Low-energy Effective Theory Research Articles

Radiative Corrections to Neutron Beta Decay and (Anti)Neutrino-Nucleon Scattering from Low-Energy Effective Field Theory

Radiative Corrections to Neutron Beta Decay and (Anti)Neutrino-Nucleon Scattering from Low-Energy Effective Field Theory

Quasisymmetry protected Ising spin-orbit coupling

Quasisymmetry is an approximated symmetry in the sense that it is not the crystalline symmetry but commutes with the Hamiltonian at a lower order. Unlike exact symmetry, quasisymmetry emerges in the context of low-energy effective theory. One of the most desirable properties added by quasisymmetry is the large Berry curvatures due to the perturbatively small band gaps, which are robust against chemical and physical perturbations. Ising spin-orbit coupling (SOC) is a special type of SOC with electron spins polarizing to out-of-plane direction and can protect the spin coherence against the relaxation. For Ising-type superconductors, Ising SOC significantly affects the superconducting properties such as Pauli limit. It is commonly believed that the out-of-plane mirror symmetry ${M}_{z}$ is necessary for Ising SOC, which puts a constraint on the allowed materials. Here we demonstrate that the strong Ising SOC exists beyond the system with ${M}_{z}$ symmetry and is protected by the quasisymmetry. Based on the group-theoretical analysis and density-functional theory calculations, we show that the lower-order SOC Hamiltonian for certain representation is Ising type, which is protected by the quasisymmetry. Several promising systems with strong Ising SOC of several hundreds of meV near the Fermi energy are identified. In addition, we propose the general design principles to search for the realistic materials. Our results advance the fundamental understanding of Ising spin-orbit physics and greatly broaden the range of the materials hosting the Ising SOC.

Remark on modular weights in low-energy effective field theory from type II string theory

We revisit the modular weights in type IIB magnetized D-brane models. The simple analysis of wave function shows that the four-dimensional matter fields have the modular weight -1/2, but it may shift as one in type IIA intersecting D-brane models. For example, the localized gauge flux as well as the localized curvature can shift the modular weight in the magnetized D-brane models. Such corrections do not affect physical couplings such as physical Yukawa couplings. However, it leads to differences in supersymmetry breaking sfermion masses, which depend on the modular weights, although the A-term coefficients and the sum of sfermion masses squared seem to be the same between two models.

Supermoiré low-energy effective theory of twisted trilayer graphene

Stacking three monolayers of graphene with a twist generally produces two moir\'e patterns. A moir\'e of moir\'e structure then emerges at larger distance where the three layers periodically realign. We devise here an effective low-energy theory to describe the spectrum at distances larger than the moir\'e lengthscale. In each valley of the underlying graphene, the theory comprises one Dirac cone at the ${\bf \Gamma}_M$ point of the moir\'e Brillouin zone and two weakly gapped points at ${\bf K}_M$ and ${\bf K}'_M$. The velocities and small gaps exhibit a spatial dependence in the moir\'e-of-moir\'e unit cell, entailing a non-abelian connection potential which ensures gauge invariance. The resulting model is numerically solved and a fully connected spectrum is obtained, which is protected by the combination of time-reversal and twofold-rotation symmetries.

Low-energy effective description of dark $Sp(4)$ theories

Strongly interacting massive particles are viable dark matter candidates. We consider a dark Sp(4)Sp(4) gauge theory with N_f=2Nf=2 fermions in the pseudo-real fundamental representation and construct the chiral low-energy effective theory. We determine the flavour multiplet structure and the chiral Lagrangian, including the Wess-Zumino-Witten term for mass-degenerate and non-degenerate flavours. We then study the possible charge assignments under a U(1)'U(1)′ gauge symmetry, emphasizing on dark state stability, and provide the full Lagrangian description for Goldstone bosons and vector resonances, including the Wess-Zumino-Witten term. Finally, we use dedicated lattice simulations to determine the chiral low-energy effective theory’s validity and low-energy constants. This work represents a self-consistent study of this non-Abelian theory. It thereby provides a framework for future phenomenological exploration in connection to the dark matter problem.

