Four-fermion Coupling Research Articles

Higgs boson origin from a gauge symmetric theory of massive composite particles and massless W± and Z0 bosons at the TeV scale

The ultraviolet completion is the Standard Model (SM) gauge-symmetric four-fermion couplings at the high-energy cutoff. Composite particles appear in the gauge symmetric phase in contrast with SM particles in the spontaneous symmetry-breaking phase. The critical point between the two phases is a weak first-order transition. It relates to an ultraviolet fixed point for an SM gauge symmetric theory of composite particles in the strong coupling regime. The low-energy SM realizes at an infrared fixed point in the weak coupling regime. Composite bosons dissolve into SM particles at the phase transition, and in the top-quark channel, they become a composite SM Higgs boson and three Goldstone bosons. Extrapolation of SM renormalization-group solutions to high energies implies that the gauge-symmetric theory of composite particles has a characteristic scale of about 5.1 TeV. We discuss the phenomenological implications of composite SM Higgs boson in the gauge symmetry-breaking phase, and massive composite bosons coupling to massless W± and Z0 gauge bosons in the gauge symmetric phase.

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.

Microscopic characterization of Ising conformal field theory in Rydberg chains

Rydberg chains provide an appealing platform for probing conformal field theories (CFTs) that capture universal behavior in a myriad of physical settings. Focusing on a Rydberg chain at the Ising transition separating charge density wave and disordered phases, we establish a detailed link between microscopics and low-energy physics emerging at criticality. We first construct lattice incarnations of primary fields in the underlying Ising CFT including chiral fermions -- a nontrivial task given that the Rydberg chain Hamiltonian does not admit an exact fermionization. With this dictionary in hand, we compute correlations of microscopic Rydberg operators, paying special attention to finite, open chains of immediate experimental relevance. We further develop a method to quantify how second-neighbor Rydberg interactions tune the sign and strength of four-fermion couplings in the Ising CFT. Finally, we determine how the Ising fields evolve when four-fermion couplings drive an instability to Ising tricriticality. Our results pave the way to a thorough experimental characterization of Ising criticality in Rydberg arrays, and can inform the design of novel higher-dimensional phases based on coupled critical chains.

Neutrino self-interactions and double beta decay

Neutrino Self-Interactions ($\nu$SI) beyond the Standard Model are an attractive possibility to soften cosmological constraints on neutrino properties and also to explain the tension in late and early time measurements of the Hubble expansion rate. The required strength of $\nu$SI to explain the $4\sigma$ Hubble tension is in terms of a point-like effective four-fermion coupling that can be as high as $10^9\, G_F$, where $G_F$ is the Fermi constant. In this work, we show that such strong $\nu$SI can cause significant effects in two-neutrino double beta decay, leading to an observable enhancement of decay rates and to spectrum distortions. We analyze self-interactions via an effective operator as well as when mediated by a light scalar. Data from observed two-neutrino double beta decay is used to constrain $\nu$SI, which rules out the regime around $10^9\, G_F$.

Dirac neutrinos and Neff

If neutrinos are Dirac particles the existence of light right-handed neutrinos νR is implied. Those would contribute to the effective number of relativistic neutrino species Neff in the early Universe. With pure standard model interactions, the contribution is negligibly small. In the presence of new interactions, however, the contribution could be significantly enhanced. We consider the most general effective four-fermion interactions for neutrinos (scalar, pseudo-scalar, vector, axial-vector and tensor), and compute the contribution of right-handed neutrinos to Neff. Taking the Planck 2018 measurement of Neff, strong constraints on the effective four-fermion coupling are obtained, corresponding to interaction strengths of 10−5∼10−3 in units of the Fermi constant. This translates in new physics scales of up to 43 TeV and higher. Future experiments such as CMB-S4 can probe or exclude the existence of effective 4-neutrino operators for Dirac neutrinos. Ways to avoid this conclusion are discussed.

Interacting two-particle states in the symmetric phase of the chiral Nambu–Jona-Lasinio model

The renormalization group flow of the chiral Nambu–Jona-Lasinio (NJL) model with one fermion flavor is mapped out in the symmetric phase with help of the Functional Renormalization Group (FRG) method using a physically motivated nonlocal trial effective action. The non-interacting infrared end-point of the flow of the four-fermion couplings is now accompanied by nonzero limiting composite couplings characteristic for interacting two-particle states with finite energy and physical size. The interaction energy of the constituents is extracted as a function of the physical size of the composite object. The propagation of a two-particle state minimizing the interaction energy has a natural bound state interpretation.

