Electromagnetic Vertex Function Research Articles

Neutrino propagation in an electron background with an inhomogeneous magnetic field

We study the electromagnetic coupling of a neutrino that propagates in a two-stream electron background medium. Specifically, we calculate the electromagnetic vertex function for a medium that consists of a normal electron background plus another electron stream background that is moving with a velocity four-vector v^mu relative to the normal background. The results can be used as the basis for studying the neutrino electromagnetic properties and various processes in such a medium. As an application, we calculate the neutrino dispersion relation in the presence of an external magnetic field (mathbf {B}), focused in the case in which B is inhomogeneous, keeping only the terms of the lowest order in 1/m^2_W and linear in the B and its gradient. We show that the dispersion relation contains additional anisotropic terms involving the derivatives of mathbf {B}, such as the gradient of {hat{k}}cdot (mathbf {v}times mathbf {B}), which involve the stream background velocity, and a term of the form {hat{k}}cdot (nabla times mathbf {B}) that can be present in the absence of the stream background, in addition to a term of the form {hat{k}}cdot mathbf {v} and the well known term {hat{k}}cdot mathbf {B} that arises in the constant mathbf {B} case. The derivative-dependent terms are even under a CP transformation. As a result, in contrast to the latter two just mentioned, they depend on the sum of the particle and antiparticle densities and therefore can be non-zero in a CP-symmetric medium in which the particle and antiparticle densities are equal.

Anomalous magnetic moment of the muon in a dispersive approach

We present a new general dispersive formalism for evaluating the hadronic light-by-light scattering contribution to the anomalous magnetic moment of the muon. In the suggested approach, this correction is related to the imaginary part of the muon's electromagnetic vertex function. The latter may be directly related to measurable hadronic processes by means of unitarity and analyticity. As a test we apply the introduced formalism to the case of meson pole exchanges and find agreement with the direct two-loop calculation.

Electromagnetic annihilation into charged leptons and scattering off nucleons of spin-3/2Majorana particles

We compute the cross section for the electromagnetic annihilation into charged leptons, and the electromagnetic scattering off nucleons, of spin-3/2 self-conjugate (Majorana) particles using the general form of the electromagnetic vertex function that was obtained previously for such particles. In addition to the restrictions imposed by common principles such as electromagnetic gauge invariance and hermiticity, the vertex function incorporates the restriction due to the Majorana condition as well as the particular properties related to the spinors in the Rarita-Schwinger representation, and is the counterpart of the so-called anapole interaction of spin-1/2 Majorana particles. The formulas obtained for the cross sections share certain similarities with the corresponding results in the spin-1/2 case, but they also reveal some important differences which are pointed out and discussed. The results given here can be useful for applications involving the electromagnetic interactions of spin-3/2 or spin-1/2 Majorana particles in several contexts that have been of interest in the recent literature such as nucleosynthesis and dark matter.

Electromagnetic properties of spin-3/2Majorana particles

The structure of the electromagnetic vertex function of spin-3/2 particles is analyzed in a general way, for the diagonal and off-diagonal couplings, of charged as well as neutral particles including the case of self-conjugate (Majorana) particles. The restrictions imposed by common principles such as electromagnetic gauge invariance and hermiticity are studied, and the implications due to the discrete space-time symmetries or the Majorana condition are deduced when they are applicable. In some cases certain features of the vertex function are analogous to the known ones for the spin-1/2 or spin-1 particles, but we find and discuss other particular properties which are related to the spin-3/2 Rarita-Schwinger representation. For example, in the diagonal Majorana case, the vertex function can contain a term of the form $\gamma_\mu\gamma_5$, which resembles the axial charge radius term for Majorana neutrinos, plus another one that resembles the vertex function for self-conjugate spin-1 particles, but with the particularity that the two terms may not appear independently of each other, but instead with a specific relative coefficient. In essence this is due to the requirement that the vertex function does not mix the genuine spin-3/2 degrees of freedom with the spurious spin-1/2 components of the Rarita-Schwinger representation. The analogous results for the other cases (off-diagonal and charged couplings) are discussed as well.

