In this paper we present the complete one-loop matching conditions, up to dimension-six operators of the Standard Model effective field theory, resulting by integrating out the two scalar leptoquarks $S_{1}$ and $S_{3}$. This allows a phenomenological study of low-energy constraints on this model at one-loop accuracy, which will be the focus of a subsequent work. Furthermore, it provides a rich comparison for functional and computational methods for one-loop matching, that are being developed. As a corollary result, we derive a complete set of dimension-six operators independent under integration by parts, but not under equations of motions, called Green's basis, as well as the complete reduction formulae from this set to the Warsaw basis.
The P2 experiment aims at high-precision measurements of the parity-violating asymmetry in elastic electron-proton and electron-$^{12}$C scatterings with longitudinally polarized electrons. We discuss here the sensitivity of P2 to leptoquarks, which within the P2 energy range can be described in the language of Standard Model Effective Field Theory (SMEFT). We give the expected P2 limits on the SMEFT operators and on the leptoquark parameters, which will test energy scales up to 15 TeV. In many cases those limits exceed current constraints from LHC and atomic parity violation (APV) experiments…
This note gives an overview of the tools for the precision matching of ultraviolet theories to the Standard Model effective field theory (SMEFT) at the tree level and one loop. Several semi- and fully automated codes are presented, as well as some supplementary codes for the basis conversion and the subsequent running and matching at low energies. A suggestion to collect information for cross-validations of current and future codes is made.
We calculate the complete tree and one-loop matching of the dimension 6 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 energ…
We explore the interplay of New Physics (NP) effects in $(g-2)_\ell$ and $h \to \ell^+ \ell^-$ within the Standard Model Effective Field Theory (SMEFT) framework, including one-loop Renormalization Group (RG) evolution of the Wilson coefficients as well as matching to the observables below the electroweak symmetry breaking scale. We include both the leading dimension six chirality flipping operators including a Higgs and $SU(2)_L$ gauge bosons as well as four-fermion scalar and tensor operators, forming a closed operator set under the SMEFT RG equations. We compare present and future experimen…
In this study we present a universal effective action for one-loop matching of all scalar leptoquarks. We use both the Universal One-Loop Effective Action (UOLEA) and covariant diagrams to evaluate the Wilson coefficients directly in the Green basis for up-to dimension-6 operators. On the technical side, we use the newly developed method of evaluating supertraces, to further validate the results stemming from the use of covariant diagrams. As an application, we perform a fully functional matching onto Standard Model Effective Field Theory (SMEFT) of a model with two scalar leptoquark fields: a…
We present a global analysis of the Higgs and electroweak sector, in the SMEFT framework and matched to a UV-completion. As the UV-model we use the triplet extension of the electroweak gauge sector. The matching is performed at one loop, employing functional methods. In the SFitter analysis, we pay particular attention to theory uncertainties arising from the matching. Our results highlight the complementarity between SMEFT and model-specific analyses.
