The assumption that the Standard Model is an Effective Field Theory (SM EFT) of a more fundamental theory at a higher, than electroweak, energy scale, implies a growth of cross-sections for electroweak Vector Boson Scattering (VBS) processes signalling the appearance of a resonance (or resonances) nearby that scale. In this article, we investigate in detail SM EFT effects from dimension-6 operators in VBS with like-sign-$W$ production in fully leptonic decay modes at the High Luminosity LHC (HL-LHC). We find that these effects are important for a handful of operators, most notably for the operator composed of three $SU(2)$ field strength tensors responsible for strong transversely polarized vector boson interactions. Current global fits on Wilson-coefficients allow for a signal immediately permissive at the HL-LHC if not accessible at the current LHC-dataset.
We investigate the Beyond Standard Model discovery potential in the framework of the Effective Field Theory (EFT) for the same-sign $WW$ scattering process in purely leptonic $W$ decay modes at the High-Luminosity and High-Energy phases of the Large Hadron Collider (LHC). The goal of this paper is to examine the applicability of the EFT approach, with one dimension-8 operator varied at a time, to describe a hypothetical new physics signal in the $WWWW$ quartic coupling. In the considered process there is no experimental handle on the $WW$ invariant mass, and it has previously been shown that t…
We review the current status of vector boson fusion and vector boson scattering studies in the frame of Run-2 of LHC. These processes are equally interesting and challenging, and new ideas have to be applied for their experimental analysis. These channels are optimal for the search of new physics, and therefore we discuss two promising techniques for this purpose: standard model effective field theory and pseudo observables. Regarding their implementation in the analyses, we also discuss briefly how these techniques should be included in the Monte Carlo generators.
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…
We generalize in several directions our recent analysis of the limitations to the use of the effective field theory approach to study dark matter at the LHC. Firstly, we study the full list of operators connecting fermion DM to quarks and gluons, corresponding to integrating out a heavy mediator in the $s$-channel; secondly, we provide analytical results for the validity of the EFT description for both $\sqrt{s}=8$ {\rm TeV} and $14$ {\rm TeV}; thirdly, we make use of a MonteCarlo event generator approach to assess the validity of our analytical conclusions. We apply our results to revisit the…
Effective field theory (EFT) formulations of dark matter interactions have proven to be a convenient and popular way to quantify LHC bounds on dark matter. However, some of the non-renormalizable EFT operators considered do not respect the gauge symmetries of the Standard Model. We carefully discuss under what circumstances such operators can arise, and outline potential issues in their interpretation and application.
Recently, the Higgs boson masses in the Minimal Supersymmetric Standard Model (MSSM) and their mixing have been calculated using the complex Two-Higgs-DoubletModel (cTHDM) as an effective field theory (EFT) of the MSSM. Here, we discuss the implementation of this calculation, which we improve in several aspects, into the hybrid framework of FeynHiggs by combing the cTHDM-EFT calculation with the existing fixed-order calculation. This combination allows accurate predictions also in the intermediate regime where some SUSY particles are relatively light, some relatively heavy and some in between.…
We review the limitations to the use of the effective field theory approach to study dark matter at the LHC. Due to the high energy reach, the low energy description breaks down, and may lead to incorrect results. The use of simplified models is suggested.
The LHC effective field theory working group gathers members of the LHC experiments and the theory community to provide a framework for the interpretation of LHC data in the context of EFT. In this note we discuss experimental observables and corresponding measurements in analysis of the Higgs, top, and electroweak data at the LHC. We review the relationship between operators and measurements relevant for the interpretation of experimental data in the context of a global SMEFT analysis. One of the goals of ongoing effort is bridging the gap between theory and experimental communities working o…
We investigate the current LHC bounds on New Physics (NP) that contributes to $\bar B \to D^{(*)} l\barν$ for $l = (e,μ,τ)$ by considering both leptoquark (LQ) models and an effective-field-theory (EFT) Hamiltonian. Experimental analyses from $l+\text{missing}$ searches with high $p_T$ are applied to evaluate the NP constraints with respect to the Wilson coefficients. A novel point of this work is to show difference between LQs and EFT for the applicable LHC bound. In particular, we find that the EFT description is not valid to search for LQs with the mass less than $\lesssim 10\,\text{TeV}$ a…
We discuss the implications of dimension-six operators of the Effective Field Theory (EFT) framework in the study of Vector Boson Scattering (VBS) in the $pp \to Z Z j j $ channel. We show that operators of dimension-six should not be neglected in favour of those of dimension-eight. We observe that this process is very sensitive to some of the operators commonly fit using LEP and Higgs data, and that it can be used to improve the bounds on the former. Further we show that other operators than the ones generating anomalous triple and quartic gauge couplings (aTGCs/aQCGs) can have a non-negligib…
With the absence of the direct detection of new physics and the large data set collected at the LHC, the search for indirect effects in precision measurements became popular. Effective field theories enable to interpret these effects that originate from physics manifested at currently unreachable energy scales in a model independent framework. In this report, an overview of new analyses performed by the ATLAS and CMS Collaborations in the field of top quark physics is given.
