arXiv subjects

Andrzej J. Buras

Publications and source records attributed to Andrzej J. Buras.

At least 55 records · Page 3Linked to original sources

arXiv2020

Isospin-breaking in $\varepsilon'/\varepsilon$: Impact of $η_0$ at the Dawn of the 2020s

For direct CP-violation in $K\toππ$ decays, the usual isospin-breaking effects at the percent level are amplified by the dynamics behind the $ΔI=1/2$ rule and conventionally encoded in $Ω_{\rm IB}$ parameters. The updated prediction $Ω_{\rm IB}^{(8)}=(15.9\pm 8.2)\times 10^{-2}$ of the Chiral Perturbation Theory for the strong isospin-breaking due to $π_3-η_8$ mixing confirms such a tendency but is quite sensitive to the theoretical input value of the low-energy constant corresponding to the flavour-singlet $η_0$ exchange contribution in this truncated octet scheme. We rather exploit the phenomenological $η_8-η_0$ mixing as a probe for the non-negligible flavour-singlet component of the physical $η$ pole to find $Ω_{\rm IB}^{(9)}=(35\pm7)\times 10^{-2}$ in a complete nonet scheme. A large central value in the nonet scheme is thus substituted for a large uncertainty in the octet one. Including the experimental $π^+-π^0$ mass difference as the dominant electromagnetic isospin-breaking, we obtain for the effective parameter entering the ratio $ε'/ε$ an improved result $\hatΩ_{\rm eff}^{(9)}=(29\pm7)\times 10^{-2}$ to be compared with $\hatΩ_{\rm eff}^{(8)}=(17\pm9)\times 10^{-2}$ used in recent analyses of $ε'/ε$. Accordingly, we get a reduction from $(ε'/ε)_{\rm SM}^{(8)}=(17.4\pm 6.1)\times 10^{-4}$ to $(ε'/ε)_{\rm SM}^{(9)}=(13.9\pm 5.2)\times 10^{-4}$ and thereby an effective suppression of $(ε'/ε)_{\rm SM}$ by isospin-breaking corrections as large as $40\%$ relative to the recent RBC-UKQCD value.

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arXiv2020

Another SMEFT Story: $Z^\prime$ Facing New Results on $\varepsilon'/\varepsilon$, $ΔM_K$ and $K\toπν\barν$

Recently the RBC-UKQCD lattice collaboration presented new results for the hadronic matrix elements relevant for the ratio $\varepsilon'/\varepsilon$ in the Standard Model (SM). With the present knowledge of the Wilson coefficients and isospin breaking effects there is still much room for new physics (NP) contributions to $\varepsilon'/\varepsilon$ which could both enhance or suppress this ratio to agree with the data. The new SM value for the $K^0-\bar K^0$ mass difference $ΔM_K$ from RBC-UKQCD is on the other hand by $2σ$ above the data hinting for NP required to suppress $ΔM_K$. Simultaneously the most recent results for $K^+\rightarrowπ^+ν\barν$ from NA62 and for $K_{L}\rightarrowπ^0ν\barν$ from KOTO still allow for significant NP contributions. We point out that the suppression of $ΔM_K$ by NP requires the presence of new CP-violating phases with interesting implications for $K\toπν\barν$, $K_S\toμ^+μ^-$ and $K_L\toπ^0\ell^+\ell^-$ decays. Considering a $Z^\prime$-scenario within the SMEFT we analyze the dependence of all these observables on the size of NP still allowed by the data on $\varepsilon'/\varepsilon$. The NP QCD penguin scenario for $\varepsilon'/\varepsilon$ is excluded by SMEFT renormalization group effects in $\varepsilon_K$ so that NP effects in $\varepsilon'/\varepsilon$ are governed by electroweak penguins. We also investigate for the first time whether the presence of a heavy $Z^\prime$ with flavour violating couplings could generate through top Yukawa renormalization group effects FCNCs mediated by the SM $Z$-boson. The outcome turns out to be very interesting.

