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arXiv · 1904.08731

Light-meson leptonic decay rates in lattice QCD+QED

M. Di Carlo·D. Giusti·V. Lubicz·G. Martinelli·C. T. Sachrajda·F. Sanfilippo·S. Simula·N. Tantalo
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Abstract

The leading electromagnetic (e.m.) and strong isospin-breaking corrections to the $π^+ \to μ^+ ν[γ]$ and $K^+ \to μ^+ ν[γ]$ leptonic decay rates are evaluated for the first time on the lattice. The results are obtained using gauge ensembles produced by the European Twisted Mass Collaboration with $N_f = 2 + 1 + 1$ dynamical quarks. The relative leading-order e.m.~and strong isospin-breaking corrections to the decay rates are 1.53(19)\% for $π_{μ2}$ decays and 0.24(10)\% for $K_{μ2}$ decays. Using the experimental values of the $π_{μ2}$ and $K_{μ2}$ decay rates and updated lattice QCD results for the pion and kaon decay constants in isosymmetric QCD, we find that the Cabibbo-Kobayashi-Maskawa matrix element $ | V_{us}| = 0.22538(46)$, reducing by a factor of about $1.8$ the corresponding uncertainty in the Particle Data Group review. Our calculation of $|V_{us}|$ allows also an accurate determination of the first-row CKM unitarity relation $| V_{ud}|^2 + | V_{us}|^2 + | V_{ub}|^2 = 0.99988(46)$. Theoretical developments in this paper include a detailed discussion of how QCD can be defined in the full QCD+QED theory and an improved renormalisation procedure in which the bare lattice operators are renormalised non-perturbatively into the (modified) Regularization Independent Momentum subtraction scheme and subsequently matched perturbatively at $O(α_{em}α_s(M_W))$ into the W-regularisation scheme appropriate for these calculations.

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M. Di Carlo, D. Giusti, V. Lubicz, G. Martinelli, C. T. Sachrajda, F. Sanfilippo, S. Simula, N. Tantalo. 2019-10-24. Light-meson leptonic decay rates in lattice QCD+QED. https://doi.org/10.1103/physrevd.100.034514

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