In this work we consider the Standard Model Effective Field Theory extended with right-handed neutrinos, the $ν$SMEFT, and calculate the full set of one-loop anomalous dimensions that are proportional to Yukawa couplings. These contributions are particularly relevant when symmetry-protected low scale seesaw models are embeded in the SMEFT, since large neutrino Yukawa couplings are expected. By combining our results with the already available gauge anomalous dimensions, we provide the complete set of one-loop renormalization group evolution equations for the dimension six $ν$SMEFT. As a possible phenomenological implication of our results, we discuss the sensitivity of lepton flavor-violating observables to $ν$SMEFT operators, focusing on the more sensitive $μ\to e$ transitions.
Using background-field method and super-heat-kernel expansion, we derive a master formula for the one-loop UV divergences of the bosonic dimension-6 operators in Standard Model Effective Field Theory (SMEFT). This approach reduces the calculation of all the UV divergences to algebraic manipulations. Using this formula we corroborate results in the literature for the one-loop anomalous dimension matrix of SMEFT obtained via diagrammatic methods, considering contributions from the operators $X^3, ϕ^6, ϕ^4 D^2, X^2 ϕ^2$ of the Warsaw basis. The formula is derived in a general way and can be appli…
The conventional oblique parameters analyses of precision electroweak data can be consistently cast in the modern framework of the Standard Model effective field theory (SMEFT) when restrictions are imposed on the SMEFT parameter space so that it describes universal theories. However, the usefulness of such analyses is challenged by the fact that universal theories at the scale of new physics, where they are matched onto the SMEFT, can flow to nonuniversal theories with renormalization group (RG) evolution down to the electroweak scale, where precision observables are measured. The departure f…
We calculate the full set of next-to-leading order (NLO) corrections to $h\to b\bar{b}$ decay in the dimension-6 Standard Model Effective Field Theory (SMEFT). Our calculation forms the basis for precision studies of this decay mode in effective field theory, providing analytic and numerical results for contributions of the 45 dimension-6 operators appearing at NLO. On the technical side, we discuss several complications in NLO SMEFT computations which have not yet been addressed in the literature. These include subtleties in Higgs-$Z$ mixing, electric charge renormalization, and especially th…
Complete two-loop Yukawa-induced running of the Higgs-gluon coupling in SMEFT
Karlsruhe Institute of Technology (KIT)（卡尔斯鲁厄理工学院）；Università degli Studi di Padova（帕多瓦大学）；Istituto Nazionale di Fisica Nucleare, Sezione di Padova（意大利国家核物理研究所帕多瓦分部）
We describe the on-shell method to deriving the Renormalization Group (RG) evolution of Wilson coefficients of high dimensional operators at one loop, which is a necessary part in the on-shell construction of the Standard Model Effective Field Theory (SMEFT), and exceptionally efficient based on the amplitude basis in hand. The UV divergence is obtained by firstly calculating the coefficients of scalar bubble integrals by unitary cuts, then subtracting the IR divergence in the massless bubbles, which can be easily read from the collinear factors we obtained for the Standard Model fields. Examp…
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…
We study implications of the four-fermion semileptonic operators at the low-energy and at electroweak (EW) scale in the framework of Standard Model Effective Field Theory (SMEFT). We show how the renormalization group (RG) running effects can play an important role in probing the \emph{generic flavour structure} of such operators. It is shown that at the 1-loop level, through RG running, depending upon the flavour structure, these operators can give rise to sizable effects at low energy in the electroweak precision (EWP) observables, the leptonic, quark, as well as the $Z$ boson flavour violat…
In this contribution to the Snowmass 2021 process we review theoretical developments in the Standard Model Effective Field Theory (SMEFT) with a focus on effects at the dimension-8 level and beyond. We review the theoretical advances that led to the complete construction of the operator bases for the dimension-8 and dimension-9 SMEFT Lagrangians. We discuss the possibility of obtaining all-orders results in the $1/Λ$ expansion for certain SMEFT observables as well as the current status of renormalization group running and implications for positivity, and briefly present the on-shell approach t…
We study Yukawa Renormalization Group (RG) running effects in the context of the Standard Model Effective Theory (SMEFT).The Yukawa running being flavour dependent leads to RG-induced off-diagonal entries, so that initially diagonal Yukawa matrices at the high scale have to be rediagonalized at the electroweak (EW) scale. Performing such flavour rotations can lead to flavour violating operators which differ from the ones obtained through SMEFT RG evolution. We show, that these flavour rotations can have a large impact on low-energy phenomenology. In order to demonstrate this effect, we compare…
