Electroweak Penguin Research Articles

Prospects for the Belle II Experiment to Further Elucidate the KM Mechanism and Beyond

Abstract We present prospects for the Belle II experiment to further elucidate the KM mechanism and beyond. Recent measurements of the CKM parameter, and the radiative and electroweak penguin decays are also reported.

The branching fraction of {B}_s^0to {K}^0{overline{K}}^0 : three puzzles

The branching fraction of the {B}_sto {K}^0{overline{K}}^0 decay has been recently measured by the LHCb and Belle experiments. We study the consistency of the measured value with three relations to other decay rates and CP asymmetries which follow from the Standard Model, and from the approximate flavor SU(3) symmetry of the strong interactions. We find that each of these relations is violated at a level of above 3σ. We argue that various subleading effects — rescattering, electroweak penguins and SU(3) breaking — if larger than theoretically expected, can account for some of these puzzles, but not for all of them simultaneously.

Electroweak Penguin Decays of b-Flavored Hadrons

In the past decade, electroweak penguin decays have provided a number of precision measurements and have become one of the most competitive ways to search for New Physics describing phenomena beyond the Standard Model. An overview of the measurements made at the B factories and hadron colliders is given, and the experimental methods are presented. Experimental measurements required to provide further insight into present indications of New Physics are discussed.

Complete analysis of all B→πK decays

The Standard Model (SM) predicts that $\Delta A_{\rm CP}$, the difference between the direct CP asymmetries for the modes $B^+\to \pi^0 K^+$ and $B^0\to \pi^- K^+$ that are related by weak isospin, should be close to zero. There has been a recent claim by the LHCb Collaboration that the measured value of $\Delta A_{\rm CP}$ shows an uncomfortable tension with the SM prediction, almost at the $8\sigma$ level. Motivated by this claim, we critically re-examine the data on all the $B\to \pi K$ modes, including the CP asymmetries and CP-averaged branching fractions. From a combined Bayesian analysis with the topological amplitudes and their phases as the free parameters, we find that the best-fit region has a large overlap with the parameter space favoured in the SM, albeit with some enhancement for the electroweak penguin and the colour-suppressed tree amplitudes, consistent with the findings of earlier studies. We find that in this SM-like region, $\Delta A_{\rm CP}$ is more than 5$\sigma$ away from zero and the tension with the global average, as well as the LHCb result, is within $2\sigma$. Thus we conclude that there is not yet enough motivation to go beyond the SM.

The \(\varepsilon '/\varepsilon \)-story: 1976–2021

The ratio $\epsilon'/\epsilon$ measures the size of the direct CP violation in $K_L\to\pi\pi$ decays $(\epsilon^\prime)$ relative to the indirect one described by $\epsilon$ 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 $\epsilon'/\epsilon$ 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 $\epsilon'/\epsilon$ 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 $\epsilon'/\epsilon$ have been expressed by different authors over last thirty years. In fact even today the uncertainty in the room left for NP contributions to $\epsilon'/\epsilon$ is very significant. My own work on $\epsilon'/\epsilon$ 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 $\epsilon'/\epsilon$ including several historical remarks not known to everybody. The present status of the $\Delta I=1/2$ 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.

Another SMEFT story: Z\u2032 facing new results on \u03b5\u2032/\u03b5, \u2206MK and K \u2192 pi nu overline{nu}