Four-Fermion Interaction Model on ℳD−1 ⊗ S1

Four-fermion interaction models are often used as simplified models of interacting fermion fields with the chiral symmetry. The chiral symmetry is dynamically broken for a larger four-fermion coupling. It is expected that the broken symmetry is restored under extreme conditions. In this paper, the finite size effect on the chiral symmetry breaking is investigated in the four-fermion interaction model. We consider the model on a flat spacetime with a compactified spatial coordinate, M D − 1 ⊗ S 1 and obtain explicit expressions of the effective potential for arbitrary spacetime dimensions in the leading order of the 1 / N expansion. Evaluating the effective potential, we show the critical lines which divide the symmetric and the broken phase and the sign-flip condition for the Casimir force.

Phases of inflation

Motivated by the 4d effective field theories for closed string axions in Type II string compactifications with D-branes, we consider chiral gauge theories coupled to multiple axions. We discuss how well-known non-perturbative dynamical phenomena, such as gauge instantons, fermion confinement and Nambu-Jona-Lasinio interactions, give rise to non-trivial vacuum configurations in the IR. The fluctuations about the IR vacuum are captured by some remaining closed string axions and infladrons (scalar chiral condensate excitations), which acquire dynamical masses. By employing the full power of the effective field theory, we investigate the applicability of these IR theories as inflationary models (natural, monodromy, Starobinsky) and connect different types of inflationary scenarios to different phases of the non-Abelian gauge theory or the Nambu-Jona-Lasinio four-fermion couplings. The back-reaction of the infladrons flattens the axion potential in natural-like inflationary models, such that the tension with current CMB data with respect to the spectral index and the tensor-to-scalar ratio can be partially alleviated.

Effective potential in ultraviolet completions for composite Higgs models

We consider a class of composite Higgs models based on asymptotically free $SO(d)$ gauge theories with $d$ odd, with fermions in two irreducible representations, and in which the Higgs field arises as a pseudo Nambu-Goldstone boson and the top quark is partially composite. The Nambu-Goldstone coset containing the Higgs field, or Higgs coset, is either $SU(4)/Sp(4)$ or $SU(5)/SO(5)$, whereas the top partners live in two-index representations of the relevant flavor group ($SU(4)$ or $SU(5)$). In both cases, there is a large number of terms in the most general four-fermion lagrangian describing the interaction of third-generation quarks with the top partners. We derive the top-induced effective potential for the Higgs coset together with the singlet pseudo Nambu-Goldstone boson associated with the non-anomalous axial symmetry, to leading order in the couplings between the third-generation quarks and the composite sector. We obtain expressions for the low-energy constants in terms of top-partner two-point functions. We revisit the effective potential of another composite Higgs model that we have studied previously, which is based on an $SU(4)$ gauge theory and provides a different realization of the $SU(5)/SO(5)$ coset. The top partners of this model live in the fundamental representation of $SU(5)$, and, as a result, the effective potential of this model is qualitatively different from the $SO(d)$ gauge theories. We also discuss the role of the isospin-triplet fields contained in the $SU(5)/SO(5)$ coset, and show that, without further constraints on the four-fermion couplings, an expectation value for the the Higgs field will trigger the subsequent condensation of an isospin-triplet field.

Phase structure of NJL model with weak renormalization group

We analyze the chiral phase structure of the Nambu–Jona-Lasinio model at finite temperature and density by using the functional renormalization group (FRG). The renormalization group (RG) equation for the fermionic effective potential V(σ;t) is given as a partial differential equation, where σ:=ψ¯ψ and t is a dimensionless RG scale. When the dynamical chiral symmetry breaking (DχSB) occurs at a certain scale tc, V(σ;t) has singularities originated from the phase transitions, and then one cannot follow RG flows after tc. In this study, we introduce the weak solution method to the RG equation in order to follow the RG flows after the DχSB and to evaluate the dynamical mass and the chiral condensate in low energy scales. It is shown that the weak solution of the RG equation correctly captures vacuum structures and critical phenomena within the pure fermionic system. We show the chiral phase diagram on temperature, chemical potential and the four-Fermi coupling constant.

Phases of a strongly coupled four-fermion theory

We present ongoing investigations of a four-dimensional lattice field theory with four massless reduced staggered fermions coupled through an SU(4)-invariant fourfermion interaction. As in previous studies of four-fermion and Higgs–Yukawa models with different lattice fermion discretizations, we observe a strong-coupling phase in which the system develops a mass gap without breaking any lattice symmetry. This symmetric strong-coupling phase is separated from the symmetric weak-coupling phase by a narrow region of four-fermi coupling in which the system exhibits long-range correlations.

