Present status of radiative and rare kaon decays

I will review recent developments in rare and radiative kaon decays from the theory side, with emphasis on those modes that are actively analyzed by the experimental collaborations.

Direct CP violation and the ΔI = 1/2 rule in K → ππ decay in the Standard Model

We discuss the RBC & UKQCD collaborations’ recent [1] lattice calculation of ϵ′, the measure of direct CP-violation in kaon decays. This result significantly improves on our previous 2015 calculation, with nearly 4× the statistics and more reliable systematic error estimates. We discuss how our results demonstrate the Standard Model origin of the ΔI = 1/2 rule, and present our plans for future calculations.

Improved Ke3 radiative corrections sharpen the Kμ2–Kl3 discrepancy

The measurements of Vus in leptonic (Kμ2) and semileptonic (Kl3) kaon decays exhibit a 3σ disagreement, which could originate either from physics beyond the Standard Model or some large unidentified Standard Model systematic effects. Clarifying this issue requires a careful examination of all existing Standard Model inputs. Making use of a newly-proposed computational framework and the most recent lattice QCD results, we perform a comprehensive re-analysis of the electroweak radiative corrections to the Ke3 decay rates that achieves an unprecedented level of precision of 10−4, which improves the current best results by almost an order of magnitude. No large systematic effects are found, which suggests that the electroweak radiative corrections should be removed from the “list of culprits” responsible for the Kμ2–Kl3 discrepancy.

Are the CKM anomalies induced by vector-like quarks? Limits from flavor changing and Standard Model precision tests

Recent high precision determinations of Vus and Vud indicate towards anomalies in the first row of the CKM matrix. Namely, determination of Vud from beta decays and of Vus from kaon decays imply a violation of first row unitarity at about 3σ level. Moreover, there is tension between determinations of Vus obtained from leptonic Kμ2 and semileptonic Kℓ3 kaon decays. These discrepancies can be explained if there exist extra vector-like quarks at the TeV scale, which have large enough mixings with the lighter quarks. In particular, extra vector-like weak singlets quarks can be thought as a solution to the CKM unitarity problem and an extra vector-like weak doublet can in principle resolve all tensions. The implications of this kind of mixings are examined against the flavour changing phenomena and SM precision tests. We consider separately the effects of an extra down-type isosinglet, up-type isosinglet and an isodoublet containing extra quarks of both up and down type, and determine available parameter spaces for each case. We find that the experimental constraints on flavor changing phenomena become more stringent with larger masses, so that the extra species should have masses no more than few TeV. Moreover, only one type of extra multiplet cannot entirely explain all the discrepancies, and some their combination is required, e.g. two species of isodoublet, or one isodoublet and one (up or down type) isosinglet. We show that these scenarios are testable with future experiments. Namely, if extra vector-like quarks are responsible for CKM anomalies, then at least one of them should be found at scale of few TeV, and anomalous weak isospin violating Z-boson couplings with light quarks should be detected if the experimental precision on Z hadronic decay rate is improved by a factor of 2 or so.

SU(3) analysis of four-quark operators: K → ππ and vacuum matrix elements

Hadronic matrix elements of local four-quark operators play a central role in non-leptonic kaon decays, while vacuum matrix elements involving the same kind of operators appear in inclusive dispersion relations, such as those relevant in τ-decay analyses. Using an SU(3)L ⊗ SU(3)R decomposition of the operators, we derive generic relations between these matrix elements, extending well-known results that link observables in the two different sectors. Two relevant phenomenological applications are presented. First, we determine the electroweak-penguin contribution to the kaon CP-violating ratio ε′/ε, using the measured hadronic spectral functions in τ decay. Second, we fit our SU(3) dynamical parameters to the most recent lattice data on K → ππ matrix elements. The comparison of this numerical fit with results from previous analytical approaches provides an interesting anatomy of the ∆I = $$ \frac{1}{2} $$ 1 2 enhancement, confirming old suggestions about its underlying dynamical origin.

Lepto-axiogenesis

We propose a baryogenenesis mechanism that uses a rotating condensate of a Peccei-Quinn (PQ) symmetry breaking field and the dimension-five operator that gives Majorana neutrino masses. The rotation induces charge asymmetries for the Higgs boson and for lepton chirality through sphaleron processes and Yukawa interactions. The dimension-five interaction transfers these asymmetries to the lepton asymmetry, which in turn is transferred into the baryon asymmetry through the electroweak sphaleron process. QCD axion dark matter can be simultaneously produced by dynamics of the same PQ field via kinetic misalignment or parametric resonance, favoring an axion decay constant fa ≲ 1010 GeV, or by conventional misalignment and contributions from strings and domain walls with fa ∼ 1011 GeV. The size of the baryon asymmetry is tied to the mass of the PQ field. In simple supersymmetric theories, it is independent of UV parameters and predicts the supersymmtry breaking mass scale to be $$ \mathcal{O} $$ O (10 − 104) TeV, depending on the masses of the neutrinos and whether the condensate is thermalized during a radiation or matter dominated era. The high supersymmetry breaking mass scale may be free from cosmological and flavor/CP problems. We also construct a theory where TeV scale supersymmetry is possible. Parametric resonance may give warm axions, and the radial component of the PQ field may give signals in rare kaon decays from mixing with the Higgs and in dark radiation.

Latest results on rare kaon decays from the NA48/2 experiment @CERN

The NA48/2 experiment at CERN reports the first observation of the [Formula: see text] decay from an exposure of [Formula: see text] charged kaon decays recorded in 2003–2004. A sample of 4919 candidates with 4.9% background contamination allows the determination of the branching ratio in the full kinematic region. The study of the kinematic space shows evidence for a structure-dependent contribution in agreement with predictions based on chiral perturbation theory. Several [Formula: see text]- and [Formula: see text]-violating asymmetries are also evaluated. The most precise measurement of the charged kaon semi-leptonic form factors obtained by NA48/2 with 4.4 million [Formula: see text] and 2.3 million [Formula: see text] events collected in 2004 will also be presented.