Operators In Field Theory Research Articles

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.

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 $\mathrm{T}_{9}$.

A CFT distance conjecture

We formulate a series of conjectures relating the geometry of conformal manifolds to the spectrum of local operators in conformal field theories in d > 2 spacetime dimensions. We focus on conformal manifolds with limiting points at infinite distance with respect to the Zamolodchikov metric. Our central conjecture is that all theories at infinite distance possess an emergent higher-spin symmetry, generated by an infinite tower of currents whose anomalous dimensions vanish exponentially in the distance. Stated geometrically, the diameter of a non-compact conformal manifold must diverge logarithmically in the higher-spin gap. In the holographic context our conjectures are related to the Distance Conjecture in the swampland program. Interpreted gravitationally, they imply that approaching infinite distance in moduli space at fixed AdS radius, a tower of higher-spin fields becomes massless at an exponential rate that is bounded from below in Planck units. We discuss further implications for conformal manifolds of superconformal field theories in three and four dimensions.

General features of the thermalization of particle detectors and the Unruh effect

We study the thermalization of smeared particle detectors that couple locally to any operator in a quantum field theory in curved spacetimes. We show that if the field state satisfies the Kubo-Martin-Schwinger condition with inverse temperature $\ensuremath{\beta}$ with respect to the detector's local notion of time evolution, reasonable assumptions ensure that the probe thermalizes to the temperature $1/\ensuremath{\beta}$ in the limit of long interaction times. Our method also imposes bounds on the size of the system with respect to its proper acceleration and spacetime curvature in order to accurately probe the Kubo-Martin-Schwinger temperature of the field. We then apply this formalism to a uniformly accelerated detector probing the Minkowski vacuum of any $CPT$ symmetric quantum field theory, and show that the detector thermalizes to the Unruh temperature, independently of the operator it couples to. This exemplifies yet again the robustness of the Unruh effect, even when arbitrary smeared detectors are used to probe general operators in a quantum field theory.

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.

Boundary Causality Violating Metrics in Holography.

Even for holographic theories that obey boundary causality, the full bulk Lorentzian path integral includes metrics that violate this condition. This leads to the following puzzle: the commutator of two field theory operators at space-like-separated points on the boundary must vanish. However, if these points are causally related in a bulk metric, then the bulk calculation of the commutator will be nonzero. It would appear that the integral over all metrics of this commutator must vanish exactly for holography to hold. This is puzzling since it must also be true if the commutator is multiplied by any other operator. Upon a careful treatment of boundary conditions in holography, we show how the bulk path integral leads to a natural resolution of this puzzle.

A basis of analytic functionals for CFTs in general dimension

We develop an analytic approach to the four-point crossing equation in CFT, for general spacetime dimension. In a unitary CFT, the crossing equation (for, say, the s- and t-channel expansions) can be thought of as a vector equation in an infinite-dimensional space of complex analytic functions in two variables, which satisfy a boundedness condition at infinity. We identify a useful basis for this space of functions, consisting of the set of s- and t-channel conformal blocks of double-twist operators in mean field theory. We describe two independent algorithms to construct the dual basis of linear functionals, and work out explicitly many examples. Our basis of functionals appears to be closely related to the CFT dispersion relation recently derived by Carmi and Caron-Huot.

Single top quark production with and without a Higgs boson * *Supported in part by the National Science Foundation of China (11725520, 11675002, 11635001)

One method of probing new physics beyond the Standard Model is to check the correlation among higher-dimensional operators in the effective field theory. We examine the strong correlation between the processes and , which both depend on the same three operators. The correlation indicates that, according to the data of , , which is significantly below the current upper limit .

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

Low energy effective field theory operator basis at d \u2264 9

We obtain the complete operator bases at mass dimensions 5, 6, 7, 8, 9 for the low energy effective field theory (LEFT), which parametrize various physics effects between the QCD scale and the electroweak scale. The independence of the operator basis regarding the equation of motion, integration by parts and flavor relations, is guaranteed by our algorithm [1, 2], whose validity for the LEFT with massive fermions involved is proved by a generalization of the amplitude-operator correspondence. At dimension 8 and 9, we list the 35058 (756) and 704584 (3686) operators for three (one) generations of fermions categorized by their baryon and lepton number violations (∆B, ∆L), as these operators are of most phenomenological relevance.

