Progress in the exploratory calculation of the rare kaon decays $K\to\pi\ell^+\ell^-$

Abstract

The rare decays of a kaon into a pion and a lepton/antilepton pair proceed via a flavour changing neutral current and therefore first arise in the Standard Model only as a second order electroweak interaction. This natural suppression makes these decays sensitive to the effects of potential New Physics. However the rare decay channels K + → π + + − are dominated by long-distance contributions, where the two electroweak processes are separated by distances over which nonperturbative QCD effects play a significant role. In this talk I provide an update on the progress of our exploratory calculations of the long-distance contributions to K + → π + + − amplitudes, which make use of the Domain Wall Fermion ensembles of the RBC and UKQCD collaborations, and outline the prospects for further progress of the calculation.

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

“…This being done on an unphysical ensemble in preparation for a later physical point computation. It is possible to use similar methods to those used in the computation of the rare Kaon decay [8][9][10][11], however there are additional techniques that could be used to improve the signal and reduce the cost of the computation. One potential technique is the use of the summed method generalised to two distinct operator insertions and arbitrary initial and final states.…”

“…Since the rare Hyperon decay is a baryonic equivalent to the rare Kaon decay [8][9][10][11], its computation can proceed via similar methods. This involves fixing the source-sink separation Δ𝑡 and the e.m. current at time 𝑡 𝐽 , and integrating the weak Hamiltonian in a window around this current…”

Progress on the exploratory calculation of the rare Hyperon decay $\Sigma^+ \to p \ell^+ \ell^-$

“…This process has been discussed in the case of the rare Kaon decay 𝐾 → 𝜋ℓ + ℓ − previously in refs. [1][2][3][4], but due to the additional spin degree of freedom of the baryons, the weak Hamiltonian matrix element has two form factors (unlike the rare Kaon decay that has only one)…”

“…Due to this suppressed SM background, new physics can have large relative effects. One example of this is the rare Hyperon decay, Σ + → 𝑝ℓ + ℓ − , which is the topic of these proceedings, and the similar rare Kaon decay 𝐾 + → 𝜋 + ℓ + ℓ − [1][2][3][4] which has seen recent progress with a physical point lattice QCD calculation [5].…”

Lattice QCD study of the rare kaon decay K+→π+νν¯Christ1, Feng2, Portelli3 et al. 2019Phys. Rev. DSelf Cite210120View full textAdd to dashboardCite

“…Since the LD contributions to K L → π 0 νν decays are negligible, we do not discuss these decays further in this paper. This paper is the latest in a series of lattice QCD studies of the rare kaon decays K → π + − and K → πνν, in which we have developed the theoretical framework and performed exploratory numerical calculations [13][14][15][16][17][18][19][20][21][22][23][24]. Here we focus on the LD contributions to the K + → π + νν decay amplitude.…”