Exploratory lattice QCD study of the rare kaon decay K+→π+ννˉK^+\to\pi^+\nu\bar{\nu}

In Ref [1] we have presented the results of an exploratory lattice QCD computation of the long-distance contribution to the $K^+\to\pi^+\nu\bar{\nu}$ decay amplitude. In the present paper we describe the details of this calculation, which includes the implementation of a number of novel techniques. The $K^+\to\pi^+\nu\bar{\nu}$ decay amplitude is dominated by short-distance contributions which can be computed in perturbation theory with the only required non-perturbative input being the relatively well-known form factors of semileptonic kaon decays. The long-distance contributions, which are the target of this work, are expected to be of O(5%) in the branching ratio. Our study demonstrates the feasibility of lattice QCD computations of the $K^+\to\pi^+\nu\bar{\nu}$ decay amplitude, and in particular of the long-distance component. Though this calculation is performed on a small lattice ($16^3\times32$) and at unphysical pion, kaon and charm quark masses, $m_\pi=420$ MeV, $m_K=563$ MeV and m_c^{\overline{\mathrm{MS}}}(\mbox{2 GeV})=863 MeV, the techniques presented in this work can readily be applied to a future realistic calculation.Comment: 74 pages, 12 figure

The pion's electromagnetic form factor at small momentum transfer in full lattice QCD

We compute the electromagnetic form factor of a "pion" with mass m_pi=330MeV at low values of Q^2\equiv -q^2, where q is the momentum transfer. The computations are performed in a lattice simulation using an ensemble of the RBC/UKQCD collaboration's gauge configurations with Domain Wall Fermions and the Iwasaki gauge action with an inverse lattice spacing of 1.73(3)GeV. In order to be able to reach low momentum transfers we use partially twisted boundary conditions using the techniques we have developed and tested earlier. For the pion of mass 330MeV we find a charge radius given by _{330MeV}=0.354(31)fm^2 which, using NLO SU(2) chiral perturbation theory, extrapolates to a value of =0.418(31)fm^2 for a physical pion, in agreement with the experimentally determined result. We confirm that there is a significant reduction in computational cost when using propagators computed from a single time-slice stochastic source compared to using those with a point source; for m_pi=330MeV and volume (2.74fm)^3 we find the reduction is approximately a factor of 12.Comment: 20 pages, 3 figure

Calculation of the hadronic vacuum polarization contribution to the muon anomalous magnetic moment

We present a first-principles lattice QCD+QED calculation at physical pion mass of the leading-order hadronic vacuum polarization contribution to the muon anomalous magnetic moment. The total contribution of up, down, strange, and charm quarks including QED and strong isospin breaking effects is found to be $a_\mu^{\rm HVP~LO}=715.4(16.3)(9.2) \times 10^{-10}$, where the first error is statistical and the second is systematic. By supplementing lattice data for very short and long distances with experimental R-ratio data using the compilation of Ref. [1], we significantly improve the precision of our calculation and find $a_\mu^{\rm HVP~LO} = 692.5(1.4)(0.5)(0.7)(2.1) \times 10^{-10}$ with lattice statistical, lattice systematic, R-ratio statistical, and R-ratio systematic errors given separately. This is the currently most precise determination of the leading-order hadronic vacuum polarization contribution to the muon anomalous magnetic moment. In addition, we present the first lattice calculation of the light-quark QED correction at physical pion mass.Comment: 12 pages, 11 figure

B -> [pi]lv and Bs -> Klv form factors and Vub from 2+1- avor lattice QCD with domain-wall light quarks and relativistic heavy quarks

We calculate the form factors for B → πlν   and Bs → Klν decay in dynamical lattice quantum chromodynamics (QCD) using domain-wall light quarks and relativistic b-quarks. We use the (2+1)-flavor gauge-field ensembles generated by the RBC and UKQCD collaborations with the domain-wall fermion action and Iwasaki gauge action. For the b-quarks we use the anisotropic clover action with a relativistic heavy-quark interpretation. We analyze data at two lattice spacings of a ~ 0.11, 0.086 fm with unitary pion masses as light as Mπ ~ 290 MeV. We simultaneously extrapolate our numerical results to the physical light-quark masses and to the continuum and interpolate in the pion/kaon energy using SU(2) “hard-pion” chiral perturbation theory for heavy-light meson form factors. We provide complete systematic error budgets for the vector and scalar form factors f+(q2) and f0(q2) for both B → πlν and Bs → Klν at three momenta that span the q2 range accessible in our numerical simulations. Next we extrapolate these results to q2=0 using a model-independent z-parametrization based on analyticity and unitarity. We present our final results for f+(q2) and f0(q2) as the coefficients of the series in z and the matrix of correlations between them; this provides a parametrization of the form factors valid over the entire allowed kinematic range. Our results agree with other three-flavor lattice-QCD determinations using staggered light quarks, and have comparable precision, thereby providing important independent cross-checks. Both B → πlν and Bs → Klν decays enable determinations of the Cabibbo-Kobayashi-Maskawa matrix element |Vub|. To illustrate this, we perform a combined z-fit of our numerical B →  πlν form-factor data with the experimental measurements of the branching fraction from BABAR and Belle leaving the relative normalization as a free parameter; we obtain |Vub| = 3.61(32) × 10-3, where the error includes statistical and all systematic uncertainties. The same approach can be applied to the decay Bs → Klν to provide an alternative determination of |Vub| once the process has been measured experimentally. Finally, in anticipation of future experimental measurements, we make predictions for B → πlν and Bs → Klν differential branching fractions and forward-backward asymmetries in the Standard Model

K to π semileptonic form factor with 2+1 flavor domain wall fermions on the lattice

We present preliminary results from the RBC and UKQCD collaborations for the Kl3 form factor f0Kπ (0) = f+Kπ (0) with 2+1 flavours of dynamical domain wall quarks. Simulations are performed on 163×32×16 and 243×64×16 lattices with three values of the light quark mass, allowing for an extrapolation to the chiral limit