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.

Comments on gauge anomalies at dimension-six in the Standard Model Effective Field Theory

We study whether higher-dimensional operators in effective field theories, in particular in the Standard Model Effective Field Theory (SMEFT), can source gauge anomalies via the modification of the interactions involved in triangle diagrams. We find no evidence of such gauge anomalies at the level of dimension-6 operators that can therefore be chosen independently to each others without spoiling the consistency of SMEFT, at variance with recent claims. The underlying reason is that gauge-invariant combinations of Goldstone bosons and massive gauge fields are allowed to couple to matter currents which are not conserved. We show this in a toy model by computing the relevant triangle diagrams, as well as by working out Wess-Zumino terms in the bosonic EFT below all fermion masses. The same approach applies directly to the Standard Model both at the renormalisable level, providing a convenient and unusual way to check that the SM is anomaly free, as well as at the non-renormalisable level in SMEFT.

Non-abelian infrared divergences on the celestial sphere

We consider the infrared factorisation of non-abelian multi-particle scattering amplitudes, and we study the form of the universal colour operator responsible for infrared divergences, when expressed in terms of coordinates on the ‘celestial sphere’ intersecting the future light-cone at asymptotic distances. We find that colour-dipole contributions to the infrared operator, to all orders in perturbation theory, have a remarkably simple expression in these coordinates, with scale and coupling dependence factorised from kinematics and colour. Generalising earlier suggestions in the abelian theory, we then show that the infrared operator can be computed as a correlator of vertex operators in a conformal field theory of Lie-algebra-valued free bosons on the celestial sphere. We verify by means of the OPE that the theory correctly predicts the all-order structure of collinear limits, and the tree-level factorisation of soft real radiation.

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.

Interface junctions in QCD${}_4$

We study 3+1 dimensional SU(N)SU(N) Quantum Chromodynamics (QCD) with N_fNf degenerate quarks that have a spatially varying complex mass. It leads to a network of interfaces connected by interface junctions. We use anomaly inflow to constrain these defects. Based on the chiral Lagrangian and the conjectures on the interfaces, characterized by a spatially varying \thetaθ-parameter, we propose a low-energy description of such networks of interfaces. Interestingly, we observe that the operators in the effective field theories on the junctions can carry baryon charges, and their spin and isospin representations coincide with baryons. We also study defects, characterized by spatially varying coupling constants, in 2+1 dimensional Chern-Simons-matter theories and in a 3+1 dimensional real scalar theory.

Field tensor network states

We define a class of tensor network states for spin systems where the individual tensors are functionals of fields. The construction is based on the path integral representation of correlators of operators in quantum field theory. These tensor network states are infinite dimensional versions of matrix product states and projected entangled pair states. We find the field-tensor that generates the Haldane-Shastry wave function and extend it to two dimensions. We give evidence that the latter underlies the topological chiral state described by the Kalmeyer-Laughlin wave function.

Implications of SU(2)L gauge invariance for constraints on Lorentz violation

Lorentz invariance may only be broken far above the electroweak scale, since violations are experimentally stringently constrained. Therefore, the Standard-Model Extension parameterizing Lorentz violation (LV) via (higher-dimensional) field theory operators is manifestly SU(2)L gauge-invariant. As a consequence, LV in neutrinos implies LV in charged leptons and vice versa. This allows us to obtain estimated sensitivities for flavour-changing operators in the charged-lepton sector from neutrino oscillations as well as sensitivities for flavour-diagonal neutrino effects from high-precision electron experiments. We also apply this method to an analysis of time-of-flight data for neutrinos (detected by IceCube) and photons from gamma ray bursts where discrepancies have been observed. Our conclusion is that an explanation of the arrival time difference between neutrino and photon events by dim-5 operators in the neutrino sector would lead to unacceptably large LV effects in the charged-lepton sector.