Recently the RBC-UKQCD lattice QCD collaboration presented new results for the hadronic matrix elements relevant for the ratio ε′/ε in the Standard Model (SM) albeit with significant uncertainties. With the present knowledge of the Wilson coefficients and isospin breaking effects there is still a sizable room left for new physics (NP) contributions to ε′/ε which could both enhance or suppress this ratio to agree with the data. The new SM value for the K0 − {overline{K}}^0 mass difference ∆MK from RBC-UKQCD is on the other hand by 2σ above the data hinting for NP required to suppress ∆MK. Simultaneously the most recent results for K+ → {pi}^{+}nu overline{nu} from NA62 and for KL → {pi}^0nu overline{nu} from KOTO still allow for significant NP contributions. We point out that the suppression of ∆MK by NP requires the presence of new CP-violating phases with interesting implications for K → pi nu overline{nu} , KS → μ+μ− and KL → π0ℓ+ℓ− decays. Considering a Z′-scenario within the SMEFT we analyze the dependence of all these observables on the size of NP still allowed by the data on ε′/ε. The hinted ∆MK anomaly together with the εK constraint implies in the presence of only left-handed (LH) or right-handed (RH) flavour-violating Z′ couplings strict correlation between K+ → {pi}^{+}nu overline{nu} and KL → {pi}^0nu overline{nu} branching ratios so that they are either simultaneously enhanced or suppressed relative to SM predictions. An anticorrelation can only be obtained in the presence of both LH and RH couplings. Interestingly, the NP QCD penguin scenario for ε′/ε is excluded by SMEFT renormalization group effects in εK so that NP effects in ε′/ε are governed by electroweak penguins. We also investigate for the first time whether the presence of a heavy Z′ 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.

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 eta _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)}(mu ) and B_8^{(3/2)}(mu ) at the mu -scales used by the RBC-UKQCD collaboration and at lower scales mathcal {O}(1, text {GeV}) used by ChPT and Dual QCD (DQCD). We present semi-analytic formulae for (varepsilon '/varepsilon )_text {SM} in terms of these parameters and hat{Omega }_text {eff} that summarizes isospin-breaking corrections to this ratio. We stress the importance of lattice calculations of the mathcal {O}(alpha _{text {em}}) contributions to the hadronic matrix elements necessary for the removal of renormalization scheme dependence at mathcal {O}(alpha _{text {em}}) in the present analyses of varepsilon '/varepsilon .

Constraining electroweak penguin graph contributions in measurements of the CKM phase alpha using B→ππ and B→ρρ decays

The unitarity of the Cabibbo-Kobayashi-Maskawa (CKM) matrix has been well established by both direct and indirect measurements without any evidence of discrepancy. The CKM weak phase $\alpha$ is directly measured using an isospin analysis in $B\rightarrow \pi\pi$ and $B\to \rho\rho$ assuming that electroweak penguin contributions are ignorable. However, electroweak penguins are sensitive to NP, hence, it is important to experimentally estimate their effects. We determine the size of both electroweak penguin and isospin amplitudes, directly from $B\rightarrow \pi\pi$ and $B\to \rho\rho$ experimental data, using in addition the indirectly measured value of $\alpha$. We find that electroweak penguin contribution are indeed small and agree with SM expectations within $1\sigma$. We also find that there is a mild enhancement of the $\Delta I=\tfrac{1}{2}$ transition amplitude.

The Optimal Strategy for ε ′/ε 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 ε ′/ε in the Standard Model. In particular, I emphasize the importance of the correct matching of the long-distance and short-distance contributions to ε ′/ε, which presently is only achieved by RBC-UKQCD lattice QCD collaboration and by the analytical Dual QCD approach. An important 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 contributions and µ t in m t (µ t ) in the case of electroweak penguin contributions play the most important roles. Presently the error on ε ′/ε is dominated by the uncertainties in the QCDP parameter and the isospin-breaking parameter . We present a table illustrating this.

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 mu _W and in particular to mu _t in m_t(mu _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 mu = m_c=1.3,, text {GeV}, we find (varepsilon '/varepsilon )_mathrm{SM} = (9.4 pm 3.5) times 10^{-4}, whereas including them results in (varepsilon '/varepsilon )_mathrm{SM} = (5.6pm 2.4)times 10^{-4}. This is an example of an anomaly at the 3.3,sigma 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 {widehat{Omega }}_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.