We study the phenomenology of the simplest renormalisable model that, at low energy, leads to the effective field theory of the Standard Model extended with right-handed neutrinos ($ν$SMEFT). Our aim is twofold. First, to contextualise new collider signatures in models with sterile neutrinos so far studied only using the bottom-up approach. And second and more important, to provide a thorough example of one-loop matching in the diagrammatic approach, of which other matching techniques and automatic tools can benefit for cross-checks. As byproducts of this work, we provide for the first time: (…
The Standard Model Effective Field Theory (SMEFT) provides a systematic and model-independent framework to study neutrino non-standard interactions (NSIs). We study the constraining power of the on-going neutrino oscillation experiments T2K, NO$ν$A, Daya Bay, Double Chooz and RENO in the SMEFT framework. A full consideration of matching is provided between different effective field theories and the renormalization group running at different scales, filling the gap between the low-energy neutrino oscillation experiments and SMEFT at the UV scale. We first illustrate our method with a top-down a…
When integrating out unknown new physics sectors, what is the minimal character of the Standard Model Effective Field Theory (SMEFT) that can result? In this paper we focus on a particular aspect of this question: "How can one obtain only one dimension six operator in the SMEFT from a consistent tree level matching onto an unknown new physics sector?" We show why this requires conditions on the ultraviolet field content that do not indicate a stand alone ultraviolet complete scenario. Further, we demonstrate how a dynamical origin of the ultraviolet scales assumed to exist in order to generate…
SUSY meets SMEFT: Complete one-loop matching of the general MSSM
Laboratoire de Physique Subatomique et de Cosmologie, Université Grenoble-Alpes, CNRS/IN2P3（亚原子与宇宙物理学实验室，格勒诺布尔阿尔卑斯大学，法国国家科学研究中心/国家核物理与粒子物理研究所）；Centro de Ciências Naturais e Humanas, Universidade Federal do ABC（自然与人文科学中心，ABC联邦大学）；Departament de Física Teòrica, IFIC (Universitat de València - CSIC)（理论物理系，瓦伦西亚大学-西班牙国家科学研究委员会联合研究所）；Institute for Theoretical Particle Physics and Cosmology, RWTH Aachen University（理论粒子物理学与宇宙学研究所，亚琛工业大学）
Matching HEFT and SMEFT in double and triple Higgs production from weak boson fusion
IFT-UAM/CSIC, Universidad Autónoma de Madrid（马德里自治大学）；IFLP, CONICET - Dpto. de Física, Universidad Nacional de La Plata（拉普拉塔国立大学）；IPARCOS, Universidad Complutense de Madrid（马德里康普顿斯大学）
We investigate model independent top-quark corrections to $ΔF = 2$ processes for the down-type quarks within the framework of the Standard Model Effective Field Theory. Dimension-six $ΔF = 1$ operators contribute to them through renormalization group evolutions and matching conditions. We provide a complete one-loop matching formula from the top quarks for $ΔF=2$ transitions. We also demonstrate these corrections on $ΔM_{B_s}$ in the left-right symmetric model, which are compared with the conventional calculation.
We study nuclear electric dipole moments induced by $ΔF=1$ effective operators in the Standard Model Effective Field Theory. Such contributions arise through renormalization group evolutions and matching conditions at the electroweak symmetry breaking scale. We provide one-loop formulae for the matching conditions. We also discuss correlations of these effects with $ΔF=2$ observables such as $ε_K$ and $ΔM_{B_d}$.
In this paper, we explore the impact of extra radiation on predictions of $pp \to t\bar{t}X, X = h/W^{\pm}/Z$ processes within the dimension-6 SMEFT framework. While full next-to-leading order calculations are of course preferred, they are not always practical, and so it is useful to be able to capture the impacts of extra radiation using leading-order matrix elements matched to the parton shower. While a matched leading-order calculation for $t\bar{t}X$ is not expected to reproduce the next-to-leading order inclusive cross section precisely, we show that it does capture the relative impact of…
Leptoquarks (LQs) provide very promising solutions to the tensions between the experimental measurements and the SM predictions of $b\to s\ell^+\ell^-$ and $b\to cτν$ processes. In this case the LQ masses are in general at the TeV scale and they can thus be produced at high energy colliders and dedicated LHC searches are ongoing. While for LQ production and decay the $O(α_s)$ corrections have been known for a long time, the $O(α_s)$ corrections to the matching on 2-quark-2-lepton operators have not been calculated, yet. In this article we close this gap by computing the QCD corrections to the …
