Search

We present results from a complete next-to-leading order (NLO) calculation of $e^+e^-\rightarrow ZH$ in the Standard Model Effective Field Theory (SMEFT) framework, including all contributions from dimension-6 operators. At NLO, there are novel dependencies on CP violating parameters in the gauge sector, on modifications to the Higgs boson self-couplings, on alterations to the top quark Yukawa couplings, and on 4-fermion operators involving the electron and the top quark, among others. We show that including only the logarithms resulting from renormalization group scaling can produce misleading results, and further, we explicitly demonstrate the constraining power of combining measurements from different energy scales., Comment: 6 pages, 5 figures

Heavy neutral gauge bosons arise in many motivated models of Beyond the Standard Model Physics. Experimental searches require that such gauge bosons are above the TeV scale in most models which means that the tools of effective field theories, in particular the Standard Model Effective Field Theory (SMEFT), are useful. We match the SMEFT to models with heavy $Z^\prime$ bosons, including effects of dimension-8 operators, and consider the restrictions on model parameters from electroweak precision measurements and from Drell Yan invariant mass distributions and forward-backward asymmetry, $A_\text{FB}$, measurements at the LHC. The results demonstrate the model dependence of the resulting limits on SMEFT coefficients and the relatively small impact of including dimension-8 matching. In all cases, the limits from invariant mass distributions are stronger than from $A_\text{FB}$ measurements in the $Z^\prime$ models we consider., Comment: 35 pages, 9 figures, v3: several sign errors corrected

The Two-Higgs Doublet Model (2HDM) is a well understood alternative to the Standard Model of particle physics. If the new particles included in the 2HDM are at an energy scale much greater than the weak scale, the theory can be matched to the Standard Model Effective Field Theory (SMEFT). We compute for the first time the complete one-loop matching at dimension-6. We compare its numerical impact with that of tree-level matching at dimension-8 by performing a global fit to single Higgs and precision electroweak measurements, and we emphasize the importance of comparing one-loop SMEFT results with corresponding one-loop results in the full 2HDM model. In the SMEFT, we consider the relative importance of both one-loop matching and the inclusion of renormalization group evolution. Our results demonstrate the necessity of studying the impact of various expansions to quantify the uncertainties of the SMEFT matching., Comment: 28 pages, 4 figures. Updated to published version. Auxiliary files at https://github.com/BDFH-2024/BDFH

Physics beyond the Standard Model (BSM) can be described in a consistent and general way through the Higgs Effective Field Theory (HEFT). Measurements of model-independent HEFT coefficients allow one to constrain the parameter space of BSM models via a matching procedure. In this work, we show that this procedure is not unique and depends on the scalings of the parameters of the Lagrangian. As examples, we consider three BSM models: the real singlet extension of the SM with a $Z_2$ symmetry, the complex singlet extension (CSE) of the SM and the 2 Higgs Doublet Model. We discuss several physical observables, and show that different scalings of the model parameters with the UV scale in the matching to the HEFT can yield quite different results. This complicates the interpretation of HEFT measurements in terms of parameters of BSM models. Additionally, as a by-product, we report the first matching of the CSE to the HEFT., Comment: Matches published version

We consider the 2 Higgs Doublet Model (2HDM) and compare two effective field theory (EFT) approaches to it, according to whether the heavy degrees of freedom are integrated out before (SMEFT) or after (HEFT) spontaneous symmetry breaking. %We show that, in the HEFT, an inconsistent EFT is obtained if one considers an expansion simply in inverse powers of the heavy masses. %We consider a HEFT expansion consistent with perturbativity %We show that, if the HEFT approach is required to comply with perturbativity, it ends up obeying the same power counting as the SMEFT one. % By requiring decoupling and perturbativity in the 2HDM, we define a consistent EFT expansion in inverse powers of the heavy masses which is applied to both the SMEFT and the HEFT matchings to the 2HDM. We organize this expansion with a dimensionless parameter $\xi$, and investigate the tree-level scatterings $hh\rightarrow hh$ and $WW\rightarrow hh$ up to $\mathcal{O}(\xi^2)$. We find no differences between the HEFT and the SMEFT approaches at this order. We show scenarios where even including dimension-8 operators of the SMEFT is insufficient to obtain an accurate matching to the 2HDM., Comment: The HEFT matching to the 2HDM is contained in the supplemental material. Version 2 is version to be published in Phys. Rev. D

