$K_{\ell 3}$ form factors at the physical point towards the continuum limit

Abstract

We present updated results for the form factors of the kaon semileptonic (K ℓ3 ) decay process calculated with N f = 2 + 1 nonperturbatively O(a)-improved Wilson quark action and Iwasaki gauge action at the physical point on large volumes of more than (10 fm) 4 . In addition to our previous calculation at the lattice spacing a = 0.085 fm, we perform a calculation at the second lattice spacing of 0.063 fm. Using the results for the form factors extracted from 3-point functions with the local and also conserved vector currents at the two lattice spacings, continuum extrapolation and interpolation of the momentum transfer are carried out simultaneously to obtain the value of the form factor f + (0) at the zero momentum transfer in the continuum limit. After investigation of stability of f + (0) against several fit forms and different data, we obtain f + (0) = 0.9615(10)( +47 −2 )( 5), where the first, second, and third errors are statistical, systematic errors from choice of the fit forms and isospin breaking effect, respectively. Furthermore, we obtain the slope and curvature of the form factors, and the phase space integral from the momentum transfer dependence of the form factors. Combining our value of f + (0) and experimental input of the K ℓ3 decay, one of the Cabibbo-Kobayashi-Maskawa matrix elements |V us | is determined as |V us | = 0.2252( +5 −12 ), whose error contains the experimental one as well as that in the lattice calculation. This value is reasonably consistent with the ones determined from recent lattice QCD results of f + (0) and also the one determined through the kaon leptonic decay process. We observe some tension between our value and |V us | evaluated from the unitarity of the CKM matrix with |V ud |, while it depends on the size of the error of |V ud |. It is also found that |V us | determined with our phase space integrals through six K ℓ3 decay processes is consistent with the above one using f + (0).

(Semi)leptonic kaon decays and neutral kaon mixing from lattice QCD

“…1 leading to the average f + (0) = 0.9698 (17) for N f = 2+1+1 and 0.9677(27) for N f = 2+1. Recently, a new study for N f = 2 + 1 became available by the PACS collaboration [11]. Its characteric feature is that they simulate the physical pion mass on a large lattice volume of (10 fm) 3 leading to good control of the chiral extrapolation and finite volume effects.…”