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arXiv2020

$\varepsilon'/\varepsilon$ in the Standard Model at the Dawn of the 2020s

We reanalyse the ratio $\varepsilon'/\varepsilon$ in the Standard Model (SM) using most recent hadronic matrix elements from the RBC-UKQCD collaboration in combination with most important NNLO QCD corrections to electroweak penguin contributions and the isospin-breaking corrections. We illustrate the importance of the latter by using their latest estimate from chiral perturbation theory (ChPT) based on the $octet$ approximation for lowest-lying mesons and a very recent estimate in the $nonet$ scheme that takes into account the contribution of $η_0$. We find $(\varepsilon'/\varepsilon)^{(8)}_\text{SM} = (17.4 \pm 6.1) \times 10^{-4}$ and $(\varepsilon'/\varepsilon)^{(9)}_\text{SM} = (13.9 \pm 5.2) \times 10^{-4}$, respectively. Despite a very good agreement with the measured value $(\varepsilon'/\varepsilon)_\text{exp} = (16.6 \pm 2.3) \times 10^{-4}$, the large error in $(\varepsilon'/\varepsilon)_\text{SM}$ still leaves room for significant new physics (BSM) contributions to this ratio. We update the 2018 master formula for $(\varepsilon'/\varepsilon)_\text{BSM}$ valid in any extension beyond the SM without additional light degrees of freedom. We provide new values of the penguin parameters $B_6^{(1/2)}(μ)$ and $B_8^{(3/2)}(μ)$ at the $μ$-scales used by the RBC-UKQCD collaboration and at lower scales $\mathcal{O}(1\,\text{GeV})$ used by ChPT and DQCD. We present semi-analytic formulae for $(\varepsilon'/\varepsilon)_\text{SM}$ in terms of these parameters and $\hatΩ_\text{eff}$ that summarizes isospin-breaking corrections to this ratio. We stress the importance of lattice calculations of the $\mathcal{O}(α_\text{em})$ contributions to the hadronic matrix elements necessary for the removal of renormalization scheme dependence at $\mathcal{O}(α_\text{em})$ in the present analyses of $\varepsilon'/\varepsilon$.

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arXiv2020

The Optimal Strategy for $\varepsilon'/\varepsilon$ in the SM: 2019

Following the recent analysis done in collaboration with Jason Aebischer and Christoph Bobeth, I summarize the optimal, in our view, strategy for the present evaluation of the ratio $\varepsilon'/\varepsilon$ in the Standard Model (SM). In particular, I emphasize the importance of the correct matching of the long-distance and short-distance contributions to $\varepsilon'/\varepsilon$, which presently is only achieved by RBC-UKQCD lattice QCD collaboration and by the analytical Dual QCD approach. An mportant role play also the isospin-breaking and QED effects, which presently are best known from chiral perturbation theory, albeit still with a significant error. Finally, it is essential to include NNLO QCD corrections in order to reduce unphysical renormalization scheme and scale dependences present at the NLO level. Here $μ_c$ in $m_c(μ_c)$ in the case of QCD penguin (QCDP) contributions and $μ_t$ in $m_t(μ_t)$ in the case of electroweak penguin (EWP) contributions play the most important roles. Presently the error on $\varepsilon'/\varepsilon$ is dominated by the uncertainties in the QCDP parameter $B_6^{(1/2)}$ and the isospin-breaking parameter $\hatΩ_\text{eff}$ We present a table illustrating this. To be published online by the Institute of Physics Proceedings.

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arXiv2020

On the Importance of NNLO QCD and Isospin-breaking Corrections in $\varepsilon'/\varepsilon$

Following the 1999 analysis of Gambino, Haisch and one of us, we stress that all the recent NLO analyses of $\varepsilon'/\varepsilon$ in the Standard Model (SM) suffer from the renormalization scheme dependence present in the electroweak penguin contributions as well as from scale uncertainties in them related to the matching scale $μ_W$ and in particular to $μ_t$ in $m_t(μ_t)$. We also reemphasize the important role of isospin-breaking and QED effects in the evaluation of $\varepsilon'/\varepsilon$. Omitting all these effects, as done in the 2015 analysis by RBC-UKQCD collaboration, and choosing as an example the QCD penguin ($Q_6$) and electroweak penguin ($Q_8$) parameters $B_6^{(1/2)}$ and $B_8^{(3/2)}$ to be $B_6^{(1/2)} = 0.80 \pm 0.08$ and $B_8^{(3/2)} = 0.76 \pm 0.04$ at $μ= m_c = 1.3$ GeV, we find $(\varepsilon'/\varepsilon)_\text{SM} = (9.4 \pm 3.5) \times 10^{-4}$, whereas including them results in $(\varepsilon'/\varepsilon)_\text{SM} = (5.6\pm 2.4) \times 10^{-4}$. This is an example of an anomaly at the $3.3\,σ$ level, which would be missed without these corrections. NNLO QCD contributions to QCD penguins are expected to further enhance this anomaly. We provide a table for $\varepsilon'/\varepsilon$ for different values of $B_6^{(1/2)}$ and the isospin-breaking parameter $\hatΩ_\text{eff}$, that should facilitate monitoring the values of $\varepsilon'/\varepsilon$ in the SM when the RBC-UKQCD calculations of hadronic matrix elements including isospin-breaking corrections and QED effects will improve with time.