Effective field theory tools are essential for exploring non-Standard Model physics at the LHC in the absence of the discovery of new light particles. Predictions for observables are typically made at the lowest order in the QCD and electroweak expansions in the Standard Model effective field theory (SMEFT) and often ignore the effects of flavor. Here, we present results for electroweak precision observables (EWPOs)at the next-to-leading order QCD and electroweak expansions (NLO) of the SMEFT with an arbitrary flavor structure for the fermion operators. Numerical NLO SMEFT fits toEWPOs have a strong dependence on the assumed flavor structures and we demonstrate this using various popular assumptions for flavor symmetries., Comment: Supplemental files contain numerical results for EWPOs, $H\rightarrow\gamma\gamma$ and $H\rightarrow Z\gamma$ at NLO QCD and electroweak order in SMEFT for arbitrary flavor structures. Version to be published in JHEP

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., Comment: 23 pages, 2 figures

Deviations from the Standard Model (SM) can be parameterized in terms of the SM effective field theory (SMEFT), which is typically truncated at dimension-6. Including higher dimension operators -- as well as considering simultaneous insertions of multiple dimension-6 operators -- may be necessary in some processes, in order to correctly capture the properties of the underlying UV theory. As a step towards clarifying this in the Higgs boson production in gluon fusion process, we study double insertions of dimension-6 operators in the 1-loop virtual amplitude. We present needed Feynman rules up to $\mathcal{O}(1/\Lambda^4)$ and we numerically study the impact of various approximations to the $\mathcal{O}(1/\Lambda^4)$ expansion., Comment: Auxiliary file replaced

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

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., Comment: 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

The Standard Model effective field theory (SMEFT) is the tool of choice for studying deviations of Higgs couplings from the Standard Model predictions. The SMEFT is an expansion in an infinite tower of higher dimension operators, which is typically truncated at dimension-6. We consider the effective theory including dimension-8 operators and examine the matching to the 2 Higgs Doublet Model (2HDM) that is assumed to be valid at some high scale. Both the limits from the direct production of single Higgs bosons and the indirect limits on the Higgs tri-linear coupling are considered in the context of the SMEFT matched to the 2HDM, and the importance of the assumptions about the expansions in powers of the high scale are examined numerically., Comment: Eq. 48 corrected

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

Electroweak precision observables (EWPO) measured at the W and Z poles provide stringent limits on possible beyond the Standard Model physics scenarios. In an effective field theory (EFT) framework, the next-to-leading order QCD and electroweak results for EWPO yield indirect limits on possible 4-fermion operators that do not contribute to the observables at tree level. Here we calculate the next-to-leading corrections to EWPO induced by flavor non-universal 4-fermion interactions and find that the extracted limits on EFT coefficients have a strong dependence on the flavor structure of the 4-fermion operators., Comment: 15 pages, 6 figures, 2 tables

The truncation of the standard-model effective field theory, its validity and the associated uncertainties have been discussed in meetings of the LHC EFT WG. Proposals were made by participants to address these issues. No consensus was reached and no formal recommendation is therefore put forward at this time. None of the proposals has been approved or validated and further work is needed to establish a prescription. This note aims at summarizing the proposals and points of debate., Comment: LHC EFT WG note, 8 pages; v2 includes a summary of the additional proposal 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

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., Comment: 26 pages, 9 figures, UFO and Feynrules files included as supplemental material; version accepted by Physical Review D

