Charge radius of the neutrino

Abstract

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 rôle of the W W box in this construction is critically examined. In particular it is shown that the exclusion of the effective W W 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 we obtain a unique decomposition of effective self-energies, vertices, and boxes, which separately respect electroweak gauge invariance. We elaborate on the tree-level origin of the mechanism which enforces at one-loop level massive cancellations among the longitudinal momenta appearing in the Feynman diagrams, and in particular those associated with the non-abelian character of the theory. Various issues related to the known connection between the pinch technique and the Background Field Method are further clarified. Explicit closed expressions for the neutrino charge radius are reported.

Probing nonstandard interactions with reactor neutrinos

“…We remind that only statistical error for the TEX-ONO measurement [6] was taken into account. One can conclude, that from the measurement of the weak mixing angle with 1% precision it is possible to find a strong evidence for the electron neutrino charge radius, which is estimated theoretically to be of the order of 0.4×10 −32 cm 2 [7][8][9].…”

“…There have been discussions in the literature on the possibility to define and to calculate a physically observable neutrino charge radius [7][8][9][10]. All relevant references can be found in Ref.…”

Electroweak pinch technique to all orders

“…In the previous formulas, i is the generation index, and the projection operators are defined according to P L,R = (1 ∓ γ 5 )/2. In this way the leptonic part of L F reads 9) with G ℓ i the Yukawa coupling. The Higgs field H will give mass to all the Standard Model fields, by acquiring a vacuum expectation value v; in particular the masses of the gauge fields are generated after absorbing the massless would-be Goldstone bosons φ ± and χ.…”

“…This definition poses in general many problems, basically related to the gauge independence/invariance of the final answer [6]. The application of the PT in this context, has allowed for an unambiguous definition of such quantities, some representative SM examples being the magnetic dipole and electric quadrupole moments of the W [7], the top-quark magnetic moment [8], and the neutrino charge radius [9]. Most notably, the gauge independent, renormalization group invariant, and target independent SM neutrino charge radius constructed through the PT constitutes a genuine physical observable, since it can be extracted (at least in principle) from experiments [10].…”

Quantum properties of a cyclic structure based on tripolar fields

“…Thus, the laws of magnetism dictate that the electron must have some physical extent to have a magnetic moment. That is why modern quantum field theories do smear the charge of the physical electron over some extended region in order to renormalise the theory and produce finite results [17].…”