The Belle II Physics Book

We present the physics program of the Belle II experiment, located on the intensity frontier SuperKEKB $e^+e^-$ collider. Belle II collected its first collisions in 2018, and is expected to operate for the next decade. It is anticipated to collect 50/ab of collision data over its lifetime. This book is the outcome of a joint effort of Belle II collaborators and theorists through the Belle II theory interface platform (B2TiP), an effort that commenced in 2014. The aim of B2TiP was to elucidate the potential impacts of the Belle II program, which includes a wide scope of physics topics: B physics, charm, tau, quarkonium, electroweak precision measurements and dark sector searches. It is composed of nine working groups (WGs), which are coordinated by teams of theorist and experimentalists conveners: Semileptonic and leptonic B decays, Radiative and Electroweak penguins, phi_1 and phi_2 (time-dependent CP violation) measurements, phi_3 measurements, Charmless hadronic B decay, Charm, Quarkonium(like), tau and low-multiplicity processes, new physics and global fit analyses. This book highlights "golden- and silver-channels", i.e. those that would have the highest potential impact in the field. Theorists scrutinised the role of those measurements and estimated the respective theoretical uncertainties, achievable now as well as prospects for the future. Experimentalists investigated the expected improvements with the large dataset expected from Belle II, taking into account improved performance from the upgraded detector.

\u03f5K and \u03f5\u2032/\u03f5 in a diquark model

Based on the calculations using the lattice QCD by the RBC-UKQCD collaboration and a large Nc dual QCD, the resulting ϵ′/ϵ, which is less than the experimental data by more than a 2σ in the standard model (SM), suggests the necessity of a new physics effect. In order to complement the insufficient ϵ′/ϵ, we study the extension of the SM with a colored scalar in a diquark model. In addition to the pure diquark box diagrams, it is found that the box diagrams with one W-boson and one diquark, ignored in the literature, play an important role in the ΔS = 2 process. The mass difference between KL and KS in the diquark model is well below the current data, whereas the Kaon indirect CP violation ϵK gives a strict constraint on the new parameters. Three mechanisms are classified in the study of ϵ′/ϵ. They include a tree-level diagram, QCD and electroweak (EW) penguins, and chromomagnetic operators (CMOs). Taking the Kobayashi-Maskawa phase as the unique CP source, we analyze each contribution of the three mechanisms in detail and conclude that with the exception of QCD and EW penguins, the tree and CMO effects can singly enhance ϵ′/ϵ to be of mathcal{O} (10−3), depending on the values of the free parameters, when the bound from ϵK is satisfied.

Exploring Brightarrow pi pi , pi K decays at the high-precision frontier

The Brightarrow pi pi ,pi K system offers a powerful laboratory to probe strong and weak interactions. Using the isospin symmetry, we determine hadronic Brightarrow pi pi parameters from data where new measurements of direct CP violation in B^0_drightarrow pi ^0pi ^0 resolve a discrete ambiguity. With the help of the SU(3) flavour symmetry, the Brightarrow pi pi parameters can be converted into their Brightarrow pi K counterparts, thereby allowing us to make predictions of observables. A particularly interesting decay is B^0_drightarrow pi ^0 K_mathrm{S} as it exhibits mixing-induced CP violation. Using an isospin relation, complemented with a robust SU(3) input, we calculate correlations between the direct and mixing-induced CP asymmetries of B^0_drightarrow pi ^0 K_mathrm{S}, which are the theoretically cleanest Brightarrow pi K probes. Interestingly, they show tensions with respect to the Standard Model. Should this Brightarrow pi K puzzle originate from New Physics, electroweak penguins offer an attractive scenario for new particles to enter. We present a strategy to determine the parameters characterising these topologies and obtain the state-of-the-art picture from current data. In the future, this method will allow us to reveal the Brightarrow pi K dynamics and to obtain insights into the electroweak penguin sector with unprecedented precision.

Towards new frontiers with B → πK decays

Exploring correlations between the CP asymmetries of Bd0→π0KS following from an isospin relation, we uncover new tensions with the Standard Model in data for neutral B→πK decays. Should this intriguing picture originate from New Physics, a modified electroweak penguin sector provides a key scenario. We present a new strategy to reveal the underlying physics, apply it to current B→πK data, and discuss the excellent prospects for Belle II.

