arXiv subjects

Andrzej J. Buras

Publications and source records attributed to Andrzej J. Buras.

At least 37 records · Page 2Linked to original sources

arXiv2023

Kaon Physics Without New Physics in $\varepsilon_K$

Despite the observation of significant suppression of $b\to sμ^+μ^-$ branching ratios no clear sign of New Physics (NP) has been identified in $ΔF=2$ observables, in particular to $\varepsilon_K$. Assuming negligible NP contributions to these observables allows us to determine CKM parameters without being involved in the tensions between inclusive and exclusive determinations of $V_{cb}$ and $V_{ub}$. Furthermore, this method avoids the impact of NP on the determination of these parameters present likely in global fits. Simultaneously it provides SM predictions for numerous rare $K$ and $B$ branching ratios that are most accurate to date. Analyzing this scenario within $Z^\prime$ models we point out, following the 2009 observations of Monika Blanke and ours of 2020, that despite the absence of NP contributions to $\varepsilon_K$, significant NP contributions to several rare Kaon decays, $\varepsilon'/\varepsilon$ and $ΔM_K$ can be present. In the simplest scenario, this is guaranteed by a single non-vanishing imaginary left-handed $Z^\prime$ coupling $g^L_{sd}$. This scenario implies very stringent correlations between the Kaon observables considered by us. In particular, the identification of NP in any of these observables implies automatically NP contributions to the remaining ones. A characteristic feature of this scenario is a strict correlation between $K^+\toπ^+ν\barν$ and $K_L\toπ^0ν\barν$ branching ratios on a branch parallel to the Grossman-Nir bound. Moreover, $ΔM_K$ is automatically suppressed as seems to be required by recent lattice QCD results.

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arXiv2023

On the Superiority of the $|V_{cb}|-γ$ Plots over the Unitarity Triangle Plots in the 2020s

The UT plots played already for three decades an important role in the tests of the SM and the determination of the CKM parameters. As of 2022, among the four CKM parameters, $V_{us}$ and $β$ are already measured with respectable precision, while this is not the case of $|V_{cb}|$ and $γ$. In the case of $|V_{cb}|$ the main obstacle are the significant tensions between its inclusive and exclusive determinations from tree-level decays. The present uncertainty in $γ$ of $4^\circ$ from tree-level decays will be reduced to $1^\circ$ by the LHCb and Belle II collaborations in the coming years. Unfortunately in the UT plots $|V_{cb}|$ is not seen and the experimental improvements in the determination of $γ$ from tree-level decays at the level of a few degrees are difficult to appreciate. In view of these deficiencies of the UT plots with respect to $|V_{cb}|$ and $γ$ and the central role these two CKM parameters will play in this decade, the recently proposed plots of $|V_{cb}|$ versus $γ$ extracted from various processes appear to be superior to the UT plots in the flavour phenomenology. We illustrate this idea with $ΔM_s$, $ΔM_d$, $ε_K$ and with rare decays $B_s\toμ^+μ^-$, $B_d\toμ^+μ^-$, $K^+\to π^+ν\barν$ and $K_L\toπ^0ν\barν$. The power of $ε_K$, $K^+\toπ^+ν\barν)$ and $K_{L}\toπ^0ν\barν)$ in the determination of $|V_{cb}|$, due to their strong dependence on $|V_{cb}|$, is transparently exhibited in this manner. Combined with future reduced errors on $γ$ and $|V_{cb}|$ from tree-level decays such plots can better exhibit possible inconsistenices between various determinations of these two parameters, caused by new physics, than it is possible with the UT plots.