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 scalar singlet model extends the Standard Model with the addition of a new gauge singlet scalar. We re-examine the limits on the new scalar from oblique parameter fits and from a global fit to precision electroweak observables and present analytic expressions for our results. For the case when the new scalar is much heavier than the weak scale, we map the model onto the dimension-six Standard Model effective field theory (SMEFT) and review the allowed parameter space from unitarity considerations and from the requirement that the electroweak minimum be stable. A global fit to precision electroweak data, along with LHC observables, is used to constrain the parameters of the high scale singlet model and we determine the numerical effects of performing the matching at both tree level and 1-loop., Comment: 24 pages, 8 figures

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., Comment: 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

In models with extended scalars and CP violation, resonance searches in double Higgs final states stand in competition with related searches in top quark final states as optimal channels for the discovery of beyond the Standard Model (BSM) physics. This complementarity is particularly relevant for benchmark scenarios that aim to highlight multi-Higgs production as a standard candle for the study of BSM phenomena. In this note, we compare interference effects in $t\bar t$ final states with correlated phenomena in double Higgs production in the complex singlet and the complex 2-Higgs-Doublet Models. Our results indicate that the BSM discovery potential in di-Higgs searches can be underestimated in comparison to $t\bar t $ resonance searches. Top pair final states are typically suppressed due to destructive signal-background interference, while $hh$ final states can be enhanced due to signal-signal interference. For parameter choices where the two heavy Higgs resonances are well separated in mass, top final states are suppressed relative to the naive signal expectation, while estimates of the production cross section times branching ratio remain accurate at the ${\cal{O}}(10\%)$ level for double Higgs final states., Comment: 12 pages, 8 figures, 3 tables, v2: version published in PRD

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

Simplified template cross sections define a framework for the measurement and dissemination of kinematic information in Higgs measurements. We benchmark the currently proposed setup in an analysis of dimension-6 effective field theory operators for $WH$ production. Calculating the Fisher information allows us to quantify the sensitivity of this framework to new physics and study its dependence on phase space. New machine-learning techniques let us compare the simplified template cross section framework to the full, high-dimensional kinematic information. We show that the way in which we truncate the effective theory has a sizable impact on the definition of the optimal simplified template cross sections., Comment: 30 pages, 12 figures. Code repository at https://github.com/shomiller/wh-madminer. Version accepted for publication in JHEP

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 study the impact of anomalous gauge boson and fermion couplings on the production of $W^+W^-$ pairs at potential future LHC upgrades and estimate the sensitivity at $\sqrt{S}=14$ TeV with $3~ab^{-1}$ and $\sqrt{S}=27$ TeV with $15~ab^{-1}$. A general technique for including NLO QCD effects in effective field theory (EFT) fits to kinematic distributions is presented, and numerical results are given for $\sqrt{S}=13$ TeV $W^+W^-$ production. Our method allows fits to anomalous couplings at NLO accuracy in any EFT basis and has been implemented in a publicly available version of the POWHEG-BOX. Analytic expressions for the $K$-factors relevant for $13$ TeV total cross sections are given for the HISZ and Warsaw EFT bases and differential $K$-factors can be obtained using the supplemental material. Our study demonstrates the necessity of including anomalous $Z$- fermion couplings in the extraction of limits on anomalous 3-gauge-boson couplings., Comment: 30 pages, 12 figures. v2: Typos fixed, discussion updated, and primitive cross sections included in submission. Results unchanged. Matches published version

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., Comment: 22 pages, 2 figures. v2: minor changes, matches version published in PRD

We review the theoretical underpinning of the Higgs mechanism of electroweak symmetry breaking and the experimental status of Higgs measurements from a pedagogical perspective. The possibilities and motivations for new physics in the symmetry breaking sector are discussed along with current measurements. A focus is on the implications of measurements in the Higgs sector for theoretical insights into extensions of the Standard Model. We also discuss of future prospects for Higgs physics and new analysis techniques., Comment: 102 pages, 64 figures, invited review for Physics Reports, v2: typos corrected, references added, v3: published version

