Neutrino Electromagnetic Properties

There is no doubt [1-3] that neutrino electromagnetic properties open a window to new physics. The most general form [1] of a neutrino electromagnetic vertex function $\Lambda_{\mu}^{ij}(q) = \left( \gamma_{\mu} - q_{\mu} {q}/q^{2} \right) \left[ f_{Q}^{ij}(q^{2}) + f_{A}^{ij}(q^{2}) q^{2} \gamma_{5} \right] \nonumber - i \sigma_{\mu\nu} q^{\nu} \left[ f_{M}^{ij}(q^{2}) + i f_{E}^{ij}(q^{2}) \gamma_{5} \right]$ , where $\Lambda_{\mu}(q)$ and form factors $f_{Q,A,M,E}(q^2)$ are $3\times 3$ matrices in the space of massive neutrinos, in the case of coupling with a real photon ($q^2=0$) provides four sets of neutrino electromagnetic characteristics: 1) the dipole magnetic moments $\mu_{ij}=f_{M}^{ij}(0)$, 2) the dipole electric moments $\epsilon_{ij}=f_{E}^{ij}(0)$, 3) the millicharges $q_{ij}=f_{Q}^{ij}(0)$ and 4) the anapole moments $a_{ij}=f_{A}^{ij}(0)$. So far, there are no indications in favour of nonzero electromagnetic properties of neutrinos from either data from laboratory experiments with neutrino fluxes from ground-based sources or from astrophysics observations. However, the study of the electromagnetic properties of neutrinos attracts considerable attention. The most well understood and studied are the dipole magnetic and electric moments. In a minimal extension of the Standard Model the diagonal magnetic moment of a Dirac neutrino is given [4] by $\mu^{D}_{ii} = \frac{3e G_F m_{i}}{8\sqrt {2} \pi ^2}\approx 3.2\times 10^{-19} \Big(\frac{m_i}{1 \mathrm{eV} }\Big) \mu_{B}$ ($\mu_B$ is the Bohr magneton). Majorana neutrinos can have only transition (off-diagonal) magnetic moments $\mu^{M}_{i\neq j}$. The most stringent constraints on the effective neutrino magnetic moment are obtained with the reactor antineutrinos: $\mu_{\nu} < 2.9 \times 10^{-11} \mu_{B}$ (GEMMA Collaboration [5]), and solar neutrinos: ${\mu}_{\nu_e}\leq 2.8 \times 10^{-11} \mu _B$ (Borexino Collaboration [6]). An astrophysical bound (for both Dirac and Majorana neutrinos) is provided [7-9] by observations of the properties of globular cluster stars: $\Big( \sum _{i,j}\left| \mu_{ij}\right| ^2\Big) ^{1/2}\leq (2.2{-}2.6) \times 10^{-12} \mu _B$. A general and termed model-independent upper bound on the Dirac neutrino magnetic moment, that can be generated by an effective theory beyond a minimal extension of the Standard Model, has been derived in [10]: $\mu_{\nu}\leq 10^{-14}\mu_B$. The corresponding limit for transition moments of Majorana neutrinos is much weaker [11]. In the theoretical framework with $CP$ violation a neutrino can have nonzero electric moments $\epsilon_{ij}$. In the laboratory neutrino scattering experiments for searching $\mu_{\nu}$ (for instance, in the GEMMA experiment) the electric moment $\epsilon_{ij}$ contributions interfere with those due to $\mu_{ij}$. Thus, these kind of experiments also provide constraints on $\epsilon_{ij}$. The astrophysical bounds on $\mu_{ij}$ are also applicable for constraining $\epsilon_{ij}$ (see [7-9] and [12]). In what follows below we give a fast flash on less know neutrino electromagnetic characteristics, namely on the neutrino millicharge, charge radius and anapole moment and give some comments on the future prospects of neutrino electromagnetic properties.

Electric and magnetic dipole moments of fundamental particles had a large influence in shaping the standard model in the past and continue to play a significant role at present by restricting the many possible expansions of the standard model. In this chapter I describe, in particular, the present status and prospects of the dipole moments in storage rings experiments, in the context of other significant electric and magnetic dipole moment efforts.

