Effective Field Theory Research Articles

Dark dimension and the effective field theory limit

In [1], we pointed out that in the Dark Dimension scenario [2] theoretical issues arise when the prediction for the vacuum energy [Formula: see text], that is obtained from swampland conjectures in string theory, is confronted with the corresponding result for [Formula: see text] in the effective field theory (EFT) limit. One of the problems concerns the widely spread belief that in higher dimensional EFTs with compact dimensions the vacuum energy is automatically finite. On the contrary, our analysis shows that [Formula: see text] contains (previously missed) UV-sensitive terms. Our work was challenged in [3]. Here we show why in our opinion the claims in [3] are flawed, and provide further support to our findings. We conclude presenting ideas on the physical mechanism that should dispose of the large UV contributions to [Formula: see text].

Hydrodynamization and resummed viscous hydrodynamics

In this paper, I review our current understanding of the applicability of hydrodynamics to modeling the quark–gluon plasma (QGP), focusing on the question of hydrodynamization/thermalization of the QGP and the anisotropic hydrodynamics (aHydro) far-from-equilibrium hydrodynamic framework. I discuss the existence of far-from-equilibrium hydrodynamic attractors and methods for determining attractors within different hydrodynamical frameworks. I also discuss the determination of attractors from exact solutions to the Boltzmann equation in relaxation time approximation and effective kinetic field theory applied to quantum chromodynamics. I then present comparisons of the kinetic attractors with the attractors obtained in standard second-viscous hydrodynamics frameworks and aHydro. I demonstrate that, due to the resummation of terms to all orders in the inverse Reynolds number, the aHydro framework can describe both the weak- and strong-interaction limits. I then review the phenomenological application of aHydro to relativistic heavy-ion collisions using both quasiparticle aHydro and second-order viscous aHydro. The phenomenological results indicate that aHydro provides a controlled extension of dissipative relativistic hydrodynamics to the early-time far-from-equilibrium stage of heavy-ion collisions. This allows one to better describe the data and to extract the temperature dependence of transport coefficients at much higher temperatures than linearized second-order viscous hydrodynamics.

Towards hypernuclei from nuclear lattice effective field theory

Understanding the strong interactions within baryonic systems beyond the up and down quark sector is pivotal for a comprehensive description of nuclear forces. This study explores the interactions involving hyperons, particularly the Λ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\varLambda $$\\end{document} particle, within the framework of nuclear lattice effective field theory (NLEFT). By incorporating Λ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\varLambda $$\\end{document} hyperons into the NLEFT framework, we extend our investigation into the S=-1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$S = -1$$\\end{document} sector, allowing us to probe the third dimension of the nuclear chart. We calculate the Λ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\varLambda $$\\end{document} separation energies (BΛ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$B_{\\varLambda }$$\\end{document}) of hypernuclei up to the medium-mass region, providing valuable insights into hyperon–nucleon (YN) and hyperon–nucleon–nucleon (YNN) interactions. Our calculations employ high-fidelity chiral interactions at N3\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ ^3$$\\end{document}LO for nucleons and extend it to Λ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\varLambda $$\\end{document} hyperons with leading-order S-wave YN interactions as well as YNN forces constrained only by the A=4,5\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$A=4,5$$\\end{document} systems. Our results contribute to a deeper understanding of the SU(3) symmetry breaking and establish a foundation for future improvements in hypernuclear calculations.

Completing the one-loop νSMEFT renormalization group evolution

In this work we consider the Standard Model Effective Field Theory extended with right-handed neutrinos, the νSMEFT, and calculate the full set of one-loop anomalous dimensions that are proportional to Yukawa couplings. These contributions are particularly relevant when symmetry-protected low scale seesaw models are embeded in the SMEFT, since large neutrino Yukawa couplings are expected. By combining our results with the already available gauge anomalous dimensions, we provide the complete set of one-loop renormalization group evolution equations for the dimension six νSMEFT. As a possible phenomenological implication of our results, we discuss the sensitivity of lepton flavor-violating observables to νSMEFT operators, focusing on the more sensitive μ → e transitions.

