Massive Gauge Fields Research Articles

Neutral current neutrino-electron scattering and generalized uncertainty principle

In this article, we study the effect of quantum gravitational corrections on neutrino electron scattering in electroweak theory SU(2) L × U(1) Y . We consider a neutrino that scatters off an electron by an exchange of a massive neutral gauge boson. In the minimal length formalism, starting from the equation of motion for a massive gauge field we obtain the propagator. And currents are obtained from the action for a massless Dirac fermion. Scattering amplitudes and differential cross sections as function of inelasticity variable y are obtained using expressions of the propagator and leptonic current. All usual expressions are recovered when the deformation parameter α tends to zero. We find that quantum gravitational effects become important only for a highly energetic process with a momentum transfer being much greater than the neutral gauge boson mass.

Gravitational wave probes of massive gauge bosons at the cosmological collider

We extend the reach of the “cosmological collider” for massive gauge boson production during inflation from the CMB scales to the interferometer scales. Considering a Chern-Simons coupling between the gauge bosons and the pseudoscalar inflaton, one of the transverse gauge modes is efficiently produced and its inverse decay leaves an imprint in the primordial scalar and tensor perturbations. We study the correlation functions of these perturbations and derive the updated constraints on the parameter space from CMB observables. We then extrapolate the tensor power spectrum to smaller scales consistently taking into account the impact of the gauge field on inflationary dynamics. Our results show that the presence of massive gauge fields during inflation can be detected from characteristic gravitational wave signals encompassing the whole range of current and planned interferometers.

Particle Creation and the Schwinger Model

We study the particle creation process in the Schwinger model coupled with an external classical source. One can approach the problem by taking advantage of the fact that the full quantized model is solvable and equivalent to a (massive) gauge field with a non-local effective action. Alternatively, one can also face the problem by following the standard semiclassical route. This means quantizing the massless Dirac field and considering the electromagnetic field as a classical background. We evaluate the energy created by a generic, homogeneous, and time-dependent source. The results match exactly in both approaches. This proves in a very direct and economical way the validity of the semiclassical approach for the (massless) Schwinger model, in agreement with a previous analysis based on the linear response equation. Our discussion suggests that a similar analysis for the massive Schwinger model could be used as a non-trivial laboratory to confront a fully quantized solvable model with its semiclassical approximation, therefore mimicking the long-standing confrontation of quantum gravity with quantum field theory in curved spacetime.

BRST formalism of Weyl conformal gravity

We present the BRST formalism of a Weyl conformal gravity in Weyl geometry. Choosing the extended de Donder gauge-fixing condition (or harmonic gauge condition) for the general coordinate invariance and the new scalar gauge-fixing for the Weyl invariance we find that there is a Poincar${\rm{\acute{e}}}$-like $\IOSp(10|10)$ supersymmetry as in a Weyl invariant scalar-tensor gravity in Riemann geometry. We also point out that there is a gravitational conformal symmetry in quantum gravity although there is a massive Weyl gauge field as a result of spontaneous symmetry breakdown of Weyl gauge symmetry and account for how the gravitational conformal symmetry is spontaneously broken to the Poincar\'e symmetry. The corresponding massless Nambu-Goldstone bosons are the graviton and the dilaton. We also prove the unitarity of the physical S-matrix on the basis of the BRST quartet mechanism.

Axion effective action

In this paper, we discuss the construction of Effective Field Theories (EFTs) in which a chiral fermion, charged under both gauge and global symmetries, is integrated out. Inspired by typical axion models, these symmetries can be spontaneously broken, and the global ones might also be anomalous. In this context, particular emphasis is laid on the derivative couplings of the Goldstone bosons to the fermions, as these lead to severe divergences and ambiguities when building the EFT. We show how to precisely solve these difficulties within the path integral formalism, by adapting the anomalous Ward identities to the EFT context. Our results are very generic, and when applied to axion models, they reproduce the non-intuitive couplings between the massive SM gauge fields and the axion. Altogether, this provides an efficient formalism, paving the way for a systematic and consistent methodology to build entire EFTs involving anomalous symmetries, as required for axion or ALP searches.

Nonperturbative renormalization of the lattice Sommerfield vector model

The lattice Sommerfield model, describing a massive vector gauge field coupled to a light fermion in 2d, is an ideal candidate to verify perturbative conclusions. In contrast with continuum exact solutions, we prove that there is no infinite field renormalization, implying the reduction of the degree of the ultraviolet divergence, and that anomalies are non renormalized. Such features are the counterpart of analogue properties at the basis of the Standard model perturbative renormalizability. The results are non-perturbative, in the sense that the averages of gauge invariant observables are expressed in terms of convergent expansions uniformly in the lattice and volume.

A bispinor formalism for spinning Witten diagrams

We develop a new embedding-space formalism for AdS4 and CFT3 that is useful for evaluating Witten diagrams for operators with spin. The basic variables are Killing spinors for the bulk AdS4 and conformal Killing spinors for the boundary CFT3. The more conventional embedding space coordinates XI for the bulk and PI for the boundary are bilinears in these new variables. We write a simple compact form for the general bulk-boundary propagator, and, for boundary operators of spin ℓ ≥ 1, we determine its conservation properties at the unitarity bound. In our CFT3 formalism, we identify an mathfrak{so} (5, 5) Lie algebra of differential operators that includes the basic weight-shifting operators. These operators, together with a set of differential operators in AdS4, can be used to relate Witten diagrams with spinning external legs to Witten diagrams with only scalar external legs. We provide several applications that include Compton scattering and the evaluation of an R4 contact interaction in AdS4. Finally, we derive bispinor formulas for the bulk-to-bulk propagators of massive spinor and vector gauge fields and evaluate a diagram with spinor exchange.