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arXiv2022

50 Years of Quantum Chromodynamics

This paper presents a comprehensive review of both the theory and experimental successes of Quantum Chromodynamics, starting with its emergence as a well defined theory in 1972-73 and following developments and results up to the present day. Topics include a review of the earliest theoretical and experimental foundations; the fundamental constants of QCD; an introductory discussion of lattice QCD, the only known method for obtaining exact predictions from QCD; methods for approximating QCD, with special focus on effective field theories; QCD under extreme conditions; measurements and predictions of meson and baryon states; a special discussion of the structure of the nucleon; techniques for study of QCD at high energy, including treatment of jets and showers; measurements at colliders; weak decays and quark mixing; and a section on the future, which discusses new experimental facilities or upgrades currently funded. The paper is intended to provide a broad background for Ph.D. students and postdocs starting their career. Some contributions include personal accounts of how the ideas or experiments were developed.

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arXiv2022

On the Standard Model Predictions for Rare K and B Decay Branching Ratios: 2022

In this decade one expects a very significant progress in measuring the branching ratios for several rare $K$ and $B$ decays, in particular for the decays $K^+\toπ^+ν\barν$, $K_L\toπ^0ν\barν$, $B_s\toμ^+μ^+$ and $B_d\toμ^+μ^+$. On the theory side a very significant progress on calculating these branching ratios has been achieved in the last thirty years culminating recently in rather precise SM predictions for them. It is then unfortunate that some papers still cite the results for $K^+\toπ^+ν\barν$ and $K_L\toπ^0ν\barν$ presented by us in 2015. They are clearly out of date. Similar comments apply to predictions for $B_{s,d}\toμ^+μ^-$. In this note I want to stress again that, in view of the tensions between various determinations of $V_{cb}$ in tree-level decays, presently, the only trustable SM predictions for the branching ratios in question can be obtained by eliminating their dependence on the CKM parameters with the help of $|\varepsilon_K|$, $ΔM_s$, $ΔM_d$ and $S_{ψK_S}$, evaluated in the SM. In this context I am astonished by statements made by some computer code practitioners that setting in this strategy these four $ΔF=2$ observables to their experimental values is an assumption. The goal of this strategy is not to make an overall SM fit but to predict the SM branching ratios. In the SM there are no new physics (NP) contributions to $ΔF=2$ transitions and no assumption on the absence of NP is needed. Moreover, presently NP is not required to describe simultaneously the very precise data on $|\varepsilon_K|$, $ΔM_s$, $ΔM_d$ and $S_{ψK_S}$. This strategy for obtaining true SM predictions for rare decay branching ratios is moreover not polluted by hadronic uncertainies and observed anomalies in semi-leptonic decays used often in global analyses as stressed recently in (arxiv: 2209.03968).

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arXiv2022

NLO QCD Renormalization Group Evolution for Non-Leptonic $ΔF=2$ Transitions in the SMEFT

We present for the first time NLO QCD Renormalization Group (RG) evolution matrices for non-leptonic $ΔF=2$ transitions in the Standard Model Effective Field Theory (SMEFT). To this end we transform first the known two-loop QCD anomalous dimension matrices (ADMs) of the BSM operators in the so-called BMU basis into the ones in the common Weak Effective Theory (WET) basis (the so-called JMS basis) for which tree-level and one-loop matching to the SMEFT are already known. This allows us subsequently to find the two-loop QCD ADMs for the SMEFT non-leptonic $ΔF=2$ operators in the Warsaw basis. Having all these ingredients we investigate the impact of these NLO QCD effects on the QCD RG evolution of SMEFT Wilson coefficients for non-leptonic $ΔF=2$ transitions from the new physics scale $Λ$ down to the electroweak scale $μ_\text{ew}$. The main benefit of these new contributions is that they allow to remove renormalization scheme dependences present both in the one-loop matchings between the WET and SMEFT and also between SMEFT and a chosen UV completion. But the NLO QCD effects, calculated here in the NDR scheme, turn out to be small, in the ballpark of a few percent but larger than one-loop Yukawa top effects when only the $ΔF=2$ operators are considered. The technology developed in our paper allows to obtain the ADMs in the SMEFT from the ones of the BMU basis also for non-leptonic $ΔF=1$ decays and the results of this more involved analysis will be presented soon in another publication.

