magnetic moment that are required for explaining the (g ? 2)_µ anomaly are in excess of the theoretical predictions for this moment.     

Neutrino-12C reactions and the LSND and KARMEN experiments on neutrino oscillations

We present new theoretical results of the flux-averaged ¹²C(ν _e , e ^?)¹²N and ¹²C(ν _μ , μ ^?)¹²N cross sections with ν _μ (ν _e ) coming from the decay-in-flight (decay-at-rest) of π ⁺(μ ⁺). These cross sections are relevant for the interpretation of the recent experiments on neutrino oscillation performed by the LSND and KARMEN collaborations. The microscopic approaches used are charge-exchange random phase approximation (RPA), charge-exchange RPA among quasiparticles (QRPA), and the Shell Model. We show that the exclusive cross sections are in nice agreement with the experimental values for both reactions when a large-scale shell-model calculation is performed. Concerning the inclusive cross section for ν _μ coming from the decay-in-flight of π ⁺, the calculated value keeps overestimating the experimental one by 20–30%, while the inclusive cross section due to ν _e coming from the decay-at-rest of μ ⁺ is in agreement within experimental error bars with the measured values. The shell-model prediction for the decay-in-flight neutrino cross section is reduced compared to the RPA one because of the different kind of correlations in the calculation of the spin modes (in particular, the quenching of the 1⁺) and partially due to the shell-model configuration basis, which is not large enough, as we show using arguments based on sum rules.     

New definition for the hadronic contribution to the muon anomalous magnetic moment

A new definition is proposed for the hadronic contribution to the muon anomalous magnetic moment that is based on the inclusion of the effects of vacuum polarization by leptons into the cross section for one-photon annihilation of a lepton pair into hadrons. The formula for the hadronic contribution includes the convolution of the measured cross section for annihilation into hadrons with a certain standard function. This remark concerns radiative correction to this function. A particular form has been proposed for this correction. It has been shown that the use of the new function makes it possible to reduce the uncertainty in such contributions due to radiative correctioins to δa _h/a _h ～ 10^?4.     

Upper limit to the cross-section for the process νμ + e− → νμ + e−

An upper limit of 3 × 10^?42E_ν cm² per electron, at 90% confidence level, has been obtained for the cross section of the process ν_μ + e^? → ν_μ + e^?, interpreted in the usual V-A framework, for an electron recoil energy larger than 0.3 GeV. This estimate is based on the observation of one candidate event in exposures of Gargamelle to the CERN PS neutrino beam.     

Muo-production of neutrino pairs and the number of generations

The cross section for production of neutrino pairs by high energy muons in the nuclear Coulomb field is calculated analytically. For right (left)-handedμ ^?(μ ⁺) helicity, the process is only mediated by neutral currents, which opens the possibility to look for the number of generations. Assuming three generations, the calculated cross section turns out to be 1.1×10^?40 cm² for⁵⁶Fe and 6.6×10^?40cm² for²⁰⁸Pb at an incident muon energy of 300 GeV. Some comments about the equivalent photon approximation are made.     

Neutrino magnetic moment and shock-wave revival in a supernova explosion

The ν _L → ν _R → ν _L double conversion of the Dirac neutrino helicity is analyzed under supernova conditions, in which case the first stage is due to the interaction of the neutrino magnetic moment with plasma electrons and protons in the supernova core, while the second stage is caused by a resonance neutrino-spin flip in the magnetic field of the supernova envelope. It is shown that, if the neutrino has a magnetic moment in the range 10^?13 µ_B < µ _ν < 10^?12 µ_B and if a magnetic field of strength 10¹³ G exists between the neutrinosphere and the region of shock-wave stagnation, an additional energy on the order of 10⁵¹ erg, which is sufficient for stimulating a damped attenuated shock wave, can be injected in this region within the stagnation time.     

Statistical theory of nuclear neutrino capture: (II). Inclusion of first-forbidden transitions

The statistical theory of nuclear neutrino capture is extended to include first-forbidden transitions. A comparison with the theory of Bahcall and Frautschi is made. It is found that the present theory predicts neutrino capture cross sections which are smaller than those of Bahcall and Frautschi by a factor 2–3 for neutrino energies less than 50 MeV when first-forbidden transitions are dominant. Calculation of the cross section is made for the process in which ³⁷Cl nuclei capture electron neutrinos that are emitted in muon decay. The present calculation gives a cross section which is around one half of that of Donnelly and Haxton. Finally the contributions of the highly excited states in ³⁷Ar to the neutrino capture cross section are evaluated. It is shown that the contributions from the highly excited states (E > 6.02 MeV) to the neutrino capture cross section amount to 60% for E_v = 50 MeV.     