Effective Field Theory (EFT) extensions of the Standard Model are tools to compute observables $\big(e.g.$ cross sections with partonic center-of-mass energy $\sqrt{\hat{s}}\,\big)$ as a systematically improvable expansion suppressed by a new physics scale $M$. If one is interested in EFT predictions in the parameter space where $M<\sqrt{\hat{s}}$, concerns of self-consistency emerge, which can manifest as a violation of perturbative partial-wave unitarity. However, when we search for the effects of an EFT at a hadron collider with center-of-mass energy $\sqrt{s}$ using an inclusive strategy, …
We propose a new approach to the LHC dark matter search analysis within the effective field theory (EFT) framework by utilising the K-matrix unitarisation formalism. This approach provides a reasonable estimate of the dark matter production cross section at high energies, and hence allows reliable bounds to be placed on the cut-off scale of relevant operators without running into the problem of perturbative unitarity violation. We exemplify this procedure for the effective operator D5 in monojet dark matter searches in the collinear approximation. We compare our bounds to those obtained using …
We present a parton-level study of electro-weak production of vector-boson pairs at the Large Hadron Collider, establishing the sensitivity to a set of dimension-six operators in the Standard Model Effective Field Theory (SMEFT). Different final states are statistically combined, and we discuss how the orthogonality and interdependence of different analyses must be considered to obtain the most stringent constraints. The main novelties of our study are the inclusion of SMEFT effects in non-resonant diagrams and in irreducible QCD backgrounds, and an exhaustive template analysis of optimal obse…
We present a study of the interplay between PDF and EFT effects in high-mass Drell-Yan at the LHC. We quantify the impact of a consistent joint determination of the PDFs and Wilson coefficients on the bounds obtained on the EFT and examine the effect on the PDFs, determining the extent to which EFT signals could be reabsorbed into the large-$x$ quark and anti-quark PDFs. Finally, we present dedicated projections for the High-Luminosity LHC and evaluate its ultimate potential to constrain the EFT parameters, while taking into account potential modifications of the proton structure.
The lightest Higgs boson mass of the Minimal Supersymmetric Standard Model has been recently computed diagrammatically at the three-loop order in the whole supersymmetric parameters space of the SUSY-QCD sector. The code FeynHiggs combines one- and two-loop fixed-order with the effective-field-theory calculations for the same Higgs mass. The two numerical predictions agree considering the scenario of only one SUSY-scale and vanishing stop mixing parameter below 10 TeV. The agreement is improved by introducing an additional supersymmetric scale and a non-zero stop mixing. Additionally, the comb…
We discuss the Standard Model Effective Field Theory (SM-EFT) contributions to neutral- and charge-current Drell-Yan production, associated production of the Higgs and a vector boson, and Higgs boson production via vector boson fusion. We consider all the dimension-six SM-EFT operators that contribute to these processes at leading order, include next-to-leading order QCD corrections, and interface them with parton showering and hadronization in Pythia8 according to the POWHEG method. We discuss existing constraints on the coefficients of dimension-six operators and identify differential and an…
Finding better ways to prove the Standard Model Effective Field Theory is a very important direction of research. This paper focuses on measurements of Electroweak triple gauge couplings, paying special attention on the regime of validity of the Effective Field Theory (EFT). In this regard, one of our goals is to find measurements leading to a large increase of the interference between the SM amplitude and the contribution of irrelevant operators in the EFT. We propose two such distributions that will lead to a better accuracy. Improvements compared to the traditional methods as well as LHC hi…
It is possible that measurements of vector boson scattering (VBS) at the LHC will reveal disagreement with Standard Model predictions, but no new particles will be observed directly. The task is then to learn as much as possible about the new physics from a VBS analysis carried within the framework of the Effective Field Theory (EFT). In this paper we discuss issues related to the correct usage of the EFT when the WW invariant mass is not directly accessible experimentally, as in purely leptonic W decay channels. The strategies for future data analyses in case such scenario indeed occurs are p…