Parity and time-reversal violating nuclear forces with explicit Δ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Delta $$\\end{document}-excitations

We emphasize the usefulness of treating delta resonances as explicit degrees of freedom in applications of chiral effective field theory (EFT) to parity-violating and time-reversal-violating (PVTV) nuclear interactions. Compared with the delta-less framework, the explicit inclusion of the delta isobar allows one to resum certain types of contributions to the PVTV two-pion exchange two- and three-nucleon potentials without at the same time introducing any unknown parameters up to next-to-next-to-leading order in the EFT expansion. We provide the corresponding expressions for the delta contributions in momentum and coordinate spaces and compare the convergence of the EFT expansion in both formulations.

Theoretical and Numerical Modeling of Optical Switching of Epitaxial Nanostructures Based on Iron-Garnet Films

The paper presents a theoretical analysis of magnetization switching in a gadolinium ferrite garnet film due to the demagnetizing effect of a femtosecond laser pulse. Using the Lagrange formalism for a two-sublattice ferrimagnet, the effective Lagrangian, thermodynamic potential, and Rayleigh dissipative function are obtained. The phase diagram of the ferrite film is analyzed, and the main states of the system are identified. Magnetization switching diagrams and trajectories of the order parameter dynamics of the magnet are constructed. The ranges of magnetic fields, temperatures, and demagnetization values for the most efficient magnetization switching are analyzed.

Measurements of inclusive and differential cross-sections of tt¯γ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ t\\overline{t}\\gamma $$\\end{document} production in pp collisions at s\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\sqrt{s} $$\\end{document} = 13 TeV with the ATLAS detector

Inclusive and differential cross-sections are measured at particle level for the associated production of a top quark pair and a photon (tt¯γ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ t\\overline{t}\\gamma $$\\end{document}). The analysis is performed using an integrated luminosity of 140 fb−1 of proton-proton collisions at a centre-of-mass energy of 13 TeV collected by the ATLAS detector. The measurements are performed in the single-lepton and dilepton top quark pair decay channels focusing on tt¯γ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ t\\overline{t}\\gamma $$\\end{document} topologies where the photon is radiated from an initial-state parton or one of the top quarks. The absolute and normalised differential cross-sections are measured for several variables characterising the photon, lepton and jet kinematics as well as the angular separation between those objects. The observables are found to be in good agreement with the Monte Carlo predictions. The photon transverse momentum differential distribution is used to set limits on effective field theory parameters related to the electroweak dipole moments of the top quark. The combined limits using the photon and the Z boson transverse momentum measured in tt¯\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ t\\overline{t} $$\\end{document} production in associations with a Z boson are also set.

D-Brane effective Lagrangian in spacetimes with boundaries

AbstractIn this study, we explore the transformation of $$D_p$$ D p -branes to $$D_{p-1}$$ D p - 1 -branes under T-duality when the D-brane is embedded in a spacetime with a boundary. Our goal is to derive the higher-derivative corrections to the Dirac–Born–Infeld (DBI) Lagrangian for both the bulk and boundary terms. For the bulk terms, we calculate the $$\alpha '$$ α ′ corrections for the massless open string fields, up to the 8th order in the dimensionless Maxwell field strength. We demonstrate that the bulk Lagrangian can satisfy the T-duality constraint without residual total derivative terms in the base space. This determines the most general independent couplings of the massless open string fields in the bulk Lagrangian, encompassing 145 coupling constants, up to three parameters. Two of these parameters are physical and are determined by disk-level S-matrix elements, while the third is unphysical and can be eliminated by field redefinitions and integration by parts. The final result for the bulk Lagrangian consists of 49 couplings. For the boundary terms, the application of T-duality symmetry to massless open and closed string fields enables us to extend the DBI Lagrangian to include the boundary unit normal vector field $$n_\mu $$ n μ and its first derivative.

