Low-energy Effective Field Theory Research Articles

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.

Universal dynamics and non-thermal fixed points in quantum fluids far from equilibrium

AbstractClosed quantum systems far from thermal equilibrium can show universal dynamics near attractor solutions, known as non-thermal fixed points, generically in the form of scaling behaviour in space and time. A systematic classification and comprehensive understanding of such scaling solutions are tasks of future developments in non-equilibrium quantum many-body theory. In this tutorial review, we outline several analytical approaches to non-thermal fixed points and summarise corresponding numerical and experimental results. The analytic methods include a non-perturbative kinetic theory derived within the two-particle irreducible effective action formalism, as well as a low-energy effective field theory framework. As one of the driving forces of this research field are numerical simulations, we summarise the main results of exemplary cases of universal dynamics in ultracold Bose gases. This encompasses quantum vortex ensembles in turbulent superfluids as well as recently observed real-time instanton solutions in one-dimensional spinor condensates.

νDoBe — A Python tool for neutrinoless double beta decay

We present νDoBe, a Python tool for the computation of neutrinoless double beta decay (0νββ) rates in terms of lepton-number-violating operators in the Standard Model Effective Field Theory (SMEFT). The tool can be used for automated calculations of 0νββ rates, electron spectra and angular correlations for all isotopes of experimental interest, for lepton-number-violating operators up to and including dimension 9. The tool takes care of renormalization-group running to lower energies and provides the matching to the low-energy effective field theory and, at lower scales, to a chiral effective field theory description of 0νββ rates. The user can specify different sets of nuclear matrix elements from various many-body methods and hadronic low-energy constants. The tool can be used to quickly generate analytical and numerical expressions for 0νββ rates and to generate a large variety of plots. In this work, we provide examples of possible use along with a detailed code documentation. The code can be accessed through:GitHub: https://github.com/OScholer/nudobeOnline User-Interface: https://oscholer-nudobe-streamlit-4foz22.streamlit.app/

Detecting Emergent Continuous Symmetries at Quantum Criticality.

New or enlarged symmetries can emerge at the low-energy spectrum of a Hamiltonian that does not possess the symmetries, if the symmetry breaking terms in the Hamiltonian are irrelevant under the renormalization group flow. We propose a tensor network based algorithm to numerically extract lattice operator approximation of the emergent conserved currents from the ground state of any quantum spin chains, without the necessity to have prior knowledge about its low-energy effective field theory. Our results for the spin-1/2 J-Q Heisenberg chain and a one-dimensional version of the deconfined quantum critical points demonstrate the power of our method to obtain the emergent lattice Kac-Moody generators. It can also be viewed as a way to find the local integrals of motion of an integrable model and the local parent Hamiltonian of a critical gapless ground state.

C and CP violation in effective field theories

The quest for new sources of the simultaneous violation of C and CP symmetry was popular in the 1960s and has since been mostly neglected for more than half a century. In this work we revisit fundamental quark-level operators that break C and CP up to and including mass dimension 8 for flavor-conserving transitions, relying on the complete operator sets of the so-called Standard Model effective field theory and the low-energy effective field theory. With the formalism of chiral perturbation theory, we match these quark operators to light-meson physics, derive C- and CP -odd Lagrangians for several processes in the η, η', and pion sectors, and furthermore, as a proof of principle, give estimates for the respective observables in explicit dependence of the underlying high-energy scale for new physics.

Entropy inside the Kerr–Sen black holes

In this paper, we consider the Kerr–Sen black hole. Unlike the AdS black hole, it is actually an exact solution for the heterotic string theory in the low energy effective field theory in four dimensions. Starting from the black hole metric in the Boyer–Lindquist coordinates, we calculate the maximal interior volume by introducing the advanced time. Further, we present the rate of change of the interior volume with the advanced time on the radius of the black hole and observe that it has a maximal value for a specific value of the radius of the black hole. It is also shown from the graph that the maximal value increases with the increase of mass, and the position of the maxima shifts towards the large radius. Moreover, we calculate the rate of loss of mass due to Hawking radiation and interpret it graphically. Finally, we compute the interior entropy and show from its variations with mass and outer horizon radius of the black hole that in the interior, the entropy decreases with mass and becomes negative, whereas, in the exterior, the entropy increases with mass and remains positive. This is further proof of the argument that was proposed in Azuma and Subramanian (2020). In this investigation, an interesting feature is that the low-mass Kerr–Sen black hole behaves like a reversible process, whatever its outer horizon also reveals.

A new gravitational action for the trace anomaly

The question of building a local diff-invariant effective gravitational action for the trace anomaly is reconsidered. General Relativity (GR) combined with the existing action for the trace anomaly is an inconsistent low energy effective field theory. This issue is addressed by extending GR into a certain scalar-tensor theory, which preserves the GR trace anomaly equation, up to higher order corrections. The extension introduces a new mass scale – assumed to be below the Planck scale – that governs four high dimensional terms in a local diff-invariant trace anomaly action. Such terms can be kept, while an infinite number of Planck-suppressed invariants are neglected. The resulting theory maintains two derivative equations of motion. In a certain approximation it reduces to the conformal Gallileon, which could have physical consequences.

An EFT hunter’s guide to two-to-two scattering: HEFT and SMEFT on-shell amplitudes

We derive the contact terms contributing to the four-point amplitudes of the standard model particles, keeping terms with up to quartic energy growth. Imposing just the unbroken low-energy symmetry, and treating the electroweak gauge bosons and the Higgs as independent degrees of freedom, we obtain the most general four-point contact-term amplitudes, corresponding to the Higgs Effective Field Theory (HEFT) framework. The contact terms are spanned by a basis of Stripped Contact Terms, which carry the polarization information, multiplied by polynomials in the Mandelstam invariants. For terms with quadratic energy growth, we also derive the low-energy Standard Model Effective Field Theory (SMEFT) predictions, via on-shell Higgsing of the massless SMEFT contact terms. We discuss several aspects of bottom-up versus top-down on-shell derivations of the HEFT and SMEFT amplitudes, highlighting in particular the simple counting of HEFT dimensions in the on-shell approach and the transparent relation between perturbative unitarity and gauge-invariance in the little-group covariant massive spinor formalism. Our results provide a formulation of Effective Field Theory analyses directly in terms of observable quantities. For terms with quadratic energy growth, we also provide the mapping to the Warsaw basis.

Hybrid metric-Palatini Higgs inflation

We propose an extension of the Higgs inflation to the hybrid metric-Palatini gravity, where we introduce non-minimal couplings between Higgs and both the metric-type and the Palatini-type Ricci scalars. We study the inflationary phenomenology of our model and find that slow-roll inflation can be realized in the large-field regime, giving the observationally favored predictions. In particular, the scalar spectral index exhibits an attractor behavior to n s ∼ 0.964, while the tensor-to-scalar ratio can take an arbitrary value depending on the non-minimal coupling parameters, with the metric-Higgs limit r ∼ 10-3 being the maximum. We also investigate the unitarity property of our model. As the ultraviolet (UV) cutoff as a low-energy effective field theory (EFT) of this model is significantly lower than the Planck scale due to a strong curvature of field-space, we consider a possible candidate of UV-extended theories with an additional scalar field introduced so as to flatten the field-space in five-dimension. While the field-space can be flatten completely and this approach can lead to a weakly-coupled EFT, we gain an implication that Planck-scale EFT can be only realized in the limit of metric-Higgs inflation. We also discuss generalizations of the model up to mass-dimension four.