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High Energy Physics - Lattice

Title: Semileptonic Kaon Decay in Staggered Chiral Perturbation Theory

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.
Comments: 33 pages, 5 figures; v2: some referencing changed
Subjects: High Energy Physics - Lattice (hep-lat); High Energy Physics - Phenomenology (hep-ph)
Cite as: arXiv:1311.7511 [hep-lat]
  (or arXiv:1311.7511v2 [hep-lat] for this version)

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)