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DOE OSTI2026

SMEFT ATLAS: The landscape beyond the Standard Model

The Standard Model Effective Field Theory (SMEFT) based on the unbroken gauge group SU(3) 𝐶 ⊗SU(2) 𝐿 ⊗U(1) 𝑌 and containing only particles of the Standard Model (SM) has developed in the last decade to a mature field. It is the framework to be used in the energy gap from scales sufficiently higher than the electroweak scale up to the lowest energy scale at which new particles show up. We summarize the present status of this theory with a particular emphasize on its role in the indirect search for new physics (NP). While flavour physics of both quarks and leptons is the main topic of our review, we also discuss electric dipole moments, anomalous magnetic moments (𝑔−2) 𝜇,𝑒 , 𝑍-pole observables, Higgs observables and high-𝑝𝑇 scattering processes within the SMEFT. We group the observables into ten classes and list for each class the most relevant operators and the corresponding renormalization group equations (RGEs). We exhibit the correlations between different classes implied both by the operator mixing and the SU(2) 𝐿 gauge symmetry. Our main goal is to provide an insight into the complicated operator structure of this framework which hopefully will facilitate the identification of valid ultraviolet completions behind possible anomalies observed in future data. Numerous colourful charts, and 85 tables, while representing rather complicated RG evolution from the NP scale down to the electroweak scale, beautify the involved SMEFT landscape. Over 1000 references to the literature underline the importance and the popularity of this field. We discuss both top-down and bottom-up approaches as well as their interplay. This allows us eventually to present an atlas of different landscapes beyond the SM that includes heavy gauge bosons and scalars, vector-like quarks and leptons and leptoquarks.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2020

Proton decay in supersymmetric SU(4) c × SU(2) L × SU(2) R

We discuss proton decay in a recently proposed model of supersymmetric hybrid inflation based on the gauge symmetry SU(4) c × SU(2) L × SU(2) R . A U(1) R symmetry plays an essential role in realizing inflation as well as in eliminating some undesirable baryon number violating operators. Proton decay is primarily mediated by a variety of color triplets from chiral superfields, and it lies in the observable range for a range of intermediate scale masses for the triplets. The decay modes include p → e + (μ + ) + π 0 , p→$\bar{ν}$+π + , p → K 0 + e + (μ + ), and p → K + +$\bar{ν}$, with a lifetime estimate of order 10 34 –10 36 yrs and accessible at Hyper-Kamiokande and future upgrades. The unification at the Grand Unified Theory (GUT) scale M GUT (~ 10 16 GeV) of the Minimal Supersymmetric Standard Model (MSSM) gauge couplings is briefly discussed.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2020

Sterile neutrino dark matter in left-right theories

SU(2) L × SU(2) R gauge symmetry requires three right-handed neutrinos (N i ), one of which, N 1 , can be sufficiently stable to be dark matter. In the early universe, W R exchange with the Standard Model thermal bath keeps the right-handed neutrinos in thermal equilibrium at high temperatures. N 1 can make up all of dark matter if they freeze-out while relativistic and are mildly diluted by subsequent decays of a long-lived and heavier right-handed neutrino, N 2 . We systematically study this parameter space, constraining the symmetry breaking scale of SU(2) R and the mass of N 1 to a triangle in the (v R , M 1 ) plane, with v R = (10 6 - 3 × 10 12 ) GeV and M 1 = (2 keV–1 MeV). Much of this triangle can be probed by signals of warm dark matter, especially if leptogenesis from N 2 decay yields the observed baryon asymmetry. The minimal value of v R is increased to 10 8 GeV for doublet breaking of SU(2) R , and further to 10 9 GeV if leptogenesis occurs via N 2 decay, while the upper bound on M 1 is reduced to 100 keV. In addition, there is a component of hot N 1 dark matter resulting from the late decay of N 2 → N 1 ℓ+ℓ- that can be probed by future cosmic microwave background observations. Interestingly, the range of v R allows both precision gauge coupling unification and the Higgs Parity understanding of the vanishing of the Standard Model Higgs quartic at scale vR. Finally, we study freeze-in production of N 1 dark matter via the WR interaction, which allows a much wider range of (v R , M 1 ).

