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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., 23 pages, 2 figures

The use of the SMEFT Lagrangian to quantify possible Beyond the Standard Model (BSM) effects is standard in LHC and future collider studies. One of the usual assumptions is to truncate the expansion with the dimension-$6$ operators. The numerical impact of the next terms in the series, the dimension-$8$ operators, is unknown in general. We consider a specific BSM model containing a charge-${2 3}$ heavy vector-like quark and compute the operators generated at dimension-$8$. The numerical effects of these operators are studied for the $t\bar{t}h$ process, where they contribute at tree level and we find effects at the ${\cal{O}}(0.5-2\%)$ level for allowed values of the parameters., 26 pages, 9 figures, UFO and Feynrules files included as supplemental material; version accepted by Physical Review D

Different sets of electroweak input parameters are discussed for SMEFT predictions at the LHC. The {Gmu,mZ,mW} one is presently recommended., Comment: LHC EFT WG note, 5 pages

Drell Yan production is a sensitive probe of new physics and as such has been calculated to high order in both the electroweak and QCD sectors of the Standard Model, allowing for precision comparisons between theory and data. Here we extend these calculations to the Standard Model Effective field theory (SMEFT) and present the NLO QCD and electroweak contributions to the neutral Drell Yan process that are linear in the Wilson coefficients of the SMEFT theory., Comment: 28 pages, auxiliary material contains fortran results, version to be published in PRD, references added

The Standard Model Effective Field Theory (SMEFT) provides a consistent framework for comparing precision measurements at the LHC to the Standard Model. The observation of statistically significant non-zero SMEFT coefficients would correspond to physics beyond the Standard Model (BSM) of some sort. A more difficult question to answer is what, if any, detailed information about the nature of the underlying high scale model can be obtained from these measurements. In this work, we consider the patterns of SMEFT operators present in five example models and discuss the assumptions inherent in using global fits to make BSM conclusions. We find that including renormalization group effects has a significant impact on the interpretation of the results. As a by-product of our study, we present an up-dated global fit to SMEFT coefficients in the Warsaw basis including some next-to-leading order QCD corrections in the SMEFT theory., 28+14 pages, 11 figures, plots updated

The production of $W^{\pm}H$, $ZH$, $W^+W^-$, and $W^\pm Z$ pairs probes non-Standard-Model interactions of quarks, gauge bosons, and the Higgs boson. New effects can be parameterized in terms of an effective field theory (EFT) where the Lagrangian is expanded in terms of higher-dimension operators suppressed by increasing powers of a high scale $\Lambda$. We examine the importance of including next-to-leading-order QCD corrections in global fits to the coefficients of the EFT. The numerical implications on the fits due to different approaches to enforcing the validity of the EFT are quantified. We pay particular attention to the dependence of the fits on the expansion in $1/\Lambda^2$ since the differences between results calculated at ${\cal {O}}(1/\Lambda^2)$ and ${\cal{O}}(1/\Lambda^4)$ may give insight into the possible significance of dimension-8 effects., Comment: 32 pages, 7 figures, 8 tables

We investigate the role of anomalous gauge boson and fermion couplings on the production of $WZ$ and $W^+W^-$ pairs at the LHC to NLO QCD in the Standard Model effective field theory, including dimension-6 operators. Our results are implemented in a publicly available version of the POWHEG-BOX. We combine our $WZ$ results in the leptonic final state $e\nu \mu^+\mu^-$ with previous $W^+W^-$ results to demonstrate the numerical effects of NLO QCD corrections on the limits on effective couplings derived from ATLAS and CMS 8 and 13 TeV differential measurements. Our study demonstrates the importance of including NLO QCD SMEFT corrections in the $WZ$ analysis, while the effects on $WW$ production are smaller. We also show that the $\mathcal{O}(1/\Lambda^4)$ contributions dominate the analysis, where $\Lambda$ is the high energy scale associated with the SMEFT., Comment: 28 pages, 10 figures. Version accepted for publication in Phys. Rev. D

We compute the next-to-leading order QCD and electroweak corrections to $Z$ and $W$ pole observables using the dimension-6 Standard Model effective field theory and present numerical results that can easily be included in global fitting programs. Limits on SMEFT coefficient functions are presented at leading order and at next-to-leading order under several assumptions., Comment: 28 pages, 2 figures, V4: Minor error in real contributions corrected with very small numerical impact. Updated auxiliary file posted

Current projections suggest that the LHC will have only limited sensitivity to di-Higgs production in the Standard Model (SM), possibly even after the completion of its high luminosity phase. Multi-Higgs final states play a fundamental role in many extensions of the SM as they are intrinsically sensitive to modifications of the Higgs sector. Therefore, any new observation in multi-Higgs final states could be linked to a range of beyond the SM (BSM) phenomena that are not sufficiently addressed by the SM. Extensions of the Higgs sector typically lead to new phenomenological signatures in multi-Higgs final states that are vastly different from the SM expectation. In this work, we provide a range of signature-driven benchmark points for resonant and non-resonant BSM di-Higgs production that motivate non-SM kinematic correlations and multi-fermion discovery channels. Relying on theoretically well-motivated assumptions, special attention is devoted to the particular case where the presence of new physics will dominantly manifest itself in multi-Higgs final states.

