arXiv subjects

Andrzej J. Buras

Publications and source records attributed to Andrzej J. Buras.

At least 19 recordsLinked to original sources

arXiv2026

Prospects for $K_{L}\toπ^{0}ν\barν$, $K_S\toμ^+μ^-$, $K_L\toπ^0 \ell^+\ell^-$ and $\varepsilon^{\prime}/\varepsilon$ after the new $K^{+}\toπ^{+}ν\barν$ result from NA62

The recently announced NA62 measurement of the $K^{+}\toπ^{+}ν\barν$ branching ratio, based on 2016--2024 data, is fully consistent with its very accurate Standard Model (SM) prediction. While it is not excluded that the final result based on 2016--2026 data will deviate from the SM prediction, the question arises whether a similar fate awaits the $K_{L}\toπ^{0}ν\barν$ decay. This decay is currently being searched for by the KOTO experiment, with the present upper bound roughly two orders of magnitude above its very precise SM prediction. The proposed KOTO II experiment aims to provide the first discovery of the $K_{L}\toπ^{0}ν\barν$ decay and measure its branching ratio. Building on the findings of several previous papers we demonstrate that in the presence of suitably chosen large new complex phases and of a small amount of new right-handed $\bar s d$ couplings, in addition to the left-handed ones, the $K_{L}\toπ^{0}ν\barν$ branching ratio can still be enhanced by one order of magnitude with respect to the SM prediction while keeping both $K^{+}\toπ^{+}ν\barν$ and $\varepsilon_K$ SM-like. Simultaneously the decays $K_S\toμ^+μ^-$, studied by LHCb, and $K_L\toπ^0\ell^+\ell^-$, searched for by KOTO II, can be strongly enhanced and the anomaly in the ratio $\varepsilon^{\prime}/\varepsilon$, as claimed by Dual QCD, removed. We illustrate this with an example of a specific $Z^\prime$ scenario.

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arXiv2026

Hunting New Animalcula with Flavour Changing Processes

This year marks the 350th anniversary of the discovery of the first animalcula (little animals) by van Leeuvanhoek in 1676.Flavour physics makes it possible to search for new animalcula at distance scales far shorter than those resolved by van Leeuwenhoek in 1676 and even shorter than those directly accessible at the Large Hadron Collider and the planned colliders in this century. I summarize various strategies for achieving this goal. While precise measurements of a wide variety of observables and their precise theoretical calculations, both within the Standard Model (SM) and beyond it, are indispensable in this context, in my view it is crucial to develop strategies for the search for New Physics (NP) that go beyond the global fits that are very popular today. While effective field theories such as WET and SMEFT are formulated in terms of Wilson coefficients of the relevant operators, with correlations characteristic of the SM and of specific NP scenarios, the most direct tests of the SM and its extensions are, in my opinion, correlations among different observables, like branching ratios of numerous decays, that are characteristic of particular new animalcula at work

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arXiv2026

Addicted to Flavour: 1976-2026

I describe my activities in Flavour Physics from 1976 to 2026. However, this 50th anniversary is not the only motivation for this writing. The second reason is the 350th anniversary of the discovery of the first animalcula by van Leeuvanhoek in 1676. Flavour physics makes it possible to search for new animalcula at distance scales far shorter than those resolved by van Leeuwenhoek in 1676 and even shorter than those directly accessible at the Large Hadron Collider. Achieving this goal requires not only precise measurements of a wide variety of processes, but also equally precise theoretical calculations, both within the Standard Model (SM) and beyond it. In this respect, next-to-leading-order (NLO) and next-to-next-to-leading-order (NNLO) QCD calculations of various Wilson coefficients in the SM and beyond it, in which I was involved for two decades, as well as reliable treatments of non-perturbative QCD effects, are indispensable. Equally important is the proper choice of observables that are best suited to revealing these new animalcula of particle physics. Moreover, in my view it is crucial to develop strategies for the search for New Physics (NP) that go beyond the global fits that are very popular today. While effective field theories such as WET and SMEFT are formulated in terms of Wilson coefficients of the relevant operators, with correlations characteristic of the SM and of specific NP scenarios, the most direct tests of the SM and its extensions are, in my opinion, correlations among different observables that are characteristic of particular new animalcula at work. Numerous colourful plots in this article illustrate this point. I hope that these ideas are clearly conveyed in my Flavour Autobiography, which also includes my memories of many conferences, workshops, and schools, as well as related anecdotes that are not always directly connected to physics.

