Low-energy Effective Theory Research Articles

Estimates on the convergence of expansions at finite baryon chemical potentials

Convergence of three different expansion schemes at finite baryon chemical potentials, including the conventional Taylor expansion, the Padé approximants, and the T′ expansion proposed recently in lattice QCD simulations, have been investigated in a low energy effective theory within the functional renormalization group approach. It is found that the convergence of the T′ expansion and the Padé approximants is consistent with the conventional Taylor expansion, within the expansion orders considered in this work. Furthermore, we find that the consistent regions of the three different expansions are in agreement with the convergence radius of the Lee-Yang edge singularities. Published by the American Physical Society 2024

Gravitational positivity for phenomenologists: Dark gauge boson in the swampland

The gravitational positivity bound gives quantitative “swampland” constraints on low-energy effective theories inside theories of quantum gravity. We give a comprehensive discussion of this bound for those interested in applications to phenomenological model building. We present a practical recipe for deriving the bound, and discuss subtleties relevant for realistic models. As an illustration, we study the positivity bound on the scattering of the massive gauge bosons in the Higgs/Stückelberg mechanism. Under certain assumptions on gravitational amplitudes at high energy, we obtain a lower bound mV≳ΛUV2/gMPl on the gauge boson mass mV, where g is the coupling constant of the gauge field, MPl is the reduced Planck mass and ΛUV is the ultraviolet cutoff of the effective field theory. This bound can strongly constrain new physics models involving a massive gauge boson. We also discuss how the bound depends on our high-energy assumptions. Published by the American Physical Society 2024

Heavy neutral leptons from kaons in effective field theory

In the framework of the low-energy effective theory containing, in addition to the Standard-Model fields, heavy neutral leptons (HNLs), we compute the decay rates of neutral and charged kaons into HNLs. We consider both lepton-number-conserving and lepton-number-violating four-fermion operators, taking into account also the contribution of active-heavy neutrino mixing. Assuming that the produced HNLs are long-lived, we perform simulations and calculate the sensitivities of future long-lived-particle (LLP) detectors at the high-luminosity LHC as well as the near detector of the Deep Underground Neutrino Experiment (DUNE-ND) to the considered scenario. When applicable, we also recast the existing bounds on the minimal mixing case obtained by NA62, T2K, and PS191. Our findings show that, while the future LHC LLP detectors can probe currently allowed parameter space only in certain benchmark scenarios, DUNE-ND should be sensitive to parameter space beyond the current bounds in almost all the benchmark scenarios, and, for some of the effective operators considered, it can even probe new-physics scales in excess of 3000 TeV. Published by the American Physical Society 2024

Ghost problem, spectrum identities and various constraints on brane-localized gravity

This paper investigates the brane-localized interactions, including DGP gravity and higher derivative (HD) gravity localized on the brane. We derive the effective action on the brane, which suggests the brane-localized HD gravity suffers the ghost problem generally. Besides, we obtain novel algebraic identities of the mass spectrum, which reveal the global nature and can characterize the phase transformation of the mass spectrum. We get a powerful ghost-free condition from the spectrum identities, which rules out one type of brane-localized HD gravity. We further prove the mass spectrum is real and non-negative m2 ≥ 0 under the ghost-free condition.Furthermore, we discuss various constraints on parameters of brane-localized gravity in AdS/BCFT and wedge holography, respectively. They include the ghost-free condition of Kaluza-Klein and brane-bending modes, the positive definiteness of boundary central charges, and entanglement entropy. The ghost-free condition imposes strict constraint, which requires non-negative couplings for pure DGP gravity and Gauss-Bonnet gravity on the brane. It also rules out one class of brane-localized HD gravity. Thus, such HD gravity should be understood as a low-energy effective theory on the brane under the ghost energy scale. Finally, we briefly discuss the applications of our results.

Neutrinoless double beta decay in multiple isotopes for fingerprints identification of operators and models

Neutrinoless double beta (0νββ) decay is the most promising way to determine whether neutrinos are Majorana particles. There are many experiments based on different isotopes searching for 0νββ decay. Combining the searches of 0νββ decay in multiple isotopes provides a possible method to distinguish operators and different models. The contributions to 0νββ decay come from standard, long-range, and short-range mechanisms. We analyze the scenario in which the standard and short-range operators exist simultaneously within the framework of low-energy effective field theory. Five specific models are considered, which can realize neutrino mass and can contribute to 0νββ decay via multiple mechanisms. A criterion to evaluate the possibilities of future experiments to discriminate operators and models is built. We find that the complementary searches for 0νββ decay in different isotopes can distinguish the cases that contain the low-energy effective operators O1,2,5\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ {\\mathcal{O}}_{1,2,5} $$\\end{document} and R-parity violating supersymmetry model. For other cases and models, the experimental searches within multiple isotopes can also more effectively constrain the parameter region than with only one isotope.