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2022

Effective field theory of Stückelberg vector bosons

We explore the effective field theory of a vector field $X^μ$ that has a Stückelberg mass. The absence of a gauge symmetry for $X^μ$ implies Lorentz-invariant operators are constructed directly from Xμ. Beyond the kinetic and mass terms, allowed interactions at the renormalizable level include $X_μX^μH^†H, (X_μX^μ)^2$, and $X_μj^μ$, where $j^μ$ is a global current of the SM or of a hidden sector. We show that all of these interactions lead to scattering amplitudes that grow with powers of $\sqrt{s}/m_X$, except for the case of $X_μj^μ$ where $j^μ$ is a nonanomalous global current. The latter is well-known when $\textit{X}$ is identified as a dark photon coupled to the electromagnetic current, often written equivalently as kinetic mixing between $\textit{X}$ and the photon. The power counting for the energy growth of the scattering amplitudes is facilitated by isolating the longitudinal enhancement. We examine in detail the interaction with an anomalous global vector current $X_μj^μ_{\text{anom}}$, carefully isolating the finite contribution to the fermion triangle diagram. We calculate the longitudinally-enhanced observables $Z → X_γ$ (when $m_X < m_Z), f\bar{f} → X_γ$, and $Z_γ → Z_γ$ when $\textit{X}$ couples to the baryon number current. Introducing a "fake" gauge-invariance by writing $X^μ = A^μ – ∂^μπ/m_X$, the would-be gauge anomaly associated with $A_μj^μ_{\text{anom}}$ is canceled by $j^μ_{\text{anom}}∂_μπ/m_X$; this is the four-dimensional Green-Schwarz anomaly-cancellation mechanism at work. Our analysis demonstrates there is a much larger set of possible interactions that an EFT with a Stückelberg vector field can have, revealing scattering amplitudes that grow with energy. The growth of these amplitudes can be tamed by a dark Higgs sector, but this requires dark Higgs boson interactions (and reintroduces fine-tuning in the dark Higgs sector) that can be separated from X interactions only in the limit $g \ll 1$ .

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2022

On ( g – 2) μ from gauged $\mathrm{U(1)_X}$

We investigate an economical explanation for the (g – 2) μ anomaly with a neutral vector boson from a spontaneously broken U(1) X gauge symmetry. The Standard Model fermion content is minimally extended by 3 right-handed neutrinos. Using a battery of complementary constraints, we perform a thorough investigation of the renormalizable, quark flavor-universal, vector-like U(1) X models, allowing for arbitrary kinetic mixing. Out of 419 models with integer charges not greater than ten, only 7 models are viable solutions, describing a narrow region in model space. These are either L μ – L τ or models with a ratio of electron to baryon number close to –2. The key complementary constraints are from the searches for nonstandard neutrino interactions. Furthermore, we comment on the severe challenges to chiral U(1) X solutions and show the severe constraints on a particularly promising such candidate.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2025

From oversimplified to overlooked: The case for exploring rich dark sectors

The Standard Model (SM) of particle physics provides a very successful description of fundamental particles and their interactions but it is incomplete, as neutrino masses, dark matter and the baryon asymmetry of the Universe indicate. In addition, the origin of masses and of the approximate fundamental symmetries call out for deeper explanations. The quest for a New SM Theory, that extends the SM to a more general theory, is ongoing. For decades the main focus has been on the TeV scale, but despite an impressive theoretical and experimental effort, no hints of new physics at such scale has been found in experiments. Dark sectors provide an interesting alternative to TeV scale extensions of the SM to explain the open questions in particle and astroparticle physics. Going beyond minimal models, rich dark sectors extend the SM to a complex theory with multiple particles and interactions, in analogy to the SM itself. They have a wealth of theoretical and astrophysical/cosmological consequences and can lead to phenomenological signatures that can be markedly different to that of minimal ones. These include short-lived particles and semi-visible decay signatures, as opposed to minimal models where new states are typically long-lived and purely visible or invisible resonances. Given the experimental configurations and analysis strategies, current dark sector searches might miss such signatures. We advocate a dedicated programme of searches for rich dark sectors that overcomes the assumptions on minimality and on the long lifetime of particles and encompasses a broader range of possibilities. Here, we discuss a prototype model that includes a complex structure akin to the SM: multiple generations of fermions charged under a new spontaneously-broken gauge symmetry.

