Lattice QCD calculation of $K\to \ellν_\ell \ell'^+ \ell'^-$ decay width

Abstract

We develop a methodology for the computation of the K → ν + − decay width using lattice QCD and present an exploratory study here. We use a scalar function method to account for the momentum dependence of the decay amplitude and adopt the infinite volume reconstruction (IVR) method to reduce the systematic errors such as the temporal truncation effects and the finitevolume effects. We then perform a four-body phase-space integral to obtain the decay width. The only remaining technical problem is the possible power-law finite-volume effects associated with the process of K → ππ ν → ν + − , where the intermediate state involves multiple hadrons. In this work, we use a gauge ensemble of twisted mass fermion with a pion mass m π = 352 MeV and a nearly-physical kaon mass. At this kinematics, the ππ in the intermediate state cannot be on shell simultaneously as 2m π > m K and the finite-volume effects associate with ππ state are exponentially suppressed. Using the developed methods mentioned above, we calculate the branching ratios for four channels of K → ν + − , and obtain the results close to the experimental measurements and ChPT predictions. Our work demonstrates the capability of lattice QCD to improve Standard Model prediction in K → ν + − decay width.

Virtual Photon Emission in Leptonic Decays of Charged Pseudoscalar Mesons

“…In our computation and also that in Ref. [13], the kaon mass is smaller that twice the pion mass, m K < 2m π , so that there are no contributions of the form K → ππ ν → ν γ, with an on-shell ππ ν intermediate state. With physical quark masses, contributions with such an intermediate state are present in the region of phase space in which k 2 > 4m 2 π , where k is the four-momentum of the virtual photon.…”

“…For kaon decays, in addition to the lattice results from the computations reported here and in Ref. [13], theoretical information about the form factors comes from Chiral Perturbation Theory (ChPT), which has been used at next-toleading order (NLO) to estimate their values and their contribution to the branching ratios [17]. It is worth noting that at NLO order in ChPT the form factors are constants, i.e.…”

“…Using these form factors one can reconstruct separately all the contributions to the branching ratios; the point-like contribution, the SD one and that coming from the interference between the two. There has been one previous lattice study of these decays, in which a method was presented and implemented to compute the branching ratio for the decays K → ν + − without separating the point-like contribution and determining the SD form factors themselves [13]. The exploratory computations in Ref.…”

“…The exploratory computations in Ref. [13] were performed on a single gauge ensemble on a 24 3 × 48 lattice with a 0.093 fm and with quark masses corresponding to m π 352 MeV and m K 506 MeV.…”

Lattice QCD Calculation of the Pion Mass Splitting

“…[28], which allows us to calculate electromagnetic corrections to stable hadron masses with only exponentially suppressed finite-volume effects. Upon its development, this method has been successfully applied and extended to various electroweak processes involving photon or massless leptonic propagators [18,[29][30][31][32]. This is the first time that we apply this methodology to the calculation of the pion mass splitting.…”