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arXiv2022

The Exclusive Vision of Rare $K$ and $B$ Decays and of the Quark Mixing in the Standard Model

The most common predictions for rare $K$ and $B$ decay branching ratios in the Standard Model are based on the CKM elements $|V_{cb}|$ and $|V_{ub}|$ resulting from global fits, that are in the ballpark of their inclusive and exclusive determinations, respectively. In the present paper we follow another route. We assume that the future true values of $|V_{cb}|$ and $|V_{ub}|$ will be both from exclusive determinations and set them equal to the most recent ones from FLAG. An unusual pattern of SM predictions results from this study with some existing tensions being dwarfed and new tensions being born. In particular using the HPQCD $B^0_{s,d}-\bar B^0_{s,d}$ hadronic matrix elements a $3.1σ$ tension in $ΔM_s$ independently of $γ$ is found. For $60^\circ\leγ\le 75^\circ$ the tension in $ΔM_d$ between $4.0σ$ and $1.1σ$ is found and in the case of $ε_K$ between $5.2σ$ and $2.1σ$. Moreover, the room for new physics in $K^+\toπ^+ν\barν$, $K_L\toπ^0ν\barν$ and $B\to K(K^*)ν\barν$ decays is significantly increased. We compare the results in this EXCLUSIVE scenario with the HYBRID one in which $|V_{cb}|$ in the former scenario is replaced by the most recent inclusive $|V_{cb}|$ and present the dependence of all observables considered by us in both scenarios as functions of $γ$. We also compare the determination of $|V_{cb}|$ from $ΔM_s$, $ΔM_d$, $ε_K$ and $S_{ψK_S}$ using $B^0_{s,d}-\bar B^0_{s,d}$ hadronic matrix elements from LQCD with $2+1+1$ flavours, $2+1$ flavours and their average. Only for the $2+1+1$ case values for $β$ and $γ$ exist for which the same value of $|V_{cb}|$ is found: $|V_{cb}|=42.6(4)\times 10^{-3}$. This in turn implies a $2.7σ$ anomaly in $B_s\toμ^+μ^-$.

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arXiv2022

Searching for New Physics in Rare $K$ and $B$ Decays without $|V_{cb}|$ and $|V_{ub}|$ Uncertainties

We reemphasize the strong dependence of the branching ratios $B(K^+\toπ^+ν\barν)$ and $B(K_L\toπ^0ν\barν)$ on $|V_{cb}|$ that is stronger than in rare $B$ decays, in particular for $K_L\toπ^0ν\barν$. Thereby the persistent tension between inclusive and exclusive determinations of $|V_{cb}|$ weakens the power of these theoretically clean decays in the search for new physics (NP). We demonstrate how this uncertainty can be practically removed by considering within the SM suitable ratios of the two branching ratios between each other and with other observables like the branching ratios for $K_S\toμ^+μ^-$, $B_{s,d}\toμ^+μ^-$ and $B\to K(K^*)ν\barν$. We use as basic CKM parameters $V_{us}$, $|V_{cb}|$ and the angles $β$ and $γ$ in the unitarity triangle (UT). This avoids the use of the problematic $|V_{ub}|$. A ratio involving $B(K^+\toπ^+ν\barν)$ and $B(B_s\toμ^+μ^-)$ while being $|V_{cb}|$-independent exhibits sizable dependence on the angle $γ$. It should be of interest for several experimental groups in the coming years. We point out that the $|V_{cb}|$-independent ratio of $B(B^+\to K^+ν\barν)$ and $B(B_s\toμ^+μ^-)$ from Belle II and LHCb signals a $1.8σ$ tension with its SM value. As a complementary test of the Standard Model, we propose to extract $|V_{cb}|$ from different observables as a function of $β$ and $γ$. We illustrate this with $ε_K$, $ΔM_d$ and $ΔM_s$ finding tensions between these three determinations of $|V_{cb}|$ within the SM. From $ΔM_s$ and $S_{ψK_S}$ alone we find $|V_{cb}|=41.8(6)\times 10^{-3}$ and $|V_{ub}|=3.65(12)\times 10^{-3}$. We stress the importance of a precise measurement of $γ$. We obtain most precise SM predictions for considered branching ratios of rare K and B decays to date.

