Massive vectors and loop observables: the g − 2 case

Carla Biggio,Luca Di Luzio,Marzia Bordone,Giovanni Ridolfi

doi:10.1007/jhep10(2016)002

Carla Biggio, Luca Di Luzio + Show 2 more

Open Access

https://doi.org/10.1007/jhep10(2016)002

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Abstract

We discuss the use of massive vectors for the interpretation of some recent experimental anomalies, with special attention to the muon $g-2$. We restrict our discussion to the case where the massive vector is embedded into a spontaneously broken gauge symmetry, so that the predictions are not affected by the choice of an arbitrary energy cut-off. Extended gauge symmetries, however, typically impose strong constraints on the mass of the new vector boson and for the muon $g-2$ they basically rule out, barring the case of abelian gauge extensions, the explanation of the discrepancy in terms of a single vector extension of the standard model. We finally comment on the use of massive vectors for $B$-meson decay and di-photon anomalies.

Highlights

Irrep is conceptually straightforward, being the SM extension automatically renormalizable and well-behaved in the ultraviolet (UV), the one of a generic Lorentz vector is less obvious and will be the subject of the present paper
We restrict our discussion to the case where the massive vector is embedded into a spontaneously broken gauge symmetry, so that the predictions are not affected by the choice of an arbitrary energy cut-off
After a brief review of the (g − 2)μ discrepancy in section 2, we discuss in section 3 the most general d ≤ 4 Lagrangian of a massive vector coupled to the SM, and show the divergence structure of the one-loop diagrams

Summary

Lagrangian of a massive vector

Before performing the actual (g − 2)μ calculation, we discuss the Lagrangian of the new vector boson, which is assumed to transform under a complex irrep of the SM gauge group. Where QX is the electric charge of X in units of the proton charge e This is enough to make the Lagrangian of eq (3.1) invariant upon local gauge transformations. It can be shown [22] that for β = 1 the above Lagrangian describes the free propagation of a massive spin 1 particle. It is easy to see that there exist extra gauge invariant terms not related to the minimal coupling. A complete classification of SM gauge invariant d ≤ 4 operators involving X and SM fields is given in appendix A, and the most general EFT should contain them all

Divergence structure of one-loop diagrams

Unitary gauge calculation

Discussion and conclusions