One-loop matching of the type-III seesaw model onto the Standard Model Effective Field Theory

In previous works [1, 2], we have performed the one-loop matching of both type-I and type-II seesaw models for neutrino masses onto the Standard Model Effective Field Theories (SMEFT). In the present paper, by matching the type-III seesaw model onto the SMEFT at the one-loop level, we complete this series of studies on the construction of low-energy effective field theories (EFTs) for the canonical seesaw models. After integrating out the heavy fermionic triplets in the type-III seesaw model via both functional and diagrammatic approaches, we find 33 dimension-six (dim-6) operators in the Warsaw basis and their Wilson coefficients, while the number of dim-6 operators is 31 (or 41) for the EFT of type-I (or type-II) seesaw model. Furthermore, we calculate the branching ratios of radiative decays of charged leptons in the EFT. Then, the relationship between the beta function of the quartic Higgs coupling λ in the full theory and that of λEFT in the EFT is clarified. Finally, we briefly discuss the phenomenological implications of three types of seesaw EFTs and propose working observables that are sensitive to the four-fermion operators, which could be used to distinguish among different seesaw models in collider experiments.

On the frozen F-theory landscape

We study 6d \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mathcal{N}$$\\end{document} = (1, 0) supergravity theories arising in the frozen phase of F-theory. For each of the known global models, we construct an F-theory compactification in the unfrozen phase with an identical non-abelian gauge algebra and massless matter content. Two such low energy effective theories are then distinguished through gauge enhancements in moduli space. We study potentially new global models obtained via compact embeddings of a plethora of 6d \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mathcal{N}$$\\end{document} = (1, 0) superconformal field theories and little string theories constructed using frozen 7-branes. In some cases, these provably do not exist, and in other cases, we explicitly construct a compact embedding, yielding 6d supergravity theories with new massless spectra. Finally, by using gravitational anomaly cancellation, we conjecture the existence of localized neutral hypermultiplets along frozen 7-brane loci.

New non-supersymmetric flux vacua from generalised calibrations

We construct a new class of non-supersymmetric ten-dimensional type II flux vacua, by studying first order differential equations which are deformations of the \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mathcal{N}$$\\end{document} = 1 supersymmetry conditions. We do so within the context of Generalised Complex Geometry, where there is a natural interpretation of the \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mathcal{N}$$\\end{document} = 1 supersymmetry conditions in terms of calibration conditions for probe D-branes, called D-string, domain-wall or space-filling branes, depending on them wrapping two, three or four non-compact dimensions. We focus on the class of non-supersymmetric vacua violating the D-string calibration condition, and write down their general equations of motion in the language of pure spinors. We solve them for a subclass of vacua, where the deformation of the calibration condition is dictated by the foliated geometry of the internal space. We also construct backgrounds violating both the domain-wall and D-string calibration conditions, generalising the one-parameter DWSB class of backgrounds introduced in Lüst et al. We present several explicit solutions with SU(2) and SU(3) structures, and we investigate briefly their associated low energy effective theories.

Testing effective field theory with the most general neutron decay correlations

Built on the seminal works by Jackson-Treiman-Wyld and Ebel-Feldman, we derive the most general free neutron differential decay rate where all massive particles (neutron, proton, and electron) are polarized. This introduces 33 new correlations in addition to the 18 existing ones, which overconstrain the coupling constants in the low-energy effective field theory of charged weak interactions, and thus provides stringent tests of the validity of the theory framework itself. We classify the correlation coefficients in terms of their Standard Model limit and discrete symmetries, and study their expansion with respect to the new physics coupling strengths, supplemented by the experiment-independent O(α) virtual electromagnetic radiative corrections. Published by the American Physical Society 2024

Quantum Electrodynamics in 2+1 Dimensions as the Organizing Principle of a Triangular Lattice Antiferromagnet

Quantum electrodynamics in 2+1 dimensions (QED3) has been proposed as a critical field theory describing the low-energy effective theory of a putative algebraic Dirac spin liquid or of quantum phase transitions in two-dimensional frustrated magnets. We provide compelling evidence that the intricate spectrum of excitations of the elementary but strongly frustrated J1−J2 Heisenberg model on the triangular lattice is in one-to-one correspondence to a zoo of excitations from QED3, in the quantum spin liquid regime. This evidence includes a large manifold of explicitly constructed monopole and bilinear excitations of QED3, which is thus shown to serve as an organizing principle of phases of matter in triangular lattice antiferromagnets and their low-lying excitations. Moreover, we observe signatures of emergent valence-bond solid (VBS) correlations, which can be interpreted either as evidence of critical VBS fluctuations of an emergent Dirac spin liquid or as a transition from the 120° Néel order to a VBS whose quantum critical point is described by QED3. Our results are obtained by comparing ansatz wave functions from a parton construction to exact eigenstates obtained using large-scale exact diagonalization up to N=48 sites. Published by the American Physical Society 2024