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arXiv2022

$\varepsilon'/\varepsilon$ in the Standard Model and Beyond: 2021

The present status of the ratio $\varepsilon'/\varepsilon$ in the Standard Model (SM) is summarized. In particular we stress the differences between three approaches that attempt to calculate $\varepsilon'/\varepsilon$ within the SM: Lattice QCD, Dual QCD and Chiral Perturbation Theory. As presently there is still a significant room left for new physics (NP) contributions, we summarize the present status of the technology that has been recently developed with the goal to analyze $\varepsilon'/\varepsilon$ and its correlations with other observables within the Weak Effective Theory (WET) and the Standard Model Effective Field Theory (SMEFT). We also make a few comments on the interpretation of the main dynamics behind the $ΔI=1/2$ rule in $K\toππ$ decays.

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arXiv2022

Standard Model Predictions for Rare $K$ and $B$ Decays without $|V_{cb}|$ and $|V_{ub}|$ Uncertainties

The persistent tensions between inclusive and exclusive determinations of $|V_{cb}|$ and $|V_{ub}|$ weaken the power of theoretically clean rare $K$ and $B$ decays in the search for new physics (NP). We demonstrate how this uncertainty can be practically removed by considering within the SM suitable ratios of various branching ratios. This includes the branching ratios for $K^+\toπ^+ν\barν$, $K_{L}\toπ^0ν\barν$, $K_S\toμ^+μ^-$, $B_{s,d}\toμ^+μ^-$ and $B\to K(K^*)ν\barν$. Also $ε_K$, $ΔM_d$, $ΔM_s$ and the mixing induced CP-asymmetry $S_{ψK_S}$, all measured already very precisely, play an important role in this analysis. The highlights of our analysis are 16 $|V_{cb}|$ and $|V_{ub}|$ independent ratios that often are independent of the CKM arameters or depend only on the angles $β$ and $γ$ in the Unitarity Triangle with $β$ already precisely known and $γ$ to be measured precisely in the coming years by the LHCb and Belle II collaborations. Once $γ$ Once $γ$ is measured precisely these 16 ratios taken together are expected to be a powerful tool in the search for new physics. Assuming no NP in $|ε_K|$ and $S_{ψK_S}$ we determine independently of $|V_{cb}|$: $\mathcal{B}(K^+\toπ^+ν\barν)_\text{SM}= (8.60\pm0.42)\times 10^{-11}$ and $\mathcal{B}(K_L\toπ^0ν\barν)_\text{SM}=(2.94\pm 0.15)\times 10^{-11}$. This are the most precise determinations to date. Assuming no NP in $ΔM_{s,d}$ allows to obtain analogous results for all $B$ decay branching ratios considered in our paper without any CKM uncertainties.