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arXiv2025

SMEFT ATLAS: The Landscape Beyond the Standard Model

The Standard Model Effective Field Theory (SMEFT) based on the unbroken gauge group $\text{SU(3)}_C\otimes\text{SU(2)}_L\otimes\text{U(1)}_Y$ and containing only particles of the Standard Model (SM) has developed in the last decade to a mature field. It is the framework to be used in the energy gap from scales sufficiently higher than the electroweak scale up to the lowest energy scale at which new particles show up. We summarize the present status of this theory with a particular emphasize on its role in the indirect search for new physics (NP). While flavour physics of both quarks and leptons is the main topic of our review, we also discuss electric dipole moments, anomalous magnetic moments $(g-2)_{μ,e}$, $Z$-pole observables, Higgs observables and high-$p_T$ scattering processes within the SMEFT. We group the observables into ten classes and list for each class the most relevant operators and the corresponding renormalization group equations (RGEs). We exhibit the correlations between different classes implied both by the operator mixing and the $\text{SU(2)}_L$ gauge symmetry. Our main goal is to provide an insight into the complicated operator structure of this framework which hopefully will facilitate the identification of valid ultraviolet completions behind possible anomalies observed in future data. Numerous colourful charts, and 85 tables, while representing rather complicated RG evolution from the NP scale down to the electroweak scale, beautify the involved SMEFT landscape. Over 950 references to the literature underline the importance and the popularity of this field. We discuss both top-down and bottom-up approaches as well as their interplay. This allows us eventually to present an atlas of different landscapes beyond the SM that includes heavy gauge bosons and scalars, vector-like quarks and leptons and leptoquarks.

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arXiv2025

On the Interplay of Constraints from $B_s$, $D$, and $K$ Meson Mixing in $Z^\prime$ Models with Implications for $b\to s ν\barν$ Transitions

Within $Z^\prime$ models, neutral meson mixing severely constrains beyond the Standard Model (SM) effects in flavour changing neutral current (FCNC) processes. However, in certain regions of the $Z^\prime$ parameter space, the contributions to meson mixing observables become negligibly small even for large $Z^\prime$ couplings. While this a priori allows for significant new physics (NP) effects in FCNC decays, we discuss how large $Z^\prime$ couplings in one neutral meson sector can generate effects in meson mixing observables of other neutral mesons, through correlations stemming from $\text{SU(2)}_L$ gauge invariance and through Renormalization Group (RG) effects in the SM Effective Field Theory (SMEFT). This is illustrated with the example of $B_s^0-\bar B_s^0$ mixing, which in the presence of both left- and right-handed $Z^\prime bs$ couplings $Δ_L^{bs}$ and $Δ_R^{bs}$ remains SM-like for $Δ_R^{bs}\approx 0.1\,Δ_L^{bs}$. We show that in this case, large $Z^\prime bs$ couplings generate effects in $D$ and $K$ meson mixing observables, but that the $D$ and $K$ mixing constraints and the relation between $Δ_R^{bs}$ and $Δ_L^{bs}$ are fully compatible with a lepton flavour universality (LFU) conserving explanation of the most recent $b\to s\ell^+\ell^-$ experimental data without violating other constraints like $e^+ e^-\to\ell^+\ell^-$ scattering. Assuming LFU, invariance under the $\text{SU(2)}_L$ gauge symmetry leads then to correlated effects in $b\to sν\barν$ observables presently studied intensively by the Belle II experiment, which allow to probe the $Z^\prime$ parameter space that is opened up by the vanishing NP contributions to $B_s^0-\bar B_s^0$ mixing. In this scenario the suppression of $B\to K(K^*)μ^+μ^-$ branching ratios implies uniquely enhancements of $B\to K(K^*)ν\barν$ branching ratios up to $20\%$.

