Operators In Effective Field Theory Research Articles

Thermal WIMPs and the scale of new physics

The non-observation of conclusive dark matter signals raises the question whether WIMPs can still account for the dark matter of the universe. In this talk I will present results from a global analysis of effective field theory operators describing the interactions between WIMPs and Standard Model particles. In this bottom-up approach, the global fitting framework GAMBIT is used to simultaneously vary the coefficients of 14 such operators, along with the WIMP mass, the scale of new physics and several nuisance parameters. The likelihood functions include the latest data from Planck, direct and indirect detection experiments, and the LHC. Although the observed relic density can be reproduced in large regions of parameter space, there cannot be a large hierarchy between the dark matter mass and the scale of new physics, which raises concerns about the validity of the effective field theory. I will discuss possible ways to address this issue in order to consistently interpret the latest results from WIMP searches at the LHC.

Probing effective field theory operators in the associated production of top quarks with a Z boson in multilepton final states at sqrt{s} = 13 TeV

A search for new top quark interactions is performed within the framework of an effective field theory using the associated production of either one or two top quarks with a Z boson in multilepton final states. The data sample corresponds to an integrated luminosity of 138 fb−1 of proton-proton collisions at sqrt{s} = 13 TeV collected by the CMS experiment at the LHC. Five dimension-six operators modifying the electroweak interactions of the top quark are considered. Novel machine-learning techniques are used to enhance the sensitivity to effects arising from these operators. Distributions used for the signal extraction are parameterized in terms of Wilson coefficients describing the interaction strengths of the operators. All five Wilson coefficients are simultaneously fit to data and 95% confidence level intervals are computed. All results are consistent with the SM expectations.

A Machine Learning approach to the EFT re-interpretation of the WZjj fully leptonic electroweak production

In this paper we study the use of Machine Learning techniques to set constraints on indirect signatures of physics beyond the Standard Model in Vector Boson Scattering (VBS), in the electroweak (EWK) production of self-interacting W ± Z bosons in association with two jets. The WZ fully leptonic channel has been extensively studied by the ATLAS Collaboration at the LHC and we are about to provide results using the full Run 2 data corresponding to an integrated luminosity of 139fb −1. The EWK production of the WZ in association with two jets has been already observed at 36fb −1 with an observed significance of 5.3 standard deviations. A factor of four increase in the integrated luminosity provides an opportunity to check for deviations from the Standard Model (SM) predictions, in particular for model independent, indirect searches for New Physics. Such searches can be realized in the context of an extension of the SM in terms of an Effective Field Theory (EFT) formalism, providing a way to quantify possible deviations from the Standard Model. The EFT Lagrangian besides the Standard Model terms comprises contributions from higher dimension operators, their effect being determined by the strength of their corresponding parameters (Wilson coefficients scaled to the appropriate power of Λ, indicating the scale of the appearance of New Physics). In this paper an attempt is made to search for New Physics effects in the WZjj production, using state-of-the-art machine learning models where diverse network architectures are effectively combined into ensembles trained on the outcomes of base learners maximizing performance. The base learners are trained to identify pure WZjj signal events originating from the effect of EFT operators, from WZjj background events originating from strong (QCD) or EWK WZjj processes. We investigate the utilization of the ensemble model response in estimating the sensitivity of WZjj events in some of the dimension-8 EFT operators and compare the results to sensitive kinematic variables traditionally used to constrain the EFT operator effects.

Thermal WIMPs and the scale of new physics: global fits of Dirac dark matter effective field theories

We assess the status of a wide class of WIMP dark matter (DM) models in light of the latest experimental results using the global fitting framework GAMBIT. We perform a global analysis of effective field theory (EFT) operators describing the interactions between a gauge-singlet Dirac fermion and the Standard Model quarks, the gluons and the photon. In this bottom-up approach, we simultaneously vary the coefficients of 14 such operators up to dimension 7, along with the DM mass, the scale of new physics and several nuisance parameters. Our likelihood functions include the latest data from Planck, direct and indirect detection experiments, and the LHC. For DM masses below 100 GeV, we find that it is impossible to satisfy all constraints simultaneously while maintaining EFT validity at LHC energies. For new physics scales around 1 TeV, our results are influenced by several small excesses in the LHC data and depend on the prescription that we adopt to ensure EFT validity. Furthermore, we find large regions of viable parameter space where the EFT is valid and the relic density can be reproduced, implying that WIMPs can still account for the DM of the universe while being consistent with the latest data.