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arXiv2022

On the Importance of Rare Kaon Decays: A Snowmass 2021 White Paper

We stress the importance of precise measurements of rare decays $K^+\rightarrowπ^+ν\barν$, $K_L\rightarrowπ^0ν\barν$, $K_{L,S}\toμ^+μ^-$ and $K_{L,S}\toπ^0\ell^+\ell^-$ for the search of new physics (NP). This includes both branching ratios and the distributions in $q^2$, the invariant mass-squared of the neutrino system in the case of $K^+\rightarrowπ^+ν\barν$ and $K_L\rightarrowπ^0ν\barν$ and of the $\ell^+\ell^-$ system in the case of the remaining decays. In particular the correlations between these observables and their correlations with the ratio $\varepsilon'/\varepsilon$ in $K_L\toππ$ decays, the CP-violating parameter $\varepsilon_K$ and the $K^0-\bar K^0$ mass difference $ΔM_K$, should help to disentangle the nature of possible NP. We stress the strong sensitivity of all observables with the exception of $ΔM_K$ to the CKM parameter $|V_{cb}|$ and list a number of $|V_{cb}|$-independent ratios within the SM which exhibit rather different dependences on the angles $β$ and $γ$ of the unitarity triangle. The particular role of these decays in probing very short distance scales far beyond the ones explored at the LHC is emphasized. In this context the role of the Standard Model Effective Field Theory (SMEFT) is very important. We also address briefly the issue of the footprints of Majorana neutrinos in $K^+\rightarrowπ^+ν\barν$ and $K_L\rightarrowπ^0ν\barν$.

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arXiv2021

General non-leptonic $ΔF=1$ WET at the NLO in QCD

We reconsider the complete set of four-quark operators in the Weak Effective Theory (WET) for non-leptonic $ΔF=1$ decays that govern $s\to d$ and $b\to d, s$ transitions in the Standard Model (SM) and beyond, at the Next-to-Leading Order (NLO) in QCD. We discuss cases with different numbers $N_f$ of active flavours, intermediate threshold corrections, as well as the issue of transformations between operator bases beyond leading order to facilitate the matching to high-energy completions or the Standard Model Effective Field Theory (SMEFT) at the electroweak scale. As a first step towards a SMEFT NLO analysis of $K\toππ$ and non-leptonic $B$-meson decays, we calculate the relevant WET Wilson coefficients including two-loop contributions to their renormalization group running, and express them in terms of the Wilson coefficients in a particular operator basis for which the one-loop matching to SMEFT is already known.

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arXiv2021

Searching for New Physics with $\overline{\mathcal{B}}(B_{s,d}\toμ\barμ)/ΔM_{s,d}$

We reemphasize that the ratio $R_{sμ} \equiv \overline{\mathcal{B}}(B_s\toμ\barμ)/ΔM_s$ is a measure of the tension of the Standard Model (SM) with latest measurements of $\overline{\mathcal{B}}(B_s\toμ\barμ)$ that does not suffer from the persistent puzzle on the $|V_{cb}|$ determinations from inclusive versus exclusive $b\to c\ell\barν$ decays and which affects the value of the CKM element $|V_{ts}|$ that is crucial for the SM predictions of both $\overline{\mathcal{B}}(B_s\toμ\barμ)$ and $ΔM_s$, but cancels out in the ratio $R_{sμ}$. In our analysis we include higher order electroweak and QED corrections und adapt the latest hadronic input to find a tension of about $2σ$ for $R_{sμ}$ measurements with the SM independently of $|V_{ts}|$. We also discuss the ratio $R_{dμ}$ which could turn out, in particular in correlation with $R_{sμ}$, to be useful for the search for New Physics, when the data on both ratios improves. Also $R_{dμ}$ is independent of $|V_{cb}|$ or more precisely $|V_{td}|$.

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arXiv2021

BSM Master Formula for $\varepsilon'/\varepsilon$ in the WET Basis at NLO in QCD

As an important step towards a complete next-to-leading order (NLO) QCD analysis of the ratio $\varepsilon'/\varepsilon$ within the Standard Model Effective Field Theory (SMEFT), we present for the first time the NLO master formula for the BSM part of this ratio expressed in terms of the Wilson coefficients of all contributing operators evaluated at the electroweak scale. To this end we use the common Weak Effective Theory (WET) basis (the so-called JMS basis) for which tree-level and one-loop matching to the SMEFT are already known. The relevant hadronic matrix elements of BSM operators at the electroweak scale are taken from Dual QCD approach and the SM ones from lattice QCD. It includes the renormalization group evolution and quark-flavour threshold effects at NLO in QCD from hadronic scales, at which these matrix elements have been calculated, to the electroweak scale.