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arXiv2019

Quark-Lepton Connections in $Z^\prime$ Mediated FCNC Processes: Gauge Anomaly Cancellations at Work

We consider scenarios with a heavy $Z^\prime$ gauge boson with flavour non-universal quark and lepton couplings with the goal to illustrate how the cancellation of gauge anomalies generated by the additional U(1)$^\prime$ gauge symmetry would imply correlations between FCNC processes in the quark sector, in the lepton sector and most interestingly between quark flavour and lepton flavour violating processes. We present scenarios with only left-handed flavour-violating $Z^\prime$ couplings and those with also right-handed flavour-violating couplings. These are characterized by a small number of free parameters but in contrast to gauge anomaly cancellation in the Standard Model, that takes place separately within each generation, in our scenarios anomaly cancellation involves simultaneously quarks and leptons of all three generations. Our models involve, beyond the ordinary quarks and leptons, three heavy right-handed neutrinos. The models with only left-handed FCNCs of $Z^\prime$ involve beyond $g_{Z^\prime}$ and $M_{Z^\prime}$ two real parameters characterizing the charges of all fermions under the U(1)$^\prime$ gauge symmetry and the CKM and PMNS ones in the quark and lepton sectors, respectively. The models with the right-handed FCNCs of $Z^\prime$ involve few additional parameters. Imposing constraints from well measured $ΔF=2$ observables we identify interesting correlations that involve e.g. $\varepsilon'/\varepsilon$, $B_{s,d}\toμ^+μ^-$, $B\to K(K^*) \ell^+\ell^-$, $K^+\rightarrowπ^+ν\barν$, $K_{L}\rightarrowπ^0ν\barν$ and purely lepton flavour violating decays like $μ\to eγ$, $μ\to 3 e$, $τ\to 3μ$ and $μ-e$ conversion} among others. Also $(g-2)_{μ,e}$ are considered. The impact of the experimental $μ\to eγ$, $μ\to 3 e$ and in particular $μ-e$ conversion bounds on rare $K$ and $B$ decays is emphasized.

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arXiv2019

Master formula for $\varepsilon'/\varepsilon$ beyond the Standard Model

We present for the first time a master formula for $\varepsilon'/\varepsilon$, the ratio probing direct CP violation in $K \to ππ$ decays, valid in any theory beyond the Standard Model (BSM). The formula makes use of hadronic matrix elements of BSM operators calculated recently in the Dual QCD approach and the ones of the SM operators from lattice QCD. We emphasize the large impact of several scalar and tensor BSM operators in the context of the emerging $\varepsilon'/\varepsilon$ anomaly. We have implemented the results in the open source code flavio.

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arXiv2019

Anatomy of $\varepsilon'/\varepsilon$ beyond the Standard Model

We present for the first time a model-independent anatomy of the ratio $\varepsilon'/\varepsilon$ in the context of the $ΔS = 1$ effective theory with operators invariant under QCD and QED and in the context of the Standard Model Effective Field Theory (SMEFT) with the operators invariant under the full SM gauge group. Our goal is to identify the new physics scenarios that are probed by this ratio and which could help to explain a possible deviation from the SM that is hinted by the data. To this end we derive a master formula for $\varepsilon'/\varepsilon$, which can be applied to any theory beyond the Standard Model (BSM) in which the Wilson coefficients of all contributing operators have been calculated at the electroweak scale. The relevant hadronic matrix elements of BSM operators are from the Dual QCD approach and the SM ones from lattice QCD. Within SMEFT, the constraints from $K^0$ and $D^0$ mixing as well as electric dipole moments limit significantly potential new physics contributions to $\varepsilon'/\varepsilon$. Correlations of $\varepsilon'/\varepsilon$ with $K\toπν\barν$ decays are briefly discussed. Building on our EFT analysis and the model-independent constraints, we discuss implications of a possible deviation from the SM in $\varepsilon'/\varepsilon$ for model building, highlighting the role of the new scalar and tensor matrix elements in models with scalar mediators.