Interacting neutrinos in cosmology: exact description and constraints

We consider the impact of neutrino self-interactions described by an effective four-fermion coupling on cosmological observations. Implementing the exact Boltzmann hierarchy for interacting neutrinos first derived in [1] into the Boltzmann solver CLASS, we perform a detailed numerical analysis of the effects of the interaction on the cosmic microwave background (CMB) anisotropies, and compare our results with known approximations in the literature. While we find good agreement between our exact approach and the relaxation time approximation used in some recent studies, the popular (ceff2,cvis2)-parameterisation fails to reproduce the correct scale dependence of the CMB temperature power spectrum. We then proceed to derive constraints on the effective coupling constant Geff using currently available cosmological data via an MCMC analysis. Interestingly, our results reveal a bimodal posterior distribution, where one mode represents the standard ΛCDM limit with Geff ≲ 108 GF, and the other a scenario in which neutrinos self-interact with an effective coupling constant Geff ≃ 3 × 109 GF.

Novel phases in strongly coupled four-fermion theories

We study a lattice model comprising four massless reduced staggered fermions in four dimensions coupled through an $SU(4)$-invariant four-fermion interaction. We present both theoretical arguments and numerical evidence that no bilinear fermion condensates are present for any value of the four-fermi coupling, in contrast to earlier studies of Higgs--Yukawa models with different exact lattice symmetries. At strong coupling we observe the formation of a four-fermion condensate and a mass gap in spite of the absence of bilinear condensates. Unlike those previously studied systems we do not find a ferromagnetic phase separating this strong-coupling phase from the massless weak-coupling phase. Instead we observe long-range correlations in a narrow region of the coupling, still with vanishing bilinear condensates. While our numerical results come from relatively small lattice volumes that call for caution in drawing conclusions, if this novel phase structure is verified by future investigations employing larger volumes it may offer the possibility for new continuum limits for strongly interacting fermions in four dimensions.

Ideal walking dynamics via a gauged NJL model

According to the Ideal Walking Technicolor paradigm large mass anomalous dimensions arise in gauged Nambu--Jona-Lasinio (NJL) models when the four-fermion coupling is sufficiently strong to induce spontaneous symmetry breaking in an otherwise conformal gauge theory. We therefore study the $SU(2)$ gauged NJL model with two adjoint fermions using lattice simulations. The model is in an infrared conformal phase at small NJL coupling while it displays a chirally broken phase at large NJL couplings. In the infrared conformal phase we find that the mass anomalous dimension varies with the NJL coupling reaching $\gamma_m \sim 1$ close to the chiral symmetry breaking transition, de facto making the present model the first explicit realization of the Ideal Walking scenario.

An effective strong-coupling theory of composite particles in UV-domain

We briefly review the effective field theory of massive composite particles, their gauge couplings and characteristic energy scale in the UV-domain of UV-stable fixed point of strong four-fermion coupling, then mainly focus the discussions on the decay channels of composite particles into the final states of the SM gauge bosons, leptons and quarks. We calculate the rates of composite bosons decaying into two gauge bosons γγ, γZ0, W+W−, Z0Z0 and give the ratios of decay rates of different channels depending on gauge couplings only. It is shown that a composite fermion decays into an elementary fermion and a composite boson, the latter being an intermediate state decays into two gauge bosons, leading to a peculiar kinematics of final states of a quark (or a lepton) and two gauge bosons. These provide experimental implications of such an effective theory of composite particles beyond the SM. We also present some speculative discussions on the channels of composite fermions decaying into W W , W Z and ZZ two boson-tagged jets with quark jets, or to four-quark jets. Moreover, at the same energy scale of composite particles produced in high-energy experiments, composite particles are also produced by high-energy sterile neutrino (dark matter) collisions, their decays lead to excesses of cosmic ray particles in space and signals of SM particles in underground laboratories.

Excitonic pairing and insulating transition in two-dimensional semi-Dirac semimetals

A sufficiently strong long-range Coulomb interaction can induce excitonic pairing in gapless Dirac semimetals, which generates a finite gap and drives semimetal-insulator quantum phase transition. This phenomenon is in close analogy to dynamical chiral symmetry breaking in high energy physics. In most realistic Dirac semimetals, including suspended graphene, Coulomb interaction is too weak to open an excitonic gap. The Coulomb interaction plays a more important role at low energies in a two-dimensional semi-Dirac semimetal, in which the fermion spectrum is linear in one component of momenta and quadratic in the other, than a Dirac semimetal, and indeed leads to breakdown of Fermi liquid theory. We study dynamical excitonic gap generation in a two-dimensional semi-Dirac semimetal by solving the Dyson-Schwinger equation, and show that a moderately strong Coulomb interaction suffices to induce excitonic pairing. Additional short-range four-fermion coupling tends to promote excitonic pairing. Among the available semi-Dirac semimetals, we find that TiO$_{2}$/VO$_{2}$ nanostructure provides a promising candidate for the realization of excitonic insulator. We also apply the renormalziation group method to analyze the strong coupling between the massless semi-Dirac fermions and the quantum critical fluctuation of excitonic order parameter at the semimetal-insulator quantum critical point, and reveal non-Fermi liquid behaviors of semi-Dirac fermions.