Cornwall-Jackiw-Tomboulis effective field theory and the nonuniversal equation of state of an ultracold Bose gas

Cornwall-Jackiw-Tomboulis effective field theory and the nonuniversal equation of state of an ultracold Bose gas

The triton lifetime from nuclear lattice effective field theory

In this work, we present a calculation of the triton β-decay lifetime using Nuclear Lattice Effective Field Theory (NLEFT) at next-to-next-to-next-to-leading order in the chiral expansion. By incorporating a non-perturbative treatment of the higher-order corrections, we achieve consistent predictions for the Fermi and Gamow-Teller matrix elements, which are crucial for determining the triton lifetime. Our results are consistent with earlier theoretical calculations, confirming the robustness of our approach. This study marks a significant advancement in the systematic application of NLEFT to nuclear β-decay processes, paving the way for future high-precision calculations in more complex nuclear systems. Additionally, we discuss potential improvements to our approach, including the explicit inclusion of two-pion exchange mechanisms and the refinement of three-nucleon forces. These developments are essential for extending the applicability of NLEFT to a broader range of nuclear phenomena, including neutrinoless double-β decay.

Impact of correlations on nuclear binding energies

A strong effort will be dedicated in the coming years to extend the reach of ab initio nuclear-structure calculations to heavy doubly open-shell nuclei. In order to do so, the most efficient strategies to incorporate dominant many-body correlations at play in such nuclei must be identified. With this motivation in mind, the present work analyses the step-by-step inclusion of many-body correlations and their impact on binding energies of Calcium and Chromium isotopes. Employing an empirically-optimal Hamiltonian built from chiral effective field theory, binding energies along both isotopic chains are studied via a hierarchy of approximations based on polynomially-scaling expansion many-body methods. More specifically, calculations are performed based on (i) the spherical Hartree–Fock–Bogoliubov mean-field approximation plus correlations from second-order Bogoliubov many-body perturbation theory or Bogoliubov coupled cluster with singles and doubles on top of it, along with (ii) the axially-deformed Hartree–Fock–Bogoliubov mean-field approximation plus correlations from second-order Bogoliubov many-body perturbation theory built on it. The corresponding results are compared to experimental data and to those obtained via valence-space in-medium similarity renormalization group calculations at the normal-ordered two-body level that act as a reference in the present study. The spherical mean-field approximation is shown to display specific shortcomings in Ca isotopes that can be understood analytically and that are efficiently corrected via the consistent addition of low-order dynamical correlations on top of it. While the same setting cannot appropriately reproduce binding energies in doubly open-shell Cr isotopes, allowing the unperturbed mean-field state to break rotational symmetry permits to efficiently capture the static correlations responsible for the phenomenological differences observed between the two isotopic chains. Eventually, the present work demonstrates that polynomially-scaling expansion methods based on unperturbed states that possibly break (and restore) symmetries constitute an optimal route to extend ab initio calculations to heavy closed- and open-shell nuclei.

Radiative corrections to proton-proton fusion in pionless effective field theory

Radiative corrections to proton-proton fusion in pionless effective field theory

Spinor–Vector Duality and Mirror Symmetry

Mirror symmetry was first observed in worldsheet string constructions, and was shown to have profound implications in the Effective Field Theory (EFT) limit of string compactifications, and for the properties of Calabi–Yau manifolds. It opened up a new field in pure mathematics, and was utilised in the area of enumerative geometry. Spinor–Vector Duality (SVD) is an extension of mirror symmetry. This can be readily understood in terms of the moduli of toroidal compactification of the Heterotic String, which includes the metric the antisymmetric tensor field and the Wilson line moduli. In terms of the toroidal moduli, mirror symmetry corresponds to mappings of the internal space moduli, whereas Spinor–Vector Duality corresponds to maps of the Wilson line moduli. In the past few of years, we demonstrated the existence of Spinor–Vector Duality in the effective field theory compactifications of string theories. This was achieved by starting with a worldsheet orbifold construction that exhibited Spinor–Vector Duality and resolving the orbifold singularities, hence generating a smooth, effective field theory limit with an imprint of the Spinor–Vector Duality. Just like mirror symmetry, the Spinor–Vector Duality can be used to study the properties of complex manifolds with vector bundles. Spinor–Vector Duality offers a top-down approach to the “Swampland” program, by exploring the imprint of the symmetries of the ultra-violet complete worldsheet string constructions in the effective field theory limit. The SVD suggests a demarcation line between (2,0) EFTs that possess an ultra-violet complete embedding versus those that do not.

