Kaon Theory News

Abstract

During the last fifteen years B s,d decays, B 0 s,d −B 0 s,d mixings, related mixing induced CP-violating asymmetries S ψK S and S ψφ and CP violation in charm decays provided the dominant information about the pattern of flavour violation within the Standard Model (SM) and its extensions. K meson physics was solely represented by the CP-violating parameter ε K which by itself could still provide a very powerful constraint on new physics (NP) models but could not offer by far as much information about the pattern of flavour violation in nature as the observables in heavy meson decays. We emphasize that in the coming years K meson physics will certainly strike back through the measurements of the branching ratios of theoretically very clean decays K + → π + νν and K L → π 0 νν and improved calculations of the ratio ε /ε provided recently by lattice QCD and large N approach. Also the improved calculations of the K 0 −K 0 mass difference ∆M K could be of help in this context. We summarize the status of K + → π + νν and K L → π 0 νν within the SM and simplified NP models and update the picture of flavour violation in the Littlest Higgs model with T-parity (LHT) taking all available constraints into account. But the highlight of this talk are new results on ε /ε from lattice QCD and large N approach that give a strong indication for a new anomaly in flavour physics, this time coming from K mesons. Indeed, ε /ε within the SM is found to be significantly below the data of NA48 and KTeV collaborations. Combining lattice results on the non-perturbative parameters B(1/2) 6 and B(3/2) 8 with the assumption that the SM dynamics dominates the ∆I = 1/2 rule a 3σ anomaly in ε /ε emerges. Moreover, the recently derived upper bounds on B(1/2) 6 and B(3/2) 8 from large N approach with B(1/2) 6 ≤ B(3/2) 8 < 1, fully consistent with lattice results, increase the confidence that the found anomaly could be an important signal of NP at work. Of particular importance are the correlations between K + → π + νν, K L → π 0 νν and ε /ε. With future precise measurements of K + → π + νν and K L → π 0 νν and improved calculations of ε /ε they will surely provide powerful tools for selecting the favourite NP models. We illustrate this with the help of the LHT model and simplified models in which NP in K → πνν and ε /ε is governed by Z with flavour violating couplings or by a heavy Z .

New physics patterns in ε′/ε and ε K with implications for rare kaon decays and ∆M K

“…While, the improvement on the estimate of isospin corrections, final state interactions (FSI) [10][11][12][13][14][15] and the inclusion of NNLO QCD corrections could in principle increase ε /ε with respect to the one in (1.1), it is rather unlikely that values of ε /ε violating the upper bound in (1.3) will be found within the SM. After all, until now, lattice QCD confirmed most of earlier results on K meson flavour physics obtained in the large N approach (see [2,16]). …”

“…2 We should emphasize that this suppression of B results from the meson evolution of the density-density operators Q 6 and Q 8 from µ ≈ 0 (strict large N limit) to scales O(1 GeV), where the hadronic matrix elements are multiplied by the Wilson coefficients. The scale dependence of both parameters is logarithmic but the one of B (1/2) 6 is stronger than of B (3/2) 8 implying at scales O(1 GeV) the inequalities in (2.12).…”

“…On the other hand, it has been advocated by the chiral perturbation theory practitioners [10,11,[13][14][15] that final state interactions (FSI), not included in the large N approach 2 On the other hand a number of other large N approaches [49][50][51] violates strongly the bounds in (2.12) with B in the dispersive approach [52,53].…”

“…A prominent example is the chromomagnetic penguin operator in supersymmetric models. The present status of ε /ε in the SM has been reviewed recently in [1,2], where references to rich literature can be found. After the new results for the hadronic matrix elements of QCDP and EWP (V − A) ⊗ (V + A) operators from RBC-UKQCD lattice collaboration [3][4][5] and the extraction of the corresponding matrix elements of penguin (V − A) ⊗ (V − A) operators from the CP-conserving K → ππ amplitudes one finds [1] (ε /ε) SM = (1.9 ± 4.5) × 10 −4 .…”

The Return of Kaon Flavour Physics

“…Therefore I changed my strategy and concentrated since 2014 [2], with few exceptions, on Kaon flavour physics. A series of reviews on our work appeared in [3][4][5][6][7].…”