Effective field theories are an incredibly powerful tool in order to study and understand the true nature of the symmetry breaking sector dynamics of the Standard Model. However, they can suffer from some theoretical problems such as that of unitarity violation. Nevertheless, in order to interpret experimental data correctly a fully unitary prescription is needed. To this purpose, unitarization methods are addressed, but each of them leads to a different (unitary) prediction. Because of this, there is an inherent theoretical uncertainty in the determination of the effective field theory parame…
We propose a parametrization of anomalous Higgs-boson couplings that is both systematic and practical. It is based on the electroweak chiral Lagrangian, including a light Higgs boson, as the effective field theory (EFT) at the electroweak scale $v$. This is the appropriate framework for the case of sizeable deviations in the Higgs couplings of order $10\%$ from the Standard Model, considered to be parametrically larger than new-physics effects in the sector of electroweak gauge interactions. The role of power counting in identifying the relevant parameters is emphasized. The three relevant sca…
Various methods are used in the literature for predicting the lightest CP-even Higgs boson mass in the Minimal Supersymmetric Standard Model (MSSM). Fixed-order diagrammatic calculations capture all effects at a given order and yield accurate results for scales of supersymmetric (SUSY) particles that are not separated too much from the weak scale. Effective field theory calculations allow a resummation of large logarithmic contributions up to all orders and therefore yield accurate results for a high SUSY scale. A hybrid approach, where both methods have been combined, is implemented in the co…
The detection of production of a pair of Higgs bosons before the end of LHC operation would be clear evidence of New Physics (NP). As searches for non-resonant production of Higgs pairs are being designed it is of particular importance to be able to conveniently present current experimental results in terms of limits in the most 'model-independent' fashion possible. In this article we provide an analytic parametrization of the {\it differential} Higgs-pair production at the LHC in the effective field theory (EFT) extension of the SM. It results from a fit to the theory prediction for the $gg \…
The usage of Effective Field Theories (EFT) for LHC new physics searches is receiving increasing attention. It is thus important to clarify all the aspects related with the applicability of the EFT formalism in the LHC environment, where the large available energy can produce reactions that overcome the maximal range of validity, i.e. the cutoff, of the theory. We show that this does forbid to set rigorous limits on the EFT parameter space through a modified version of the ordinary binned likelihood hypothesis test, which we design and validate. Our limit-setting strategy can be carried on in …
Projecting measurements of the interactions of the known Standard Model (SM) states into an effective field theory (EFT) framework is an important goal of the LHC physics program. The interpretation of measurements of the properties of the Higgs-like boson in an EFT allows one to consistently study the properties of this state, while the SM is allowed to eventually break down at higher energies. In this review, basic concepts relevant to the construction of such EFTs are reviewed pedagogically. Electroweak precision data is discussed as a historical example of some importance to illustrate cri…
Precise predictions for Higgs boson masses in the Minimal Supersymmetric Standard Model can be obtained by combining fixed-order calculations with effective field theory (EFT) methods for the resummation of large logarithms in case of heavy superpartners. This hybrid approach is implemented in the computer code FeynHiggs and has been applied in previous studies for calculating the mass of the lightest CP-even Higgs boson for low, intermediate and high SUSY scales. In these works it was assumed that the non-standard Higgs bosons share a common mass scale with the supersymmetric squark particles…
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 study the validity of effective field theory (EFT) interpretations of monojet searches for dark matter at the LHC for vector and axial-vector interactions. We show that the EFT approach is valid when the mediator has mass m_med greater than 2.5 TeV. We find that the current limits on the contact interaction scale Lambda in the EFT apply to theories that are perturbative for dark matter mass m_DM < 800 GeV. However, for all values of m_DM in these theories, the mediator width is larger than the mass, so that a particle-like interpretation of the mediator is doubtful. Furthermore, consistency…
