CP asymmetry in τ→KSπντ decays within the standard model and beyond

Abstract

This work aims to explore the 2.8σ discrepancy observed between the BaBar measurement and the Standard Model prediction of the CP asymmetry in τ → K S πν τ decays. Firstly, we reproduce the known CP asymmetry due to K 0 −K 0 mixing by means of the reciprocal basis, which is convenient when a K S(L) is involved in the final state. As the Kπ tensor form factor plays a crucial role in generating an extra direct CP asymmetry that can arise only from the interference of vector and tensor operators, we then present a dispersive representation of this form factor, with its phase obtained in the context of chiral theory with resonances, which fulfills the requirements of unitarity and analyticity. Finally, the τ → K S πν τ decays are analyzed both within a model-independent low-energy effective theory framework and in a scalar leptoquark scenario. It is observed that the CP anomaly can be accommodated in the model-independent framework, even at the 1σ level, together with the constraint from the branching ratio of this decay; it can be, however, marginally reconciled only at the 2σ level, due to the specific relation between the scalar and tensor operators in the scalar leptoquark scenario.

Lepton-flavour violation in hadronic tau decays and μ-τ conversion in nuclei

“…The value of Λ 2 has been determined in ref. [87]: Λ 2 = (11.1 ± 0.4) MeV (see also [88]). If we assume resonance saturation, we can, in fact, use this relation to get a value for the coupling…”

CP asymmetry in the angular distribution of τ → KSπντ decays

“…Here we shall investigate for the first time whether an observable CP asymmetry in the angular distribution of τ → K S πν τ decays could be generated by the well-measured CP violation in K 0 −K 0 mixing. To this end, we shall employ the reciprocal basis [40][41][42][43][44][45], which is most convenient when a K S(L) is involved in the final state and has been used to reproduce conveniently the decay-rate asymmetry [33]. It is then found that a non-zero CP asymmetry would appear in the angular observable of the decays considered, even within the SM.…”

“…While the formalism of the former is quite clear [43], a precise description of the latter requires information about the Kπ vector and scalar form factors, including both their moduli and phases. As the form-factor phases fitted via a superposition of Breit-Wigner functions with complex coefficients do not vanish at threshold and violate Watson's final-state interaction theorem before the higher resonances start to play an effect [31][32][33], we cannot rely on the formalism developed in refs. [46][47][48][49] the CP asymmetry in τ → K S πν τ decays.…”

“…Within the SM, this asymmetry is predicted to be non-zero [23][24][25], due to the CP violation in K 0 −K 0 mixing [1,26], but is found to be 2.8 σ away from the BaBar measurement [22]. Such a discrepancy has motivated many studies of possible direct CP asymmetries in τ → K S πν τ decays induced by non-standard tensor interactions [27][28][29][30][31][32][33], finding that such a large asymmetry cannot be explained by a tensor coupling under the combined constraints from other observables [31][32][33]. With the integrated luminosity of the data sample increased, it is expected that measurements of CP -violating effects in hadronic τ decays will be improved at the Belle II experiment [34].…”

Effective-field theory analysis of the τ−→K−(η(′),K0<

“…Several recent works [16][17][18][19][20] have put forward that semileptonic tau decays offer also an interesting scenario to set bounds on nonstandard weak charged current interactions complementary to other low-energy semileptonic probes considered before, such as nuclear beta decays, purely leptonic lepton, pion, and kaon decays or hyperon decays (see, e.g., Refs. [21][22][23][24][25][26][27][28][29][30][31]).…”