We report the first calculation using physical light-quark masses of the electromagnetic form factor $V(z)$ describing the long-distance contributions to the ${K}^{+}\ensuremath{\rightarrow}{\ensuremath{\pi}}^{+}{\ensuremath{\ell}}^{+}{\ensuremath{\ell}}^{\ensuremath{-}}$ decay amplitude. The calculation is performed on a $2+1$ flavor domain wall fermion ensemble with inverse lattice spacing ${a}^{\ensuremath{-}1}=1.730(4)\text{ }\text{ }\mathrm{GeV}$. We implement a Glashow-Iliopoulos-Maiani cancellation by extrapolating to the physical charm-quark mass from three below-charm masses. We obtain $V(z=0.013(2))=\ensuremath{-}0.87(4.44)$, achieving a bound for the value. The large statistical error arises from stochastically estimated quark loops. 

Simulating rare kaon decays 
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msup><mml:mi>K</mml:mi><mml:mo>+</mml:mo></mml:msup><mml:mo stretchy="false">→</mml:mo><mml:msup><mml:mi>π</mml:mi><mml:mo>+</mml:mo></mml:msup><mml:msup><mml:mo>ℓ</mml:mo><mml:mo>+</mml:mo></

Abstract Kaon physics is at a turning point – while the rare-kaon experiments NA62 and KOTO are in full swing, the end of their lifetime is approaching and the future experimental landscape needs to be defined. With HIKE, KOTO-II and LHCb-Phase-II on the table and under scrutiny, it is a very good moment in time to take stock and contemplate about the opportunities these experiments and theoretical developments provide for particle physics in the coming decade and beyond. This paper provides a compact summary of talks and discussions from the Kaons@CERN 2023 workshop, held in September 2023 at CERN. 

Workshop summary: Kaons@CERN 2023

Kaon physics is at a turning point -- while the rare-kaon experiments NA62 and KOTO are in full swing, the end of their lifetime is approaching and the future experimental landscape needs to be defined. With HIKE, KOTO-II and LHCb-Phase-II on the table and under scrutiny, it is a very good moment in time to take stock and contemplate about the opportunities these experiments and theoretical developments provide for particle physics in the coming decade and beyond. This paper provides a compact summary of talks and discussions from the Kaons@CERN 2023 workshop. 

Workshop summary -- Kaons@CERN 2023

This is an overview of quark flavor physics as presented in a plenary talk at Lattice 2023. In the first part, I discuss the main processes and lattice-QCD inputs used to determine the Wolfenstein parameters of the Cabibbo-Kobayashi-Maskawa matrix. In the second part, I review selected further processes that are being used to search for physics beyond the Standard Model. New results presented at Lattice 2023 are referenced throughout, but detailed discussions are limited to selected work published prior to the conference. QED corrections, inclusive decays on the lattice, and processes involving hadronic resonances are not discussed in detail here, as they were covered in other plenary talks at Lattice 2023 and Lattice 2022.

Quark flavor physics with lattice QCD

The NA62 experiment at CERN collected the world's largest data set of charged kaon decays in 2016-2018, leading to the most precise measurement of the branching fraction of the ultra-rare K+→π+νν‾ decay, based on 20 candidates. This provides evidence for the observation of the K+→π+νν‾ decay with a significance of 3.4σ. This measurement is also used to set limits on B(K+→π+X), where X is a scalar or pseudo-scalar particle. The analysis of the full 2016-2018 data sample is reviewed. More recent results from NA62 analyses of K+→π0e+νγ, K+→π+μ+μ− and K+→π+γγ decays, using data samples recorded in 2017–2018, are also reported. The radiative kaon decay K+→π0e+νγ (Ke3γ) is studied with a data sample of O(100k) Ke3γ candidates with sub-percent background contamination. Final results of the most precise measurements of the Ke3γ branching ratios and T-asymmetry are presented. The K+→π+μ+μ− sample comprises about 27k signal events with negligible background contamination, and the results presented include the most precise determination of the branching fraction and the decay form factor. The K+→π+γγ sample contains about 4k signal events with 10% background contamination, and the preliminary analysis results improve the precision of the branching fraction measurement by a factor of 3 with respect to previous measurements. An overview of the latest NA62 results and future prospects for the experiment is presented. 

Recent results from the NA62 experiment at CERN

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