Lattice QCD study of the rare kaon decay K+→π+νν¯

Abstract

The rare kaon decay K + → π + νν is an ideal process in which to search for signs of new physics and is the primary goal of the NA62 experiment at CERN. In this paper we report on a lattice QCD calculation of the long-distance contribution to the K + → π + νν decay amplitude at the near-physical pion mass m π = 170 MeV. The calculations are however, performed on a coarse lattice and hence with a lighter charm quark mass (m MS c (3 GeV) = 750 MeV) than the physical one. The main aims of this study are two-fold. Firstly we study the momentum dependence of the amplitude and conclude that it is very mild so that a computation at physical masses even at a single kinematic point would provide a good estimate of the long-distance contribution to the decay rate. Secondly we compute the contribution to the branching ratio from the two-pion intermediate state whose energy is below the kaon mass and find that it is less than 1% after its exponentially growing unphysical contribution has been removed and that the corresponding non-exponential finite-volume effects are negligibly small.

Quark flavor physics and lattice QCD

“…However, long-distance effects could contribute to K + → π + νν at the 5-10% level. The NA62 experiment has just reported evidence for this decay at the 3.4σ level [140], and are reported to be aiming for a 10% measurement eventually [141]. It is timely for lattice QCD to determine these nonlocal contributions.…”

“…It is timely for lattice QCD to determine these nonlocal contributions. In their recent paper [141] have carried out a calculation with quark masses corresponding to nearly physical pion mass. They investigated several effects, such as momentum dependence, the contributions from disconnected diagrams, and their ability to control unphysical effects.…”

Towards a lattice determination of the form factors of the rare Hyperon decay $Σ^+ \to p \ell^+ \ell^-$

“…which can be obtained from 3-point functions with insertions of the e.m. current and weak Hamiltonian respectively. The 𝑁 𝜋 state can then be constructed in a similar manner to the 𝜋𝜋 state removal in [12]. In addition, there are finite volume corrections that stem from these same 𝑁 𝜋 intermediate state.…”

Access to the Kaon Radius with Kaonic Atoms

“…Associated studies could give access to the strangeness sector of quantum chromodynamics, [ 1 ] CP, [ 2,3 ] and lepton number violation, [ 4 ] properties of other particles, [ 5 ] they could allow to probe dark matter, [ 6 ] and would also help in other fields. [ 7,8 ] Despite their short lifetime of the order of 10 −8 s, negatively charged kaons can be captured by a nucleus and form a kaonic atom. Experimental studies of kaonic hydrogen and kaonic helium were performed lately by the SIDDHARTA collaboration at the DAΦNE collider at INFN‐LNF, testing kaon‐nucleon strong interaction.…”