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arXiv2025

Kaon Physics: A Cornerstone for Future Discoveries

The kaon physics programme, long heralded as a cutting-edge frontier by the European Strategy for Particle Physics, continues to stand at the intersection of discovery and innovation in high-energy physics (HEP). With its unparalleled capacity to explore new physics at the multi-TeV scale, kaon research is poised to unveil phenomena that could reshape our understanding of the Universe. This document highlights the compelling physics case, with emphasis on exciting new opportunities for advancing kaon physics not only in Europe but also on a global stage. As an important player in the future of HEP, the kaon programme promises to drive transformative breakthroughs, inviting exploration at the forefront of scientific discovery.

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arXiv2025

Hunting New Animalcula with Rare K and B Decays

We summarize the recent strategy for an efficient hunting of new animalcula with the help of rare K and B decays that avoids the use of the $V_{cb}$ and $V_{ub}$ parameters that are subject to tensions between their determinations from inclusive and exclusive decays. In particular we update the values of the $V_{cb}$-independent ratios of various K and B decay branching ratios predicted by the Standard Model. We also stress the usefulness of the $V_{cb}-γ$ plots in the search for new physics. We select the magnificant seven among rare K and B decays that should play a leading role in the search for new physics due to their theoretical cleanness: $B^+\to K^+(K^*)ν\barν$ and $K^+\toπ^+ν\barν$ measured recently by Belle II and NA62, respectively, $K_L\toπ^0ν\barν$ investigated by KOTO and also $B_{s,d}\toμ^+μ^-$ and $K_S\toμ^+μ^-$ measured by the LHCb, CMS and ATLAS experiments at CERN. %

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arXiv2024

Disentangling new physics in $K\rightarrowπ\barνν$ and $B\rightarrow K(K^*)\barνν$ observables

We investigate the possibility of disentangling different new physics contributions to the rare meson decays $K\rightarrowπ+\displaystyle{\not}E$ and $B\rightarrow K(K^*)+\displaystyle{\not}E$ through kinematic distributions in the missing energy $\displaystyle{\not}E$. We employ dimension-$6$ operators within the Low-Energy Effective Field Theory (LEFT), identifying the invisible part of the final state as either active or sterile neutrinos. Special emphasis is given to lepton-number violating (LNV) operators with scalar and tensor currents. We show analytically that contributions from scalar, vector, and tensor quark currents can be uniquely determined from experimental data of kinematic distributions. In addition, we present new correlations of branching ratios for $K$ and $B$-decays involving scalar and tensor currents. As there could a priori also be new invisible particles in the final states, we include dark-sector operators giving rise to two dark scalars, fermions, or vectors in the final state. In this context, we present new calculations of the inclusive decay rate $B\rightarrow X_s+\displaystyle{\not}E$ for dark operators. We show that careful measurements of kinematic distributions make it theoretically possible to disentangle the contribution from LEFT operators from most of the dark-sector operators, even when multiple operators are contributing. We revisit sum rules for vector currents in LEFT and show that the latter are also satisfied in some new dark-physics scenarios that could mimic LEFT. Finally, we point out that an excess in rare meson decays consistent with a LNV hypothesis would point towards highly flavor non-democratic physics in the UV, and could put high-scale leptogenesis under tension.

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arXiv2024

Expedition to the Zeptouniverse

Flavour experiments promise insights into energy scales as high as 200 TeV and distances as small as Zeptometer and offer the chance to identify New Physics

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arXiv2024

Two-Loop QCD Anomalous Dimensions of Flavour-Changing Four-Quark Operators Within and Beyond the Standard Model

We calculate the two-loop QCD anomalous dimension matrix (ADM) gamma^(1)_NDR in the NDR-MSbar scheme for all the flavour-changing four-quark dimension-six operators that are relevant in both the Standard Model and its extensions. Both current-current and penguin diagrams are included. Some of our NDR-MSbar results for Delta F=1 operators overlap with the previous calculations, but several others have never been published before. In the case of Delta F=2 operators, our results are compatible with the ones obtained by Ciuchini et al. in the Regularization-Independent renormalization scheme, but differ from their NDR-MSbar results. In order to explain the difference, we calculate the ADM of Delta F=2 operators again, extracting it from the ADM of Delta F=1 operators.