One of the stiffest equations of state for matter in a compact star is constant energy density and this generates the interior Schwarzschild radius to mass relation and the Misner maximum mass for relativistic compact stars. If dark matter populates the interior of stars, and this matter is supersymmetric or of some other type, some of it possessing a tiny electric charge, there is the possibility that highly compact stars can trap a small but non-negligible electric charge. In this case the radius to mass relation for such compact stars should get modifications. We use an analytical scheme to investigate the limiting radius to mass relation and the maximum mass of relativistic stars made of an incompressible fluid with a small electric charge. The investigation is carried out by using the hydrostatic equilibrium equation, i.e., the Tolman–Oppenheimer–Volkoff (TOV) equation, together with the other equations of structure, with the further hypothesis that the charge distribution is proportional to the energy density. The approach relies on Volkoff and Misner’s method to solve the TOV equation. For zero charge one gets the interior Schwarzschild limit, and supposing incompressible boson or fermion matter with constituents with masses of the order of the neutron mass one finds that the maximum mass is the Misner mass. For a small electric charge, our analytical approximating scheme, valid in first order in the star’s electric charge, shows that the maximum mass increases relatively to the uncharged case, whereas the minimum possible radius decreases, an expected effect since the new field is repulsive, aiding the pressure to sustain the star against gravitational collapse.

We investigate dimension-five Lorentz-violating (LV) nonminimal interactions in the electroweak sector, in connection with the possible generation of electric dipole moment (EDM), weak electric dipole moment (WEDM), magnetic dipole moment (MDM) and weak magnetic dipole moment (WMDM) for leptons. These couplings are composed of the physical fields in the Standard Model and LV tensors of ranks ranging from 1 to 4. The CPT-odd couplings do not generate EDM behavior nor provide the correct MDM signature, while the CPT-even ones are compatible with EDM and MDM behavior, being subject to improved constraining. Tau lepton experimental data is used to constrain the WEDM and WMDM couplings to the level of 10−4(GeV)−1, whereas electron MDM and EDM data are employed to improve constraints to the level of 10−10(GeV)−1 and 10−16(GeV)−1, respectively.

In modern physics there have developed two complementary—and apparently mutually contradictory—modes of description of radiation processes and of the motion of molecules, atoms, electrons and protons. How far can the parallelism in description of photons (light quanta) and members of the second group of entities be carried ? It is now well known that the physical effects by which an entity is recognised are, in all cases, atomic and individual, e. g ., photoelectric and Compton effects, Scintillation on a fluorescent screen, effect on a photographic plate. Such effects are quite naturally correlated with the concept of a moving particle with energy and momentum. On the other hand, the motion of these particles can only be completely described by the wave method. Except in the case of very long wireless waves, the waves are never observed directly as waves with periodic physical effects in space and time, and even in the case of the exception it seem probable that the periodicity observed is only a large scale phenomenon (for comparatively large numbers of particles). The development of the analogy between photons and entities of the second class (atoms, electrons, etc.) has already reached the stage where it is possible to give a wave description of the motion of the particles in all cases and to assign to the particles an energy-momentum four-vector within the limits of Heisenberg's principle. There remains, however, a fundamental distinction in current theory. All the entities in the second class have electro-magnetic particle properties while none have been assigned to the photon. Electrons, ions, and protons have electric charge which is quantised in integral multiples of the electronic charge ± e . Atoms possess the electromagnetic particle properties, magnetic moment and possibly electric moment, while molecules have magnetic and electric moments and mechanical moments of inertia. Since the photon is assumed to be electromagnetic in origin, and can produce electromagnetic effects, it is necessary to assign to it some electro-magnetic character. The simplest particle properties which one can postulate are those of electric moment and magnetic moment; free electric charge is excluded by the fact that light is not deflected in a uniform electric or magnetic field. The present investigation was carried out with the object of detecting, if possible, the existence of the magnetic moment of a photon. The Stern-Gerlach method of the non-uniform field involving the deflection of particles moving with velocity of light, presents obvious difficulties. The method actually adopted depends for its sensitiveness on the interference properties of light, and the principle was the following. Light was passed through a Fabry-Perot étalon placed in a strong magnetic field which was perpendicular to the direction of propagation of the light. A particle with a magnetic moment μ parallel or antiparallel to the field H, would undergo a change in energy ΔE = ± μH on entering the field and in accordance with the principles of the quantum theory would experience a change in frequency Δ v = ±μH/ h . This would involve an effective change in wave-length Δλ = ±μHλ 2 / hc and a change in the interference pattern formed by the interferometer of the type observed in the normal Zeeman effect.

Precision measurements of the anomalous electromagnetic moment of leptons (al) may serve as one of the most promising directions in the search for new physics beyond the Standard Model. While the experimental value of the electron magnetic moment agrees with theoretical predictions with up to 11 significant digits, the muon magnetic moment shows deviations from the Standard Model value at the level of 4.2 sigma, indicating the possible occurrence of new physics effects. Although the aτ of the tau lepton with its heavy mass is expected to be ${{m_\tau ^2} \mathord{\left/ {\vphantom {{m_\tau ^2} {m_\mu ^2}}} \right. \kern-\nulldelimiterspace} {m_\mu ^2}} \approx 280$ times more sensitive to new physics effects than aμ, measurements of this quantity are rare. This is because the standard spin precession methods are not suitable for aτ measurements due to the very short tau lifetime. Ultra-peripheral collisions of heavy ions at the LHC may serve as an alternative tool to measure aτ. In ultra-peripheral collisions, hadronic interactions are strongly suppressed and long-distance electromagnetic processes dominate, providing an environment to study the electromagnetic properties of the tau lepton. The di-tau production process PbPb → PbPbγγ → PbPbττ contains two gamma-tau vertices and hence provides enhanced sensitivity to the anomalous magnetic and electric moments. In this contribution we discuss the feasibility of the aτ measurement in ultraperipheral collisions with the ALICE experiment and present projections of the sensitivity of the measurement for the upcoming heavy ion run in 2022 at LHC.

