0000000000269867
AUTHOR
Luis G. Cabral-rosetti
Charge radius of the neutrino
Using the pinch technique we construct at one-loop order a neutrino charge radius, which is finite, depends neither on the gauge-fixing parameter nor on the gauge-fixing scheme employed, and is process independent. This definition stems solely from an effective proper photon-neutrino one-loop vertex, with no reference to box or self-energy contributions. The role of the $\mathrm{WW}$ box in this construction is critically examined. In particular it is shown that the exclusion of the effective $\mathrm{WW}$ box from the definition of the neutrino charge radius is not a matter of convention but is in fact dynamically realized when the target fermions are right-handedly polarized. In this way …
Generalized hypergeometric functions and the evaluation of scalar one-loop integrals in Feynman diagrams
Present and future high-precision tests of the Standard Model and beyond for the fundamental constituents and interactions in Nature are demanding complex perturbative calculations involving multi-leg and multi-loop Feynman diagrams. Currently, large effort is devoted to the search for closed expressions of loop integrals, written whenever possible in terms of known - often hypergeometric-type - functions. In this work, the scalar three-point function is re-evaluated by means of generalized hypergeometric functions of two variables. Finally, use is made of the connection between such Appell functions and dilogarithms coming from a previous investigation, to recover well-known results.
Charge and magnetic moment of the neutrino in the background field method and in the linear R-xi(L) gauge
We present a computation of the charge and the magnetic moment of the neutrino in the recently developed electro-weak Background Field Method and in the linear $R_{\xi}^L$ gauge. First, we deduce a formal Ward-Takahashi identity which implies the immediate cancellation of the neutrino electric charge. This Ward-Takahashi identity is as simple as that for QED. The computation of the (proper and improper) one loop vertex diagrams contributing to the neutrino electric charge is also presented in an arbitrary gauge, checking in this way the Ward-Takahashi identity previously obtained. Finally, the calculation of the magnetic moment of the neutrino, in the minimal extension of the Standard Model…
Appell Functions and the Scalar One-Loop Three-point Integrals in Feynman Diagrams
The scalar three-point function appearing in one-loop Feynman diagrams is compactly expressed in terms of a generalized hypergeometric function of two variables. Use is made of the connection between such Appell function and dilogarithms coming from a previous investigation. Special cases are obtained for particular values of internal masses and external momenta.