Dark matter↗

DOE OSTI2021

Generalising G 2 geometry: involutivity, moment maps and moduli

We analyse the geometry of generic Minkowski N = 1, D = 4 flux compactifications in string theory, the default backgrounds for string model building. In M-theory they are the natural string theoretic extensions of G2 holonomy manifolds. In type II theories, they extend the notion of Calabi-Yau geometry and include the class of flux backgrounds based on generalised complex structures first considered by Graña et al. (GMPT). Using E 7(7) × $\mathbb{R}$ + generalised geometry we show that these compactifications are characterised by an SU(7) ⊂ E 7(7) structure defining an involutive subbundle of the generalised tangent space, and with a vanishing moment map, corresponding to the action of the diffeomorphism and gauge symmetries of the theory. The Kähler potential on the space of structures defines a natural extension of Hitchin’s G 2 functional. Using this framework we are able to count, for the first time, the massless scalar moduli of GMPT solutions in terms of generalised geometry cohomology groups. It also provides an intriguing new perspective on the existence of G 2 manifolds, suggesting possible connections to Geometrical Invariant Theory and stability.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2022

Index-like theorem for massless fermions in spherically symmetric monopole backgrounds

In this paper we study massless fermions coupled to spherically symmetric SU(N) monopoles without Yukawa couplings between the Higgs and fermion fields. The corresponding Dirac operator is not Fredholm and the associated eigenfunctions are not L 2 -normalizable. Here we derive a formula for the dimension of the plane-wave normalizable kernel of such a Dirac operator for fermions of any representation of SU(N) in the presence of any spherically symmetric monopole background. Notably, our results also apply to fermions coupled to monopoles that preserve non-abelian gauge symmetry.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2022

Milli-magnetic monopole dark matter and the survival of galactic magnetic fields

A bstract Dark sectors with Abelian gauge symmetries can interact with ordinary matter via kinetic mixing. In such scenarios, magnetic monopoles of a broken dark U(1) will appear in our sector as confined milli-magnetically charged objects under ordinary electromagnetism. Halo ellipticity constraints are shown to significantly bound the strength of dark magnetic Coulomb monopole interactions. The bound magnetic monopole ground state, which in vacuum is stable and has no magnetic charge or moment, is shown to become quantum mechanically unstable in the presence of an external, ordinary magnetic field. If these states contribute sizably to the local dark matter density, they extract significant energy from the galactic magnetic field. We revise and extend this “Parker Bound” on galactic magnetic energy loss to milli-magnetic monopoles which leads to the strongest existing constraints on these states, satisfying our halo ellipticity bounds, over a wide range of magnetic monopole masses.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2021

How dark is the $ν_R$-philic dark photon?

We consider a generic dark photon that arises from a hidden U(1) gauge symmetry imposed on right-handed neutrinos ($ν_R$). Such a $ν_R$-philic dark photon is naturally dark due to the absence of tree-level couplings to normal matter. However, loop-induced couplings to charged leptons and quarks are inevitable, provided that $ν_R$ mix with left-handed neutrinos via Dirac mass terms. We investigate the loop-induced couplings and find that the $ν_R$-philic dark photon is not inaccessibly dark, which could be of potential importance to future dark photon searches at SHiP, FASER, Belle-II, LHC 14 TeV, etc.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2021

