CP asymmetry in the angular distributions of τ → KSπντ decays. Part II. General effective field theory analysis

Abstract

In this work, we proceed to study the CP asymmetry in the angular distributions of τ → KSπντ decays within a general effective field theory framework including four-fermion operators up to dimension-six. It is found that, besides the commonly considered scalar-vector interference, the tensor-scalar interference can also produce a non-zero CP asymmetry in the angular distributions, in the presence of complex couplings. Using the dispersive representations of the Kπ form factors as inputs, and taking into account the detector efficiencies of the Belle measurement, we firstly update our previous SM predictions for the CP asymmetries in the same four Kπ invariant-mass bins as set by the Belle collaboration. Bounds on the effective couplings of the non-standard scalar and tensor interactions are then obtained under the combined constraints from the CP asymmetries measured in the four bins and the branching ratio of τ−→ KSπ−ντ decay, with the numerical results given respectively by $$ \operatorname{Im}\left[{\hat{\upepsilon}}_S\right] $$ Im ϵ ̂ S = −0.008 ± 0.027 and $$ \operatorname{Im}\left[{\hat{\upepsilon}}_T\right] $$ Im ϵ ̂ T = 0.03 ± 0.12, at the renormalization scale μτ = 2 GeV in the $$ \overline{\mathrm{MS}} $$ MS ¯ scheme. Using the best-fit values, we also find that the distributions of the CP asymmetries can deviate significantly from the SM expectation in almost the whole Kπ invariant-mass region. Nevertheless, the current bounds on $$ \operatorname{Im}\left[{\hat{\upepsilon}}_S\right] $$ Im ϵ ̂ S and $$ \operatorname{Im}\left[{\hat{\upepsilon}}_T\right] $$ Im ϵ ̂ T are still plagued by large experimental uncertainties, but will be improved with more precise measurements from the Belle II experiment as well as the proposed Tera-Z and STCF facilities. Assuming further that the non-standard scalar and tensor interactions originate from a weakly-coupled heavy new physics well above the electroweak scale, the SU(2)L invariance of the resulting SMEFT Lagrangian would indicate that very strong limits on $$ \operatorname{Im}\left[{\hat{\upepsilon}}_S\right] $$ Im ϵ ̂ S and $$ \operatorname{Im}\left[{\hat{\upepsilon}}_T\right] $$ Im ϵ ̂ T could also be obtained from the neutron electric dipole moment and the $$ {D}^0-{\overline{D}}^0 $$ D 0 − D ¯ 0 mixing. With the bounds from these processes taken into account, it is then found that, unless there exist extraordinary cancellations between the new physics contributions, neither the scalar nor the tensor interaction can produce any significant effects on the CP asymmetries (relative to the SM predictions) in the processes considered, especially under the “single coefficient dominance” assumption.

Radiative corrections and new physics tests in semileptonic tau decays

“…NSI have been studied either in two-meson tau decays or using the inclusive (non-)strange tau decay width [41][42][43][61][62][63][64][65][66][67][68]. In particular, Ref.…”

Electromagnetic corrections in hadronic tau decays

“…Semileptonic tau decays are a valuable tool for studying QCD hadronization at low energies [1,2], as the τ lepton is the only known lepton that is heavy enough to decay into hadrons. With the high-precision measurements achieved in recent years [3][4][5][6][7][8][9][10], one-and two-meson decays of tau leptons have become increasingly useful for testing new physics scenarios [11][12][13][14][15][16][17][18][19][20][21][22][23]. To this end, it is crucial to account for radiative corrections in the theoretical predictions.…”

Triple-product asymmetry in the radiative two-pion tau decay

“…Up to now the CPV in the lepton sector is yet to be discovered, and its establishment will definitely extend our understanding of the CPV in particle physics. The charge-conjugate decay rate asymmetries in various channels are expected to provide promising opportunities to establish the CPV of the τ lepton [1][2][3][4][5][6]. Another distinct way to probe the CPV relies on the nontrivial kinematical measurements of the T-odd quantities.…”