New tools for dissecting the general 2HDM

Two Higgs doublet models (2HDM) provide the low energy effective theory (EFT) description in many well motivated extensions of the Standard Model. It is therefore relevant to study their properties, as well as the theoretical constraints on these models. In this article we concentrate on three relevant requirements for the validity of the 2HDM framework, namely the perturbative unitarity bounds, the bounded from below constraints, and the vacuum stability constraints. In this study, we concentrate on the most general renormalizable version of the 2HDM — without imposing any parity symmetry, which may be violated in many UV extensions. We derive novel analytical expressions that generalize those previously obtained in more restrictive scenarios to the most general case. We also discuss the phenomenological implications of these bounds, focusing on mathcal{CP} violation.

Dimension-8 SMEFT matching conditions for the low-energy effective field theory

In particle physics, the modern view is to categorize things in terms of effective field theories (EFTs). Above the weak scale, we have the SMEFT, formed when the heavy new physics (NP) is integrated out, and for which the Standard Model (SM) is the leading part. Below MW, we have the LEFT (low-energy EFT), formed when the heavy SM particles (W±, Z0, H, t) are also integrated out. In order to determine how low-energy measurements depend on the underlying NP, it is necessary to compute the matching conditions of LEFT operators to SMEFT operators. These matching conditions have been worked out for all LEFT operators up to dimension 6 in terms of SMEFT operators up to dimension 6 at the one-loop level. However, this is not sufficient for all low-energy observables. In this paper we present the momentum-independent matching conditions of all such LEFT operators to SMEFT operators up to dimension 8 at tree level.

Shift-Invariant Orders of an Axionlike Particle.

It is generally believed that global symmetries, in particular, axion shift symmetries, can only be approximate. This motivates one to quantify the breaking of the shift invariance that characterizes the flavorful effective couplings of an axionlike particle to standard model fermions. We identify a minimal set of Jarlskog-like flavor invariants that vanish if and only if the axion is shift symmetric. Therefore, they represent order parameters for the breaking of the axion shift symmetry. We illustrate properties of the invariants by matching to a UV model, studying the CP transformation of the invariants, calculating their renormalization group evolution, and investigating similar conditions in the low-energy effective field theory below the electroweak scale. Finally, we discuss the order parameter associated to the nonperturbative shift-breaking induced by the axion-gluons coupling, which is also flavorful.

Pseudoscalar MSSM Higgs Production at NLO SUSY-QCD

One of the most important mechanisms at the Large Hadron Collider (LHC) for the production of the pseudoscalar Higgs boson of the Minimal Supersymmetric Standard Model (MSSM) is the loop-induced gluon fusion process gg → A. The higher-order QCD corrections have been obtained a long time ago and turned out to be large. However, the genuine supersymmetric (SUSY–)QCD corrections have been obtained only in the limit of large SUSY particle masses so far. We describe our calculation of the next-to-leading-order (NLO) SUSY-QCD results with full mass dependence and present numerical results for a few representative benchmark points. We also address the treatment of the effective top and bottom Yukawa couplings, in the case of heavy SUSY particles, in terms of effective low-energy theories where the heavy degrees of freedom have been decoupled. Furthermore, we include a discussion of the relation between the SUSY-QCD corrections that we have computed and the Adler-Bardeen theorem for the axial anomaly. In addition, we apply our results to the gluonic and photonic pseudoscalar Higgs decays A → gg, γγ at NLO.

