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Register a new userKaon Flavour Physics Strikes Back
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Andrzej J. Buras
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In this short presentation I emphasize the increased importance of kaon flavour physics in the search for new physics (NP) that we should witness in the rest of this decade and in the next decade. The main actors will be the branching ratios for the rare decays $K^+rightarrowpi^+ ubar u$ and $K_{L}rightarrowpi^0 ubar u$, to be measured by NA62 and KOTO, and their correlations with the ratio $varepsilon/varepsilon$ on which recently progress by lattice QCD and large $N$ dual QCD approach has been made implying a new flavour anomaly. Further correlations of $K^+rightarrowpi^+ ubar u$, $K_{L}rightarrowpi^0 ubar u$ and $varepsilon/varepsilon$ with $varepsilon_K$, $Delta M_K$, $K_Ltomu^+mu^-$ and $K_Ltopi^0ell^+ell^-$ will help us to identify indirectly possible NP at short distance scales. This talk summarizes the present highlights of this fascinating field including some results from concrete NP scenarios.
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Kaon flavour physics has played in the 1960s and 1970s a very important role in the construction of the Standard Model (SM) and in the 1980s and 1990s in SM tests with the help of CP violation in $K_Ltopipi$ decays represented by $varepsilon_K$ and the ratio $varepsilon/varepsilon$. In this millennium this role has been taken over by $B_{s,d}$ and $D$ mesons. However there is no doubt that in the coming years we will witness the return of kaon flavour physics with the highlights being the measurements of the theoretically clean branching ratios for the rare decays $K^+rightarrow pi^+ ubar u$ and $K_{L}rightarrowpi^0 ubar u$ and the improved SM predictions for the ratio $varepsilon/varepsilon$, for $varepsilon_K$ and the $K^0-bar K^0$ mixing mass difference $Delta M_K$. Theoretical progress on the decays $K_{L,S}tomu^+mu^-$ and $K_Ltopi^0ell^+ell^-$ is also expected. They all are very sensitive to new physics (NP) contributions and the correlations between them should help us to identify new dynamics at very short distance scales. These studies will be enriched when theory on the $Ktopipi$ isospin amplitudes ${rm Re} A_0$ and ${rm Re} A_2$ improves. This talk summarizes several aspects of this exciting field. In particular we emphasize the role of the Dual QCD approach in getting the insight into the numerical Lattice QCD results on $K^0-bar K^0$ mixing and $Ktopipi$ decays.
We present the Flavour Les Houches Accord (FLHA) which specifies a unique set of conventions for flavour-related parameters and observables. The FLHA uses the generic SUSY Les Houches Accord (SLHA) file structure. It defines the relevant Standard Model masses, Wilson coefficients, decay constants, bag parameters, flavour observables, etc. The accord provides a universal and model-independent interface between codes evaluating and/or using flavour-related observables.
We give a brief introduction to flavour physics. The first part covers the flavour structure of the Standard Model, how the Kobayashi-Maskawa mechanism is tested and provides examples of searches for new physics using flavour observables, such as meson mixing and rare decays. In the second part we give a brief overview of the recent flavour anomalies and how the Higgs can act as a new flavour probe.
LHCb found hints for physics beyond the Standard Model (SM) in $Bto K^*mu^+mu^-$, $R(K)$ and $B_stophimu^+mu^-$. These intriguing hints for NP have recently been confirmed by the LHCb measurement of $R(K^*)$ giving a combined significance for NP above the $5,sigma$ level. In addition, the BABAR, BELLE and LHCb results for $Bto D^{(*)}tau u$ also point towards lepton flavour universality (LFU) violating new physics (NP). Furthermore, there is the long-standing discrepancy between the measurement and the theory prediction of the anomalous magnetic moment of the muon ($a_mu$) at the $3,sigma$ level. Concerning NP effects, $bto smu^+mu^-$ data can be naturally explained with a new neutral gauge bosons, i.e. a $Z^prime$ but also with heavy new scalars and fermions contributing via box diagrams. Another promising solution to $bto smu^+mu^-$, which can also explain $Bto D^{(*)}tau u$, are leptoquarks. Interestingly, leptoquarks provide also a viable explanation of $a_mu$ which can be tested via correlated effects in $Ztomu^+mu^-$ at future colliders. Considering leptoquark models, we show that an explanation of $Bto D^{(*)}tau u$ predicts an enhancement of $bto stau^+tau^-$ processes by around three orders of magnitude compared to the SM. In case of a simultaneous explanation of $Bto D^{(*)}tau u$ and $bto smu^+mu^-$ data, sizable effects in $bto staumu$ processes are predicted.
Let $G$ be any $n$-vertex graph whose random walk matrix has its nontrivial eigenvalues bounded in magnitude by $1/sqrt{Delta}$ (for example, a random graph $G$ of average degree~$Theta(Delta)$ typically has this property). We show that the $expBig(c frac{log n}{log Delta}Big)$-round Sherali--Adams linear programming hierarchy certifies that the maximum cut in such a~$G$ is at most $50.1%$ (in fact, at most $tfrac12 + 2^{-Omega(c)}$). For example, in random graphs with $n^{1.01}$ edges, $O(1)$ rounds suffice; in random graphs with $n cdot text{polylog}(n)$ edges, $n^{O(1/log log n)} = n^{o(1)}$ rounds suffice. Our results stand in contrast to the conventional beliefs that linear programming hierarchies perform poorly for maxcut and other CSPs, and that eigenvalue/SDP methods are needed for effective refutation. Indeed, our results imply that constant-round Sherali--Adams can strongly refute random Boolean $k$-CSP instances with $n^{lceil k/2 rceil + delta}$ constraints; previously this had only been done with spectral algorithms or the SOS SDP hierarchy.
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