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arXiv2019

Emerging $ΔM_{d}$-Anomaly from Tree-Level Determinations of $|V_{cb}|$ and the Angle $γ$

We point out that the recently increased value of the angle $γ$ in the Unitarity Triangle (UT), determined in tree-level decays to be $γ=(74.0^{+5.0}_{-5.8})^\circ$ by the LHCb collaboration, combined with the most recent value of $|V_{cb}|$ implies an enhancement of $ΔM_{d}$ over the data in the ballpark of $30\%$. This is roughly by a factor of two larger than the enhancement of $ΔM_{s}$ that is independent of $γ$. This disparity of enhancements is problematic for models with Constrained Minimal Flavour Violation (CMFV) and also for $U(2)^3$ models. In view of the prospects of measuring $γ$ with the precision of $\pm 1^\circ$ by Belle II and LHCb in the coming years, we propose to use the angles $γ$ and $β$ together with $|V_{cb}|$ and $|V_{us}|$ as the fundamental parameters of the CKM matrix until $|V_{ub}|$ from tree-level decays will be known precisely. Displaying $ΔM_{s,d}$ as functions of $γ$ clearly demonstrates the tension between the value of $γ$ from tree-level decays, free from new physics (NP) contributions, and $ΔM_{s,d}$ calculated in CMFV and $U(2)^3$ models and thus exhibits the presence of NP contributions to $ΔM_{s,d}$ beyond these frameworks. We calculate the values of $|V_{ub}|$ and $|V_{td}|$ as functions of $γ$ and $|V_{cb}|$ and discuss the implications of our results for $\varepsilon_K$ and rare $K$ and $B$ decays. We also briefly discuss a future strategy in which $β$, possibly affected by NP, is replaced by $|V_{ub}|$.

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arXiv2019

BSM Hadronic Matrix Elements for $ε'/ε$ and $K\toππ$ Decays in the Dual QCD Approach

We calculate for the first time all four-quark hadronic matrix elements of local operators possibly contributing to $K\toππ$ decays and in particular to the ratio $ε'/ε$ beyond the Standard Model (BSM). To this end we use the Dual QCD (DQCD) approach. In addition to 7 new mirror operators obtained from the SM ones by flipping the chirality, we count 13 BSM four-quark operators of a given chirality linearly independent of each other and of the aforesaid 14 operators for which hadronic matrix elements are already known. We present results in two bases for all these operators, one termed DQCD basis useful for the calculation of the hadronic matrix elements in the DQCD approach and the other called SD basis suited to the short distance renormalization group evolution above the 1~GeV scale. We demonstrate that the pattern of long distance evolution (meson evolution) matches the one of short distance evolution (quark-gluon evolution), a property which to our knowledge cannot be presently achieved in any other analytical framework. The highlights of our paper are chirally enhanced matrix elements of tensor-tensor and scalar-scalar BSM operators. They could thereby explain the emerging $ε'/ε$ anomaly which is strongly indicated within DQCD with some support from lattice QCD. On the other hand we do not expect the BSM operators to be relevant for the $ΔI=1/2$ rule.

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arXiv2018

$ε^\prime/ε$-2018: A Christmas Story

I was supposed to review the status of $ε^\prime/ε$ both at the CKM Workshop in September in Heidelberg and recently at the Discrete 2018 Conference in Vienna. Unfortunately I had to cancel both talks for family reasons. My main goal in these talks was to congratulate NA48 and KTeV collaborations for the discovery of new sources of CP violation through their heroic efforts to measure the ratio $ε^\prime/ε$ in the 1980s and 1990s with final results presented roughly 16 years ago. As I will not attend any other conferences this year I will reach this goal in this writing. In this context I will give arguments, why I am convinced about the presence of new physics in $ε^\prime/ε$ on the basis of my work with Jean-Marc Gerard within the context of the Dual QCD (DQCD) approach and why RBC-UKQCD collaboration and in particular Chiral Perturbation Theory practitioners are still unable to reach this conclusion. I will demonstrate that even in the presence of pion loops, as large as advocated recently by Gilbert and Pich, the value of $ε^\prime/ε$ is significantly below the data, when the main non-factorizable QCD dynamics at long distance scales, represented in DQCD by {the meson evolution}, is taken into account. As appriopriate for a Christmas story, I will prophesy the final value of $ε^\prime/ε$ within the SM, which should include in addition to the correct matching between long and short distance contributions, isospin breaking effects, NNLO QCD corrections to both QCD penguin and electroweak penguin contributions and final state interactions. Such final SM result will probably be known from lattice QCD only in the middle of 2020s, but already in 2019 we should be able to see some signs of NP in the next result on $ε^\prime/ε$ from RBC-UKQCD.