Measurement of the electroweak production of Zγ and two jets in proton-proton collisions at s=13 TeV and constraints on anomalous quartic gauge couplings

The first observation of the electroweak (EW) production of a Z boson, a photon, and two forward jets (Z$\gamma$jj) in proton-proton collisions at a center-of-mass energy of 13 TeV is presented. A data set corresponding to an integrated luminosity of 137 fb$^{-1}$, collected by the CMS experiment at the LHC in 2016-2018 is used. The measured fiducial cross section for EW Z$\gamma$jj is $\sigma_{\mathrm{EW}}$ = 5.21 $\pm$ 0.52 (stat) $\pm$ 0.56 (syst) fb = 5.21 $\pm$ 0.76 fb. Single-differential cross sections in photon, leading lepton, and leading jet transverse momenta, and double-differential cross sections in $m_{\mathrm{jj}}$ and $\lvert\Delta\eta_{\mathrm{jj}}\rvert$ are also measured. Exclusion limits on anomalous quartic gauge couplings are derived at 95% confidence level in terms of the effective field theory operators $\mathrm{M}_{0}$ to $\mathrm{M}_{5}$, $\mathrm{M}_{7}$, $\mathrm{T}_{0}$ to $\mathrm{T}_{2}$, and $\mathrm{T}_{5}$ to $\mathrm{T}_{9}$.

Observing t{bar{t}}Z spin correlations at the LHC

Spin correlations in the production of top-antitop quark (t{bar{t}}) pairs at the Large Hadron Collider (LHC) are an experimentally verified prediction of the Standard Model. In this paper, we compute the full spin density matrix for t{bar{t}}Z production at next-to-leading order precision in QCD, for center-of-mass energies of 13 and 14 text {TeV}. We find that the additional emission of a Z boson leads to significantly different spin correlations with respect to the t{bar{t}} case, and induces small longitudinal polarisations of the top quarks. We further propose an analysis strategy that could lead to the observation of spin correlations in t{bar{t}}Z events at the end of Run 3 of the LHC, or possibly earlier by combining the ATLAS and CMS datasets. In addition, we show that the pure angular information contained in the spin density matrix provides novel constraints on the dimension-6 effective field theory operators relevant to the t-Z interaction, without any reference to the total production rates.

Complete set of dimension-eight operators in the standard model effective field theory

We present a complete list of the dimension 8 operator basis in the standard model effective field theory using group theoretic techniques in a systematic and automated way. We adopt a new form of operators in terms of the irreducible representations of the Lorentz group, and identify the Lorentz structures as states in a $SU(N)$ group. In this way, redundancy from equations of motion is absent and that from integration-by-part is treated using the fact that the independent Lorentz basis forms an invariant subspace of the $SU(N)$ group. We also decompose operators into the ones with definite permutation symmetries among flavor indices to deal with subtlety from repeated fields. For the first time, we provide the explicit form of independent flavor-specified operators in a systematic way. Our algorithm can be easily applied to higher dimensional standard model effective field theory and other effective field theories, making these studies more approachable.

Complete set of dimension-nine operators in the standard model effective field theory

We present a complete and independent list of the dimension 9 operator basis in the Standard Model effective field theory by an automatic algorithm based on the amplitude-operator correspondence. A complete basis (y-basis) is first constructed by enumerating Young tableau of an auxiliary $SU(N)$ group and the gauge groups, with the equation-of-motion and integration-by-part redundancies all removed. In the presence of repeated fields, another basis (p-basis) with explicit flavor symmetries among them is derived from the y-basis, which further induces a basis of independent monomial operators through a systematic process called de-symmetrization. Our form of operators have advantages over the traditional way of presenting operators constrained by flavor relations, in the simplicity of both eliminating flavor redundancies and identifying independent flavor-specified operators. We list the 90456 (560) operators for three (one) generations of fermions, all of which violate baryon number or lepton number conservation; among them we find new violation patterns as $\Delta B = 2$ and $\Delta L = 3$, which only appear at the dimensions $d \ge 9$.

Effective field theory analysis of the first LUX dark matter search

The Large Underground Xenon (LUX) dark matter search was a 250-kg active mass dual-phase time projection chamber that operated by detecting light and ionization signals from particles incident on a xenon target. In December 2015, LUX reported a minimum 90% upper C.L. of 6×10−46 cm2 on the spin-independent WIMP-nucleon elastic scattering cross section based on a 1.4×104 kg·day exposure in its first science run. Tension between experiments and the absence of a definitive positive detection suggest it would be prudent to search for WIMPs outside the standard spin-independent/spin-dependent paradigm. Recent theoretical work has identified a complete basis of 14 independent effective field theory (EFT) operators to describe WIMP-nucleon interactions. In addition to spin-independent and spin-dependent nuclear responses, these operators can produce novel responses such as angular-momentum-dependent and spin-orbit couplings. Here we report on a search for all 14 of these EFT couplings with data from LUX’s first science run. Limits are placed on each coupling as a function of WIMP mass.Received 26 March 2020Revised 5 May 2021Accepted 25 May 2021DOI:https://doi.org/10.1103/PhysRevD.103.122005© 2021 American Physical SocietyPhysics Subject Headings (PhySH)Research AreasParticle astrophysicsParticle dark matterTechniquesDark matter detectorsGravitation, Cosmology & Astrophysics