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arXiv2024

Standard Model Predictions for Rare K and B Decays without New Physics Infection

The Standard Model (SM) does not contain by definition any new physics (NP) contributions to any observable but contains four CKM parameters which are not predicted by this model. We point out that if these four parameters are determined in a global fit that includes processes which are infected by NP, the resulting SM contributions to rare decay branching ratios cannot be considered as true SM contributions to the latter. On the other hand true SM predictions, that are free from the CKM dependence, can be obtained for suitable ratios of the $K$ and $B$ rare decay branching ratios to $ΔM_s$, $ΔM_d$ and $|\varepsilon_K|$, all calculated within the SM. These three observables contain by now only small hadronic uncertainties and are already well measured so that rather precise true SM predictions for the ratios in question can be obtained. In this context the rapid test of NP infection in the $ΔF=2$ sector is provided by a $|V_{cb}|-γ$ plot that involves $ΔM_s$, $ΔM_d$, $|\varepsilon_K|$, and the mixing induced CP-asymmetry $S_{ψK_S}$. As with the present hadronic matrix elements this test turns out to be negative, assuming negligible NP infection in the $ΔF=2$ sector and setting the values of these four observables to the experimental ones, allows to obtain SM predictions for all $K$ and $B$ rare decay branching ratios that are most accurate to date and as a byproduct to obtain the full CKM matrix on the basis of $ΔF=2$ transitions alone. Using this strategy we obtain SM predictions for 26 branching ratios for rare semileptonic and leptonic $K$ and $B$ decays with the $μ^+μ^-$ pair or the $ν\barν$ pair in the final state. Most interesting turn out to be the anomalies in the low $q^2$ bin in $B^+\to K^+μ^+μ^-$ ($4.4σ$) and $B_s\to ϕμ^+μ^-$ ($4.8σ$).

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arXiv2023

Kaon Theory: 50 Years Later

We summarize the status of the Kaon Theory 50 years after the seminal paper of Kobayashi and Maskawa who pointed out that six quarks are necessary to have CP violation in the Standard Model (SM) and presented a parametrization of a $3\times 3$ unitary matrix that after the discovery of the charm quark in 1974 and the $b$ quark in 1977 dominated the field of flavour changing processes. One of the main goals of flavour physics since then was the determination of the four parameters of this matrix, which we will choose here to be $|V_{us}|$, $|V_{cb}|$ and the two angles of the unitarity triangle, $β$ and $γ$ with $|V_{us}|$ introduced by Cabibbo in 1963. I will summarize recent strategy for determination of these parameters without new physics (NP) infection. It is based on the conjecture of the absence of relevant NP contributions to $ΔF=2$ processes that indeed can be demonstrated by a negative rapid test: the $|V_{cb}|-γ$ plot. This in turn allows to obtain SM predictions for rare $K$ and $B$ decays that are most precise to date. We present strategies for the explanation of the anticipated anomaly in the ratio $\varepsilon'/\varepsilon$ and the observed anomalies in $b\to sμ^+μ^-$ transitions that are consistent with our $ΔF=2$ conjecture. In particular, the absence of NP in the parameter $\varepsilon_K$, still allows for significant NP effects in $\varepsilon'/\varepsilon$ and in rare Kaon decays, moreover in a correlated manner. Similar the absence of NP in $ΔM_s$ combined with anomalies in $b\to sμ^+μ^-$ transitions hints for the presence of right-handed quark currents. We also discuss how the nature of neutrinos, Dirac vs. Majorana one, can be probed in $K\toπν\barν$ and $B\to K(K^*)ν\barν$ decays. The present status of the $ΔI=1/2$ rule and of $\varepsilon'/\varepsilon$ is summarized.

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arXiv2023

Climbing NLO and NNLO Summits of Weak Decays: 1988-2023

I describe the history of the calculations of NLO and NNLO QCD corrections to weak decays of mesons and particle-antiparticle mixing in the period 1988-2023. Also existing calculations of electroweak and QED corrections to these processes are included in this presentation. These efforts bear some analogies to the climbing of Himalayas and various expeditions by several teams of strongly motivated "climbers" allowed to move this field from the LO through the NLO to the NNLO level. We also summarize the most recent calculations within the Standard Model Effective Field Theory. The material is meant to be an up to date review of this very advanced field in non-technical terms as much as possible and a guide to the rich literature on NLO and NNLO corrections in question. In particular we stress for which processes these calculations are crucial for the tests of the Standard Model and to be able to differentiate between numerous New Physics models. It includes several anecdotes related to the climbs that I was involved in. I hope that some of the comments made in the course of the presentation could turn out to be not only amusing but also instructive.

