Low-energy Effective Field Theory Research Articles

Eternal inflation, entropy bounds and the swampland

It has been suggested that low energy effective field theories should satisfy given conditions in order to be successfully embedded into string theory. In the case of a single canonically normalized scalar field this translates into conditions on its potential and the derivatives thereof. In this Letter we revisit small field hilltop models of eternal inflation including stochastic effects and study the compatibility of the swampland constraints with entropy considerations. We show that these stochastic inflation scenarios either violate entropy bounds or the swampland criterion on the slope of the scalar field potential. Furthermore, we illustrate that such models are faced with a graceful exit problem: any patch of space which exits the region of eternal inflation is either not large enough to explain the isotropy of the cosmic microwave background, or has a spectrum of fluctuations with an unacceptably large red tilt.

Non-canonical kinetic structures in the swampland

We consider how the swampland criteria might be applied to models in which scalar fields have nontrivial kinetic terms, particularly in the context of P(ϕ,X) theories, popularly used in approaches to inflation, to its alternatives, and to the problem of late-time cosmic acceleration. By embedding such theories in canonical multi-field models, from which the original theory emerges as a low-energy effective field theory, we derive swampland constraints, and study the circumstances under which these might be evaded while preserving cosmologically interesting phenomenology. We further demonstrate how these successes are tied to the phenomenon of turning in field space in the multi-field picture. We study both the general problem and specific examples of particular interest, such as DBI inflation.

Extending low energy effective field theory with a complete set of dimension-7 operators

We present a complete and independent set of dimension-7 operators in the low energy effective field theory (LEFT) where the dynamical degrees of freedom are the standard model five quarks and all of the neutral and charged leptons. All operators are non-Hermitian and are classified according to their baryon (∆B) and lepton (∆L) numbers violated. Including Hermitian-conjugated operators, there are in total 3168, 750, 588, 712 operators with (∆B, ∆L) = (0, 0), (0, ±2), (±1, ∓1), (±1, ±1) respectively. We perform the tree-level matching with the standard model effective field theory (SMEFT) up to dimension-7 (dim-7) operators in both LEFT and SMEFT. As a phenomenological application we study the effective neutrino-photon interactions due to dim-7 lepton number violating operators that are induced and much enhanced at one loop from dim-6 operators that in turn are matched from dim-7 SMEFT operators. We compare various neutrino-photon scattering cross sections with their counterparts in the standard model and highlight the new features. Finally, we illustrate how these effective interactions could arise from ultraviolet completion.

Shadows of charged rotating black holes: Kerr–Newman versus Kerr–Sen

Celebrating the centennial of its first experimental test, the theory of General Relativity (GR) has successfully and consistently passed all subsequent tests with flying colors. It is expected, however, that at certain scales new physics, in particular, in the form of quantum corrections, will emerge, changing some of the predictions of GR, which is a classical theory. In this respect, black holes (BHs) are natural configurations to explore the quantum effects on strong gravitational fields. BH solutions in the low-energy effective field theory description of the heterotic string theory, which is one of the leading candidates to describe quantum gravity, have been the focus of many studies in the last three decades. The recent interest in strong gravitational lensing by BHs, in the wake of the Event Horizon Telescope (EHT) observations, suggests comparing the BH lensing in both GR and heterotic string theory, in order to assess the phenomenological differences between these models. In this work, we investigate the differences in the shadows of two charged BH solutions with rotation: one arising in the context of GR, namely the Kerr–Newman (KN) solution, and the other within the context of low-energy heterotic string theory, the Kerr–Sen (KS) solution. We show and interpret, in particular, that the stringy BH always has a larger shadow, for the same physical parameters and observation conditions.