Lepton mixing under the lepton charge nonconservation, neutrino masses and oscillations and the “forbidden” decay µ− → e − + γ

The lepton-charge (L _e , L _μ , L _τ ) nonconserving interaction leads to the mixing of the electron, muon, and tau neutrinos, which manifests itself in spatial oscillations of a neutrino beam, and also to the mixing of the electron, negative muon, and tau lepton, which, in particular, may be the cause of the “forbidden” radiative decay of the negative muon into the electron and γ quantum. Under the assumption that the nondiagonal elements of the mass matrices for neutrinos and ordinary leptons, connected with the lepton charge nonconservation, are the same, and by performing the joint analysis of the experimental data on neutrino oscillations and experimental restriction for the probability of the decay µ^? → e ^? + γ per unit time, the following estimate for the lower bound of neutrino mass has been obtained: m ^(ν) > 1.5 eV/c ².     

New determination of the upper limit for the muon neutrino mass

We have measured the muon momentum in pion decay at rest using a magnetic spectrometer. From the result, p_μ⁺ = (29.787±0.005) MeV/c, we deduce a squared muon neutrino mass of (0.23±0.54) MeV²/c⁴.     

Searching for effects of neutrino magnetic moments at reactors and accelerators

The sensitivity of the νe elastic scattering experiments to possible effects of nonzero neutrino magnetic moment (μ) is analyzed and the optimal experimental condition under which such effects are relatively enhanced are found. New, somewhat more restrictive than the previously derived bounds on μ, are obtained on the basis of existing data by the use of selfconsistent statistical analyses: μ_νe < 1.52 × 10^?10e/2m_e and μ_νμ < 1.19 × 10^?9e/2m_e. These bounds are expected to be improved approximately by an order of magnitude in experiments planned to be performed in the near future.     

Measurement of weak meson form factors in spacelike regions

With the construction of high energy, high intensity accelerators (NAL & CERN, SPS) investigation of neutrino scattering on virtual pions, á la Chew-Low, becomes experimentally possible. We propose to analyse the process ν + N → μ^? + K + Δ to extract the usual K_?3 form factor(s) for spacelike momentum transfer. A model calculation suggests that f₊(T) can be determined reasonably well from a triple differential cross section, whereas only rough information on f_?(T) may be obtained from the transverse polarization of the muon. The experiment proposed requires scanning of several millions of bubble chamber pictures.     

Superstring induced mass and magnetic moment of the neutrino and the time modulation of the solar neutrino flux

The new Yukawa couplings involving heavy matter E₆ fields predicted in the framework of superstring theories are considered as a source of mass and magnetic moment for the neutrino. Given the experimental bound m_ve < 46 eV bounds are derived on the neutrino magnetic moment thus generated. Finally, a scenario is produced where the induced magnetic moment has the correct magnitude (∼10⁻¹¹ μ_B) to explain an alleged depletion or solar neutrino flux during periods of maximum solar activity.     

Lepton and pion pair production in γγ collisions measured near the threshold at DCI

This paper reports a complete analysis of data taken at DCI to measure lepton and pion pair production close to the threshold in two-photon processes: e⁺e⁻→e⁺e⁻(e⁺e⁻, μ⁺μ⁻,π⁺π⁻). Preliminary results have been previously published including one-half of the total statistics. Final results presented here are in good agreement with QED for lepton pair production. The measured cross section for pion pair production is twice as large as that expected from Born terms only — a two standard deviation effect.     

Heavy muon as a possible cause of two anomalies

We propose to explain two observed anomalies that suggest extension of the minimal gauge scheme, the eμ production in the e⁺e^? reaction and the anomalous y-distribution in $\text{ν}{}_{\mathrm{\mu }}$ reactions, as being caused by a single object, a heavy muon. With more accurate neutrino data this explanation can readily be distinguished from that of a new quark production.     

Precision measurement of the muon momentum in pion decay at rest

A new series of precision measurements of the muon momentum p_μ⁺ in the decay π→μ⁺v_μ at rest have been made using a magnetic spectrometer. The result is p_μ⁺=(29.79139 ± 0.00083) MeV/c. The consequences of this value for the rest masses of the muon neutrino and of the charged pion are discussed.