The neutrino magnetic and electric moments are zero at tree level but can arise in radiative corrections. Any deviation from the Standard Model prediction would provide another indication of neutrino-related new physics in addition to the neutrino oscillation and masses. Especially, Dirac and Majorana neutrinos have quite different structures in their electromagnetic moments. Nevertheless, the recoil measurements and astrophysical stellar cooling can only constrain combinations of neutrino magnetic and electric moments with the limitation of not seeing their detailed structures. We propose using the atomic radiative emission of neutrino pair to serve as a unique probe of the neutrino electromagnetic moments with the advantage of not just separating the magnetic and electric moments but also identifying their individual elements. Both searching strategy and projected sensitivities are illustrated in this letter.

Precise measurements of magnetic and electric dipole moments are important tests of the Standard Model and beyond Standard Model physics, particularly for the electron and the muon. However, the situation presents distinctive challenges when dealing with the tau lepton due to its very short lifetime and relatively high mass. Here, we review the theoretical predictions and experimental measurements of both the anomalous magnetic and electric dipole moments of the tau lepton.

The new derivation of the equation of the spin precession is given for a particle possessing electric and magnetic dipole moments. Contributions from classical electrodynamics and from the Thomas effect are explicitly separated. A fully covariant approach is used. The final equation is expressed in a very simple form in terms of the fields in the instantaneously accompanying frame. The Lorentz transformations of the electric and magnetic dipole moments and of the spin are derived from basic equations of classical electrodynamics. For this purpose, the Maxwell equations in matter are used and the result is confirmed by other methods. An antisymmetric four-tensor is correctly constructed from the electric and magnetic dipole moments.

The electromagnetic properties of the SU(3)-flavor baryon decuplet are examined within a lattice simulation of quenched QCD. Electric charge radii, magnetic moments, and magnetic radii are extracted from the E0 and M1 form factors. Preliminary results for the E2 and M3 moments are presented giving the first model independent insight to the shape of the quark distribution in the baryon ground state. As in our octet baryon analysis, the lattice results give evidence of spin-dependent forces and mass effects in the electromagnetic properties. The quark charge distribution radii indicate these effects act in opposing directions. Some baryon dependence of the effective quark magnetic moments is seen. However, this dependence in decuplet baryons is more subtle than that for octet baryons. Of particular interest are the lattice predictions for the magnetic moments of $\Omega^-$ and $\Delta^{++}$ for which new recent experimental measurements are available. The lattice prediction of the $\Delta^{++}/p$ ratio appears larger than the experimental ratio, while the lattice prediction for the $\Omega^-/p$ magnetic moment ratio is in good agreement with the experimental ratio.

We consider the massive Dirac neutrino electric charge and magnetic moment within the context of the standard model supplied with an SU(2)-singlet right-handed neutrino in an arbitrary ${R}_{\ensuremath{\xi}}$ gauge. Using the dimensional-regularization scheme we start with the calculations of the one-loop contributions to the neutrino electromagnetic vertex function exactly accounting for the neutrino mass. We examine the decomposition of the massive neutrino electromagnetic vertex function. It is found by means of direct calculations that the massive neutrino vertex function contains only the four form factors. Then we derive the closed integral expressions for different contributions to the neutrino electric form factor, electric charge, and magnetic moment. For several one-loop contributions to the neutrino charge and magnetic moment that were calculated previously with mistakes by the other authors, we find the correct results. We show that the electric charge for the massive neutrino is a gauge independent and vanishing parameter in the first two orders of the expansion over the neutrino mass parameter ${b=(m}_{\ensuremath{\nu}}{/M}_{W}{)}^{2}.$ From the obtained closed two-integral expression for a massive neutrino electric form factor it is also possible to derive the neutrino charge radius. In the particular choice of the 't Hooft--Feynman gauge we also demonstrate that the neutrino charge is zero in all orders of expansion over b, i.e., for an arbitrary mass of neutrino. For each of the diagrams contributing to the neutrino magnetic moment, we obtain the expressions accounting for the leading (zeroth) and next-to-leading (first) order in b, where the gauge dependence is shown explicitly. Each of the contributions is finite and the sum of all contributions turns out to be gauge independent. Our calculations also enable us to obtain the neutrino magnetic moment in theoretical models that differ from each other by the values of particles' masses, including the case of a very heavy neutrino. The general expression for the massive neutrino magnetic form factor is presented.