Black hole gravitational waves in the effective field theory of gravity

We investigate the propagation of gravitational waves on a black hole background within the low-energy effective field theory of gravity, where effects from heavy fields are captured by higher-dimensional curvature operators. Depending on the spin of the particles integrated out, the speed of gravitational waves at low energy can be either superluminal or subluminal as compared to the causal structure observed by other species. Interestingly, however, gravitational waves are always exactly luminal at the black hole horizon, implying that the horizon is identically defined for all species. We further compute the corrections on quasinormal frequencies caused by the higher-dimensional curvature operators and highlight the corrections arising from the low-energy effective field.

Ekpyrotic cosmology with a zero-shear S-brane

In a recent paper [R. Brandenberger and Z. Wang, Phys. Rev. D 101, 063522 (2020)] we proposed a mechanism for a continuous transition between a contracting ekpyrotic phase and the standard big bang phase of expansion: the bounce is generated by an S-brane which represents the effects of higher-mass string states in the low-energy effective field theory. We showed that gravitational waves on cosmological scales obtain a nearly scale-invariant spectrum. Here, we study the cosmological fluctuations in this setup, assuming that the S-brane has zero shear. We find a nearly scale-invariant spectrum of cosmological perturbations with a slight red tilt. The scenario yields two consistency relations for cosmological observations: one relating the tensor-to-scalar ratio with the scalar spectral tilt, and one relating the tensor tilt to the scalar tilt. The predicted tensor-to-scalar ratio is within the reach of upcoming cosmic microwave background observations. The tensor tilt is blue.

Lattice-QCD determination of the hyperon axial couplings in the continuum limit

We present the first chiral-continuum--finite-volume extrapolation of the hyperon octet axial couplings (${g}_{\mathrm{\ensuremath{\Sigma}}\mathrm{\ensuremath{\Sigma}}}$ and ${g}_{\mathrm{\ensuremath{\Xi}}\mathrm{\ensuremath{\Xi}}}$) from ${N}_{f}=2+1+1$ lattice QCD. These couplings are important parameters in the low-energy effective field theory description of the octet baryons and are fundamental to the nonleptonic decays of hyperons and to hyperon-hyperon and hyperon-nucleon scattering with applications to neutron stars. We use clover lattice fermion action for the valence quarks with sea quarks coming from configurations of ${N}_{f}=2+1+1$ highly improved staggered quarks generated by MILC Collaboration. Our work includes the first calculation of ${g}_{\mathrm{\ensuremath{\Sigma}}\mathrm{\ensuremath{\Sigma}}}$ and ${g}_{\mathrm{\ensuremath{\Xi}}\mathrm{\ensuremath{\Xi}}}$ directly at the physical pion mass on the lattice, and a full account of systematic uncertainty, including excited-state contamination, finite-volume effects, and continuum extrapolation, all addressed for the first time. We find the ratio of the continuum-limit hyperon coupling constants with respect to the nucleon axial charges to be ${g}_{\mathrm{\ensuremath{\Sigma}}\mathrm{\ensuremath{\Sigma}}}/{g}_{A}=0.351(6)(2)$ and ${g}_{\mathrm{\ensuremath{\Xi}}\mathrm{\ensuremath{\Xi}}}/{g}_{A}=\ensuremath{-}0.213(5)(1)$, where the first error includes the statistical and extrapolation systematic uncertainties, and the second error corresponds to systematics associated with varying lattice parameters. The SU(3) symmetry breaking derived from these axial charges is 9%, which is about a factor of 2 smaller than earlier lattice estimates.

General neutrino interactions with sterile neutrinos in light of coherent neutrino-nucleus scattering and meson invisible decays