Neutrino electromagnetic properties

The main goal of the paper is to give a short review on neutrino electromagnetic properties. In the introductory part of the paper a summary on what we really know about neutrinos is given: we discuss the basics of neutrino mass and mixing as well as the phenomenology of neutrino oscillations. This is important for the following discussion on neutrino electromagnetic properties that starts with a derivation of the neutrino electromagnetic vertex function in the most general form, that follows from the requirement of Lorentz invariance, for both the Dirac and Majorana cases. Then, the problem of the neutrino form factors definition and calculation within gauge models is considered. In particular, we discuss the neutrino electric charge form factor and charge radius, dipole magnetic and electric and anapole form factors. Available experimental constraints on neutrino electromagnetic properties are also discussed, and the recently obtained experimental limits on neutrino magnetic moments are reviewed. The most important neutrino electromagnetic processes involving a direct neutrino coupling with photons (such as neutrino radiative decay, neutrino Cherenkov radiation, spin light of neutrino and plasmon decay into neutrino-antineutrino pair in media) and neutrino resonant spin-flavor precession in a magnetic field are discussed at the end of the paper.

Electromagnetic vertex function of the pion at T>0

The matrix element of the electromagnetic current between pion states is calculated in quenched lattice QCD at a temperature of $T = 0.93 T_c$. The nonperturbatively improved Sheikholeslami-Wohlert action is used together with the corresponding ${\cal O}(a)$ improved vector current. The electromagnetic vertex function is extracted for pion masses down to $360 {\rm MeV}$ and momentum transfers $Q^2 \le 2.7 {\rm GeV}^2$.

Nucleon contribution to the induced charge of neutrinos in a matter background and a magnetic field

We study the nucleon contribution to the electromagnetic vertex function of neutrinos that propagate in a matter background in the presence of a magnetic field. Starting from the one-loop expression for the corresponding terms of the vertex function, and taking into account the anomalous magnetic coupling of the nucleons, we calculate the B-dependent part of the form factors that determine the induced charge of the neutrino. A formula for the neutrino induced charge is obtained, and it is evaluated for various illustrative situations. The terms due to the nucleons can be important in some cases, depending on the physical conditions of the environment.

Electric charge and magnetic moment of a massive neutrino

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.

Electromagnetic vertex of neutrinos in an electron background and a magnetic field

We study the electromagnetic vertex function of a neutrino that propagates in an electron background in the presence of a static magnetic field. The structure of the vertex function under the stated conditions is determined and it is written down in terms of a minimal and complete set of tensors. The one-loop expressions for all the form factors is given, up to terms that are linear in the magnetic field, and the approximate integral formulas that hold in the long wavelength limit are obtained. We discuss the physical interpretation of some of the form factors and their relation with the concept of the neutrino induced charge. The neutrino acquires a longitudinal and a transverse charge, due to the fact that the form factors depend on the transverse and longitudinal components of the photon momentum independently. We compute those form factors explicitly in various limiting cases and find that the longitudinal and transverse charge are the same for the case of a non-relativistic electron gas, but not otherwise.

Off-shell pion electromagnetic form factor from a gauge-invariant Nambu-Jona-Lasinio model

The off-shell electromagnetic vertex function of pions and kaons is studied in a bosonized Nambu-Jona-Lasinio model with a gauge-invariant proper-time cutoff. In the chiral limit, the off-shell slope of the pion form factor with respect to the pion 4-momentum is equal to the on-shell slope in the photon momentum. The off-shell slope of the K 0 form factor is zero, that of the K ± about 0.85 times that of the pion. We compare with results of a recent calculation in chiral perturbation theory.

Infrared structure of the leading conformal contribution to the electromagnetic vertex function

We treat the infrared problem directly related to the asymptotic behavior of the form factor of a particle belonging to the fermion-antifermion channel, with anomalous dimension $\overline{d}$. For $\overline{d}<2$ we relate it to the off-shell vertex function; for $\overline{d}>2$ we examine the triangle graph which is considered to be the most infrared divergent. We show that the leading ${\ensuremath{\gamma}}_{5}$-even conformal contribution to the wave function does not give rise to infrared divergences, provided the dimensions of the various fields satisfy the conformal bounds. Thus the ensuing contribution to the asymptotic form factor is ${(\ensuremath{-}{q}^{2})}^{1\ensuremath{-}\overline{d}}$.

Boson Electromagnetic Vertex Function in the Veneziano Model

A possible way of deriving the electromagnetic vertex function of boson is proposed within the operator formalism of the Veneziano model, by introducing an indefinite number of spurions. It is shown that the method leads us to the modification of trajectory intercept as assumed in a previous work, and the boson electromagnetic form factor of the dipole type. The introduction of electromagnetic field in the present method may be accepted on the basis of the conventional field theory.

Simple Relativistic Calculation of the Electromagnetic Form Factors of the Deuteron

A simple method of extracting anomalous singularities from the electromagnetic vertex function of bound states is proposed. The method has been applied to the electromagnetic form factors of the deuteron and its relevance has been proven by a thorough comparison with the experimental data.