Coupling a Cosmic String to a TQFT

A common framework of particle physics consists of two sectors of particles, such as the Standard Model and a dark sector, with some interaction between them. In this work, we initiate the study of a qualitatively different setup in which one of the sectors is a topological quantum field theory (TQFT). Instead of particles, the physics of a TQFT only manifests itself in non-trivial spacetime topologies or in the presence of topological defects. In particular, we consider two possible ways in which axionic cosmic strings can interact with a ℤn TQFT. One of them, by extending the structure of the axion coupling, leads to specific predictions for the localized degrees of freedom on the cosmic string, which can in turn effect their evolution and leave observable signals. The second approach, by gauging a discrete subgroup of the axionic shift symmetry, leads to dramatic changes in the string spectrum. We stress that the scenario considered here should be regarded as a plausible way for new physics to arise since it can be the low energy effective field theory for quite generic scenarios at high energies. To demonstrate this point and further illustrate the physical implications, we construct UV completions for both of the cases of couplings to TQFTs. While detailed predictions for observable signals of such scenarios require further investigation, our results demonstrate that there are rich new phenomena in this scenario.

A Lattice Formulation of Weyl Fermions on a Single Curved Surface

Abstract In the standard lattice domain-wall fermion formulation, one needs two flat domain-walls where both of the left- and right-handed massless modes appear. In this work we investigate a single domain-wall system with a nontrivial curved background. Specifically we consider a massive fermion on a 3D square lattice, whose domain-wall is a 2D sphere. In the free theory, we find that a single Weyl fermion is localized at the wall and it feels gravity through the induced spin connection. With a topologically nontrivial U(1) link gauge field, however, we find a zero mode with the opposite chirality localized at the center where the gauge field is singular. In the latter case, the low-energy effective theory is not chiral but vectorlike. We discuss how to circumvent this obstacle in formulating lattice chiral gauge theory in the single domain-wall fermion system.

Bounds on scattering of neutral Goldstones

We study the space of 2 → 2 scattering amplitudes of neutral Goldstone bosons in four space-time dimensions. We establish universal bounds on the first two non-universal Wilson coefficients of the low energy Effective Field Theory (EFT) for such particles. We reconstruct the analytic, crossing-symmetric, and unitary amplitudes saturating our bounds, and we study their physical content. We uncover non-perturbative Regge trajectories by continuing our numerical amplitudes to complex spins. We then explore the consequence of additional constraints arising when we impose the knowledge about the EFT up to the cut-off scale. In the process, we improve on some aspects of the numerical S-matrix bootstrap technology for massless particles.

Mott insulator-density ordered superfluid transition and ‘shamrock transition’ in a frustrated triangle lattice

Density order is usually a consequence of the competition between long-range and short-range interactions. Here we report a density ordered superfluid emergent from a homogeneous Mott insulator due to the competition between frustrations and local interactions. This transition is found in a Bose–Hubbard model on a frustrated triangle lattice with an extra pairing term. Furthermore, we find a quantum phase transition between two different density ordered superfluids, which is beyond the Landau–Ginzburg (LG) paradigm. A U(1) symmetry is emergent at the critical point, while the symmetry in each density ordered superfluid is Z 2 × Z 3. We call the transition a ‘shamrock transition’, due to its degenerate ground state in the parameter space being a shamrock-like curve rather than a circle in an LG-type transition. Effective low energy theories are established for the two transitions mentioned above and we find their resemblance and differences with clock models.

Dynamical t/U Expansion of the Doped Hubbard Model

We construct a new U(1) slave-spin representation for the single-band Hubbard model in the large-U limit. The mean-field theory in this representation is more amenable to describe both the spin-charge-separation physics of the Mott insulator at half-filling and the strange metal behavior at finite doping. By employing a dynamical Green’s function theory for slave spins, we calculate the single-particle spectral function of electrons. The result is comparable to that in dynamical mean field theories. We then formulate a dynamical t/U expansion for the doped Hubbard model that reproduces the mean-field results at the lowest order of expansion. To the next order of expansion, it naturally yields an effective low-energy theory of a t–J model for spinons self-consistently coupled to an XXZ model for the slave spins. We show that the superexchange J is renormalized by doping, in agreement with the Gutzwiller approximation. Surprisingly, we find a new ferromagnetic channel of exchange interactions which survives in the infinite U limit, as a manifestation of the Nagaoka ferromagnetism.