Inflaton as a pseudo-Nambu-Goldstone boson

In the realistic model of cosmic inflation the inflaton potential should be flat and stable under quantum corrections. It is natural to imagine that there is some symmetry behind and an idea of the inflaton as a Nambu-Goldstone boson of spontaneous breaking of some symmetry has been examined. We give a general formulation of this idea using the non-linear realization of Nambu-Goldstone boson in low-energy effective theory with some explicit symmetry breaking to generate non-trivial potential. The potential is naturally a simple function, typically the mass term of inflaton, and the scenario of “warm inflation” should necessarily be applied under the present observational constraints. We investigate the generation mechanism of necessary thermal dissipation term in inflaton field equation for “warm inflation” without large thermal corrections to inflaton potential. A simple numerical analysis is given to investigate the viability of this scenario.

Solutions to axion electromagnetodynamics and new search strategies of sub-μeV axion

The Witten effect implies the electromagnetic interactions between axions and magnetic monopoles, and the quantum electromagnetodynamics (QEMD) properly describes interactions of electric charges, magnetic charges and photons. Based on the QEMD, a generic low-energy axion-photon effective field theory was built by introducing two four-potentials (Aμ and Bμ) to describe a photon. More anomalous axion-photon interactions and couplings (gaAA, gaBB and gaAB) arise in contrary to the ordinary axion coupling {g}_{agamma gamma}{a F}^{mu nu}{overset{sim }{F}}_{mu nu} . As a consequence, the conventional axion Maxwell equations are further modified. We properly solve the new axion-modified Maxwell equations and obtain the axion-induced electromagnetic fields given a static electric or magnetic field. It turns out that the dominant couplings gaAB and gaBB can be probed in the presence of external magnetic field and electric field, respectively. The induced oscillating magnetic fields are always suppressed compared with the electric fields for the axions with large Compton wavelengths. This is contrary to the situation in conventional experiments searching for the oscillating magnetic fields induced by sub-μeV axions. Thus, we propose new strategies to measure the new couplings for sub-μeV axion in haloscope experiments.

Generalized Spin-Wave Theory for the Hubbard Model and D-theory Formulation

It is pointed out that the low energy effective theory of a generalized spin system relates to the more generalized system shown by the Hubbard-like model. When the onsite repulsion is assumed to be provided by hard-core repulsion, a generalized fermion with flavour and colour degrees of freedom is used to define the Hubbard-like Hamiltonian in this case. In the strong coupling limit and at half filling this reduces to an antiferromagnet. The <I>D</I>-theory then helps us to associate the continuum limit of the <i>(4+1)D </i>aniferromagnet to <i>4D </i>principal chiral model. It has been observed that in the strong coupling limit the problem of finding the ground state of lattice QCD is identical to that of solving the generalized antiferromagnet with Neel order playing the role of chiral symmetry breaking. In view of this, now formulate the Hubbard-like model Hamiltonian in terms of the gener- alized fermions with flavor and color degrees of freedom also shall consider the<i> D</i>-theoretical framework to show that the antiferromagnetic system which arises in the strong coupling limit and at half filling corresponds to the principal chiral model in the continuum limit with dimensional reduction. Also pointed out that at strong coupling and half filling the system reduces to a Heisenberg antiferromagnet. This result is analogous to the result obtained in standard Hubbard model.

Low-Energy Effective Theories of the 1/2 - Filled Hubbard Model in the Continuum Limit

It has been observed that when the gauge fields are present on the link, fermion propagation is possible in the weak coupling limit due to the dominance of the hopping term, which corresponds to the colour gauge interaction in the lattice QCD formulation. The production of low energy skyrmionic excitation at the fermionic site destroys the underlying antiferromagnetic order. In the continuum limit, the kinetic term in the lattice QCD corresponds to the rearrangement of the fermionic constituents through their propagation within the confined domain of the bound stateconfigurations of the interacting system which gives rise to a running coupling constant leading to asymptotic freedom. When one can assign a colour to a particular quantum number of a fermionic component in a limited state, it shows that QCD may be thought of as a generalised non-Abelian gauge field theory since these degrees of freedom play a part in the restricted area of the system and examines the continuous limit of the Hubbard-like model and the weak coupling limit that results from the abolition of the antiferromagnetic order and fermion propagation. This is equivalent to the non-Abelian color gauge field interaction. It is noted that the generalised spin fluctuation may be linked to the colour gauge field. This formalism's discovery of pseudoscalar Goldstone bosons associated with chiral symmetry breaking is in line with (3+1)D continuum QCD.