The shift in focus towards searches for physics beyond the Standard Model (SM) employing model-independent Effective Field Theory (EFT) methods necessitates a rigorous approach to matching to guarantee the validity of the obtained results and constraints. The limits on the leading dimension-six EFT effects can be rather inaccurate for LHC searches that suffer from large uncertainties while exploring an extensive energy range. Similarly, precise measurements can, in principle, test the subleading effects of the operator expansion. In this work, we present an algorithmic approach to automatise m…
Institute for Theoretical Physics, Karlsruhe Institute of Technology（卡尔斯鲁厄理工学院理论物理研究所）；Institute for Particle Physics Phenomenology, Durham University（达勒姆大学粒子物理现象学研究所）
We present a basis of dimension-eight Green's functions involving Standard Model (SM) bosonic fields, consisting of 86 new operators. Rather than using algebraic identities and integration by parts, we prove the independence of these interactions in momentum space, including a discussion on evanescent bosonic operators. Our results pave the way for renormalising the SM effective field theory (SMEFT), as well as for performing matching of ultraviolet models onto the SMEFT, to higher order. To demonstrate the potential of our construction, we have implemented our basis in matchmakereft and used …
We investigate the high-$p_T$ tails of the $pp\to \ell ν$ and $pp \to \ell \ell$ Drell-Yan processes as probes of New Physics in semileptonic interactions with an arbitrary flavor structure. For this purpose, we provide a general decomposition of the $2\to2$ scattering amplitudes in terms of form-factors that we match to specific scenarios, such as the Standard Model Effective Field Theory (SMEFT), including all relevant operators up to dimension-$8$, as well as ultraviolet scenarios giving rise to tree-level exchange of new bosonic mediators with masses at the TeV scale. By using the latest L…
The interpretation of electroweak precision data in the Standard Model Effective Field Theory is discussed. One loop corrections $\propto y_t^2, λ$ to the partial $Z$ decay widths and ratios of partial widths in this theory are discussed. A reparameterization invariance and the non-minimal character of matching onto this theory is reviewed.
Leptoquarks provide viable solutions to the flavour anomalies, i.e. they can explain the tensions between the measurements and the Standard Model predictions of the anomalous magnetic moment of the muon as well as $b\to s\ell^+\ell^-$ and $b\to cτν$ processes. However, leptoquarks also contribute to other flavour observables, such as $ΔF=2$ processes, at the loop-level. In particular, $B_s-\bar B_s$ mixing provides a crucial bound in setups addressing $b\to cτν$ data, often excluding a big portion of the parameter space that could otherwise account for it. In this article, we first derive the …
We simplify the one-loop functional matching formalism to develop a streamlined prescription. The functional approach is conceptually appealing: all calculations are performed within the UV theory at the matching scale, and no prior determination of an Effective Field Theory (EFT) operator basis is required. Our prescription accommodates any relativistic UV theory that contains generic interactions (including derivative couplings) among scalar, fermion, and vector fields. As an example application, we match the singlet scalar extended Standard Model (SM) onto SMEFT.
The equations of motion for the Standard Model Effective Field Theory (SMEFT) differ from those in the Standard Model. Corrections due to local contact operators modify the equations of motion and impact matching results at sub-leading order in the operator expansion. As a consequence, a matching coefficient in $\mathcal{L}^{(n)}$ (for operators of dimension $n$) can be dependent on the basis choice for $\mathcal{L}^{(m<n)}$. We report the SMEFT equations of motion with corrections due to $\mathcal{L}^{(5,6)}$. We demonstrate the effect of these corrections when matching to sub-leading order b…
Flavorful Lepton-Number-Violating SMEFT: Loop Mixing, $0νββ$ and Rare Meson Decays
Institute of Particle and Nuclear Physics (IPNP), Faculty of Mathematics and Physics, Charles University in Prague（布拉格查理大学数学物理学院粒子与核物理研究所）；Institute of Physics, Silesian University in Opava（奥帕瓦西里西亚大学物理研究所）；Instituto de Física Corpuscular (IFIC), Universitat de València–CSIC（巴伦西亚大学-西班牙国家科学研究委员会粒子物理研究所）；Department of Physics, University of California, Berkeley（加州大学伯克利分校物理学系）
