Weak Effective Theory Research Articles

Effective theory tower for μ → e conversion

Abstract We present theoretical predictions for μ → e conversion rates using a tower of effective field theories connecting the UV to nuclear physics scales. The interactions in nuclei are described using a recently developed nonrelativistic effective theory (NRET) that organizes contributions according to bound nucleon and muon velocities, $$ {\overrightarrow{v}}_N $$ v → N and $$ {\overrightarrow{v}}_{\mu } $$ v → μ , with $$ \left|{\overrightarrow{v}}_N\right| $$ v → N >$$ \left|{\overrightarrow{v}}_{\mu}\right| $$ v → μ . To facilitate the top-down matching, we enlarge the set of Lorentz covariant nucleon-level interactions mapped onto the NRET operators to include those mediated by tensor interactions, in addition to the scalar and vector interactions already considered previously, and then match NRET nonperturbatively onto the Weak Effective Theory (WET). At the scale μ ≈ 2 GeV WET is formulated in terms of u, d, s quarks, gluons and photons as the light degrees of freedom, along with the flavor-violating leptonic current. We retain contributions from WET operators up to dimension 7, which requires the full set of 26 NRET operators. The results are encoded in the open-source Python- and Mathematica-based software suite MuonBridge, which we make available to the theoretical and experimental communities interested in μ → e conversion.

Constraining |Vcs| and physics beyond the Standard Model from exclusive (semi)leptonic charm decays

We study the available data on exclusive leptonic and semileptonic c → sℓ+ν decays within the Standard Model and beyond. Our analysis accounts for theory correlations between the relevant hadronic matrix elements through application of dispersive bounds. We find that, within a global analysis, the dispersive bounds are generally well respected and only mildly affect the extraction of the Cabibbo-Kobayashi-Maskawa (CKM) matrix element |Vcs|. Assuming Standard Model dynamics, we obtainVcs=0.957±0.003,\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\left|{V}_{cs}\\right|=0.957\\pm 0.003, $$\\end{document}which is compatible with the HFLAV/PDG reference value |Vcs| = 0.975 ± 0.006 at the 2.7σ level. Our findings lead to significant deficits in the second-row and second-column unitarity relations of the CKM matrix. Allowing for beyond the SM contributions in the Weak Effective Theory, we find very strong constraints on potential (pseudo)scalar and tensor effects. However, the data still permits sizeable CP-violating right-handed currents.

Electric dipole moments in 5+3 flavor weak effective theory

A fully generic treatment of electric dipole moments (EDMs) is presented in the CP-violating and flavor-conserving weak effective field theory (WET) with five flavors of quarks and three flavors of leptons. We systematically analyze leading contributions to EDMs originating from QCD and QED renormalization group running between the electroweak scale and low energy scales of about 2 GeV. We include the full one-loop anomalous dimension and a subset of two-loop corrections, as well as threshold corrections at the bottom, charm and τ masses. This allows us to derive master formulae in the space of generic WET for the neutron and proton EDMs, for EDMs of diamagnetic atoms, and for the precession frequencies constrained in molecular EDM experiments, from which bounds on the electron EDM are extracted. In particular, our master formulae capture the contributions of WET CP-violating operators with heavy quark and lepton flavors. As an application, we study EDM constraints on the Yukawa couplings of the Higgs boson, in both the linear and non-linear realizations of electroweak symmetry breaking.

Toward a complete description of b → uℓ− overline{nu} within the Weak Effective Theory decays

We fit the available data on exclusive semileptonic b → uℓ− overline{nu} decays within the Standard Model and in the Weak Effective Theory. Assuming Standard Model dynamics, we find left|{V}_{ub}right|={3.59}_{-0.12}^{+0.13}times {10}^{-3} . Lifting this assumption, we obtain stringent constraints on the coefficients of the ubℓν sector of the Weak Effective Theory. Performing a Bayesian model comparison, we find that a beyond the Standard Model interpretation is favoured over a Standard Model interpretation of the available data. We provide a Gaussian mixture model that enables the efficient use of our fit results in subsequent analyses beyond the Standard Model, within and beyond the framework of the Standard Model Effective Field Theory.

