Low-energy Effective Field Theory Research Articles

Non-perpetual eternal inflation and the emergent de Sitter Swampland conjecture

We introduce a novel correlation, ns\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$n_{\ ext {s}}$$\\end{document} - ΔN\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Delta N$$\\end{document}, connecting CMB parameters to the required total e-folds for eternal inflation. This correlation provides a robust tool for evaluating eternal (string) inflation models using CMB data and explores the impact of quantum fluctuations on non-attractor phases. By generalizing eternal inflation criteria, our parameterization simplifies rigorous testing of predictions and reveals a link between refined de Sitter conjecture parameters and the eternal nature of the cosmic landscape. This points to a general tendency towards eternal behavior in low-energy effective field theories within the landscape, opening the possibility for our cosmic stage to potentially embrace a ’multiverse’ scenario.

Baryon-number-violating nucleon decays in ALP effective field theories

The search for baryon-number-violating (BNV) nucleon decay is an intriguing probe of new physics beyond the SM in future neutrino experiments with enhanced sensitivity. The dark sector states such as an axion or axion-like particle (ALP) can induce nucleon decays with distinct signature and kinematics from the conventional nucleon decays. In this work, we study the ALP effective field theories (EFTs) with baryon number violation and the impact of light ALP on BNV nucleon decays. We revisit the dimension-8 BNV operators in the extended EFTs with an ALP field a respecting shift symmetry. The low-energy EFT operators with |∆(B – L)| = 2 and |∆(B – L)| = 0 are matched to the baryon chiral perturbation theory. We obtain the effective chiral Lagrangian and the BNV interactions between ALP and baryons/mesons. The ALP interactions lead to two-body baryon decays B → ℓ (or ν) a and three-body nucleon decays N → M ℓ (or ν) a. We obtain the constraints on the UV scale from the invisible Λ0 decay search at BESIII, the invisible neutron decay search at KamLAND and proton decay search at Super-K. We also show the projections of some other baryon/nucleon decays and present the distinct distributions of kinematic observable.

CP asymmetries in τ→KSπντ decays

We present here the CP asymmetries in the decay rate and angular distributions of [Formula: see text] decays in the Standard Model (SM) and beyond (BSM). The CP asymmetries in the SM are induced by the CP violation in [Formula: see text] mixing. To investigate the BSM CP-violating (CPV) effects, a model-independent analysis is performed by using the low-energy effective field theory (LEFT) framework at [Formula: see text] GeV. If one further assumes the BSM physics to stem from above the electroweak scale, the LEFT shall then be matched onto the SM effective field theory (SMEFT), the operators of which contributing to [Formula: see text] decays will also contribute to the neutron electric dipole moment (EDM) and [Formula: see text] mixing. The stringent bounds from the latter suggest that no remarkable CPV effects can be observed in either the decay rate or the angular distributions. The prospects for future measurements of these observables are also mentioned.

Study of τ− → ωπ−ντ decay in resonance chiral theory with tensor sources

In this work, we make a study of the τ− → ωπ−ντ decay in the framework of low-energy effective field theory. The JPG\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ {J}^{\\mathcal{P}G} $$\\end{document} decompositions of the quark currents and the ωπ final state show that, besides the Standard Model vector interaction, only the non-standard tensor interaction can have a non-zero contribution to the decay. To discuss its effect, a reliable calculation of the ωπ tensor form factors is necessary. After constructing the Lagrangian of resonance chiral theory with external tensor sources, we calculate both the vector and tensor form factors with the relevant resonance couplings determined by combining the QCD short-distance constraints, the fit to the spectral function of τ− → ωπ−ντ decay, as well as the matching between the Op4\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{O}\\left({p}^4\\right) $$\\end{document} odd-intrinsic-parity operators after integrating out the vector resonances and the Op6\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{O}\\left({p}^6\\right) $$\\end{document} operators of chiral perturbation theory. The new physics effect is then investigated in the distributions of the spectral function and the forward-backward asymmetry of τ− → ωπ−ντ decay. We find that the spectral function is dominated by the Standard Model, and the non-standard tensor contribution is negligible. However, since the forward-backward asymmetry can be only generated with a non-zero tensor interaction, the observable is quite sensitive to this kind of new physics. A future measurement of the observable at the Belle II experiment as well as at the proposed Tera-Z and STCF facilities is, therefore, strongly called for to check the existence of such a non-standard tensor interaction.