We analyse the constraints on models of WIMP Dark Matter that can be derived from upper bounds on the "monojet" cross section at the LHC. These constraints were originally interpreted in the context of an effective field theory (EFT) where the Standard Model is extended by a dimension--6 operator whose coefficient is $1/Λ^2$. We show that combining the 8 TeV data of the ATLAS and CMS collaborations improves the bounds only slightly. We then analyze this final state in the context of simplified models with $s-$channel mediator. We show that if the decay width of the mediator is small, these sim…
The present approach relies on the SM chiral symmetry breaking pattern $SU(2)_L\otimes SU(2)_R\to SU(2)_{L+R}$, with the EW Goldstone bosons given in a non-linear realization and the Higgs boson described by an EW singlet field. In addition, we assume the presence of new physics heavy states around the TeV scale that do not couple to the SM fermions, only to the SM bosonic sector. However, the mixing between gauge bosons and BSM resonances induces a small indirect interaction between the BSM sector and the SM fermions. This leads to an important suppression of the fermionic operators in the lo…
We investigate single Higgs and Higgs pair production at the LHC in models of Universal Extra Dimensions. After calculating the relevant cross sections, we use the UED model as a testing ground for the Effective Field Theory approach to physics beyond the Standard Model. We show how the UED contributions to Higgs production can be matched to a dimension-6 operator. We then discuss the range of validity of this approach, in particular for Higgs pair production, and determine the sensitivity to the number of KK modes in the loop.
Electroweak Sudakov logarithms at high energy, of the form alpha/sin^2 theta_W^n log^m s/M_{Z,W}^2, are summed using effective theory (EFT) methods. The exponentiation of Sudakov logarithms and factorization is discussed in the EFT formalism. Radiative corrections are computed to scattering processes in the standard model involving an arbitrary number of external particles. The computations include non-zero particle masses such as the t-quark mass, electroweak mixing effects which lead to unequal W and Z masses and a massless photon, and Higgs corrections proportional to the top quark Yukawa c…
I review the main features of the effective field theory (EFT) behind scenarios of dynamical electroweak symmetry breaking, placing particular emphasis on the systematics and the parallels that can be drawn with Chiral Perturbation Theory. The notion of chiral dimensions will be introduced and shown to be the right tool to describe nonlinear expansions. I will also discuss why such an EFT is of interest in phenomenological studies at the LHC. The most important aspect is that the EFT is engineered to recover the Standard Model in a particular limit, and therefore provides a general framework t…
The high-energy tails of charged- and neutral-current Drell-Yan processes provide important constraints on the light quark and anti-quark parton distribution functions (PDFs) in the large-x region. At the same time, short-distance new physics effects such as those encoded by the Standard Model Effective Field Theory (SMEFT) would induce smooth distortions to the same high-energy Drell-Yan tails. In this work, we assess for the first time the interplay between PDFs and EFT effects for high-mass Drell-Yan processes at the LHC and quantify the impact that the consistent joint determination of PDF…
In this paper, we present the computation of the Higgs boson pair production cross section, both inclusive as well as differential on the invariant mass distribution, at next-to-next-to-leading order (NNLO) in QCD including effects of new physics beyond the standard model. We parametrize the effects of new physics with the relevant dimension 6 operators in a standard model effective field theory (EFT) approach and examine their phenomenology. The dependence of the NNLO $K$-factor on the EFT couplings is analysed, finding that, while rather flat for a number of EFT coefficients, it can consider…
Effective field theory (EFT) approaches are widely used at the LHC, such that it is important to study their validity, and ease of matching to specific new physics models. In this paper, we consider an extension of the SM in which a top quark couples to a new heavy scalar. We find the dimension six operators generated by this theory at low energy, and match the EFT to the full theory up to NLO precision in the simplified model coupling. We then examine the range of validity of the EFT description in top pair production, finding excellent validity even if the scalar mass is only slightly above …
Effective field theories (EFT) are commonly used to parameterize effects of BSM physics in vector boson scattering (VBS). For Wilson coefficients which are large enough to produce presently observable effects, the validity range of the EFT represents only a fraction of the energy range covered by the LHC, however. In order to shed light on possible extrapolations into the high energy region, a class of UV-complete toy models, with extra SU(2) multiplets of scalars or of fermions with vector-like weak couplings, is considered. By calculating the Wilson coefficients up to energy-dimension eight,…