Revisiting final state interaction in charmless Bq→PP decays

Various new measurements in charmless ${B}_{u,d,s}\ensuremath{\rightarrow}PP$ modes, where $P$ is a low lying pseudoscalar meson, are reported by Belle and LHCb. These include the rates of ${B}^{0}\ensuremath{\rightarrow}{\ensuremath{\pi}}^{0}{\ensuremath{\pi}}^{0}$, $\ensuremath{\eta}{\ensuremath{\pi}}^{0}$, ${B}_{s}\ensuremath{\rightarrow}{\ensuremath{\eta}}^{\ensuremath{'}}{\ensuremath{\eta}}^{\ensuremath{'}}$, ${B}^{0}\ensuremath{\rightarrow}{K}^{+}{K}^{\ensuremath{-}}$ and ${B}_{s}^{0}\ensuremath{\rightarrow}{\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{\ensuremath{-}}$ decays. Some of these modes are highly suppressed and are among the rarest $B$ decays. Direct $CP$ asymmetries on various modes are constantly updated. It is well known that direct $CP$ asymmetries and rates of suppressed modes are sensitive to final state interaction (FSI). As new measurements are reported and more data will be collected, it is interesting and timely to revisit the rescattering effects in ${B}_{u,d,s}\ensuremath{\rightarrow}PP$ states. We perform a ${\ensuremath{\chi}}^{2}$ analysis with all available data on $CP$-averaged rates and $CP$ asymmetries in ${\overline{B}}_{u,d,s}\ensuremath{\rightarrow}PP$ decays. Our numerical results are compared to data and those from factorization approach. The quality of the fit is improved significantly from the factorization results in the presence of rescattering. The relations on topological amplitudes and rescattering are explored and they help to provide a better understanding of the effects of FSI. As suggested by U(3) symmetry on topological amplitudes and FSI, a vanishing exchange rescattering scenario is considered. The exchange, annihilation, $u$-penguin, $u$-penguin annihilation, and some electroweak penguin amplitudes are enhanced significantly via annihilation and total annihilation rescatterings. In particular, the $u$-penguin annihilation amplitude is sizably enhanced by the tree amplitude via total annihilation rescattering. These enhancements affect rates and $CP$ asymmetries. Predictions can be checked in the near future.

Gluino-mediated electroweak penguin with flavor-violating trilinear couplings

In light of a discrepancy of the direct CP violation in K → ππ decays, ε′/εK , we investigate gluino contributions to the electroweak penguin, where flavor violations are induced by squark trilinear couplings. Top-Yukawa contributions to ΔS = 2 observables are taken into account, and vacuum stability conditions are evaluated in detail. It is found that this scenario can explain the discrepancy of ε′/εK for the squark mass smaller than 5.6 TeV. We also show that the gluino contributions can amplify mathrm{mathcal{B}}left(Kto pi nu overline{nu}right) , ℬ(KS → μ+μ−)eff and ΔACP(b → sγ). Such large effects could be measured in future experiments.

Disentangling weak and strong interactions in Brightarrow K^{*}(rightarrow Kpi )pi Dalitz-plot analyses

Dalitz-plot analyses of Brightarrow Kpi pi decays provide direct access to decay amplitudes, and thereby weak and strong phases can be disentangled by resolving the interference patterns in phase space between intermediate resonant states. A phenomenological isospin analysis of Brightarrow K^*(rightarrow Kpi )pi decay amplitudes is presented exploiting available amplitude analyses performed at the BaBar, Belle and LHCb experiments. A first application consists in constraining the CKM parameters thanks to an external hadronic input. A method, proposed some time ago by two different groups and relying on a bound on the electroweak penguin contribution, is shown to lack the desired robustness and accuracy, and we propose a more alluring alternative using a bound on the annihilation contribution. A second application consists in extracting information on hadronic amplitudes assuming the values of the CKM parameters from a global fit to quark flavour data. The current data yields several solutions, which do not fully support the hierarchy of hadronic amplitudes usually expected from theoretical arguments (colour suppression, suppression of electroweak penguins), as illustrated from computations within QCD factorisation. Some prospects concerning the impact of future measurements at LHCb and Belle II are also presented. Results are obtained with the CKMfitter analysis package, featuring the frequentist statistical approach and using the Rfit scheme to handle theoretical uncertainties.

