Abstract
We propose a new method to probe the magnetic and electric dipole moments of the $\tau$ lepton using precise measurements of the differential rates of radiative leptonic $\tau$ decays at high-luminosity $B$ factories. Possible deviations of these moments from the Standard Model values are analyzed in an effective Lagrangian approach, thus providing model-independent results. Analytic expressions for the relevant non-standard contributions to the differential decay rates are presented. Earlier proposals to probe the $\tau$ dipole moments are examined. A detailed feasibility study of our method is performed in the conditions of the Belle and Belle II experiments at the KEKB and Super-KEKB colliders, respectively. This study shows that our approach, applied to the planned full set of Belle II data for radiative leptonic $\tau$ decays, has the potential to improve the present experimental bound on the $\tau$ anomalous magnetic moment. On the contrary, its foreseen sensitivity is not expected to lower the current experimental limit on the $\tau$ electric dipole moment.
Highlights
JHEP03(2016)140 would be direct evidence of new physics
This study shows that our approach, applied to the planned full set of Belle II data for radiative leptonic τ decays, has the potential to improve the present experimental bound on the τ anomalous magnetic moment
We examine the feasibility of earlier proposals; in particular, one based on the study of the Pauli form factor of the τ via τ +τ − production in e+e− collisions at the Υ resonances [25, 26], and another relying on the analysis of the radiation zero which occurs in radiative leptonic τ decays [27]
Summary
Let us consider the structure of the f fγ coupling. The most general vertex function describing the interaction between a photon and the initial and final states of an arbitrary on-shell spin 1/2 fermion f , with four-momenta p and p , respectively, can be written in the form. The operator Q3lW3 in (2.5) generates an additional chirality-flipping coupling between the τ and the W boson, and a four-point vertex that couples the τ and the W to the photon or the Z (other four- and five-point vertices, involving the physical Higgs boson, will not be considered since they do not contribute to the τ dipole moments nor to the decays τ → lνν(γ)). These additional τ -W couplings at−iro(en√sp2rvbo/τpΛo=2r)tiso−inn(aθ2lW mtIτom/etC)h(l3e√W3 2c=vom/Λspi2nl)e2xsθiW npdθaτWra+RmeseiCtnel3θrW3WCc=l3oW3s and, to the real combinasin2θWaτ − sin θW cos θWaW τ and cτ = θWdW τ. We will neglect these new τ -W couplings
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