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

Peter Boyle, Matteo Di Carlo+11 more|arXiv (Cornell University)|Nov 23, 2022

Particle physics theoretical and experimental studies4 citations

TL;DR

This paper presents the first lattice QCD calculation of isospin-breaking corrections to light-meson leptonic decays at physical quark masses, using $N_f=2+1$ dynamical quarks and Möbius domain wall fermions. It finds that finite-volume electromagnetic corrections are a dominant systematic uncertainty, and that isospin-breaking effects are potentially sub-dominant in the precision of $|V_{\mathrm{us}}|/|V_{\mathrm{ud}}|$ if these systematics are controlled.

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 $\mathrm{O}(1\%)$, 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 with $N_\mathrm{f}=2+1$ 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 $\mathrm{QED_L}$ 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 $|V_\mathrm{us}|/|V_\mathrm{ud}|$ 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.

Motivation & Objective

• To compute isospin-breaking corrections to the ratio of leptonic decay rates of kaons and pions into muons and neutrinos with high precision.
• To address the growing tension in CKM matrix unitarity by including subleading QCD and QED effects in lattice calculations.
• To quantify the impact of finite-volume electromagnetic corrections, which are identified as a major source of systematic uncertainty.
• To assess whether isospin-breaking corrections will be sub-dominant in the final precision of $|V_{\mathrm{us}}|/|V_{\mathrm{ud}}|$ when other systematics are reduced.
• To provide an ab initio, first-principles lattice determination of $f_K/f_\pi$ corrections including electromagnetism and quark mass splitting at physical masses.

Proposed method

• Perform lattice QCD simulations with $N_f=2+1$ dynamical quarks at physical quark masses using Möbius domain wall fermions for exact chiral symmetry.
• Implement long-distance QED interactions via the $\mathrm{QED}_{\mathrm{L}}$ prescription to include electromagnetic corrections in the hadronic matrix elements.
• Use a genetic algorithm (GA) with AIC-weighted optimization to explore fit ranges for correlator analyses and estimate systematic uncertainties from fit selection.
• Cache and analyze results from multiple GA runs (GA 5-2000, GA 25-2000, GA 25-5000) to ensure convergence and robustness of the fit uncertainty estimation.
• Compute the leptonic decay rate ratio $\Gamma(K^\pm \to \mu^\pm \nu)/\Gamma(\pi^\pm \to \mu^\pm \nu)$ including virtual and real photon contributions to handle infrared divergences.
• Compare AIC-weighted histograms of $\delta R_{K\pi}^{\mathrm{latt}}$ from different GA setups to validate convergence and stability of systematic error estimates.

Experimental results

Research questions

• RQ1 What is the magnitude of isospin-breaking corrections to the ratio of kaon and pion leptonic decay rates at physical quark masses?
• RQ2 How do finite-volume electromagnetic corrections affect the precision of $|V_{\mathrm{us}}|/|V_{\mathrm{ud}}|$ in lattice QCD calculations?
• RQ3 Can ab initio lattice QCD calculations at physical quark masses reliably include QED and strong isospin-breaking effects without relying on chiral perturbation theory?
• RQ4 To what extent are isospin-breaking corrections sub-dominant in the total uncertainty of $|V_{\mathrm{us}}|/|V_{\mathrm{ud}}|$ when finite-volume effects are controlled?
• RQ5 How robust are the systematic uncertainties from fit range selection in the lattice correlator analysis, and can they be reliably estimated using genetic algorithms?

Key findings

• This is the first lattice QCD calculation of isospin-breaking corrections to $f_K/f_\pi$ at physical quark masses, including both QED and quark mass splitting effects.
• Finite-volume electromagnetic corrections are identified as a dominant source of systematic uncertainty in the determination of leptonic decay rates.
• The genetic algorithm-based fit uncertainty estimation shows convergence, with GA 25-5000 producing stable and representative results for $\delta R_{K\pi}^{\mathrm{latt}}$.
• AIC-weighted histograms from top fits in GA 25-2000 and GA 25-5000 setups show consistent medians and systematic spreads, indicating robustness of the uncertainty estimation.
• The study concludes that if finite-volume systematics are reduced, isospin-breaking corrections are potentially sub-dominant in the final precision of $|V_{\mathrm{us}}|/|V_{\mathrm{ud}}|$.
• The inclusion of long-distance QED interactions via the $\mathrm{QED}_{\mathrm{L}}$ prescription enables a consistent treatment of infrared divergences in leptonic decay amplitudes.