To (b)e or not to (b)e: no electrons at LHCb

We discuss the impact of the recent LHCb update on the two lepton-flavour universality ratios R_K and R_{K^*}, and the CMS update of B({B_s rightarrow mu ^+mu ^-}) regarding the possibility of New Physics in brightarrow sell ^+ell ^- decays. We perform global fits of the New Physics Wilson coefficients defined in the model-independent approach of the Weak Effective Theory at the b-quark mass. We discuss three different frameworks for this analysis: (i) an update limited to the experimental data but using the same theoretical framework as in earlier works, (ii) a full update concerning both the experimental inputs and the theoretical framework, (iii) an analysis without the LHCb results on electron modes. The comparison between these various sets of results allows us to identify the differences stemming from the various components of the analysis: new experimental results, new inputs for the hadronic form factors, the role played by LHCb data on electron modes. As expected, the significance of all New Physics hypotheses gets reduced after the LHCb announcements on R_{K^{(*)}} while the hypothesis of a lepton-flavour-universal contribution to the Wilson coefficient of the semileptonic O_{9ell } operators (possibly with a very small lepton-flavour-universality violating component) is clearly reinforced. We also discuss the possibility of a long-distance charm-loop contribution through a mode-by-mode analysis and we find that the preferred values for the {mathcal C}_{9mu } Wilson coefficient are consistent throughout the different brightarrow smu ^+mu ^- modes and that there is no significant evidence of non-constant q^2 dependencies, which would indicate the presence of a long-distance charm-loop contribution beyond those already included.

NLO QCD renormalization group evolution for nonleptonic ΔF=2 transitions in the SMEFT

We present for the first time Next-to-Leading (NLO) QCD renormalization group (RG) evolution matrices for nonleptonic $\mathrm{\ensuremath{\Delta}}F=2$ 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 (Beyond the SM) operators in the so-called Buras Misiak Urban basis into the ones in the common weak effective theory (WET) basis (the so-called Jenkins Manohar Stoffer basis) for which tree-level and one-loop matching to the SMEFT are already known. This subsequently allows us to find the two-loop QCD ADMs for the SMEFT nonleptonic $\mathrm{\ensuremath{\Delta}}F=2$ 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 nonleptonic $\mathrm{\ensuremath{\Delta}}F=2$ transitions from the new physics scale $\mathrm{\ensuremath{\Lambda}}$ down to the electroweak scale ${\ensuremath{\mu}}_{\mathrm{ew}}$. The main benefit of these new contributions is that they allow one to remove renormalization scheme dependences present in the one-loop matchings both between the WET and SMEFT and also between SMEFT and a chosen UV completion. But the Next-to-Leading (NLO) QCD effects, calculated here in the Naive dimensional regularisation minimal subtraction scheme, turn out to be small, in the ballpark of a few percent but larger than one-loop Yukawa top effects when only the $\mathrm{\ensuremath{\Delta}}F=2$ operators are considered. The more complicated class of nonleptonic $\mathrm{\ensuremath{\Delta}}F=1$ decays will be presented soon in another publication.

BSM master formula for \u03b5\u2032/\u03b5 in the WET basis at NLO in QCD

As an important step towards a complete next-to-leading (NLO) QCD analysis of the ratio ε′/ε 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.

General non-leptonic \u2206F = 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 ∆F = 1 decays that govern s → d and b → 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 Nf 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 → ππ 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.

Lepton-flavour non-universality of {bar{B}}rightarrow D^*ell {{bar{nu }}} angular distributions in and beyond the Standard Model

We analyze in detail the angular distributions in {bar{B}}rightarrow D^*ell {{bar{nu }}} decays, with a focus on lepton-flavour non-universality. We investigate the minimal number of angular observables that fully describes current and upcoming datasets, and explore their sensitivity to physics beyond the Standard Model (BSM) in the most general weak effective theory. We apply our findings to the current datasets, extract the non-redundant set of angular observables from the data, and compare to precise SM predictions that include lepton-flavour universality violating mass effects. Our analysis shows that the number of independent angular observables that can be inferred from current experimental data is limited to only four. These are insufficient to extract the full set of relevant BSM parameters. We uncover a sim 4sigma tension between data and predictions that is hidden in the redundant presentation of the Belle 2018 data on {bar{B}}rightarrow D^*ell {{bar{nu }}} decays. This tension specifically involves observables that probe e-mu lepton-flavour universality. However, we find inconsistencies in these data, which renders results based on it suspicious. Nevertheless, we discuss which generic BSM scenarios could explain the tension, in the case that the inconsistencies do not affect the data materially. Our findings highlight that e-mu non-universality in the SM, introduced by the finite muon mass, is already significant in a subset of angular observables with respect to the experimental precision.