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arXiv2023

Waiting for Precise Measurements of $β$ and $γ$

During the last three decades the determination of the Unitarity Triangle (UT) was dominated by the measurements of its sides $R_b$ and $R_t$ through tree-level $B$ decays and the $ΔM_d/ΔM_s$ ratio, respectively, with some participation of the measurements of the angle $β$ through the mixing induced CP-asymmetries like $S_{ψK_S}$ and $\varepsilon_K$. However, as pointed out already in 2002 by Fabrizio Parodi, Achille Stocchi and the present author, the most efficient strategy for a precise determination of the apex of the UT, that is $(\bar\varrho,\barη)$, is to use the measurements of the angles $β$ and $γ$. The second best strategy would be the measurements of $R_b$ and $γ$. However, in view of the tensions between different determinations of $|V_{ub}|$ and $|V_{cb}|$, that enter $R_b$, the $(β,γ)$ strategy should be a clear winner once LHCb and Belle II will improve the measurements of these two angles. In this note we recall our finding of 2002 which should be finally realized in this decade through precise measurements of both angles by these collaborations. In this context we present two very simple formulae for $\bar\varrho$ and $\barη$ in terms of $β$ and $γ$ which could be derived by high-school students, but to my knowledge never appeared in the literature on the UT, not even in our 2002 paper. We also emphasize the importance of precise measurements of both angles that would allow to perform powerful tests of the SM through numerous $|V_{cb}|$-independent correlations between $K$ and $B$ decay branching ratios $R_i(β,γ)$ recently derived by Elena Venturini and the present author. The simple findings presented here will appear in a subsection of a much longer contribution to the proceedings of KM50 later this year. I exhibited them here so that they are not lost in the latter.

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arXiv2023

331 Model Predictions for Rare $B$ and $K$ Decays, and $ΔF=2$ Processes: an Update

Motivated by the improved results from the HPQCD lattice collaboration on the hadronic matrix elements entering $ΔM_{s,d}$ in $B_{s,d}^0-\bar B_{s,d}^0$ mixings and the increase of the experimental branching ratio for $B_s\toμ^+μ^-$, we update our 2016 analysis of various flavour observables in four 331 models, M1, M3, M13 and M16 based on the gauge group $SU(3)_C\times SU(3)_L\times U(1)_X$. These four models, which are distinguished by the quantum numbers, are selected among 24 331 models through their consistency with the electroweak precision tests and simultaneously by the relation $C_9^\text{NP}=-b\, C_{10}^\text{NP}$ with $b\ge 2$, which after new result on $B_s\toμ^+μ^-$ from CMS is favoured over the popular relation $C_9^\text{NP}=- C_{10}^\text{NP}$ predicted by several leptoquark models. In this context we investigate in particular the dependence of various observables on $|V_{cb}|$, varying it in the broad range $[0.0386,\,0.043]$, that encompasses both its inclusive and exclusive determinations. Imposing the experimental constraints from $\varepsilon_K$, $ΔM_s$, $ΔM_d$ and the mixing induced CP asymmetries $S_{ψK_S}$ and $S_{ψK_S}$, we investigate for which values of $|V_{cb}|$ the four models can be made compatible with these data and what is the impact on $B$ and $K$ branching ratios. In particular we analyse NP contributions to the Wilson coefficients $C_9$ and $C_{10}$ and the decays $B_{s,d}\toμ^+μ^-$, $K^+\rightarrowπ^+ν\barν$ and $K_L\rightarrowπ^0ν\barν$. This allows us to illustrate how the value of $|V_{cb}|$ determined together with other parameters of these models is infected by NP contributions and compare it with the one obtained recently under the assumption of the absence of NP in $\varepsilon_K$, $ΔM_s$, $ΔM_d$ and $ S_{ψK_S}$.

