Comparison of lattice QCD+QED predictions for radiative leptonic decays of light mesons with experimental data

Abstract

We present a comparison of existing experimental data for the radiative leptonic decays P → ν γ, where P = K or π and = e or µ, from the KLOE, PIBETA, E787, ISTRA+ and OKA collaborations with theoretical predictions based on the recent non-perturbative determinations of the structure-dependent vector and axial-vector form factors, F V and F A respectively. These were obtained using lattice QCD+QED simulations at order O(α em ) in the electromagnetic coupling. We find good agreement with the KLOE data on K → eν e γ decays from which the form factor F + = F V + F A can be determined. For K → µν µ γ decays we observe differences of up to 3 -4 standard deviations at large photon energies between the theoretical predictions and the data from the E787, ISTRA+ and OKA experiments and similar discrepancies in some kinematical regions with the PIBETA experiment on radiative pion decays. A global study of all the kaon-decay data within the Standard Model results in a poor fit, largely because at large photon energies the KLOE and E787 data cannot be reproduced simultaneously in terms of the same form factor F + . The discrepancy between the theoretical and experimental values of the form factor F − = F V − F A is even more pronounced. These observations motivate future improvements of both the theoretical and experimental determinations of the structure-dependent form factors F + and F − , as well as further theoretical investigations of models of "new physics" which might for example, include possible flavor changing interactions beyond V − A and/or non-universal corrections to the lepton couplings.

Lattice QCD calculation of $K\to \ellν_\ell \ell'^+ \ell'^-$ decay width

“…Besides, other processes involving both weak and electromagnetic interactions, e.g. the radiative corrections to the leptonic and semileptonic decays, have also been investigated recently [14][15][16][17][18][19][20][21]. It is interesting to have the lattice QCD study extend its horizon to include the K → ν + − decay, where the final state involves four daughter particles.…”

Isospin Breaking in Lattice QCD Computations of Decay Amplitudes

“…Since the corresponding experimental rates are fully inclusive in the energy of the final state photon, structure-dependent contributions to the real photon emission should be included, however the Chiral Perturbation Theory (ChPT) predictions of Ref. [35] indicate that these structure-dependent contributions are negligible for both kaon and pion decays into muons, an expectation explicitly verified in a recent lattice computation [32], where the structure dependent contributions to Γ 1 were shown to be negligible. The same is not true to the same extent for decays into final-state electrons (see Ref.…”

“…( 35)). The most recent development has been the calculation of the radiative decays P → ν γ for light and charmed mesons, and a phenomenological comparison of our results with those from experimental measurements [30,32].…”

“…While this is practicable for the decays of pions and kaons, particularly into muons for which the rate for large E γ is suppressed [15], this is not the case for the decays of heavy mesons. More recently we have demonstrated that the structure-dependent contributions to Γ 1 can be calculated [30,32], thus extending the framework to the decays of heavy mesons.…”

QCD factorization for the four-body leptonic $B$-meson decays

“…We will therefore employ the potentialsubtracted (PS) renormalization scheme for the bottom-quark mass [71] and then convert the obtained expressions of the hard functions from the pole scheme to the PS scheme for the mass parameter accordingly (see [72] for an overview of the leading renormalon-free and short-distance mass definitions for nearly on-shell heavy quarks). Another important hadronic quantity governing the factorized result for the four-body rare B-meson decay amplitude in the entire kinematic region is the leptonic decay constant of the charged bottom-meson f Bu , whose interval collected in Table 1 is borrowed from the lattice-QCD computation with the number of dynamical quark flavours N f = 2 + 1 + 1 in the isospin symmetry limit [24] (see [73] for the further discussion on the strong-isospin violating effect and [74][75][76] on the technical strategies to address the more complicated electromagnetic correction).…”