EFT asymptotics: the growth of operator degeneracy

We establish formulae for the asymptotic growth (with respect to the scaling dimension) of the number of operators in effective field theory, or equivalently the number of S-matrix elements, in arbitrary spacetime dimensions and with generic field content. This we achieve by generalising a theorem due to Meinardus and applying it to Hilbert series---partition functions for the degeneracy of (subsets of) operators. Although our formulae are asymptotic, numerical experiments reveal remarkable agreement with exact results at very low orders in the EFT expansion, including for complicated phenomenological theories such as the standard model EFT. Our methods also reveal phase transition-like behaviour in Hilbert series. We discuss prospects for tightening the bounds and providing rigorous errors to the growth of operator degeneracy, and of extending the analytic study and utility of Hilbert series to EFT.

Revisiting electroweak radiative corrections to b \u2192 s\u2113\u2113 in SMEFT

We revisit electroweak radiative corrections to Standard Model Effective Field Theory (SMEFT) operators which are relevant for the B-meson semileptonic decays. The one-loop matching formulae onto the low-energy effective field theory are provided without imposing any flavor symmetry. The on-shell conditions are applied especially in dealing with quark-flavor mixings. Also, the gauge independence is shown explicitly in the Rξ gauge.

Low-Energy Effective Field Theory below the Electroweak Scale: dimension-8 operators

We construct a complete basis of dimension-8 operators in the Low-Energy Effective Field Theory below the Electroweak Scale (LEFT). We find there are 35058 dimension-8 operators in the LEFT for two generations of up-type quarks and three generations of down-type quarks, charged leptons, and left-handed neutrinos. The existence of this operator basis is a necessary prerequisite for matching to the Standard Model Effective Field Theory at the dimension-8 level.

Search for new physics in top quark production with additional leptons in proton-proton collisions at sqrt{s} = 13 TeV using effective field theory

Events containing one or more top quarks produced with additional prompt leptons are used to search for new physics within the framework of an effective field theory (EFT). The data correspond to an integrated luminosity of 41.5 fb−1 of proton-proton collisions at a center-of-mass energy of 13 TeV at the LHC, collected by the CMS experiment in 2017. The selected events are required to have either two leptons with the same charge or more than two leptons; jets, including identified bottom quark jets, are also required, and the selected events are divided into categories based on the multiplicities of these objects. Sixteen dimension-six operators that can affect processes involving top quarks produced with additional charged leptons are considered in this analysis. Constructed to target EFT effects directly, the analysis applies a novel approach in which the observed yields are parameterized in terms of the Wilson coefficients (WCs) of the EFT operators. A simultaneous fit of the 16 WCs to the data is performed and two standard deviation confidence intervals for the WCs are extracted; the standard model expectations for the WC values are within these intervals for all of the WCs probed.

Precision Higgs couplings in neutral naturalness models: an effective field theory approach

The Higgs sector in neutral naturalness models provides a portal to the hidden sectors, and thus measurements of Higgs couplings at current and future colliders play a central role in constraining the parameter space of the model. We investigate a class of neutral naturalness models, in which the Higgs boson is a pseudo-Goldstone boson from the universal SO(N)/SO(N − 1) coset structure. Integrating out the radial mode from the spontaneous global symmetry breaking, we obtain various dimension-six operators in the Standard Model effective field theory, and calculate the low energy Higgs effective potential with radiative corrections included. We perform a χ2 fit to the Higgs coupling precision measurements at current and future colliders and show that the new physics scale could be explored up to 2.3 (2.4) TeV without (with) the Higgs invisible decay channels at future Higgs factories. The limits are comparable to the indirect constraints obtained via electroweak precision measurements.