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arXiv2023

Simple Rules for Evanescent Operators in One-Loop Basis Transformations

Basis transformations often involve Fierz and other relations which are only valid in $D=4$ dimensions. In general $D$ space-time dimensions however, evanescent operators have to be introduced, in order to preserve such identities. Such evanescent operators contribute to one-loop basis transformations as well as to two-loop renormalization group running. We present a simple procedure on how to systematically change basis at the one-loop level by obtaining shifts due to evanescent operators. As an example we apply this method to derive the one-loop basis transformation from the BMU (Buras, Misiak and Urban) basis useful for NLO QCD calculations, to the JMS (Jenkins, Manohar and Stoffer) basis used in the matching to the SMEFT.

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arXiv2023

$Z^\prime$-Tandem Mechanism for the Suppression of New Physics in Quark Mixing with Implications for K, D and B Decays

$Z^\prime$ models belong to the ones that can most easily explain the anomalies in $b\to s μ^+μ^-$ transitions. However, such an explanation by a single $Z^\prime$ gauge boson, as done in the literature, is severly constrained by the $B^0_s-\bar B_s^0$ mixing. Also the recent finding, hat the mass differences $ΔM_s$, $ΔM_d$, the CP-violating parameter $\varepsilon_K$, and the mixing induced CP-asymmetries $S_{ψK_S}$ and $S_{ψϕ}$ can be simultaneously well described within the SM without new physics (NP) contributions, is a challenge for $Z^\prime$ models with a single $Z^\prime$ contributing at tree-level to quark mixing. We point out that including a second $Z^\prime$ in the model allows to eliminate simultaneously tree-level contributions to the five $ΔF=2$ observables used in the determination of the CKM parameters while leaving the room for NP in $ΔM_K$ and $ΔM_D$. The latter one can be removed at the price of infecting $ΔM_s$ or $ΔM_d$ by NP which is presently disfavoured. This pattern is transparently seen using the new mixing matrix for $Z^\prime$ interactions with quarks. This strategy allows significant tree-level contributions to $K$, $B_s$ and $B_d$ decays thereby allowing to explain the existing anomalies in $b\to sμ^+μ^-$ transitions and the anticipated anomaly in the ratio $\varepsilon'/\varepsilon$ much easier than in $Z^\prime$-Single scenarios. The proposed $Z^\prime$-Tandem mechanism bears some similarities to the GIM mechanism for the suppression of the FCNCs in the SM with the role of the charm quark played here by the second $Z^\prime$. However, it differs from the latter profoundly in that only NP contributions to quark mixing are eliminated at tree-level. We discuss briefly the implied flavour patterns in $K$ and $B$ decay observables in this NP scenario.

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arXiv2023

Natural Suppression of FCNCs at the One-Loop Level in $Z^\prime$ Models with Implications for K, D and B Decays

We analyse $Z^\prime$ contributions to FCNC processes at the one-loop level. In analogy to the CKM matrix we introduce two $3\times3$ unitary matrices $\hatΔ_d(Z^\prime)$ and $\hatΔ_u(Z^\prime)$ which are also hermitian. They govern the flavour interactions mediated by $Z^\prime$ between down-quarks and up-quarks, respectively, with $\hatΔ_d(Z^\prime)=\hatΔ_u(Z^\prime)\equiv \hatΔ_L(Z^\prime)$ for left-handed currents due to the unbroken $\text{SU(2)}_L$ gauge symmetry. This assures the suppression of these contributions to all $Z^\prime$ mediated FCNC processes at the one-loop level. As, in contrast to the GIM mechanism, one-loop $Z^\prime$ contributions to flavour observables in $K$ and $B_{s,d}$ systems are governed by down-quark masses, they are ${\cal O}(m^2_b/M^2_{Z^\prime})$ and negligible. With the ${\cal O}(m^2_t/M^2_{Z^\prime})$ suppression they are likely negligible also in the $D$ system. We present an explicit parametrization of $\hatΔ_L(Z^\prime)$ in terms of two mixing angles and two complex phases that distinguishes it profoundly from the CKM matrix. This framework can be generalized to purely leptonic decays with matrices analogous to the PMNS matrix but profoundly different from it. Interestingly, the breakdown of flavour universality between the first two generations and the third one, both for quark and lepton couplings to $Z^\prime$, is identified as a consequence of $\hatΔ_L(Z^\prime)$ being hermitian. The importance of the unitarity for both $\hatΔ_L(Z^\prime)$ and the CKM matrix in the light of the Cabibbo anomaly is emphasized.

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