Cross-Channel Constraints on Resonant Antikaon-Nucleon Scattering.

Chiral perturbation theory and its unitarized versions have played an important role in our understanding of the low-energy strong interaction. Yet, so far, such studies typically deal exclusively with perturbative or nonperturbative channels. In this Letter, we report on the first global study of meson-baryon scattering up to one-loop order. It is shown that covariant baryon chiral perturbation theory, including its unitarization for the negative strangeness sector, can describe meson-baryon scattering data remarkably well. This provides a highly nontrivial check on the validity of this important low-energy effective field theory of QCD. We show that the K[over ¯]N related quantities can be better described in comparison with those of lower-order studies, and with reduced uncertainties due to the stringent constraints from the πN and KN phase shifts. In particular, we find that the two-pole structure of Λ(1405) persists up to one-loop order reinforcing the existence of two-pole structures in dynamically generated states.

On the impact of meson mixing on Bs→ ϕee angular observables at low q2

Decays based on the b → sγ transition are expected to yield left-handed photons in the Standard Model, but could be particularly sensitive to New Physics contributions modifying the short-distance Wilson coefficients mathcal{C} 7 and mathcal{C} 7′ defined in the low-energy Effective Field Theory. These coefficients can be determined by combining observables of several modes, among which Bs → ϕee at low q2, in a kinematic range where the photon-pole is dominant. We investigate the impact of Bs − overline{B} s mixing on the angular observables available for this mode, which induces a time-dependent modulation governed by interference terms between mixing and decay that are sensitive to the moduli and phases of mathcal{C} 7 and mathcal{C} 7′. These interference terms can be extracted through a time-dependent analysis but they also affect time-integrated observables. In particular, we show that the asymmetries {A}_T^{(2)} and {A}_T^{left(operatorname{Im}right); CP} receive terms of potentially similar size from mixing-independent and mixing-induced terms, and we discuss how the constraints coming from the angular analysis of Bs→ ϕee at low q2 should be interpreted in the presence of mixing.

Gravity as a Quantum Field Theory

Classical gravity is understood as the geometry of spacetime, and it seems very different from the other known interactions. In this review, I will instead stress the analogies: Like strong interactions, the low energy effective field theory of gravity is related to a nonlinearly realized symmetry, and like electroweak interactions, it is a gauge theory in Higgs phase, with a massive connection. I will also discuss the possibility of finding a UV complete quantum field theoretic description of all interactions.

Slow-rotating black holes with potential in dynamical Chern-Simons modified gravitational theory

The Chern-Simons amended gravity theory appears as a low-energy effective theory of string theory.The effective theory includes an anomaly-cancelation correction to the Einstein-Hilbert action.The Chern-Simons expression consists of the product φRR̃ of the Pontryagin density RR̃ with a scalar field φ, where the latter is considered a background field(dynamical construction or non-dynamical construction).Many different solutions to Einstein's general relativity continue to be valid in the amended theories.The Kerr metric is, however, considered an exceptional case that raised a search for rotating black hole solutions.We generalize the solution presented in Phys. Rev. D 77 (2008) 064007 by allowing the potential V to have a non-vanishing value,and we discuss three different cases of the potential, that is, V = const., V ∝ φ, and V ∝ φ 2 cases.This study presents, for the first time, novel solutions prescribing rotating black holes in the frame of the dynamical formulation of the Chern-Simons gravity,where we include a potential and generalize the previously derived solutions.We derive solutions in the slow-rotation limit, where we write the parameter of the slow-rotation expansion by ε.These solutions are axisymmetric and stationary, and they make a distortion of the Kerr solution by a dipole scalar field.Furthermore, we investigate that the correction to the metric behaves in the inverse of the fourth order of radial distance from the centerof the black hole as V ∝ φ. This suggests that any meaningful limits from the weak-field experiments could be passed.We show that the energy conditions associated with the scalar field of the case V ∝ φ are non-trivial and have non-trivial values to the leading order.These non-trivial values come mainly from the contribution of the potential. Finally, we derived the stability condition using the geodesic deviations.We conclude this study by showing that other choices of the potential, i.e., V ∝ φn , where n > 2 are not allowedbecause all the solutions to these cases will be of order \U0001d4aa(ε 2), which is not covered in this study.