The Λc → Λ ℓ+νℓ weak decay including new physics

We investigate the Λc → Λℓ+νℓ decay with a focus on potential new physics (NP) effects in the ℓ = μ channel. We employ an effective Hamiltonian within the framework of the Standard Model Effective Field Theory (SMEFT) to consider generalized dimension-6 semileptonic c → s operators of scalar, pseudoscalar, vector, axial-vector and tensor types. We rely on Lattice QCD (LQCD) for the hadronic transition form factors, using heavy quark spin symmetry (HQSS) to determine those that have not yet been obtained on the lattice. Uncertainties due to the truncation of the NP Hamiltonian and different implementations of HQSS are taken into account. As a result, we unravel the NP discovery potential of the Λc → Λ semileptonic decay in different observables. Our findings indicate high sensitivity to NP in lepton flavour universality ratios, probing multi-TeV scales in some cases. On the theoretical side, we identify LQCD uncertainties in axial and vector form factors as critical for improving NP sensitivity, alongside better SMEFT uncertainty estimations.

Magnetic polarizability of octet baryons via lattice QCD

Drawing on recent advances in lattice QCD background-field techniques, the magnetic polarizability of octet baryons is calculated from the first principles of QCD. The results are presented in the context of new constituent quark model calculations providing a framework for understanding the lattice results and a direct comparison with simulation results at unphysical quark masses. Using smeared quark sources, low-lying Laplacian eigenmode projection and final-state Landau-mode projection, considerable attention is devoted to ensuring single-state isolation in the lattice correlation functions. We also introduce new weighting methods to reduce the sensitivity to correlation-function fits, averaging over many fits based on merit drawn from the full correlated χ2 of the fits. The techniques are implemented on the 323×64, 2+1-flavor dynamical-fermion lattices provided by the PACS-CS Collaboration following the introduction of uniform magnetic fields quantized to the lowest nontrivial values available. After some scaling of the constituent quark model parameters, we find the model captures the patterns observed in the lattice QCD results very well, providing important insights into the physics underpinning the magnetic polarizabilities. Finally, comparison with the most recent results from experiment proceeds through an effective field theory formalism which incorporates estimates of finite-volume corrections and small electroquenching corrections as the results are brought to the physical point. We find excellent agreement with experiment where available, including the proton and neutron polarizabilities. Published by the American Physical Society 2024

Effective field theory descriptions of Higgs boson pair production

Higgs boson pair production is traditionally considered to be of particular interest for a measurement of the trilinear Higgs self-coupling. Yet it can offer insights into other couplings as well, since – in an effective field theory (EFT) parameterisation of potential new physics – both the production cross section and kinematical properties of the Higgs boson pair depend on various other Wilson coefficients of EFT operators. This note summarises the ongoing efforts related to the development of EFT tools for Higgs boson pair production in gluon fusion, and provides recommendations for the use of distinct EFT parameterisations in the Higgs boson pair production process. This document also outlines where further efforts are needed and provides a detailed analysis of theoretical uncertainties. Additionally, benchmark scenarios are updated. We also re-derive a parameterisation of the next-to-leading order (NLO) QCD corrections in terms of the EFT Wilson coefficients both for the total cross section and the distribution in the invariant mass of the Higgs boson pair, providing for the first time also the covariance matrix. A reweighting procedure making use of the newly derived coefficients is validated, which can be used to significantly speed up experimental analyses.