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arXiv2021

The charm of 331

We perform a detailed analysis of flavour changing neutral current processes in the charm sector in the context of 331 models. As pointed out recently, in the case of $Z^\prime$ contributions in these models there are no new free parameters beyond those already present in the $B_{d,s}$ and $K$ meson systems analyzed in the past. As a result, definite ranges for new Physics (NP) effects in various charm observables could be obtained. While generally NP effects turn out to be small, in a number of observables they are much larger than the tiny effects predicted within the Standard Model. In particular we find that the branching ratio of the mode $D^0 \to μ^+ μ^-$, despite remaining tiny, can be enhanced by 6 orders of magnitude with respect to the SM. We work out correlations between this mode and rare $B_{d,s}$ and $K$ decays. We also discuss neutral charm meson oscillations and CP violation in the charm system. In particular, we point out that 331 models provide new weak phases that are a necessary condition to have non-vanishing CP asymmetries. In the case of $ΔA_{CP}$, the difference between the CP asymmetries in $D^0 \to K^+ K^-$ and $D^0 \to π^+ π^-$, we find that agreement with experiment can be obtained provided that two conditions are verified: the phases in the ranges predicted in 331 models and large hadronic matrix elements.

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arXiv2021

Global Analysis of Leptophilic Z' Bosons

New neutral heavy gauge bosons ($Z^\prime$) are predicted within many extensions of the Standard Model. While in case they couple to quarks the LHC bounds are very stringent, leptophilic $Z^\prime$ bosons (even with sizable couplings) can be much lighter and therefore lead to interesting quantum effects in precision observables (like $(g-2)_μ$) and generate flavour violating decays of charged leptons. In particular, $\ell\to\ell^\primeν\barν$ decays, anomalous magnetic moments of charged leptons, $\ell\to\ell^\primeγ$ and $\ell\to3\ell^\prime$ decays place stringent limits on leptophilic $Z^\prime$ bosons. Furthermore, in case of mixing $Z^\prime$ with the SM $Z$, $Z$ pole observables are affected. In light of these many observables we perform a global fit to leptophilic $Z^\prime$ models with the main goal of finding the bounds for the $Z^\prime$ couplings to leptons. To this end we consider a number of scenarios for these couplings. While in generic scenarios correlations are weak, this changes once additional constraints on the couplings are imposed. In particular, if one considers an $L_μ-L_τ$ symmetry broken only by left-handed rotations, or considers the case of $τ-μ$ couplings only. In the latter setup, on can explain the $(g-2)_μ$ anomaly and the hint for lepton flavour universality violation in $τ\toμν\barν/τ\to eν\barν$ without violating bounds from electroweak precision observables.

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arXiv2021

The $ε'/ε$-Story: 1976-2021

The ratio $ε'/ε$ measures the size of the direct CP violation in $K_L\toππ$ decays $(ε^\prime)$ relative to the indirect one described by $ε$ and is very sensitive to new sources of CP violation. As such it played a prominent role in particle physics already for 45 years. Due to the smallness of $ε'/ε$ its measurement required heroic efforts in the 1980s and the 1990s on both sides of the Atlantic with final results presented by NA48 and KTeV collaborations 20 years ago. Unfortunately, even 45 years after the first calculation of $ε'/ε$ we do not know to which degree the Standard Model agrees with this data and how large is the room left for new physics contributions to this ratio. This is due to significant non-perturbative (hadronic) uncertainties accompanied by partial cancellation between the QCD penguin contributions and electroweak penguin contributions. While the significant control over the short distance perturbative effects has been achieved already in the early 1990s, with several improvements since then, different views on the non-perturbative contributions to $ε'/ε$ have been expressed by different authors over last thirty years. In fact even today the uncertainty in the room left for NP contributions to $ε'/ε$ is very significant. My own work on $ε'/ε$ started in 1983 and involved both perturbative and non-perturbative calculations. This writing is a non-technical recollection of the steps which led to the present status of $ε'/ε$ including several historical remarks not known to everybody. The present status of the $ΔI=1/2$ rule is also summarized. This story is dedicated to Jean-Marc Gerard on the occasion of the 35th anniversary of our collaboration and his 64th birthday.