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arXiv2018

The Dual QCD @ Work

The Dual QCD (DQCD) framework, based on the ideas of 't Hooft and Witten, and developed by Bill Bardeen, Jean-Marc Gerard and myself in the 1980s is not QCD, a theory of quarks and gluons, but a successful low energy approximation of it when applied to $K\toππ$ decays and $K^0-\bar K^0$ mixing. After years of silence, starting with 2014, this framework has been further developed in order to improve the SM prediction for the ratio $ε'/ε$, the $ΔI=1/2$ rule and $\hat B_K$. Most importantly, this year it has been used for the calculation of all $K\toππ$ hadronic matrix elements of BSM operators which opened the road for the general study of $ε'/ε$ in the context of the SM effective theory (SMEFT). This talk summarizes briefly the past successes of this framework and discusses recent developments which lead to a master formula for $ε'/ε$ valid in any extension of the SM. This formula should facilitate the search for new physics responsible for the $ε'/ε$ anomaly hinted by 2015 results from lattice QCD and DQCD.

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arXiv2018

Analytic inclusion of the scale dependence of the anomalous dimension matrix in Standard Model Effective Theory

The renormalization group equations (RGEs) in Standard Model effective theory are usually either solved analytically, neglecting the scale dependence of gauge and Yukawa couplings, or numerically without such approximations. We present analytic solutions of RGEs that take into account the dominant scale dependence of the anomalous-dimension matrix due to the running of the QCD coupling and of the top-Yukawa coupling. We consider first the case for which a given operator is generated directly through mixing with the parent operator whose Wilson coefficient is non-vanishing at the new physics scale. Subsequently we consider the case of two-step running, in which two operators do not mix directly, but only via a third mediator operator. We generalize these solutions to an arbitrary number of operators and show how even in this case analytic solutions can be obtained.

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arXiv2018

The Return of Kaon Flavour Physics

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 $K_L\toππ$ 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 $K^+\rightarrow π^+ν\barν$ and $K_{L}\rightarrowπ^0ν\barν$ and the improved SM predictions for the ratio $\varepsilon'/\varepsilon$, for $\varepsilon_K$ and the $K^0-\bar K^0$ mixing mass difference $ΔM_K$. Theoretical progress on the decays $K_{L,S}\toμ^+μ^-$ and $K_L\toπ^0\ell^+\ell^-$ 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 $K\toππ$ 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 $K\toππ$ decays.

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arXiv2018

Dual QCD Insight into BSM Hadronic Matrix Elements for $K^0-\bar K^0$ Mixing from Lattice QCD

We calculate BSM hadronic matrix elements for $K^0-\bar K^0$ mixing in the Dual QCD approach (DQCD). The ETM, SWME and RBC-UKQCD lattice collaborations find the matrix elements of the BSM density-density operators $\mathcal{O}_i$ with $i=2-5$ to be rather different from their vacuum insertion values (VIA) with $B_2\approx 0.5$, $B_3\approx B_5\approx 0.7$ and $B_4\approx 0.9$ at $μ=3~GeV$ to be compared with $B_i=1$ in the VIA. We demonstrate that this pattern can be reconstructed within the DQCD through the non-perturbative meson evolution from very low scales, where factorization of matrix elements is valid, to scales of order $(1~GeV)$ with subsequent perturbative quark-gluon evolution to $μ=3~GeV$. This turns out to be possible in spite of a very different pattern displayed at low scales with $B_2=1.2$, $B_3=3.0$, $B_4=1.0$ and $B_5\approx 0.2$ in the large $N$ limit, $N$ being the number of colours. Our results imply that the inclusion of meson evolution in the phenomenology of any non-leptonic transition like $K^0-\bar K^0$ mixing and $K\toππ$ decays is mandatory. While meson evolution, as demonstrated in our paper, is hidden in LQCD results, to our knowledge DQCD is the only analytic approach for non-leptonic transitions and decays which takes this important QCD dynamics into account.

