Semileptonic Kaon Decay in Staggered Chiral Perturbation Theory

Abstract

The determination of $|V_{us}|$ from kaon semileptonic decays requires the value of the form factor $f_{+}(q^2=0)$, which can be calculated precisely on the lattice. We provide the one-loop partially quenched staggered chiral perturbation theory expressions that may be employed to analyze staggered simulations of $f_{+}(q^2)$ with three light flavors. We consider both the case of a mixed action, where the valence and sea sectors have different staggered actions, and the standard case where these actions are the same. The momentum transfer $q^2$ of the form factor is allowed to have an arbitrary value. We give results for the generic situation where the $u$, $d$, and $s$ quark masses are all different, $N_f=1+1+1$, and for the isospin limit, $N_f=2+1$. The expression we obtain for $f_{+}(q^2)$ is independent of the mass of the (valence) spectator quark. In the limit of vanishing lattice spacing, our results reduce to the one-loop continuum partially quenched expression for $f_{+}(q^2)$, which has not previously been reported in the literature for the $N_f=1+1+1$ case. Our expressions have already been used in staggered lattice analyses of $f_{+}(0)$, and should prove useful in future calculations as well.

33 pages, 5 figures; v2: some referencing changed

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Cited by in corpus (8)

• FLAG Review 2019
• FLAG Review 2021
• FLAG Review 2024
• $|V_{us}|$ from $K_{\ell 3}$ decay and four-flavor lattice QCD
• Nucleon Mass with Highly Improved Staggered Quarks
• Twisted finite-volume corrections to $K_{l3}$ decays with partially-quenched and rooted-staggered quarks
• K semileptonic form factor with HISQ fermions at the physical point
• Kaon semileptonic decays with $N_f=2+1+1$ HISQ fermions and physical light-quark masses