We show that for asymptotically vanishing Maxwell fields in Minkowski space with non-vanishing total charge, one can find a unique geometric structure, a null direction field, at null infinity. From this structure a unique complex analytic world line in complex Minkowski space can be found and then identified as the complex centre of charge. By ‘sitting’—in an imaginary sense—on this world line both the electric and intrinsic magnetic dipole moments vanish. The intrinsic magnetic dipole moment is (in some sense) obtained from the ‘distance’ the complex world line is from the real space (times the charge). This point of view unifies the asymptotic treatment of the dipole moments. For electromagnetic fields with vanishing magnetic dipole moments the world line is real and defines the real (ordinary centre of charge). We illustrate these ideas with the Lienard–Wiechert Maxwell field. In the conclusion we discuss its generalization to general relativity where the complex centre of charge world line has its analogue in a complex centre of mass allowing a definition of the spin and orbital angular momentum—the analogues of the magnetic and electric dipole moments.

We derive relative upper bounds on the effective magnetic moment of Dirac neutrinos from comparison of the standard weak and electromagnetic mechanisms of the neutrino luminosity due to the Compton-like photoproduction of neutrino pairs in a degenerate gas of electrons on the lowest Landau level in a strong magnetic field. These bounds are close to the known astrophysical and laboratory ones. 1. Neutrino emission is the main source of energy losses of stars in the late stages of their evolution [1]. As is well known, neutron stars (NSs) can have strong magnetic fields H >∼ 10 12 G, the NSs with H ∼ 10− 10 G are called magnetars [2]. In this report, we consider one of the main processes of neutrino emission in the outer regions of NSs (for a review of various neutrino processes, see [3]) that is photoproduction of neutrino pairs (γe → eνν) in a degenerate gas of electrons through two mechanisms: the weak one via standard charged and neutral weak currents and the electromagnetic one via neutrino electromagnetic dipole moments arising in extended versions of the Standard Model [1,4] (for a recent review, see [5]). By comparison of the neutrino luminosities due to these two mechanism, Lw and Lem, we derive relative upper bounds on the neutrino effective magnetic moment (NEMM) μν = (μ 2 ν + d 2 ν) , (1) restricting ourselves to the case of Dirac neutrinos. Here μν and dν are the neutrino magnetic and electric dipole moments, respectively. 2. We assume that the electron gas is degenerate and strongly magnetized: T ≪ μ−m, H > ((μ/m) − 1)H0/2, (2) where T and μ ≃ μ(T = 0) ≡ eF = (m 2 + p F ) are the temperature and chemical potential of the gas, eF and pF are the Fermi energy and momentum, H0 = m /e ≃ 4.41×10 G, m and −e are the electron mass and charge (we use the units with h = c = kB = 1). Under the conditions (2), electrons occupy only the lowest Landau level in the magnetic field with pF = 2π 2ne/(eH), where ne is the electron concentration, and the effective photon mass is generated which e-mail: borisov@phys.msu.ru late e-mail: mstranger@list.ru is equal to the plasmon frequency ωp = ((2α/π)(pF/eF)H/H0) m, α is the fine-structure constant. For the nonrelativistic case, pF ≪ m and ωp ≪ T , the neutrino luminosities are expressed as follows: Lw = 3.49× 10 H 13 ρ 6 T 9 8 erg cm s, (3) Lem = 4.06× 10 30(μν/μB) 2ρ26T 3 8 erg cm −3 s, (4) where H13 = H/(10 13 G), ρ6 = ρ/ (

BLMSSM is introduced as a supersymmetric extension of the Standard Model (SM), where local gauged baryon number B and lepton number L are considered. Extending BLMSSM with exotic Higgs superfields (ΦNL, φNL) and superfields (Y, Y′), one obtains the new model called EBLMSSM, where exotic leptons are heavy enough and have tree level couplings with the SM leptons. In this model, some new parameters with CP-violating phases are considered, so there are new contributions to lepton anomalous magnetic dipole moments (MDMs) and electric dipole moments (EDMs). Therefore, we study the one-loop, two-loop Barr-Zee and two-loop Rainbow type corrections to lepton MDMs and EDMs in the EBLMSSM. Considering the constraints from the lightest CP-even Higgs mass and decays, we discuss the numerical results of lepton MDMs and EDMs. In our used parameter space, the new physics contributions to lepton MDMs are large, which can remedy the deviation between the SM prediction and experimental result well. New introduced CP-violating phases also affect the lepton EDMs in a certain degree.

Elastic neutrino–electron scattering of solar neutrinos and potential effects of magnetic and electric dipole moments