In this work we study the current bounds from the CEνNS process and meson invisible decays on generic neutrino interactions with sterile neutrinos in effective field theories. The interactions between quarks and left-handed SM neutrinos and/or right-handed neutrinos are first described by the low-energy effective field theory (LNEFT) between the electroweak scale and the chiral symmetry breaking scale. We complete the independent operator basis for the LNEFT up to dimension-6 by including both the lepton-number-conserving (LNC) and lepton-number-violating (LNV) operators involving right-handed neutrinos. We translate the bounds on the LNEFT Wilson coefficients from the COHERENT observation and calculate the branching fractions of light meson invisible decays. The bounds on LNEFT are then mapped onto the SM effective field theory with sterile neutrinos (SMNEFT) to constrain new physics above the electroweak scale. We find that the meson invisible decays can provide the only sensitive probe for τ neutrino flavor component and s quark component in the quark-neutrino interactions involving two (one) active neutrinos and for the effective operators without any active neutrino fields. The CEνNS process places the most stringent bound on all other Wilson coefficients. By assuming one dominant Wilson coefficient at a time in SMNEFT and negligible sterile neutrino mass, the most stringent limits on the new physics scale are 2.7–10 TeV from corresponding dipole operator in LNEFT and 0.5–1.5 TeV from neutrino-quark operator in LNEFT.

Scalar and tensor neutrino interactions

We constrain general Dirac neutrino interactions based on the Standard Model Effective Field Theory framework extended with right-handed neutrinos N (SMNEFT) using deep inelastic and coherent elastic neutrino scattering, nuclear beta decay, and meson decay data, and high energy electron-proton and proton-proton collider data. We compute the one-loop anomalous dimensions of the low-energy effective field theory (LEFT) below the electroweak scale and of SMNEFT above the electroweak scale. The tree-level matching between LEFT and SMNEFT is performed at the electroweak scale. Currently, the most stringent limits on scalar and tensor interactions arise from pseudoscalar meson decays and the LHC measurements at the per mille level. In the future, the upcoming High-Luminosity LHC (HL-LHC) has the potential to reach the 10−4 level and LHeC can play an important role under certain theoretical assumptions.

Interfaces and the extended Hilbert space of Chern-Simons theory

The low energy effective field theories of (2 + 1) dimensional topological phases of matter provide powerful avenues for investigating entanglement in their ground states. In [1] the entanglement between distinct Abelian topological phases was investigated through Abelian Chern-Simons theories equipped with a set of topological boundary conditions (TBCs). In the present paper we extend the notion of a TBC to non-Abelian Chern-Simons theories, providing an effective description for a class of gapped interfaces across non-Abelian topological phases. These boundary conditions furnish a defining relation for the extended Hilbert space of the quantum theory and allow the calculation of entanglement directly in the gauge theory. Because we allow for trivial interfaces, this includes a generic construction of the extended Hilbert space in any (compact) Chern-Simons theory quantized on a Riemann surface. Additionally, this provides a constructive and principled definition for the Hilbert space of effective ground states of gapped phases of matter glued along gapped interfaces. Lastly, we describe a generalized notion of surgery, adding a powerful tool from topological field theory to the gapped interface toolbox.

Nucleon decay and n−n¯ oscillations in a left-right symmetric model with large extra dimensions

We study baryon-number-violating processes, including proton and bound neutron decays and $n-\bar n$ oscillations, in a left-right-symmetric (LRS) model in which quarks and leptons have localized wavefunctions in extra dimensions. In this model we show that, while one can easily suppress baryon-number-violating nucleon decays well below experimental bounds, this does not suppress $n-\bar n$ transitions, which may occur at levels comparable to current limits. This is qualitatively similar to what was found in an extra-dimensional model with a Standard-Model low-energy effective field theory (SMEFT). We show that experimental data imply a lower limit on the mass scale $M_{n \bar n}$ characterizing the physics responsible for $n-\bar n$ oscillations in the LRS model that is significantly higher than in the extra-dimensional model using a SMEFT and explain the reason for this. Our results provide further motivation for new experiments to search for $n - \bar n$ oscillations.

Escape from the swampland with a spectator field

In the context of string theory, several conjectural conditions have been proposed for low energy effective field theories not to be in swampland, the UV-incomplete class. The recent ones represented by the de Sitter and trans-Planckian censorship conjectures in particular seem to conflict with the inflation paradigm of the early universe. We first point out that scenarios where inflation is repeated several times (multi-phase inflation) can be easily compatible with these conjectures. In other words, we relax the constraint on the single inflation for the large scale perturbations to only continue at least around 10 e-folds. In this context, we then investigate if a spectator field can be a source of the almost scale-invariant primordial perturbations on the large scale. As a consequence of such an isocurvature contribution, the resultant perturbations exhibit the non-vanishing non-Gaussianity in general. Also the perturbation amplitude on smaller scales can be completely different from that on the large scale due to the multiplicity of inflationary phases. These signatures will be a smoking gun of this scenario by the future observations.