Non-equilibrium effective field theory and second sound

We investigate the phenomenon of second sound in various states of matter from the perspective of non-equilibrium effective field theory (EFT). In particular, for each state of matter considered, we find that at least two (though sometimes multiple) qualitatively different EFTs exist at finite temperature such that there is always at least one EFT with a propagating second-sound wave and at least one with no such second-sound wave. To aid in the construction of these EFTs, we use the method of cosets developed for non-equilibrium systems. It turns out that the difference between the EFTs with and without second-sound modes can be understood as arising from different choices of a new kind of inverse Higgs constraint. Finally, we demonstrate that it is possible to bypass the need for new inverse Higgs constraints by formulating EFTs on a new kind of manifold that is like the usual fluid worldvolume, but with reduced gauge symmetries.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2022

Forbidden scalar dark matter and dark Higgses

As experimental searches for WIMP dark matter continue to yield null results, models beyond the WIMP paradigm have proliferated in order to elude ever improving observational constraints, among them that of sub-GeV dark matter mediated by a massive vector portal (a dark photon) associated with a new dark U(1) gauge symmetry. It has been previously noted that for a significant range of the parameter space of this class of models, the annihilation of dark matter particles into a pair of dark photons can dominate the freeze-out process even when this process is kinematically forbidden for dark matter at rest — this is known as the “forbidden dark matter” (FDM) regime. Prior studies of this regime, however, assume that any “dark Higgs” associated with breaking the dark U(1) and imparting mass to the dark photon is decoupled from the dark matter and as such plays no role in the freeze-out process. In this paper, we explore the effects of a dark Higgs on sub-GeV dark matter phenomenology in this FDM regime by considering the simplest possible construction in which there exist non-trivial dark matter-dark Higgs couplings: a model with a single complex scalar DM candidate coupled directly to the dark Higgs field. We find that for a wide range of parameter space, the dark Higgs can alter the resulting relic abundance by many orders of magnitude, and that this effect can remain significant even for a small dark matter-dark Higgs coupling constant. Considering measurements from direct detection and measurements of the CMB, we further find that points in this model’s parameter space which recreate the appropriate dark matter relic abundance suffer only mild constraints from other sources at present, but may become accessible in near-future direct detection experiments.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2023

One-loop corrections to the celestial chiral algebra from Koszul Duality

We consider self-dual Yang-Mills theory (SDYM) in four dimensions and its lift to holomorphic BF theory on twistor space. Following the work of Costello and Paquette, we couple SDYM to a quartic axion field, which guarantees associativity of the (extended) celestial chiral algebra at the quantum level. We demonstrate how to reproduce their one-loop quantum deformation to the chiral algebra using Koszul duality.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2024

The QCD axion sum rule

Abstract We demonstrate that the true QCD axion that solves the strong CP problem can be found in all generality outside the customary standard QCD band, with QCD being the sole source of Peccei-Quinn breaking. The essential reason is that the basis of axion-gluon interactions does not need to coincide with the mass basis. Specifically, we consider the case in which the QCD axion field is not the only singlet scalar in Nature but it mixes with other singlet scalars (besides theη′). We determine the exact mathematical condition for an arbitraryN-scalar potential to be Peccei-Quinn invariant. Such potentials provide extra sources of mass for the customary axion without enlarging the Standard Model gauge symmetry. The contribution to the axion mass stemming from the QCD topological susceptibility is shown to be shared then among theNaxion eigenstates through a precise sum rule. Their location can only be displaced to the right of the standard QCD band. We demonstrate that the axion closest to this band can be displaced from it by a factor of$$ \sqrt{N} $$ N at most, and this corresponds to the case in which all axion signals are maximally deviated. Conversely, if one axion is found on the standard QCD band, the other eigenstates will be out of experimental reach. Our results imply that any ALP experiment which finds a signal to the right of the standard QCD axion band can be solving the strong CP problem within QCD, with the associatedN− 1 excitations to be found in an area of parameter space that we determine. We illustrate the results and phenomenology in some particular cases.