In this work the vector boson scattering process is investigated through the reaction $pp\rightarrow 2 \mathrm{jets} + W^\ast W^\ast \rightarrow 2 \mathrm{jets} + lν_l l'ν_l'$, where $W^\ast$ denote in general off-shell $W^+$, in the EFT approach with the HL-LHC and HE-LHC experiments in mind. We have investigated the discovery potential of certain classes of the EFT "models" of both the SMEFT and HEFT bases with the particular emphasis on using the EFT "models" in their region of validity. A novel method has been proposed for determining the discovery regions of physics beyond the SM, describ…
Assuming the presence of physics beyond the Standard Model (SM) with a characteristic scale M ~ O(10) TeV, we investigate the naturalness of the Higgs sector at scales below M using an effective field theory (EFT) approach. We obtain the leading 1-loop EFT contributions to the Higgs mass with a Wilsonian-like hard cutoff, and determine the constraints on the corresponding operator coefficients for these effects to alleviate the little hierarchy problem up to the scale of the effective action Λ< M, a condition we denote by "EFT-naturalness". We also determine the types of physics that can lead …
State-of-the-art predictions for the mass of the lightest MSSM Higgs boson usually involve the resummation of higher-order logarithmic contributions obtained within an effective-field-theory (EFT) approach, often combined with a fixed-order calculation into a hybrid result. For the phenomenologically interesting case of a significant hierarchy between the gluino mass and the masses of the scalar top quarks the predictions suffer from large theoretical uncertainties related to non-decoupling power-enhanced gluino contributions in the EFT results employing the $\overline{\text{DR}}$ renormalisat…
In these proceedings we review the interplay between LHC searches for dark matter and direct detection experiments. For this purpose we consider two prime examples: the effective field theory (EFT) approach and the minimal supersymmetric standard model (MSSM). In the EFT scenario we show that for operators which do not enter directly direct detection at tree-level, but only via loop effects, LHC searches give complementary constraints. In the MSSM stop and Higgs exchange contribute to the direct detection amplitude. Therefore, LHC searches for supersymmetric particles and heavy Higgses place c…
We discuss effective field theories (EFTs) for the Higgs particle, which is not necessarily the Higgs of the Standard Model. We distinguish two different consistent expansions: EFTs that describe decoupling new-physics effects and EFTs that describe non-decoupling new-physics effects. We briefly discuss the first case, the SM-EFT. The focus of this thesis is on the non-decoupling EFTs. We argue that the loop expansion is the consistent expansion in the second case. We introduce the concept of chiral dimensions, equivalent to the loop expansion. Using the chiral dimensions, we expand the electr…
Measurements carried out or reinterpreted within the framework of effective field theory (EFT) will constitute a key component of the LHC legacy in the quest towards physics beyond the standard model. Numerous EFT measurements were already published by the CMS Collaboration. In the top quark sector, four distinct approaches to EFT have been identified, each successfully applied in several analyses. We review the pros and cons of each approach, while illustrating them with recent analyses in which they were adopted.
With an expected rate of about one event per 100,000 top-quark pairs, four top-quark final states very rarely arise at the LHC. Though scarce, they offer a unique window onto top-quark compositeness, self-interactions and more generically, onto any top-philic new physics. By employing simplified models featuring heavy resonances, we study the range of validity of effective theory interpretations of current four top-quark analyses at the LHC and establish their future reach at the HL-LHC. We find that for the class of models under consideration, the effective field theory interpretations are no…
The gauge singlet right-handed neutrinos (RHNs) are essential fields in several neutrino mass models that explain the observed eV scale neutrino mass. We assume RHN field to be present in the vicinity of the electroweak scale and all the other possible beyond the standard model (BSM) fields arise at high energy scale $\geΛ$. In this scenario, the BSM physics can be described using effective field theory (EFT) where the set of canonical degrees of freedoms consists of both RHN and SM fields. EFT of this kind is usually dubbed as $N_{R}$-EFT. We systematically construct relevant operators that c…