A new B-flavour anomaly in Bd,s \u2192 {K}^{ast 0}{overline{K}}^{ast 0} : anatomy and interpretation

In the context of the recently measured non-leptonic decays Bd→ {K}^{ast 0}{overline{K}}^{ast 0} and Bs→ {K}^{ast 0}{overline{K}}^{ast 0} we analyse the anatomy of the LVV observable that compares the longitudinal components of Bs→VV and Bd→VV decays. This observable is cleaner than the longitudinal polarisation fraction as it is afflicted only at subleading order in a 1/mb expansion by the theoretical uncertainties arising in the transverse components entering the polarisation fraction. Focusing on the particular case of Bd→ {K}^{ast 0}{overline{K}}^{ast 0} and Bs→ {K}^{ast 0}{overline{K}}^{ast 0} , we discuss the main sources of hadronic uncertainty in the SM. We find for the SM prediction {L}_{K^{ast }{overline{K}}^{ast }}={19.5}_{-6.8}^{+9.3} , which implies a 2.6σ tension with respect to the most recent data, pointing to a deficit in the b→s transition of the non-leptonic decay versus the corresponding b→d transition. We discuss possible New Physics explanations for this deviation, first at the level of the Weak Effective Theory and we identify that the two Wilson coefficients {mathcal{C}}_4 and {mathcal{C}}_{8g} can play a central role in explaining this anomaly. Finally, we briefly explore two different simplified New Physics models which can explain the anomaly through a contribution either in {mathcal{C}}_4 (Kaluza-Klein gluon) or in {mathcal{C}}_{8g} , with a significant amount of fine tuning, but possible connections to the b→sℓℓ anomalies.

B-decay discrepancies after Moriond 2019

Following the updated measurement of the lepton flavour universality (LFU) ratio R_K in Brightarrow Kell ell decays by LHCb, as well as a number of further measurements, e.g. R_{K^*} by Belle and B_s rightarrow mu mu by ATLAS, we analyse the global status of new physics in brightarrow s transitions in the weak effective theory at the b-quark scale, in the Standard Model effective theory above the electroweak scale, and in simplified models of new physics. We find that the data continues to strongly prefer a solution with new physics in semi-leptonic Wilson coefficients. A purely muonic contribution to the combination C_9 = -C_{10}, well suited to UV-complete interpretations, is now favoured with respect to a muonic contribution to C_9 only. An even better fit is obtained by allowing an additional LFU shift in C_9. Such a shift can be renormalization-group induced from four-fermion operators above the electroweak scale, in particular from semi-tauonic operators, able to account for the potential discrepancies in b rightarrow c transitions. This scenario is naturally realized in the simplified U_1 leptoquark model. We also analyse simplified models where a LFU effect in brightarrow sell ell is induced radiatively from four-quark operators and show that such a setup is on the brink of exclusion by LHC di-jet resonance searches.

New Physics in {varvec{b rightarrow s ell ^+ ell ^-}} confronts new data on lepton universality

In light of the very recent updates on the R_K and R_{K^*} measurements from the LHCb and Belle collaborations, we systematically explore here imprints of New Physics in b rightarrow s ell ^+ ell ^- transitions using the language of effective field theories. We focus on effects that violate Lepton Flavour Universality both in the Weak Effective Theory and in the Standard Model Effective Field Theory. In the Weak Effective Theory we find a preference for scenarios with the simultaneous presence of two operators, a left-handed quark current with vector muon coupling and a right-handed quark current with axial muon coupling, irrespective of the treatment of hadronic uncertainties. In the Standard Model Effective Field Theory we select different scenarios according to the treatment of hadronic effects: while an aggressive estimate of hadronic uncertainties points to the simultaneous presence of two operators, one with left-handed quark and muon couplings and one with left-handed quark and right-handed muon couplings, a more conservative treatment of hadronic matrix elements leaves room for a broader set of scenarios, including the one involving only the purely left-handed operator with muon coupling.