Physics↗

DOE OSTI2021

Measurements of differential cross-sections in four-lepton events in 13 TeV proton-proton collisions with the ATLAS detector

Measurements of four-lepton differential and integrated fiducial cross-sections in events with two same-flavour, opposite-charge electron or muon pairs are presented. The data correspond to 139 fb -1 of $ \sqrt{s} $ = 13 TeV proton-proton collisions, collected by the ATLAS detector during Run 2 of the Large Hadron Collider (2015–2018). The final state has contributions from a number of interesting Standard Model processes that dominate in different four-lepton invariant mass regions, including single Z boson production, Higgs boson production and on-shell ZZ production, with a complex mix of interference terms, and possible contributions from physics beyond the Standard Model. The differential cross-sections include the four-lepton invariant mass inclusively, in slices of other kinematic variables, and in different lepton flavour categories. Also measured are dilepton invariant masses, transverse momenta, and angular correlation variables, in four regions of four-lepton invariant mass, each dominated by different processes. The measurements are corrected for detector effects and are compared with state-of-the-art Standard Model calculations, which are found to be consistent with the data. The Z → 4 ℓ branching fraction is extracted, giving a value of (4.41 ± 0.30) × 10 -6 . Constraints on effective field theory parameters and a model based on a spontaneously broken B – L gauge symmetry are also evaluated. Further reinterpretations can be performed with the provided information.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2026

Shadow sectors of gauge theories

We show that both abelian and non-abelian gauge theories admit configurations in which the fields behave as if in the presence of static charge densities, or “shadow charges”. These correspond to nontrivial initial conditions for the fields that generate gauge transformations, the Gauss’ law operators. In non-abelian theories, such configurations seem to demand additional physical fields with exactly static charge densities. In contrast with this expectation, we show that gauge theory alone provides a consistent and gauge-invariant description of shadow charges. Canonical quantization then yields continuous shadow charges for abelian theories and quantized ones for non-abelian theories. In general, our findings indicate that all local conservation laws give rise to gauge symmetries, even in the presence of second-class constraints.

Del Grosso, Loris [Johns Hopkins U.] (ORCID:000000↗

DOE OSTI2024

Non-compact gauge groups, tensor fields and Yang-Mills-Einstein amplitudes

Abstract Scattering amplitudes in Yang-Mills-Einstein theories have been investigated mostly for compact gauge groups. While non-compact gauge groups are not physically viable in Yang-Mills theory, non-compact gaugings feature prominently in the supergravity literature, where any choice of perturbative vacuum spontaneously breaks the gauge group to a compact subgroup. In this paper, we formulate double-copy constructions for several five-dimensional$$ \mathcal{N} $$ N = 2 supergravities with non-compact gauge groups. On one side of the double copy, we employ amplitudes from a super-Yang-Mills theory with a massive hypermultiplet. On the other, we use amplitudes from particular non-supersymmetric Yang-Mills-scalar theories with massive fermions, chosen to obey constraints coming from color/kinematics duality. Supergravities with massive self-dual tensors in five dimensions are also considered, showing that tensors are straightforwardly realized as double copies of gauge-theory fermions with suitable choices of signs in the corresponding solutions of the Dirac equation. We present several examples of these constructions, noting in particular the appearance of Heisenberg groups in the supergravity gauge symmetry and, in some cases, the possibility of exotic tensor-vector matter couplings.

Physics↗

DOE OSTI2020

Heterotic backgrounds via generalised geometry: moment maps and moduli

We describe the geometry of generic heterotic backgrounds preserving minimal supersymmetry in four dimensions using the language of generalised geometry. They are characterised by an SU(3) × Spin(6 + n) structure within O(6, 6 + n) x $\mathbb{R}$ + generalised geometry. Supersymmetry of the background is encoded in the existence of an involutive subbundle of the generalised tangent bundle and the vanishing of a moment map for the action of diffeomorphisms and gauge symmetries. We give both the superpotential and the Kähler potential for a generic background, showing that the latter defines a natural Hitchin functional for heterotic geometries. Intriguingly, this formulation suggests new connections to geometric invariant theory and an extended notion of stability. Finally we show that the analysis of infinitesimal deformations of these geometric structures naturally reproduces the known cohomologies that count the massless moduli of supersymmetric heterotic backgrounds.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