This paper presents STrEAM (SuperTrace Evaluation Automated for Matching), a Mathematica package that calculates all functional supertraces which arise when matching a generic UV model onto a relativistic Effective Field Theory (EFT) at one loop and to arbitrary order in the heavy mass expansion. STrEAM implements the covariant derivative expansion to automate the most tedious step of the streamlined functional matching prescription presented in arXiv:2011.02484 . The code and an example notebook are available at https://www.github.com/EFTMatching/STrEAM .
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.
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 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 …
We present SuperTracer, a Mathematica package aimed at facilitating the functional matching procedure for generic UV models. This package automates the most tedious parts of one-loop functional matching computations. Namely, the determination and evaluation of all relevant supertraces, including loop integration and Dirac algebra manipulations. The current version of SuperTracer also contains a limited set of output simplifications. However, a further reduction of the output to a minimal basis using Fierz identities, integration by parts, simplification of Dirac structures, and/or light field …
IFAE and BIST, Universitat Autònoma de Barcelona（巴塞罗那自治大学）；School of Physics, Peking University（北京大学物理学院）；International Centre for Theoretical Physics Asia-Pacific (ICTP-AP), University of Chinese Academy of Sciences (UCAS)（中国科学院大学亚太理论物理中心）；School of Physics and State Key Laboratory of Nuclear Physics and Technology, Peking University（北京大学物理学院）；Center for High Energy Physics, Peking University（北京大学高能物理中心）；Beijing Laser Acceleration Innovation Center（北京激光加速创新中心）；CAS Key Laboratory of Theoretical Physics, Institute of Theoretical Physics, Chinese Academy of Sciences（中国科学院理论物理研究所）；School of Physical Sciences, University of Chinese Academy of Sciences（中国科学院大学物理科学学院）
Low-energy effective field theories (EFT) encode information about the physics at high energies--i.e., the high-energy theory (HET). To extract this information the EFT and the HET have to be matched to each other. At the one-loop level, general results for the matching of renormalizable operators have already been obtained in the literature. In the present paper, we take a step towards a better understanding of renormalizable operator matching at the two-loop level: Focusing on the diagrammatic method, we discuss in detail the various contributions to two-loop matching conditions and compare …
In this paper, we continue to construct the low-energy effective field theories (EFTs) of the canonical seesaw models, which are natural extensions of the Standard Model (SM) to accommodate tiny but nonzero neutrino masses. Different from three right-handed neutrino singlets in the type-I seesaw model, the Higgs triplet in the type-II seesaw model participates directly in the electroweak gauge interactions, rendering the EFT construction more challenging. By integrating out the heavy Higgs triplet in the functional-integral formalism, we carry out a complete one-loop matching of the type-II se…
We develop tools for performing effective field theory (EFT) calculations in a manifestly gauge-covariant fashion. We clarify how functional methods account for one-loop diagrams resulting from the exchange of both heavy and light fields, as some confusion has recently arisen in the literature. To efficiently evaluate functional traces containing these "mixed" one-loop terms, we develop a new covariant derivative expansion (CDE) technique that is capable of evaluating a much wider class of traces than previous methods. The technique is detailed in an appendix, so that it can be read independen…
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）
Extensions of the Standard Model (SM) often contain new particles with masses far above the electroweak scale. Due to the presence of a mass hierarchy, effective field theory (EFT) is a suitable tool for the study of such extensions. In this thesis, we provide a solution to the matching problem at the one-loop level in the form of the Bispinor Universal One-Loop Effective Action (BSUOLEA), which is a pre-computed expression for the effective action, parameterised in terms of derivatives of the Lagrangian of the ultraviolet (UV) model. The BSUOLEA is derived using functional methods and is suff…
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…
Many studies of possible new physics employ effective field theory (EFT), whereby corrections to the Standard Model take the form of higher-dimensional operators, suppressed by a large energy scale. Fits of such a theory to data typically use parton level observables, which limits the datasets one can use. In order to theoretically model search channels involving many additional jets, it is important to include tree-level matrix elements matched to a parton shower algorithm, and a suitable matching procedure to remove the double counting of additional radiation. There are then two potential pr…
Mapping UV theories onto low energy effective descriptions is a procedure known as matching. The last decade has seen tremendous progress in the development of new tools for efficiently performing matching calculations, by relying on so-called functional methods. This white paper summarizes the status of functional matching. Specifically, matching for relativistic theories is a fully solved problem up to one-loop order in perturbation theory, and to arbitrary order in the effective field theory expansion. A streamlined prescription that has been partially automated facilitates the application …
We present a practical three-step procedure of using the Standard Model effective field theory (SM EFT) to connect ultraviolet (UV) models of new physics with weak scale precision observables. With this procedure, one can interpret precision measurements as constraints on a given UV model. We give a detailed explanation for calculating the effective action up to one-loop order in a manifestly gauge covariant fashion. This covariant derivative expansion method dramatically simplifies the process of matching a UV model with the SM EFT, and also makes available a universal formalism that is easy …