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 …
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…
Standard Model Neutrino Effective Field Theory (SMNEFT) is an effective theory with Standard Model (SM) gauge-invariant operators constructed only from SM and right-handed neutrino fields. For the full set of dimension-six SMNEFT operators, we present the gauge coupling terms of the one-loop anomalous dimension matrix for renormalization group evolution (RGE) of the Wilson coefficients between a new physics scale and the electroweak scale. We find that the SMNEFT operators can be divided into five subsets which are closed under RGE. Our results apply for both Dirac and Majorana neutrinos. We a…
We describe on-shell methods for computing one- and two-loop anomalous dimensions in the context of effective field theories containing higher-dimension operators. We also summarize methods for computing one-loop amplitudes, which are used as inputs to the computation of two-loop anomalous dimensions, and we explain how the structure of rational terms and judicious renormalization scheme choices can lead to additional vanishing terms in the anomalous dimension matrix at two loops. We describe the two-loop implications for the Standard Model Effective Field Theory (SMEFT). As a by-product of th…
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…
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…
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 calculate one loop contributions to $Γ(h \rightarrow γ\, γ)$ from higher dimensional operators, in the Standard Model Effective Field Theory (SMEFT). Some technical challenges related to determining Electroweak one loop "finite terms" are discussed and overcome. Although we restrict our attention to $Γ(h \rightarrow γ\, γ)$, several developments we report have broad implications. Firstly, the running of the vacuum expectation value modifies the $\log(μ)$ dependence of processes in a manner that is not captured in some past SMEFT Renormalization Group (RG) calculations. Secondly, higher dime…
Starting from the one-loop divergences we obtained previously, we work out the renormalization of the Higgs-Electroweak Chiral Lagrangian explicitly and in detail. This includes the renormalization of the lowest-order Lagrangian, as well as the decomposition of the remaining divergences into a complete basis of next-to-leading-order counterterms. We provide the list of the corresponding beta functions. We show how our results match the one-loop renormalization of some of the dimension-6 operators in SMEFT. We further point out differences with related work in the literature and discuss them. A…
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 …
In the Standard Model, the renormalization of the QCD vacuum angle $θ$ is extremely tiny, and small $θ$ is technically natural. In the general Standard Model effective field theory (SMEFT), however, $Δθ$ is quadratically divergent, reflecting the fact that new sources of hadronic CP-violation typically produce $\mathcal O(1)$ threshold corrections to $θ$. The observation of such CP-violating interactions would therefore be in tension with solutions to the strong CP problem in which $θ=0$ is an ultraviolet boundary condition, pointing to the Peccei-Quinn mechanism as the explanation for why $θ$…
We perform a model-independent analysis of the magnetic and electric dipole moments of the muon and electron. We give expressions for the dipole moments in terms of operator coefficients of the low-energy effective field theory (LEFT) and the Standard Model effective field theory (SMEFT). We use one-loop renormalization group improved perturbation theory, including the one-loop matching from SMEFT onto LEFT, and one-loop lepton matrix elements of the effective-theory operators. Semileptonic four-fermion operators involving light quarks give sizable non-perturbative contributions to the dipole …
Symmetry-restoring finite counterterms of SMEFT four-fermion operator insertions at one loop
Universitat de València – Consejo Superior de Investigaciones Científicas（瓦伦西亚大学 - 西班牙国家研究委员会）；University of Sussex（萨塞克斯大学）；Universidad Cardenal Herrera-CEU（卡迪纳尔埃雷罗大学-CEU）
Challenging Majorana neutrino effects in $B\to K^{(\ast)}νν$ and $K\to πνν$ decays
Université Paris-Saclay（巴黎萨克雷大学）；CNRS/IN2P3（法国国家科学研究中心/粒子物理研究所）；IJCLab（伊凡·斯夸尔实验室）；Institut Universitaire de France (IUF)（法兰西学院）；Universidade de São Paulo（圣保罗大学）
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 $ΔB = ΔS = 1,2$ and $ΔB = ΔC = 1$ operators of the Weak Effective Theory at the electroweak sca…
$\tt DsixTools$ is a Mathematica package for the handling of the Standard Model Effective Field Theory (SMEFT) and the Low-energy Effective Field Theory (LEFT) with operators up to dimension six, both at the algebraic and numerical level. $\tt DsixTools$ contains a visually accessible and operationally convenient repository of all operators and parameters of the SMEFT and the LEFT. This repository also provides information concerning symmetry categories and number of degrees of freedom, and routines that allow to implement this information on global expressions (such as decay amplitudes and cr…