We compute the one-loop corrections to $Z$ decay properties from dimension-6 operators in the Standard Model Effective Field Theory (SMEFT) that contribute also to anomalous 3-gauge boson couplings and examine the relative sensitivity of the two processes to the anomalous couplings. The size of the contributions is of order a few percent, of the same size as Standard Model electroweak corrections. This is part of a program of computing electroweak quantities to one-loop in the SMEFT: these calculations are needed for a future global fit to limit the coefficients of the dimension-six Wilson coefficients consistently at one loop., 22 pages, 2 figures. v2: minor changes, matches version published in PRD

We calculate the complete one-loop electroweak corrections to the inclusive $H\rightarrow ZZ$ and $H\rightarrow Z��$ decays in the dimension-$6$ extension of the Standard Model Effective Field Theory (SMEFT). The corrections to $H\rightarrow ZZ$ are computed for on-shell $Z$ bosons and are a precursor to the physical $H\rightarrow Z f {\overline{f}}$ calculation. We present compact numerical formulas for our results and demonstrate that the logarithmic contributions that result from the renormalization group evolution of the SMEFT coefficients are larger than the finite NLO contributions to the decay widths. As a by-product of our calculation, we obtain the first complete result for the finite corrections to $G_��$ in the SMEFT., Published Version. The results for $\Delta r$ in the SMEFT are now given in $R_\xi$ gauge; V3: corrected a typo in eq 38 and 39, updated eq. 41

Higgs decays to gauge boson pairs are a crucial ingredient in the study of Higgs properties, with the decay $H\rightarrow����$ being particularly sensitive to new physics effects. Assuming all potential new physics occurs at energies much above the weak scale, deviations from Standard Model predictions can be parameterized in terms of the coefficients of an effective field theory (SMEFT). When experimental limits on the SMEFT coefficients reach an accuracy of a few percent, predictions must be done beyond the lowest order in the SMEFT in order to match theory and experimental accuracy. This paper completes a program of computing the one-loop electroweak SMEFT corrections to $H\rightarrow VV^\prime$, $V=W^\pm,Z,��$. The calculation of the real contribution to $H\rightarrow W^+W^-��$ is performed by mapping two-loop amplitudes to the $3-$ body phase space., 21 pages, 3 figures; V2: Version accepted for publication

We study the impact of anomalous gauge boson and fermion couplings on the production of $W^+W^-$ pairs at the LHC. Helicity amplitudes are presented separately to demonstrate the sources of new physics contributions and the impact of QCD and electroweak corrections. The QCD corrections have important effects on the fits to anomalous couplings, in particular when one $W$ boson is longitudinally polarized and the other is transversely polarized. In effective field theory language, we demonstrate that the dimension-6 approximation to constraining new physics effects in $W^+W^-$ pair production fails at $p_T\sim 500-1000$ GeV., Comment: 23 pages, version published in journal, code posted at https://quark.phy.bnl.gov/Digital_Data_Archive/dawson/ww_2017/WWEFT_NLO.tar.gz

The ATLAS and CMS collaborations have recently published new limits on CP conserving anomalous couplings from the $W��$ and $Z��$ production processes. We study the corresponding limits that can be placed on the CP violating anomalous couplings $��_tilde_��$ and $h^1_{��, Z}$ at the LHC. We find that the process $pp --> W��$ at 14 TeV can place the 95% CL limit $|��_tilde_��| Z��$ can place the 95% CL limits $|h^1_��, 16 LaTex pages, 4 figures, 5 tables, accepted version for publication in Physical Review D

We present a complete next-to-leading order (NLO) calculation for the total cross section for inclusive Higgs pair production via bottom-quark fusion at the CERN Large Hadron Collider (LHC) in the minimal supersymmetric standard model (MSSM) and the minimal supergravity model (mSUGRA). We emphasize the contributions of squark and gluino loops (SQCD) and the decoupling properties of our results for heavy squark and gluino masses. The enhanced couplings of the b quark to the Higgs bosons in supersymmetric models with large tanb yield large NLO SQCD corrections in some regions of parameter space., Comment: 24 pages, 10 figures

The cross section for the reaction $e^+e^- \to t\bar{t} H$ depends sensitively on the top quark Yukwawa coupling $\lambda_t$. We calculate the rate for $t\bar{t}H$ production, followed by the decay $H\to b\bar{b}$, for a Standard Model Higgs boson with 100 < m_H, Comment: 24 pages, 11 figures

This report, as part of the 2021 Snowmass Process, summarizes the current status of collider physics at the Energy Frontier, the broad and exciting future prospects identified for the Energy Frontier, the challenges and needs of future experiments, and indicates high priority research areas., Comment: 128 pages, 41 figures, 17 tables, contribution to Snowmass 2021

The International Linear Collider (ILC) is on the table now as a new global energy-frontier accelerator laboratory taking data in the 2030s. The ILC addresses key questions for our current understanding of particle physics. It is based on a proven accelerator technology. Its experiments will challenge the Standard Model of particle physics and will provide a new window to look beyond it. This document brings the story of the ILC up to date, emphasizing its strong physics motivation, its readiness for construction, and the opportunity it presents to the US and the global particle physics community., Comment: 356 pages, Large pdf file (40 MB) submitted to Snowmass 2021; v2 references to Snowmass contributions added, additional authors; v3 references added, some updates, additional authors

A future Higgs Factory will provide improved precision on measurements of Higgs couplings beyond those obtained by the LHC, and will enable a broad range of investigations across the fields of fundamental physics, including the mechanism of electroweak symmetry breaking, the origin of the masses and mixing of fundamental particles, the predominance of matter over antimatter, and the nature of dark matter. Future colliders will measure Higgs couplings to a few per cent, giving a window to beyond the Standard Model (BSM) physics in the 1-10 TeV range. In addition, they will make precise measurements of the Higgs width, and characterize the Higgs self-coupling. This report details the work of the EF01 and EF02 working groups for the Snowmass 2021 study., 44 pages, 40 figures, Report of the Topical Group on Higgs Physics for Snowmass 2021. The first four authors are the Conveners, with Contributions from the other authors