Symmetric scalars

We provide a complete classification of Poincar'e-invariant scalar field theories with an enlarged set of classical symmetries to leading order in derivatives, namely for the so-called P(X,ϕ) theories, in two or more spacetime dimensions. We find only three possibilities: Dirac-Born-Infeld, Cuscuton and Scaling theories. The latter two classes of actions involve an arbitrary function of the scalar field. As an application, we use the scaling symmetry to derive an infinite set of constraints on the Wilsonian coefficients of the low-energy Effective Field Theory. Furthermore, we study the extension of these results to cosmological (FLRW) and (Anti-)de Sitter spacetimes. We find in particular that the Cuscuton action has a generic set of symmetries around any background spacetime that possesses Killing vector fields, while the DBI actions have well-known analogues that we summarize explicitly.

How to renormalize integral equations with singular potentials in effective field theory

We briefly review general concepts of renormalization in quantum field theory and discuss their application to solutions of integral equations with singular potentials in the few-nucleon sector of the low-energy effective field theory of QCD. We also describe a particular subtractive renormalization scheme and consider a specific application to a toy-model with a singular potential serving as its effective field theoretical leading-order approximation.

One-loop matching in the SMEFT extended with a sterile neutrino

We study the phenomenology of the simplest renormalisable model that, at low energy, leads to the effective field theory of the Standard Model extended with right-handed neutrinos (νSMEFT). Our aim is twofold. First, to contextualise new collider signatures in models with sterile neutrinos so far studied only using the bottom-up approach. And second and more important, to provide a thorough example of one-loop matching in the diagrammatic approach, of which other matching techniques and automatic tools can benefit for cross-checks. As byproducts of this work, we provide for the first time: (i) a complete off-shell basis for the νSMEFT and explicit relations between operators linked by equations of motion; (ii) a complete basis for the low-energy effective field theory (νLEFT) and the tree-level matching onto the νSMEFT; (iii) partial one-loop anomalous dimensions in the νLEFT. This way, our work comprises a new step forward towards the systematisation of one-loop computations in effective field theories, especially if the SM neutrinos are Dirac.

Braneworld effective field theories \u2014 holography, consistency and conformal effects

Braneworld theories are often described as low-energy effective field theories (EFTs) featuring an infinitely thin 3-brane and 4D fields exactly localized on it. We investigate whether an exactly localized braneworld can arise as a limit of a theory of 5D fields. Using a holographic formalism we argue that such limit does not exist in the presence of gravity, therefore implying a discontinuity in the space of EFTs. We then present specific models involving exactly localized fields in which inconsistencies appear, which are solved when fields are taken as quasilocalized. Part of our arguments rely on conjectures from the “swampland” program. Our investigation motivates braneworld EFTs built from 5D fields, i.e. quasilocalized braneworlds. Observable effects from quasilocalization are significant for warped braneworlds such as Randall-Sundrum II (RSII), and are reminiscent of a conformal hidden sector. Focusing on the gauge-gravity sector we show that manifestations of the quasilocalized warped braneworld include i) an anomalous running of SM gauge couplings ii) a conformal contribution to SM gauge boson scattering induced by 5D gravity. Constraining these effects puts an upper bound on the 5D EFT cutoff, implying that the warped braneworld hypothesis could — at least in principle — be tested completely.