Dual QED3 at “N F = 1/2” is an interacting CFT in the infrared

We study the fate of weakly coupled dual QED3 in the infrared, that is, a single two-component Dirac fermion coupled to an emergent U(1) gauge field, but without Chern-Simons term. This theory has recently been proposed as a dual description of 2D surfaces of certain topological insulators. Using the renormalization group, we find that the interplay of gauge fluctuations with generated interactions in the four-fermi sector stabilizes an interacting conformal field theory (CFT) with finite four-fermi coupling in the infrared. The emergence of this CFT is due to cancellations in the $\beta$-function of the four-fermi coupling special to "NF = 1/2". We also quantify how a possible "strong" Dirac fermion duality between a free Dirac cone and dual QED3 would constrain the universal constants of the topological current correlator of the latter.

Hierarchy spectrum of SM fermions: from top quark to electron neutrino

In the SM gauge symmetries and fermion content of neutrinos, charged leptons and quarks, we study the effective four-fermion operators of Einstein-Cartan type and their contributions to the Schwinger-Dyson equations of fermion self-energy functions. The study is motivated by the speculation that these four-fermion operators are probably originated due to the quantum gravity that provides the natural regularization for chiral-symmetric gauge field theories. In the chiral-gauge symmetry breaking phase, as to achieve the energetically favorable ground state, only the top-quark mass is generated via the spontaneous symmetry breaking, and other fermion masses are generated via the explicit symmetry breaking induced by the top-quark mass, four-fermion interactions and fermion-flavor mixing matrices. A phase transition from the symmetry breaking phase to the chiral-gauge symmetric phase at TeV scale occurs and the drastically fine-tuning problem can be resolved. In the infrared fixed-point domain of the four-fermion coupling for the SM at low energies, we qualitatively obtain the hierarchy patterns of the SM fermion Dirac masses, Yukawa couplings and family-flavor mixing matrices with three additional right-handed neutrinos $\nu^f_R$. Large Majorana masses and lepton-symmetry breaking are originated by the four-fermion interactions among $\nu^f_R$ and their left-handed conjugated fields $\nu^{fc}_R$. Light masses of gauged Majorana neutrinos in the normal hierarchy ($10^{-5}-10^{-2}$ eV) are obtained consistently with neutrino oscillations. We present some discussions on the composite Higgs phenomenology and forward-backward asymmetry of $t\bar t$-production, as well as remarks on the candidates of light and heavy dark matter particles (fermions, scalar and pseudoscalar bosons).

Critical end point in the presence of a chiral chemical potential

A class of Polyakov-loop-modified Nambu--Jona-Lasinio (PNJL) models have been used to support a conjecture that numerical simulations of lattice-regularized quantum chromodynamics (QCD) defined with a chiral chemical potential can provide information about the existence and location of a critical endpoint in the QCD phase diagram drawn in the plane spanned by baryon chemical potential and temperature. That conjecture is challenged by conflicts between the model results and analyses of the same problem using simulations of lattice-regularized QCD (lQCD) and well-constrained Dyson-Schwinger equation (DSE) studies. We find the conflict is resolved in favor of the lQCD and DSE predictions when both a physically-motivated regularization is employed to suppress the contribution of high-momentum quark modes in the definition of the effective potential connected with the PNJL models and the four-fermion coupling in those models does not react strongly to changes in the mean-field that is assumed to mock-up Polyakov loop dynamics. With the lQCD and DSE predictions thus confirmed, it seems unlikely that simulations of lQCD with $\mu_5>0$ can shed any light on a critical endpoint in the regular QCD phase diagram.

Fermion masses through four-fermion condensates

Fermion masses can be generated through four-fermion condensates when symmetries prevent fermion bilinear condensates from forming. This less explored mechanism of fermion mass generation is responsible for making four reduced staggered lattice fermions massive at strong couplings in a lattice model with a local four-fermion coupling. The model has a massless fermion phase at weak couplings and a massive fermion phase at strong couplings. In particular there is no spontaneous symmetry breaking of any lattice symmetries in both these phases. Recently it was discovered that in three space-time dimensions there is a direct second order phase transition between the two phases. Here we study the same model in four space-time dimensions and find results consistent with the existence of a narrow intermediate phase with fermion bilinear condensates, that separates the two asymptotic phases by continuous phase transitions.