New physics contributions to bar{B}_s rightarrow pi ^0(rho ^0 ),eta ^{(')} decays

The decay modes bar{B}_s rightarrow pi ^0(rho ^0 ),eta ^{(')} are dominated by electroweak penguins that are small in the standard model. In this work we investigate the contributions to these penguins from a model with an additional U(1)' gauge symmetry and show there effects on the branching ratios of bar{B}_s rightarrow pi ^0(rho ^0 ),eta ^{(')} . In a scenario of the model, where Z^prime couplings to the left-handed quarks vanish, we show that the maximum enhancement occurs in the branching ratio of bar{B}^0_srightarrow ,pi ^0,eta ' where it can reach 6 times the SM prediction. On the other hand, in a scenario of the model where Z^prime couplings to both left-handed and right-handed quarks do not vanish, we find that Z^prime contributions can enhance the branching ratio of B^0_srightarrow ,rho ^0,eta up to one order of magnitude comparing to the SM prediction for several sets of the parameter space where both Delta M_{B_s} and S_{psi phi } constraints are satisfied. This kind of enhancement occurs for a rather fine-tuned point where the Delta M_{B_s} constraint on mid S_mathrm{SM} (B_s) + S_{Z'} (B_s)mid is fulfilled by overcompensating the SM via S_{Z'} (B_s) simeq -2 S_mathrm{SM} (B_s).

Flavor changing neutral current transition of B to a1 with light-cone sum rules

The $B\to a_1 \ell^+ \ell^-$ decays occur by the electroweak penguin and box diagrams which can be performed through the flavor changing neutral current (FCNC). We calculate the form factors of the FCNC $B \to a_1$ transitions in the light--cone sum rules approach, up to twist--4 distribution amplitudes of the axial vector meson $a_1$. Forward--backward asymmetry, as well as branching ratios of $B\to a_1\ell^{+}\ell^{-}$, and $B\to a_1 \gamma$ decays are considered. A comparison is also made between our results and the predictions of other methods.

Singularity-free next-to-leading order ΔS = 1 renormalization group evolution and ϵ K ′ /ϵK in the Standard Model and beyond

The standard analytic solution of the renormalization group (RG) evolution for the $\Delta S = 1$ Wilson coefficients involves several singularities, which complicate analytic solutions. In this paper we derive a singularity-free solution of the next-to-leading order (NLO) RG equations, which greatly facilitates the calculation of $\epsilon_K^{\prime}$, the measure of direct $CP$ violation in $K\to \pi\pi$ decays. Using our new RG evolution and the latest lattice results for the hadronic matrix elements, we calculate the ratio $\epsilon_{K}^{\prime}/\epsilon_{K}$ (with $\epsilon_{K}$ quantifying indirect $CP$ violation) in the Standard Model (SM) at NLO to $\epsilon_{K}^{\prime}/\epsilon_{K} = (1.06 \pm 5.07) \times 10^{-4} $, which is $2.8\,\sigma$ below the experimental value. We also present the evolution matrix in the high-energy regime for calculations of new physics contributions and derive easy-to-use approximate formulae. We find that the RG amplification of new-physics contributions to Wilson coefficients of the electroweak penguin operators is further enhanced by the NLO corrections: If the new contribution is generated at the scale of 1-10 TeV, the RG evolution between the new-physics scale and the electroweak scale enhances these coefficients by 50-100 %. Our solution contains a term of order $\alpha_{EM}^2/\alpha_s^2$, which is numerically unimportant for the SM case but should be included in studies of high-scale new-physics.