Isospin-breaking corrections to light-meson leptonic decays from lattice simulations at physical quark masses

Abstract

The decreasing uncertainties in theoretical predictions and experimental measurements of several hadronic observables related to weak processes, which in many cases are now smaller than O(1%), require theoretical calculations to include subleading corrections that were neglected so far. Precise determinations of leptonic and semi-leptonic decay rates, including QED and strong isospin-breaking effects, can play a central role in solving the current tensions in the first-row unitarity of the CKM matrix. In this work we present the first RBC/UKQCD lattice calculation of the isospin-breaking corrections to the ratio of leptonic decay rates of kaons and pions into muons and neutrinos. The calculation is performed at fixed lattice spacing (a−1 ≃ 1.730 GeV) on a 483× 96 volume with Nf = 2 + 1 dynamical quarks close to the physical point and domain wall fermions in the Möbius formulation are employed. Long-distance QED interactions are included according to the QEDL prescription and the crucial role of finite-volume electromagnetic corrections in the determination of leptonic decay rates, which produce a large systematic uncertainty, is extensively discussed. Finally, we study the different sources of uncertainty on |Vus|/|Vud| and observe that, if finite-volume systematics can be reduced, the error from isospin-breaking corrections is potentially sub-dominant in the final precision of the ratio of the CKM matrix elements.

First results on QCD+QED with C* boundary conditions

“…[5,7,9,11,[13][14][15][16][17][18][19][20]. By now, a vast literature exists on numerical calculations that include electromagnetic effects to various hadronic observables, as in the case of hadron masses [3,6,15,[21][22][23][24][25][26][27][28][29][30][31][32][33], decay rates of light mesons [16,18,[34][35][36], the hadronic-vacuum-polarization contribution to the muon anomalous magnetic moment [20,22,[37][38][39][40][41][42][43].…”

Towards $K\pi$ scattering with domain-wall fermions at the physical point using distillation

“…The choice of fit range is done by a scan over the time extension with an acceptable signal-to-noise ratio. Then, using an AIC weighting of the correlated fits [24,25], we choose fit ranges yielding the results illustrated in Fig. 2, where we picked only levels with reasonable quality of fit.…”