Effective Field Theories

This paper represents a pedagogical introduction to low-energy effective field theories. In some of them, heavy particles are “integrated out” (a typical example—the Heisenberg–Euler EFT); in some, heavy particles remain but some of their degrees of freedom are “integrated out” (Bloch–Nordsieck EFT). A large part of these lectures is, technically, in the framework of QED. QCD examples, namely decoupling of heavy flavors and HQET, are discussed only briefly. However, effective field theories of QCD are very similar to the QED case, and there are just some small technical complications: more diagrams, color factors, etc. The method of regions provides an alternative view at low-energy effective theories; this is also briefly introduced.

Implication of K→πνν¯ for generic neutrino interactions in effective field theories

In this work we investigate the implication of $K\to \pi \nu \bar{\nu}$ from the recent KOTO and NA62 measurements for generic neutrino interactions and the new physics scale in effective field theories. The interactions between quarks and left-handed Standard Model (SM) neutrinos are first described by the low energy effective field theory (LEFT) below the electroweak scale. We match them to the chiral perturbation theory ($\chi$PT) at the chiral symmetry breaking scale to calculate the branching fractions of Kaon semi-invisible decays and match them up to the SM effective field theory (SMEFT) to constrain new physics above the electroweak scale. In the framework of effective field theories, we prove that the Grossman-Nir bound is valid for both dim-6 and dim-7 LEFT operators, and the dim-6 vector and scalar operators dominantly contribute to Kaon semi-invisible decays based on LEFT and chiral power counting rules. They are induced by multiple dim-6 lepton-number-conserving operators and one dim-7 lepton-number-violating operator in the SMEFT, respectively. In the lepton-number-conserving $s\to d$ transition, the $K\to \pi \nu \bar{\nu}$ decays provide the most sensitive probe for the operators with $\tau\tau$ component and point to a corresponding new physics scale of $\Lambda_{\rm NP} \in[47~\text{TeV},~72~\text{TeV}]$ associated with a single effective coefficient. The lepton-number-violating operator can also explain the observed $K\to\pi\nu\bar{\nu}$ discrepancy with the SM prediction within a narrow range $\Lambda_{\rm NP}\in [19.4~\text{TeV},~21.5~\text{TeV}]$, which is consistent with constraints from Kaon invisible decays.

Anomalous anomalies from virtual black holes

We investigate gravitational UV/IR mixing models that predict a breakdown of low energy effective field theory, from loop-level, nonlocal gravitational corrections to particle processes. We determine how the choice of IR cutoff in these theories alters predictions for lepton magnetic moments. Using Brookhaven E821 muon magnetic moment data, we exclude models of UV/IR mixing with an IR cutoff set by a spherical volume enclosing the experiment. On the other hand, an IR cutoff defined by the simply connected spatial volume containing the trajectories of the muons implies a correction to the muon magnetic moment which may have already been observed.

Effective field theory approach to lepton number violating decays {K}^{pm}to {pi}^{mp }{l}_{alpha}^{pm }{l}_{beta}^{pm }: long-distance contribution

This is a sequel to our recent work [1] in which we calculated the lepton number violating (LNV) K± decays due to contact dimension-9 (dim-9) quark-lepton effective interactions that are induced at a high energy scale. In this work we investigate the long- distance contribution to the decays arising from the exchange of a neutrino. These decays can probe LNV interactions involving the second generation of fermions that are not reach- able in nuclear neutrinoless double-β decays. Our study is completely formulated in the framework of effective field theories (EFTs), from the standard model effective field theory (SMEFT) through the low energy effective field theory (LEFT) to chiral perturbation theory (χPT). We work to the first nontrivial orders in each effective field theory, collect along the way the matching conditions and renormalization group effects, and express the decay branching ratios in terms of the Wilson coefficients associated with the dim-5 and dim-7 operators in SMEFT. Our result is general in that it does not depend on dynamical details of physics at a high scale that induce the effective interactions in SMEFT and in that it does not appeal to any hadronic models. We find that the long-distance contribution overwhelmingly dominates over the contact or short-distance one. Assuming the new physics scale to be around a TeV, the branching ratios are predicted to be below the current experimental upper bounds by several orders of magnitude.