Anomalous U(1) extension of the Standard Model

We present a set of example models in which the Standard Model (SM) symmetry group is extended by a new abelian symmetry. This additional symmetry appears anomalous in the effective low-energy theory; however, the anomalies cancel out when massive chiral fermions not present in the effective low-energy theory are taken into account. These chiral fermions under the new abelian gauge group, are chosen to be vector-like under the SM symmetries, and reside in the same representations as quarks and leptons. This allows us to quantitatively determine the magnitude of tree-level interactions between three vector bosons induced in low-energy effective field theory by the integration of chiral heavy fermions. We also examine the perturbativity constraints of the theory and the ultraviolet cut-off. We conclude by highlighting possible extensions of our work.

Probing heavy neutrino magnetic moments at the LHC using long-lived particle searches

We explore long-lived particle (LLP) searches using non-pointing photons at the LHC as a probe for sterile-to-sterile and active-to-sterile transition magnetic dipole moments of sterile neutrinos. We consider heavy sterile neutrinos with masses ranging from a few GeV to several hundreds of GeV. We discuss transition magnetic dipole moments using the Standard Model effective field theory and low-energy effective field theory extended by sterile neutrinos (NRSMEFT and NRLEFT) and also provide a simplified UV-complete model example. LLP searches at the LHC using non-pointing photons will probe sterile-to-sterile dipole moments two orders of magnitude below the current best constraints from LEP, while an unprecedented sensitivity to sterile neutrino mass of about 700 GeV is expected for active-to-sterile dipole moments. For the UV model example with one-loop transition magnetic moments, the searches for charged lepton flavour violating processes in synergy with LLP searches at the LHC can probe new physics at several TeV mass scales and provide valuable insights into the lepton flavour structure of new physics couplings.

Neural network learning and Quantum Gravity

The landscape of low-energy effective field theories stemming from string theory is too vast for a systematic exploration. However, the meadows of the string landscape may be fertile ground for the application of machine learning techniques. Employing neural network learning may allow for inferring novel, undiscovered properties that consistent theories in the landscape should possess, or checking conjectural statements about alleged characteristics thereof. The aim of this work is to describe to what extent the string landscape can be explored with neural network-based learning. Our analysis is motivated by recent studies that show that the string landscape is characterized by finiteness properties, emerging from its underlying tame, o-minimal structures. Indeed, employing these results, we illustrate that any low-energy effective theory of string theory is endowed with certain statistical learnability properties. Consequently, several local learning problems therein formulated, including interpolations and multi-class classification problems, can be concretely addressed with machine learning, delivering results with sufficiently high accuracy.

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.

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.

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.

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.

On the importance of heavy fields in pseudo-scalar inflation

Pseudo-scalar inflation coupled with U(1) gauge fields through the Chern-Simons term has been extensively studied. However, new physics arising from UV theories may still influence the pseudo-scalar field at low-energy scales, potentially impacting predictions of inflation. In the realm of effective field theory (EFT), we investigated axion inflation, where operators from heavy fields are also present, in addition to the axion and gauge fields. The integrated out fields have two significant effects: the non-linear dispersion regime and coupling heavy modes to the Chern-Simons term. The first effect changes the propagation of the curvature fluctuation, while the second one results in additional operators that contribute to curvature fluctuation via inverse decay. We derived the power spectrum and magnitude of equilateral non-Gaussianity in this low-energy EFT. We found that the second effect could become significant as the mass of heavy fields approaches Hubble scale.

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.

Entropy-current for dynamical black holes in Chern-Simons theories of gravity

We construct an entropy current and establish a local version of the classical second law of thermodynamics for dynamical black holes in Chern-Simons (CS) theories of gravity. We work in a chosen set of Gaussian null coordinates and assume the dynamics to be small perturbations around the Killing horizon. In explicit examples of both purely gravitational and mixed gauge gravity CS theories in (2 + 1) and (4 + 1)-dimensions, the entropy current is obtained by studying the off-shell structure of the equations of motion evaluated on the horizon. For the CS theory in (2 + 1) dimensions, we argue that the second law holds to quadratic order in perturbations by considering it as a low energy effective field theory with the leading piece given by Einstein gravity. In all such examples, we show that the construction of entropy current is invariant under the reparameterization of the null horizon coordinates. Finally, extending an existing formalism for diffeomorphism invariant theories, we construct an abstract proof for the linearised second law in arbitrary Chern-Simons theories in any given odd dimensions by studying the off-shell equations of motion. As a check of consistency, we verify that the outcome of this algorithmic proof matches precisely with the results obtained in explicit examples.