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arXiv2017

Yukawa enhancement of $Z$-mediated New Physics in $ΔS = 2$ and $ΔB = 2$ Processes

We discuss Yukawa-enhanced contributions from $Z$-mediated new physics to down-type quark $ΔF=2$ processes in the framework of the standard model gauge-invariant effective theory (SMEFT). Besides the renormalization group (RG) mixing of the $Z$-mediating $ψ^2 H^2 D$ operators into $ΔF = 2$ operators, we include at the electroweak scale one-loop (NLO) matching corrections consistently, necessary for the removal of the matching scale dependence. We point out that the right-handed $Z$-mediated interactions generate through Yukawa RG mixing $ΔF=2$ left-right operators, which are further enhanced through QCD RG effects and chirally enhanced hadronic matrix elements. We investigate the impact of these new effects on the known correlations between $ΔF=2$ and $ΔF=1$ transitions in the SMEFT framework and point out qualitative differences to previous parameterizations of $Z$-mediated new physics that arise for the left-handed case. We illustrate how specific models fit into our model-independent framework by using four models with vector-like quarks. We carry out model-independent analyses of scenarios with purely left-handed and purely right-handed new-physics $Z$ couplings for each of the three sectors $s\to d$, $b\to s$ and $b\to d$. Specifically we discuss the correlations between $\varepsilon'/\varepsilon$, $\varepsilon_K$, $K_L\to μ^+μ^-$ $K^+\to π^+ν\barν$ and $K_L\toπ^0ν\barν$ in the Kaon sector, and $ϕ_s$, $B_s\toμ^+μ^-$ and $B\to K^{(*)} (μ^+μ^-, ν\barν)$ in the $b\to s$ sector and $B_d\toμ^+μ^-$ in the $b\to d$ sector.

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arXiv2017

Patterns of Flavour Violation in Models with Vector-Like Quarks

We study the patterns of flavour violation in renormalisable extensions of the Standard Model (SM) that contain vector-like quarks (VLQs) in a single complex representation of either the SM gauge group $G_{SM}$ or $G_{SM}' = G_{SM} \times U(1)_{L_μ- L_τ}$. We first decouple VLQs in the $M=(1-10)$ TeV range and then at the electroweak scale also $Z, Z'$ gauge bosons and additional scalars to study the resulting phenomenology that depends on the relative size of $Z$- and $Z'$-induced flavour-changing neutral currents, as well as the size of $ΔF=2$ contributions including the effects of renormalisation group Yukawa evolution from $M$ to the electroweak scale that turn out to be very important for models with right-handed currents through the generation of left-right operators. In addition to rare decays like $P\to \ell\bar\ell$, $P\to P' \ell\bar\ell$, $P\to P'ν\barν$ with $P=K, B_s, B_d$ and $ΔF=2$ observables we analyze the ratio $\varepsilon'/\varepsilon$ which appears in the SM to be significantly below the data. We study patterns and correlations between these observables which taken together should in the future allow for differentiating between VLQ models. In particular the patterns in models with left-handed and right-handed currents are markedly different from each other. Among the highlights are large $Z$-mediated new physics effects in Kaon observables in some of the models and significant effects in $B_{s,d}$-observables. $\varepsilon'/\varepsilon$ can easily be made consistent with the data, implying then uniquely the suppression of $K_L\to π^0 ν\barν$. Significant enhancements of $Br(K^+\to π^+ ν\barν)$ are still possible. We point out that the combination of $ΔF=2$ and $ΔF=1$ observables in a given meson system generally allows to determine the masses of VLQs independently of the size of VLQ couplings.

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arXiv2016

Final State Interactions in $K\toππ$ Decays: $ΔI=1/2$ Rule vs. $\varepsilon^\prime/\varepsilon$

Dispersive effects from strong $ππ$ rescattering in the final state (FSI) of weak $K\toππ$ decays are revisited with the goal to have a global view on their {\it relative} importance for the $ΔI=1/2$ rule and the ratio $\varepsilon^\prime/\varepsilon$ in the Standard Model (SM). We point out that this goal cannot be reached within a pure effective (meson) field approach like chiral perturbation theory in which the dominant current-current operators governing the $ΔI=1/2$ rule and the dominant density-density (four-quark) operators governing $\varepsilon^\prime/\varepsilon$ cannot be disentangled from each other. But in the context of a dual QCD approach, which includes both long distance dynamics and the UV completion, that is QCD at short distance scales, such a distinction is possible. We find then that beyond the strict large $N$ limit, $N$ being the number of colours, FSI are likely to be important for the $ΔI=1/2$ rule but much less relevant for $\varepsilon^\prime/\varepsilon$. The latter finding diminishes significantly hopes that improved calculations of $\varepsilon^\prime/\varepsilon$ would bring its SM prediction to agree with the experimental data, opening thereby an arena for important new physics contributions to this ratio.

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