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arXiv2021

Leptoquarks meet $\varepsilon'/\varepsilon$ and rare Kaon processes

We analyse for the first time the CP violating ratio $\varepsilon'/\varepsilon$ in $K\to ππ$ decays in leptoquark (LQ) models. Assuming a mass gap to the electroweak (EW) scale, the main mechanism for LQs to contribute to $\varepsilon'/\varepsilon$ is EW gauge-mixing of semi-leptonic into non-leptonic operators, which we treat in the Standard Model effective theory (SMEFT). We perform also the one-loop decoupling for scalar LQs, finding that in all models with both left-handed and right-handed LQ couplings box-diagrams generate numerically strongly enhanced EW-penguin operators $Q_{8,8'}$ already at the LQ scale. We then investigate correlations of $\varepsilon'/\varepsilon$ with rare Kaon processes ($K_L\toπ^0ν\barν$, $K^+\toπ^+ν\barν$, $K_L\toπ^0\ell\bar\ell$, $K_S\toμ\barμ$, $ΔM_K$ and $\varepsilon_K$) and find that even imposing only a moderate enhancement of $(\varepsilon'/\varepsilon)_{\rm NP} = 5 \times 10^{-4}$ to explain the current anomaly hinted by the Dual QCD approach and RBC-UKQCD lattice QCD calculations leads to conflicts with experimental upper bounds on rare Kaon processes. They exclude all LQ models with only a single coupling as an explanation of the $\varepsilon'/\varepsilon$ anomaly and put strong-to-serious constraints on parameter spaces of the remaining models. Future results on $K^+\toπ^+ν\barν$ from the NA62 collaboration, $K_L\toπ^0ν\barν$ from the KOTO experiment and $K_S\toμ\barμ$ from LHCb will even stronger exhibit the difficulty of LQ models in explaining the measured $\varepsilon'/\varepsilon$, in case the $\varepsilon'/\varepsilon$ anomaly will be confirmed by improved lattice QCD calculations. Hopefully also improved measurements of $K_L\toπ^0\ell\bar\ell$ decays will one day help in this context.

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arXiv2020

SMEFT ATLAS of $ΔF=2$ Transitions

We present a model-independent anatomy of the $ΔF=2$ transitions $K^0-\bar K^0$, $B_{s,d}-\bar B_{s,d}$ and $D^0-\bar D^0$ in the context of the Standard Model Effective Field Theory (SMEFT). We present two master formulae for the mixing amplitude $\big[M_{12} \big]_\text{BSM}$. One in terms of the Wilson coefficients (WCs) of the Low-Energy Effective Theory (LEFT) operators evaluated at the electroweak scale $μ_\text{ew}$ and one in terms of the WCs of the SMEFT operators evaluated at the BSM scale $Λ$. The coefficients $P_a^{ij}$ entering these formulae contain all the information below the scales $μ_\text{ew}$ and $Λ$, respectively. Renormalization group effects from the top-quark Yukawa coupling play the most important role. The collection of the individual contributions of the SMEFT operators to $\big[M_{12}\big]_\text{BSM}$ can be considered as the SMEFT ATLAS of $ΔF=2$ transitions and constitutes a travel guide to such transitions far beyond the scales explored by the LHC. We emphasize that this ATLAS depends on whether the down-basis or the up-basis for SMEFT operators is considered. We illustrate this technology with tree-level exchanges of heavy gauge bosons ($Z^\prime$, $G^\prime$) and corresponding heavy scalars.

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