Localised gravity and resolved braneworlds

Deriving an effective massless field theory for fluctuations about a braneworld spacetime requires analysis of the transverse-space-wavefunction’s second-order differential equation. There can be two strikingly different types of effective theory. For a supersymmetric braneworld, one involves a technically consistent embedding of a supergravity theory on the worldvolume; the other can produce, in certain situations, a genuine localisation of gravity near the worldvolume but not via a technically consistent embedding. So, in the latter situation, the theory’s dynamics remains higher-dimensional but there can still be a lower-dimensional effective-theory interpretation of the dynamics at low worldvolume momenta / large worldvolume distances.This paper examines the conditions for such a gravity localisation to be possible. Localising gravity about braneworld spacetimes requires finding solutions to transverse-space self-adjoint Sturm-Liouville problems admitting a normalisable zero mode in the noncompact transverse space. This in turn requires analysis of Sturm-Liouville problems with radial singular endpoints following a formalism originating in the work of Hermann Weyl. Examples of such gravity-localising braneworld systems are found and analysed in this formalism with underlying “skeleton” braneworlds of Salam-Sezgin, resolved D3-brane and Randall-Sundrum II types.

Renormalization of three-body interaction in DDK system

In systems comprising three identical particles, the Efimov effect emerges in the unitary limit. This article, utilizing the method of effective field theory along with the effective range expansion (ERE) and low-momentum expansion, reproduces the Efimov effect beyond unitary limit and identical case and applies to DDK system. It also links the high-energy scale with the ultraviolet cutoff in the three-body system. We discuss a method for obtaining exact solutions for the three-body wave function below the threshold of dimer production, that is D and Ds0⁎(2317). It turns out that introducing this scale is a necessary condition for the emergence of DDK three-body bound state. Since without this scale, the wave function would be solved below threshold with arbitrary binding energy, which violates the conditions of unitarity and energy quantization. The calculation involving this scale results in a discrete spectrum below the threshold and restores unitarity, making the effects induced by this scale significant for the formation of DDK bound state. In order to establish this in a complete formalism, the paper further gives an analytical expression for the three-body coupling constant, and compares it to the numerical calculation in DDK system.

Complex dark photon dark matter EFT

We construct an effective field theory for complex Stueckelberg dark photon dark matter. Such an effective construction can be realized by writing down a complete set of operators up to dimension six built with the complex dark photon and Standard Model fields. Classifying the effective operators, we find that in order to properly take into account the non-renormalizable nature of an interacting massive vector, the size of the Wilson coefficients should be naturally smaller than naively expected. This can be consistently taken into account by a proper power counting, that we suggest. First we apply this to collider bounds on light dark matter, then to direct detection searches by extending the list of non-relativistic operators to include the case of complex vectors. In the former we correctly find scaling limits for small masses, while in the latter we mostly focus on electric dipole interactions, that are the signatures of this type of dark matter. Simple UV completions that effectively realize the above scenarios are also outlined.

Fiducial and differential cross-section measurements of electroweak Wγjj\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$W\\gamma jj$$\\end{document} production in pp collisions at s=13\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\sqrt{s} = 13$$\\end{document} TeV with the ATLAS detector

The observation of the electroweak production of a W boson and a photon in association with two jets, using pp collision data at the Large Hadron Collider at a centre of mass energy of s=13\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\sqrt{s}=13$$\\end{document} TeV, is reported. The data were recorded by the ATLAS experiment from 2015 to 2018 and correspond to an integrated luminosity of 140 fb-1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$^{-1}$$\\end{document}. This process is sensitive to the quartic gauge boson couplings via the vector boson scattering mechanism and provides a stringent test of the electroweak sector of the Standard Model. Events are selected if they contain one electron or muon, missing transverse momentum, at least one photon, and two jets. Multivariate techniques are used to distinguish the electroweak Wγjj\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$W\\gamma jj$$\\end{document} process from irreducible background processes. The observed significance of the electroweak Wγjj\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$W\\gamma jj$$\\end{document} process is well above six standard deviations, compared to an expected significance of 6.3 standard deviations. Fiducial and differential cross sections are measured in a fiducial phase space close to the detector acceptance, which are in reasonable agreement with leading order Standard Model predictions from MadGraph5+Pythia8 and Sherpa. The results are used to constrain new physics effects in the context of an effective field theory.