### References & Citations

# High Energy Physics - Lattice

# Title: Semileptonic Kaon Decay in Staggered Chiral Perturbation Theory

(Submitted on 29 Nov 2013 (v1), last revised 8 Dec 2013 (this version, v2))

Abstract: The determination of $\vert V_{us}\vert$ 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.

## Submission history

From: Elvira Gamiz [view email]**[v1]**Fri, 29 Nov 2013 10:10:32 GMT (68kb,D)

**[v2]**Sun, 8 Dec 2013 16:24:22 GMT (68kb,D)