One-loop matching of the CP-odd three-gluon operator to the gradient flow

The calculation of the neutron electric dipole moment within effective field theories for physics beyond the Standard Model requires non-perturbative hadronic matrix elements of effective operators composed of quark and gluon fields. In order to use input from lattice computations, these matrix elements must be translated from a scheme suitable for lattice QCD to the minimal-subtraction scheme used in the effective-field-theory framework. The accuracy goal in the context of the neutron electric dipole moment necessitates at least a one-loop matching calculation. Here, we provide the one-loop matching coefficients for the CP-odd three-gluon operator between two different minimally subtracted 't Hooft–Veltman schemes and the gradient flow. This completes our program to obtain the one-loop gradient-flow matching coefficients for all CP-violating and flavor-conserving operators in the low-energy effective field theory up to dimension six.

ALP-LEFT Interference and the Muon (g − 2)

The low-energy effective field theory (LEFT) provides the appropriate framework to describe particle interactions below the scale of electroweak symmetry breaking, μw ~ v. By matching the Standard Model onto the LEFT, non-zero Wilson coefficients of higher-dimensional operators are generated, suppressed by the corresponding power of 1/v. An axion or axion-like particle (ALP) with mass ma ≪ μw that interacts with the Standard Model via classically shift-invariant dimension-five operators would also contribute to the LEFT Wilson coefficients, since it can appear as a virtual particle in divergent Green’s functions and thus has an impact on the renormalization of the LEFT operators. We present the full set of one-loop ALP-induced source terms modifying the renormalization-group evolution equations of the LEFT Wilson coefficients up to dimension-six order. Our framework allows for model-independent ALP searches at low energies from current bounds on LEFT Wilson coefficients. As a concrete application, we present an improved prediction for ALP effects on the anomalous magnetic moment of the muon.

Quantum calculation of axion-photon transition in electromagnetodynamics for cavity haloscope* *T. L. is supported by the National Natural Science Foundation of China (12375096, 11975129, 12035008) and “the Fundamental Research Funds for the Central Universities”, Nankai University (63196013)

The Witten effect implies the presence of electric charge of magnetic monople and the possible relationship between axion and dyon. The axion-dyon dynamics can be reliably built based on the quantum electromagnetodynamics (QEMD) which was developed by Schwinger and Zwanziger in the 1960's. A generic low-energy axion-photon effective field theory can also be realized in the language of “generalized symmetries” with higher-form symmetries and background gauge fields. In this work, we implement the quantum calculation of the axion-single photon transition rate inside a homogeneous electromagnetic field in terms of the new axion interaction Hamiltonian in QEMD. This quantum calculation can clearly imply the enhancement of conversion rate through resonant cavity in axion haloscope experiments. We also show the promising potentials on the cavity search of new axion-photon couplings.

Adiabatic and isocurvature perturbations in extended theories with kinetic couplings

The scalar field sector in low-energy effective field theories motivated by string theory often contains several scalar fields, some of which possess non-standard kinetic terms. In this paper we study theories with two scalar fields, in which one of the fields has a non-canonical kinetic term. The kinetic coupling is allowed to depend on both fields, going beyond the work in the literature, which usually considers the case of the coupling to depend on the other field only. Our aim is to study adiabatic and isocurvature perturbations in these extended theories. Our results show that the evolution equation for the curvature perturbation does not change when allowing the coupling to depend on both fields, while the effective mass of the entropy perturbation changes. We find expressions for the spectral index and its running at horizon crossing and at the end of inflation. We apply the formalism and study three phenomenological models, with different kinetic couplings.

Revisiting the refined Distance Conjecture

The Distance Conjecture of Ooguri and Vafa holds that any infinite-distance limit in the moduli space of a quantum gravity theory must be accompanied by a tower of exponentially light particles, which places tight constraints on the low-energy effective field theories in these limits. One attempt to extend these constraints to the interior of moduli space is the refined Distance Conjecture, which holds that the towers of light particles predicted by the Distance Conjecture must appear any time a modulus makes a super-Planckian excursion in moduli space. In this note, however, we point out that a tower which satisfies the Distance Conjecture in an infinite-distance limit of moduli space may be parametrically heavier than the Planck scale for an arbitrarily long geodesic distance. This means that the refined Distance Conjecture, in its most naive form, does not place meaningful constraints on low-energy effective field theory. This motivates alternative refinements of the Distance Conjecture, which place an absolute upper bound on the tower mass scale in the interior of moduli space. We explore two possibilities, providing evidence for them and briefly discussing their implications.