BCF anomaly and higher-group structure in the low energy effective theories of mesons

We discuss the BCF anomaly of massless QCD-like theories, first obtained by Anber and Poppitz, from the viewpoint of the low energy effective theories. We assume that the QCD-like theories exhibit spontaneous chiral symmetry breaking due to a quark bilinear condensate. Using the ’t Hooft anomaly matching condition for the BCF anomaly, we find that the low energy effective action is composed of a chiral Lagrangian and a Wess-Zumino-Witten term together with an interaction term of the η′ meson with the background gauge field for a discrete one-form symmetry. It is shown that the low energy effective action cancels the quantum inconsistencies associated with η′ due to an ambiguity of how to uplift the action to a five-dimensional spacetime with a boundary. The η′ term plays a substantial role in exploring the emergent higher-group structure at low energies.

Domain-wall skyrmions in chiral magnets

Domain-wall skyrmions are skyrmions trapped inside a domain wall. We investigate domain-wall skyrmions in chiral magnets using a fully analytic approach. Treating the Dzyaloshinskii-Moriya (DM) interaction perturbatively, we construct the low-energy effective theory of a magnetic domain wall in an $O(3)$ sigma model with the DM interaction and an easy-axis potential term, yielding a sine-Gordon model. We then construct domain-wall skyrmions as sine-Gordon solitons along the domain wall. We also construct domain-wall skyrmions on top of a pair of a domain wall and an anti-domain wall. One characteristic feature of domain-wall skyrmions is that both skyrmions and antiskyrmions are equally stable inside the domain wall, unlike the bulk in which only one of them is stable.

Field-theoretic functional renormalization group formalism for non-Fermi liquids and its application to the antiferromagnetic quantum critical metal in two dimensions

To capture the universal low-energy physics of metals within effective field theories, one has to generalize the usual notion of scale invariance and renormalizable field theory due to the presence of intrinsic scales (Fermi momenta). In this paper, we develop a field-theoretic functional renormalization group formalism for full low-energy effective field theories of non-Fermi liquids that include all gapless modes around the Fermi surface. The formalism is applied to the non-Fermi liquid that arises at the antiferromagnetic quantum critical point in two space dimensions. In the space of coupling functions, an interacting fixed point arises at a point with momentum-independent couplings and vanishing nesting angle. In theories deformed with non-zero nesting angles, coupling functions acquire universal momentum profiles controlled by the bare nesting angles at low energies before flowing to superconducting states in the low-energy limit. The superconducting instability is unavoidable because lukewarm electrons that are coherent enough to be susceptible to pairing end up being subject to a renormalized attractive interaction with its minimum strength set by the nesting angle irrespective of the bare four-fermion coupling. Despite the inevitable superconducting instability, theories with small bare nesting angles and bare four-fermion couplings that are repulsive or weakly attractive must pass through the region with slow RG flow due to the proximity to the non-Fermi liquid fixed point. The bottleneck region controls the scaling behaviours of the normal state and the quasi-universal pathway from the non-Fermi liquid to superconductivity. In the limit that the nesting angle is small, the non-Fermi liquid scaling dictates the physics over a large window of energy scale above the superconducting transition temperature.