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

Motivated by the 2.86 discrepancy observed between the BABAR measurement and the standard model prediction of the CP asymmetry in tau -> K-S pi nu(tau), decays, as well as the prospects of future measurements at Belle II, we revisit this observable in this paper. Firstly, we reproduce the known CP asymmetry due to K-0 - (K) over bar (0) mixing by means of the reciprocal basis, which is convenient when a K-S(L) is involved in the final state. As the K pi tensor form factor plays a crucial role in generating a nonzero 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 tau -> K-S pi nu(tau) 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 1 sigma level, together with the constraint from the branching ratio of tau(-) -> K-S pi(-)nu(tau) decay; it can be, however, marginally reconciled only at the 2 sigma level, due to the specific relation between the scalar and tensor operators in the scalar leptoquark scenario. Once the combined constraints from the branching ratio and the decay spectrum of this decay arc taken into account, these possibilities are, however, both excluded, even without exploiting further the stronger bounds from the (semi)leptonic kaon decays under the assumption of lepton-flavor universality, as well as from the neutron electric dipole moment and D - (D) over bar mixing under the assumption of SU(2) invariance of the weak interactions.