Positivity and the electroweak hierarchy

We point out that an unnatural hierarchy between certain higher-dimensional operator coefficients in a low-energy effective field theory (EFT) would automatically imply that the Higgs’ vacuum expectation value is hierarchically smaller than the EFT cutoff, assuming the EFT emerged from a unitary, causal and local UV completion. Future colliders may have the sensitivity to infer such a pattern of coefficients for a little hierarchy with an EFT cutoff up to O(10) TeV. Published by the American Physical Society 2024

Low-energy effective field theory below the electroweak scale: one-loop renormalization in the ’t Hooft-Veltman scheme

The low-energy effective field theory below the electroweak scale (LEFT) describes the effects at low energies of both the weak interaction and physics beyond the Standard Model. We study the one-loop renormalization of the LEFT in the ’t Hooft-Veltman scheme, which offers an algebraically consistent definition of the Levi-Civita symbol and γ5 in dimensional regularization. However, in connection with minimal subtraction this scheme leads to a spurious breaking of chiral symmetry in intermediate steps of the calculation. Based on the ’t Hooft-Veltman prescription, we define a renormalization scheme that restores chiral symmetry by including appropriate finite counterterms. To this end, we extend the physical LEFT operator basis by a complete set of off-shell and one-loop-evanescent operators and we perform the renormalization at one loop. We determine the finite counterterms to the physical parameters that compensate both the insertions of evanescent operators, as well as the chiral-symmetry-breaking terms from the renormalizable part of the Lagrangian in D dimensions. Our results can be applied in next-to-leading-log calculations in the ’t Hooft-Veltman scheme: using our renormalization scheme instead of pure minimal subtraction separates the physical sector from the unphysical evanescent sector and leads to results that are manifestly free of spurious chiral-symmetry-breaking terms.

Searching for high-frequency axion in quantum electromagnetodynamics through interface haloscopes

The so-called Witten effect implies a close relationship between the axion and magnetic monopole. A sound quantization in the presence of magnetic monopoles, called quantum electromagnetodynamics (QEMD), was utilized to construct a more generic axion-photon Lagrangian in the low-energy axion effective field theory. This generic axion-photon Lagrangian introduces the interactions between axion and two four-potentials, and leads to new axion-modified Maxwell equations. The interface haloscopes place an interface between two electromagnetic media with different properties and are desirable to search for high-mass axions ma≳O(10) μeV. In this work, for the generic axion-photon couplings built under QEMD, we perform comprehensive calculations of the axion-induced propagating waves and energy flux densities in different interface setups. We also obtain the sensitivity to new axion-photon couplings for high-mass axions. Published by the American Physical Society 2024

Effective brane field theory with higher-form symmetry

We propose an effective field theory for branes with higher-form symmetry as a generalization of ordinary Landau theory, which is an extension of the previous work by Iqbal and McGreevy for one-dimensional objects to an effective theory for p-dimensional objects. In the case of a p-form symmetry, the fundamental field ψ[Cp] is a functional of p-dimensional closed brane Cp embedded in a spacetime. As a natural generalization of ordinary field theory, we call this theory the brane field theory. In order to construct an action that is invariant under higher-form transformation, we generalize the idea of area derivative for one-dimensional objects to higher-dimensional ones. Following this, we discuss various fundamental properties of the brane field based on the higher-form invariant action. It is shown that the classical solution exhibits the area law in the unbroken phase of U(1) p-form symmetry, while it indicates a constant behavior in the broken phase for the large volume limit of Cp. In the latter case, the low-energy effective theory is described by the p-form Maxwell theory. We also discuss brane-field theories with a discrete higher-form symmetry and show that the low-energy effective theory becomes a BF-type topological field theory, resulting in topological order. Finally, we present a concrete brane-field model that describes a superconductor from the point of view of higher-form symmetry.

Dark sector effective field theory

We introduce the effective field theory of two different light dark particles interacting with the standard model (SM) light states in a single vertex, termed dark sector effective field theory (DSEFT). We focus on the new light particles with spin up to 1 and being real in essence, namely, new real scalars ϕ and S, Majorana fermions χ and ψ, and real vectors Xμ and Vμ. In the framework of low energy effective field theory with QED and QCD symmetry, the DSEFT can be classified into six categories, including the scalar-scalar-SM (ϕS-SM), fermion-fermion-SM (χψ-SM), vector-vector-SM (XV-SM), scalar-fermion-SM (ϕχ-SM), scalar-vector-SM (ϕX-SM), and fermion-vector-SM (χX-SM) cases. For each case, we construct the effective operator basis up to canonical dimension 7, which will cover most interesting phenomenology at low energy. As a phenomenological example, we investigate the longstanding neutron lifetime anomaly through the neutron dark decay modes n → χϕ or χX from the effective interactions in the fermion-scalar-SM or fermion-vector-SM case. When treating the light fermion as a dark matter candidate, we also explore the constraints from DM-neutron annihilation signal at Super-Kamiokande. We find the neutron dark decay in each scenario can accommodate the anomaly, at the same time, without contradicting with the Super-Kamiokande limit.