Evidence for electroweak production of four charged leptons and two jets in proton-proton collisions at [formula omitted

Evidence is presented for the electroweak (EW) production of two jets (jj) in association with two Z bosons and constraints on anomalous quartic gauge couplings are set. The analysis is based on a data sample of proton-proton collisions at s=13TeV collected with the CMS detector in 2016–2018, and corresponding to an integrated luminosity of 137fb−1. The search is performed in the fully leptonic final state ZZ→ℓℓℓ′ℓ′, where ℓ,ℓ′=e,μ. The EW production of two jets in association with two Z bosons is measured with an observed (expected) significance of 4.0 (3.5) standard deviations. The cross sections for the EW production are measured in three fiducial volumes and the result is σEW(pp→ZZjj→ℓℓℓ′ℓ′jj)=0.33−0.10+0.11(stat)−0.03+0.04(syst)fb in the most inclusive volume, in agreement with the standard model prediction of 0.275±0.021fb. Measurements of total cross sections for jj production in association with two Z bosons are also reported. Limits on anomalous quartic gauge couplings are derived in terms of the effective field theory operators T0, T1, T2, T8, and T9.

Observation of electroweak production of Wγ with two jets in proton-proton collisions at [formula omitted] TeV

A first observation is presented for the electroweak production of a W boson, a photon, and two jets in proton-proton collisions. The W boson decays are selected by requiring one identified electron or muon and an imbalance in transverse momentum. The two jets are required to have a high dijet mass and a large separation in pseudorapidity. The measurement is based on data collected with the CMS detector at a center-of-mass energy of 13 TeV, corresponding to an integrated luminosity of 35.9 fb−1. The observed (expected) significance for this process is 4.9 (4.6) standard deviations. After combining with previously reported CMS results at 8 TeV, the observed (expected) significance is 5.3 (4.8) standard deviations. The cross section for the electroweak Wγjj production in a restricted fiducial region is measured as 20.4±4.5fb and the total cross section for Wγ production in association with 2 jets in the same fiducial region is 108±16fb. All results are in good agreement with recent theoretical predictions. Constraints are placed on anomalous quartic gauge couplings in terms of dimension-8 effective field theory operators.

An explicit construction of the dimension-9 operator basis in the standard model effective field theory

We investigate systematically dimension-9 operators in the standard model effective field theory which contains only standard model fields and respects its gauge symmetry. With the help of the Hilbert series approach to classifying operators according to their lepton and baryon numbers and their field contents, we construct the basis of operators explicitly. We remove redundant operators by employing various kinematic and algebraic relations including integration by parts, equations of motion, Schouten identities, Dirac matrix and Fierz identities, and Bianchi identities. We confirm counting of independent operators by analyzing their flavor symmetry relations. All operators violate lepton or baryon number or both, and are thus non-Hermitian. Including Hermitian conjugated operators there are {left.384right|}_{Delta B=0}^{Delta L=pm 2}+{left.10right|}_{Delta B=pm 2}^{Delta L=0}+{left.4right|}_{Delta B=pm 1}^{Delta L=pm 3}+{left.236right|}_{Delta B=pm 1}^{Delta L=mp 1} operators without referring to fermion generations, and {left.44874right|}_{Delta B=0}^{Delta L=pm 2}+{left.2862right|}_{Delta B=pm 2}^{Delta L=0}+{left.486right|}_{Delta B=pm 1}^{Delta L=pm 3}+{left.42234right|}_{Delta B=mp 1}^{Delta L=pm 1} operators when three generations of fermions are referred to, where ∆L, ∆B denote the net lepton and baryon numbers of the operators. Our result provides a starting point for consistent phenomenological studies associated with dimension-9 operators.

Dimension-8 operators in the Standard Model Effective Field Theory

We present a complete basis of dimension-8 operators in the Standard Model Effective Field Theory. Attention is paid to operators that vanish in the absence of flavor structure. The 44,807 operators are encoded in 1,031 Lagrangian terms. We also briefly discuss a few aspects of phenomenology involving dimension-8 operators, including light-by-light scattering and electroweak precision data.

EFT anomalous dimensions from the S-matrix

We use the on-shell S-matrix and form factors to compute anomalous dimensions of higher dimension operators in the Standard Model Effective Field Theory. We find that in many instances, these computations are made simple by using the on-shell method. We first compute contributions to anomalous dimensions of operators at dimension-six that arise at one-loop. Then we calculate two-loop anomalous dimensions for which the corresponding one-loop contribution is absent, using this powerful method.

One-loop running of dimension-six Higgs-neutrino operators and implications of a large neutrino dipole moment

We compute the one-loop running of the dimension-six CP-even Higgs operators in the Standard Model effective field theory involving the right-handed component of the would-be Dirac neutrinos. Then, on the basis of naturalness arguments, for some operators we obtain bounds that surpass direct constraints by orders of magnitude. We also discuss the implications of a large Dirac neutrino magnetic dipole moment. In particular, we demonstrate that a neutrino magnetic moment explaining the recent XENON1T excess induces Higgs and Z invisible decays with branching ratios in the range [10−18, 10−12]. These numbers are unfortunately beyond the reach of current and near future facilities.