We present the results of the first complete one-loop matching calculation between the real singlet scalar extension of the Standard Model and the Standard Model effective field theory (SMEFT) at dimension six. Beyond their immediate relevance to the precision calculation of observables in singlet extensions of the Standard Model, our results illustrate a variety of general features of one-loop matching. We explore the interplay between non-supersymmetric non-renormalization theorems, the logarithmic dependence of Wilson coefficients, and the relevance of mixed diagrams in theories with large …
A complete one-loop matching calculation for real singlet scalar extensions of the Standard Model to the Standard Model effective field theory (SMEFT) of dimension-six operators is presented. We compare our analytic results obtained by using Feynman diagrams to the expressions derived in the literature by a combination of the universal one-loop effective action (UOLEA) approach and Feynman calculus. After identifying contributions that have been overlooked in the existing calculations, we find that the pure diagrammatic approach and the mixed method lead to identical results. We highlight some…
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. Ha…
In this paper we consider semileptonic lepton flavor violating operators of the type $q^2l^2$ in low energy effective theory (LEFT). At the chiral scale, we match these operators to chiral perturbation theory ($χ$PT) and place constraints from the process $π^0\rightarrow μ^+ \,\, e^-$. These bounds are shown to depend on the chiral nature of the operators. The scalar operators are significantly more constrained compared to the vector operators. We then compare the limits from $μ\to e$ conversion in Nuclei and show that the limits on scalar operators are within an order of magnitude of the corr…
We calculate one loop $y_t$ and $λ$ dependent corrections to $\barΓ_Z,\bar{R}_f^0$ and the partial $Z$ widths due to dimension six operators in the Standard Model Effective Field Theory (SMEFT), including finite terms. We assume $\rm CP$ symmetry and a $\rm U(3)^5$ symmetry in the UV matching onto the dimension six operators, dominantly broken by the Standard Model Yukawa matrices. Corrections to these observables are predicted using the input parameters $\{\hatα_{ew}, \hat{M}_Z, \hat{G}_F, \hat{m}_t, \hat{m}_h\}$ extracted with one loop corrections in the same limit. We show that at one loop …
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…
We perform a complete study of the low-energy phenomenology of $S_1$ and $S_3$ lepto-quarks, aimed at addressing the observed deviations in $B$-meson decays and the muon magnetic dipole moment. Leptoquark contributions to observables are computed at one-loop accuracy in an effective field theory approach, using the recently published complete one-loop matching of these leptoquarks to the Standard Model effective field theory. We present several scenarios, discussing in each case the preferred parameter space and the most relevant observables.
Effective field theories offer a rationale to classify new physics models based on the size of their contribution to the effective Lagrangian, and therefore to experimental observables. A complete classification can be obtained, at a fixed order in perturbation theory, in the form of IR/UV dictionaries. We report on the first step towards the calculation of the one loop, dimension 6 IR/UV dictionary in the SMEFT. We consider dimension-six operators in the SMEFT that cannot be generated at tree level in weakly coupled extensions of the Standard Model. This includes operators with three gauge fi…
An Effective Field Theory (EFT) analysis of the magnetic moment of the muon is discussed. The expression for the dipole moment is given in terms of operator coefficients of the low-energy effective field theory (LEFT) and the Standard Model effective field theory (SMEFT), where one-loop renormalization group improved perturbation theory, the one-loop matching from SMEFT onto LEFT as well as one-loop lepton matrix elements of the effective-theory operators were taken into account. Interestingly only a very limited set of the SMEFT operators is able to explain the current deviation of the magnet…
In this paper, we accomplish the complete one-loop matching of the type-I seesaw model onto the Standard Model Effective Field Theory (SMEFT), by integrating out three heavy Majorana neutrinos with the functional approach. It turns out that only 31 dimension-six operators (barring flavor structures and Hermitian conjugates) in the Warsaw basis of the SMEFT can be obtained, and most of them appear at the one-loop level. The Wilson coefficients of these 31 dimension-six operators are computed up to $\mathcal{O}\left( M^{-2}\right)$ with $M$ being the mass scale of heavy Majorana neutrinos. As th…
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 SME…
