SMEFTsim 3.0 — a practical guide

Published for SISSA by Springer Received: January 23, 2021 Accepted: March 8, 2021 Published: April 9, 2021 Ilaria Brivio Institut für Theoretische Physik, Universität Heidelberg. Philosophenweg 16, 69120 Heidelberg, Germany E-mail: Abstract: The SMEFTsim package [1] is designed to enable automated computations in the Standard Model Effective Field Theory (SMEFT), where the SM Lagrangian is extended with a complete basis of dimension six operators. It contains a set of models written in FeynRules and pre-exported to the UFO format, for usage within Monte Carlo event generators. The models differ in the flavor assumptions and in the input parameters chosen for the electroweak sector. The present document provides a self-contained, pedagogical reference that collects all the theoretical and technical aspects relevant to the use of SMEFTsim and it documents the release of version 3.0. Compared to the previous release, the description of Higgs production via gluon-fusion in the SM has been significantly improved, two flavor assumptions for studies in the top quark sector have been added, and a new feature has been implemented, that enables the treatment of linearized SMEFT corrections to the propagators of unstable particles. SMEFTsim 3.0 is available on the Github website https://SMEFTsim.github.io and on the FeynRules database http://feynrules.irmp.ucl.ac.be/wiki/SMEFT. Keywords: Beyond Standard Model, Effective Field Theories, Higgs Physics ArXiv ePrint: 2012.11343 Open Access, c The Authors. Article funded by SCOAP3 . https://doi.org/10.1007/JHEP04(2021)073 JHEP04(2021)073 SMEFTsim 3.0 — a practical guide Contents 1 3 2 EWSB, field and parameter redefinitions 2.1 Higgs sector 2.2 Gauge sector 6 6 7 3 Flavor assumptions 3.1 general: general flavor structure 3.2 U35: maximal U(3)5 symmetry 3.3 MFV: linear minimal flavor violation 3.4 top, topU3l: U(2)3 symmetry in the quark sector 3.5 Comparison with the literature 9 10 12 14 18 25 4 Input parameters 4.1 Implementation in SMEFTsim 4.2 Higgs and EW sectors 4.2.1 {αem , mZ , GF } scheme 4.2.2 {mW , mZ , GF } scheme 4.3 Yukawa sector 27 30 31 32 34 35 5 SM loop-generated Higgs interactions 5.1 Validity of the approximations used 5.2 Comparison to previous versions of SMEFTsim 36 38 39 6 Propagator corrections 6.1 Implementation in SMEFTsim 40 41 7 Usage in Mathematica 44 8 Usage in MadGraph5_aMC@NLO 49 8.1 Parameter cards and restrictions 50 8.2 Interaction orders 51 8.2.1 Definitions 52 8.2.2 Recommended use 53 8.3 Propagator corrections and decay widths 54 8.3.1 Method (a): linearized corrections 54 8.3.2 Method (b): full corrections 55 8.4 Example: Higgs production and decay including W, Z propagator corrections 56 8.4.1 STXS for q̄q → hq̄q 56 + − + − 8.4.2 h → e e µ µ 58 –i– JHEP04(2021)073 1 Introduction 1.1 Basics and notation 59 A Analytic expressions of decay width corrections A.1 Z boson A.2 W boson A.3 Higgs boson A.4 Top quark 59 59 61 62 63 B What’s new in version 3.0 64 C Conversion tables between flavor assumptions 64 D Parameter definitions in the code implementation 71 E Comparison to other SMEFT UFO models E.1 dim6top E.2 SMEFT@NLO 79 79 80 F Validation of the UFO models 89 1 Introduction LHC physics is about to enter a precision era that will span over the next two decades. During this time, new opportunities to hunt for new physics will arise: direct searches of new particles will be complemented by indirect searches, that target possible deviations from the predictions of the Standard Model (SM). While the isolation of this kind of signatures is not without challenges, indirect searches present some very attractive features. Most notably, they do not rely on specific assumptions about the nature of the new physics under scrutiny and, at the same time, their sensitivity in terms of new physics scales can potentially extend beyond the energy reach of the collider. The Standard Model Effective Field Theory (SMEFT) is the best established theory framework to describe such effects. Its formulation employs the degrees of freedom and gauge symmetries of the SM and it is structured as an infinite series of operators sorted by canonical dimension. At the observables level, it reproduces a series expansion in (E/Λ), being E the typical energy exchanged in a process and Λ the mass scale that characterizes the beyond-SM (BSM) dynamics. The condition (E/Λ)  1, indicating the near decoupling of the new physics sector, is necessarily assumed. The SMEFT has been developed extensively in the past ten years, laying the ground for a systematic program for indirect searches [2–4]. The ultimate goal is to measure as many EFT parameters as possible, in a manner that enables the extraction of unbiased information about the underlying physics. The crucial aspect of this program is its transversality: the SMEFT contains a large number of parameters, each typically entering the description –1– JHEP04(2021)073 9 Summary 1 The original release contained two fully equivalent implementations, that were called model sets A and B. Both were provided for debugging and cross-validation. Set B is not supported anymore starting from version 3.0, which is based on set A. –2– JHEP04(2021)073 of several processes. Combining measurements of different observables is then mandatory in order to preserve the model-independence of the analysis. To date, this principle has been applied within individual sectors as well as across Higgs, electroweak (EW) and top quark measurements, see refs. [5–15] for recent examples. The incorporation of data from flavor observables (including non-LHC experiments) would be very valuable in this context, as most of the SMEFT parameter space is “flavorful”. First steps in this direction were taken in [16–19]. The theory developments have been accompanied by the publication of a number of computing tools that automate most stages of a SMEFT study [20]. These include the definition of non-redundant operator bases and the translation between them [21–24], the matching to concrete BSM models or to the low-energy EFT and the renormalization group running [25–31], the extraction of the Feynman rules in Rξ gauges [32, 33] and in the background field gauge [34], Monte Carlo simulations [1, 35–37] and global analyses [13, 38–41]. The SMEFTsim package [1] was designed in order to enable the Monte Carlo simulation of arbitrary processes in the effective theory, in the spirit of providing a unified, generalpurpose tool for SMEFT physics at the LHC. It provides complete tree level, unitary gauge predictions at O(Λ−2 ), including all the dimension six operators in the so-called Warsaw basis [42]. The field and parameter redefinitions that are required in order to compute physical observables in the SMEFT are conveniently performed internally. The package contains FeynRules [43, 44] source files and a set of models pre-exported to the UFO format [45]. Although the latter are in (...truncated)