Higgs decays to gauge boson pairs are a crucial ingredient in the study of Higgs properties, with the decay $H\rightarrow\gamma\gamma$ 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 $H\rightarrow VV^\prime$, $V=W^\pm,Z,\gamma$. The calculation of the real contribution to $H\rightarrow W^+W^-\gamma$ is performed by mapping two-loop amplitudes to the $3-$ body phase space., Comment: 21 pages, 3 figures; V2: Version accepted for publication

We calculate the complete one-loop electroweak corrections to the inclusive $H\rightarrow ZZ$ and $H\rightarrow Z\gamma$ 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 $G_\mu$ in the SMEFT., Comment: 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; V4: corrected a typo in eq 39 (global minus sign)

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

One of the simplest extensions of the Standard Model is the inclusion of an additional scalar multiplet, and we consider scalars in the $SU(2)_L$ singlet, triplet, and quartet representations. We examine models with heavy neutral scalars, $m_H\sim 1-2$ TeV, and the matching of the UV complete theories to the low energy effective field theory. We demonstrate the agreement of the kinematic distributions obtained in the singlet models for the gluon fusion of a Higgs pair with the predictions of the effective field theory. The restrictions on the extended scalar sectors due to unitarity and precision electroweak measurements are summarized and lead to highly restricted regions of viable parameter space for the triplet and quartet models., Comment: 28 pages, 12 figures, 5 tables; v2: references added, other minor changes, version to appear in PRD

Higgs production from gluon fusion is sensitive to the properties of heavy colored fermions and to the Yukawa couplings, (Y_F M_F)/v, of these particles to the Higgs boson. We compute the two--loop, ${\cal O}((Y_F M_F)^3/v^3)$ contributions of new high mass fermions to Higgs production. In the Standard Model, these contributions are part of the well-known electroweak corrections and are negligible. However, in models with TeV scale fermions, such as top partner or composite models, Yukawa corrections are enhanced by effects of ${\cal O}((Y_F M_F)^3/v^3)$ and are potentially significant due to the large mass of the new quarks. We examine the size of these top partner Yukawa corrections to Higgs production for parameter choices which are allowed by precision electroweak constraints., Comment: 27 pages, 7 figures, matches the published version

The ATLAS and CMS collaborations have recently published new limits on CP conserving anomalous couplings from the $W\gamma$ and $Z\gamma$ production processes. We study the corresponding limits that can be placed on the CP violating anomalous couplings $\kappa_tilde_\gamma$ and $h^1_{\gamma, Z}$ at the LHC. We find that the process $pp --> W\gamma$ at 14 TeV can place the 95% CL limit $|\kappa_tilde_\gamma| <~ 0.05$ with 10 fb^{-1} which is comparable to the existing LHC bound on the CP conserving anomalous couplings $\kappa_\gamma$. Similarly, the process $pp --> Z\gamma$ can place the 95% CL limits $|h^1_\gamma| <~ 20$ and $|h^1_Z| <~ 40$ respectively. None of these limits is derived from a truly CP-odd observable so that it is not possible to separate the effects of the CP violating anomalous couplings from the rest., Comment: 16 LaTex pages, 4 figures, 5 tables, accepted version for publication in Physical Review D

In many new physics scenarios, the particle content of the Standard Model is extended and the Higgs couplings are modified, sometimes without affecting single Higgs production. We analyse two models with additional quarks. In these models, we compute double Higgs production from gluon fusion exactly at leading-order, and present analytical results in the heavy-quark mass ap- proximation. The experimental bounds from precision electroweak measurements and from the measured rate of single Higgs production combine to give significant restrictions for the allowed deviation of the double Higgs production rate from the Standard Model prediction as well as on the branching ratio for the Higgs decay into photons. The two models analysed eventually present a similar Higgs phenomenology as the Standard Model. We connect this result to the magnitude of the dimension six operators contributing to the gluon-fusion Higgs production., Comment: 39 pages, 15 figures. Minor correction to Fig. 3