Matching for FCNC effects in the flavour-symmetric SMEFT

We calculate the complete tree and one-loop matching of the dimension-six Standard Model Effective Field Theory (SMEFT) with unbroken U(3)5 flavour symmetry to the operators of the Weak Effective Theory (WET) which are responsible for flavour changing neutral current effects among down-type quarks. We also explicitly calculate the effects of SMEFT corrections to input observables on the WET Wilson coefficients, a necessary step on the way to a well-defined, complete prediction. These results will enable high-precision flavour data to be incorporated into global fits of the SMEFT at high energies, where the flavour symmetry assumption is widespread.

: a Python package for the running and matching of Wilson coefficients above and below the electroweak scale

wilson is a Python library for matching and running Wilson coefficients of higher-dimensional operators beyond the Standard Model. Provided with the numerical values of the Wilson coefficients at a high new physics scale, it automatically performs the renormalization group evolution within the Standard Model effective field theory (SMEFT), matching onto the weak effective theory (WET) at the electroweak scale, and QCD/QED renormalization group evolution below the electroweak scale down to hadronic scales relevant for low-energy precision tests. The matching and running encompasses the complete set of dimension-six operators in both SMEFT and WET. The program builds on the Wilson coefficient exchange format (WCxf) and can thus be easily combined with a number of existing public codes.

Anomalies in bottom from new physics in top

We analyze the possibility to accommodate current b→sℓ+ℓ− anomalies with TeV-scale mediators that couple to right-handed top quarks and muons, contributing to b→sℓ+ℓ− at the one-loop level. We use the Standard Model Effective Field Theory (SMEFT) framework but also look at specific scenarios by taking into account all possible irreducible representations of the Lorentz and Standard Model gauge group for the mediators. From a global fit of b→sℓ+ℓ− data and LEP-I observables we find that the Wilson coefficients of two SMEFT operators: Oℓu=(ℓ¯LμγαℓLμ)(t¯RγαtR) and Oeu=(μ¯RγαμR)(t¯RγαtR) need to satisfy Ceu∼Cℓu. New physics enters then in b→sℓ+ℓ− mainly through the operator O9=(s¯γμPLb)(ℓ¯γμℓ) of the Weak Effective Theory. After discussing all possible mediators, we concentrate on two scenarios: A vector boson in the irreducible representation Zμ′∼(1,1,0) of the Standard Model gauge group with vectorial coupling to muons, and a combination of two leptoquarks: the scalar R2∼(3,2,7/6) and the vector U˜1μ∼(3,1,5/3). We derive LHC constraints by recasting di-muon resonance, pp→tt¯tt¯ and SUSY searches. Additionally, we analyze the prospects for discovering these mediators during the high-luminosity phase of the LHC.

WCxf: An exchange format for Wilson coefficients beyond the Standard Model

We define a data exchange format for numerical values of Wilson coefficients of local operators parameterising low-energy effects of physics beyond the Standard Model. The format facilitates interfacing model-specific Wilson coefficient calculators, renormalisation group (RG) runners, and observable calculators. It is designed to be unambiguous (defining a non-redundant set of operators with fixed normalisation in each basis), extensible (allowing the addition of new EFTs or bases by the user), and robust (being based on industry standard file formats with parsers implemented in many programming languages). We have implemented the format for the Standard Model EFT (SMEFT) and for the weak effective theory (WET) below the electroweak scale and have added interfaces to a number of public codes dealing with SMEFT or WET. We also provide command-line utilities and a Python module for convenient manipulation of WCxf files, including translation between different bases and matching from SMEFT to WET.

DsixTools: the standard model effective field theory toolkit

We present DsixTools, a Mathematica package for the handling of the dimension-six standard model effective field theory. Among other features, DsixTools allows the user to perform the full one-loop renormalization group evolution of the Wilson coefficients in the Warsaw basis. This is achieved thanks to the SMEFTrunner module, which implements the full one-loop anomalous dimension matrix previously derived in the literature. In addition, DsixTools also contains modules devoted to the matching to the Delta B = Delta S = 1,2 and Delta B = Delta C = 1 operators of the Weak Effective Theory at the electroweak scale, and their QCD and QED Renormalization group evolution below the electroweak scale.