Bounds on Lorentz-violating Yukawa couplings via lepton electromagnetic moments

Abstract

The effective-Lagrangian description of Lorentz-invariance violation provided by the so-called Standard-Model Extension covers all the sectors of the Standard Model, allowing for modelindependent studies of high-energy phenomena that might leave traces at relatively-low energies. In this context, the quantification of the large set of parameters characterizing Lorentz-violating effects is well motivated. In the present work, effects from the Lorentz-nonconserving Yukawa sector on the electromagnetic moments of charged leptons are calculated, estimated, and discussed. Following a perturbative approach, explicit expressions of leading contributions are derived and upper bounds on Lorentz violation are estimated from current data on electromagnetic moments. Scenarios regarding the coefficients of Lorentz violation are considered. In a scenario of two-point insertions preserving lepton flavor, the bound on the electron electric dipole moment yields limits as stringent as 10 −28 , whereas muon and tau-lepton electromagnetic moments determine bounds as restrictive as 10 −14 and 10 −6 , respectively. Another scenario, defined by the assumption that Lorentz-violating Yukawa couplings are Hermitian, leads to less stringent bounds, provided by the muon anomalous magnetic moment, which turn out to be as restrictive as 10 −14 .

Vacuum polarization in Yang-Mills theories with Lorentz violation

“…The ingredient in our result that is not common to conventional field theories is the presence of IR divergences. As it was commented in the introduction, IR divergences in the context of the mSME also arise in physical quantities as anomalous magnetic moments [26]. The presence of this type of divergences in physical observables seems to be an undesirable characteristic of the mSME, which will require the implementation of complicated cancelation mechanisms [26].…”

“…On the other hand, to consider effects on SM observables, that is, observables that are invariant under both observer and particle Lorentz transformations, it is necessary to include second-order effects in the T µ1µ2••• coefficients. It is expected that first-order effects of T µ1µ2••• impact experiments designed to detect Lorentz violation, such as those aforementioned, but second-order effects of these coefficients can, in addition, contribute to SM observables, such as the static electromagnetic properties of elementary particles [25][26][27]. For instance, in the mSME the electromagnetic f f γ vertex, with f stands for a lepton or quark, can develop at the one-loop level new electromagnetic structures proportional to the T µ1µ2••• coefficients [25] and new contributions that modify the usual ones if second order effects of the form [26,27].…”

“…It is expected that first-order effects of T µ1µ2••• impact experiments designed to detect Lorentz violation, such as those aforementioned, but second-order effects of these coefficients can, in addition, contribute to SM observables, such as the static electromagnetic properties of elementary particles [25][26][27]. For instance, in the mSME the electromagnetic f f γ vertex, with f stands for a lepton or quark, can develop at the one-loop level new electromagnetic structures proportional to the T µ1µ2••• coefficients [25] and new contributions that modify the usual ones if second order effects of the form [26,27]. Although these quantities do not carry information on spatial directions or relative motion, they can provide useful information about the importance of LV effects when constrained from high precision experiments, such as, for example, magnetic and electric dipole moments of charged leptons and nucleons.…”

“…Although these quantities do not carry information on spatial directions or relative motion, they can provide useful information about the importance of LV effects when constrained from high precision experiments, such as, for example, magnetic and electric dipole moments of charged leptons and nucleons. In particular, bounding these effects is particulary useful in cases of antisymmetric 2-tensors T µν = −T νµ , since this types of objects are made of two spatial e and b vectors and thus bounds for |e| and |b| can be derived [26]. As we will see later, the study of second-order effects is valuable in itself since it can shed light on the very structure of the theory.…”

“…It is a well-known fact that in the SM (and in any Lorentz-invariant QFT) the anomalous magnetic moment of a spin-1 2 charged particle is a one-loop prediction that is free of both ultraviolet (UV) divergences and infrared (IR) divergences, that is, it is a physical observable. However, it has been shown in [26] that LV induces contributions to the anomalous magnetic moments of leptons and quarks that are not free of IR divergences, showing that these quantities are no longer observable. We think that this type of result constitute a strong incentive to study one-loop LV effects on standard observables (in the sense that they are invariant under both observer and particle Lorentz transformations) beyond the first order in the T µ1µ2••• coefficients.…”