The Polyakov loop dependence of bulk viscosity of QCD matter

In this work, we show the dependence of bulk viscosity on Polyakov loop in 3+1 dimensional topologically massive model (TMM). This model contains equally massive non-Abelian gauge fields without spontaneous symmetry breaking. In earlier works, the bulk viscosity was found from the trace anomaly in massless ϕ4 model and Yang-Mills (YM) theory and its dependence on the quantum corrections was established. In TMM, the trace anomaly is absent due to the presence of kinetic term of a two-form field B in the action. This model also provides the dependence of bulk viscosity on the mass of the gauge bosons. The mass of the gauge bosons in TMM acts as magnetic mass in the perturbative thermal field theory. This magnetic mass is gauge independent unlike what is found in massless YM theory. We also observe that the strong coupling constant has the same behaviour at high energy limit (i.e. asymptotic freedom) as that of massless YM theory at zero temperature.

Condensates, massive gauge fields, and confinement in the SU(3) gauge theory

Abstract SU(3) gauge theory in the nonlinear gauge of the Curci–Ferrari type is studied. In the low-energy region, ghost condensation and subsequent gauge field condensation can happen. The latter condensation makes classical gauge fields massive. If the color electric potential with a string is chosen as the classical gauge field, it produces the static potential with the linear potential. We apply this static potential to the three-quark system, and show, differently from the Y-type potential, that infrared divergence remains in the Δ-type potential. The color electric flux is also studied, showing that a current which plays the role of the magnetic current appears

A differential relation between the energy and electric charge of a dyon

The differential relation between the energy and electric charge of a dyon is derived. The relation expresses the derivative of the energy with respect to the electric charge in terms of the boundary value for the temporal component of the dyon's electromagnetic potential. The use of the Hamiltonian formalism and transition to the unitary gauge make it possible to show that this derivative is proportional to the phase frequency of the electrically charged massive gauge fields forming the dyon's core. It follows from the differential relation that the energy and electric charge of the non-BPS dyon cannot be arbitrarily large. Finally, the dyon's properties are investigated numerically at different values of the model parameters.

Massive double copy in three spacetime dimensions

Recent explorations on how to construct a double copy of massive gauge fields have shown that, while any amplitude can be written in a form consistent with colour-kinematics duality, the double copy is generically unphysical. In this paper, we explore a new direction in which we can obtain a sensible double copy of massive gauge fields due to the special kinematics in three-dimensional spacetimes. To avoid the appearance of spurious poles at 5-points, we only require that the scattering amplitudes satisfy one BCJ relation. We show that the amplitudes of Topologically Massive Yang-Mills satisfy this relation and that their double copy at three, four, and five-points is Topologically Massive Gravity.

The anomalous case of axion EFTs and massive chiral gauge fields

We study axion effective field theories (EFTs), with a focus on axion couplings to massive chiral gauge fields. We investigate the EFT interactions that participate in processes with an axion and two gauge bosons, and we show that, when massive chiral gauge fields are present, such interactions do not entirely originate from the usual anomalous EFT terms. We illustrate this both at the EFT level and by matching to UV-complete theories. In order to assess the consistency of the Peccei-Quinn (PQ) anomaly matching, it is useful to introduce an auxiliary, non-dynamical gauge field associated to the PQ symmetry. When applied to the case of the Standard Model (SM) electroweak sector, our results imply that anomaly-based sum rules between EFT interactions are violated when chiral matter is integrated out, which constitutes a smoking gun of the latter. As an illustration, we study a UV-complete chiral extension of the SM, containing an axion arising from an extended Higgs sector and heavy fermionic matter that obtains most of its mass by coupling to the Higgs doublets. We assess the viability of such a SM extension through electroweak precision tests, bounds on Higgs rates and direct searches for heavy charged matter. At energies below the mass of the new chiral fermions, the model matches onto an EFT where the electroweak gauge symmetry is non-linearly realised.

Comments on gauge anomalies at dimension-six in the Standard Model Effective Field Theory

We study whether higher-dimensional operators in effective field theories, in particular in the Standard Model Effective Field Theory (SMEFT), can source gauge anomalies via the modification of the interactions involved in triangle diagrams. We find no evidence of such gauge anomalies at the level of dimension-6 operators that can therefore be chosen independently to each others without spoiling the consistency of SMEFT, at variance with recent claims. The underlying reason is that gauge-invariant combinations of Goldstone bosons and massive gauge fields are allowed to couple to matter currents which are not conserved. We show this in a toy model by computing the relevant triangle diagrams, as well as by working out Wess-Zumino terms in the bosonic EFT below all fermion masses. The same approach applies directly to the Standard Model both at the renormalisable level, providing a convenient and unusual way to check that the SM is anomaly free, as well as at the non-renormalisable level in SMEFT.

Dynamically emergent gravity from hidden local Lorentz symmetry

Gravity can be regarded as a consequence of local Lorentz (LL) symmetry, which is essential in defining a spinor field in curved spacetime. The gravitational action may admit a zero-field limit of the metric and vierbein at a certain ultraviolet cutoff scale such that the action becomes a linear realization of the LL symmetry. Consequently, only three types of term are allowed in the four-dimensional gravitational action at the cutoff scale: a cosmological constant, a linear term of the LL field strength, and spinor kinetic terms, whose coefficients are in general arbitrary functions of LL and diffeomorphism invariants. In particular, all the kinetic terms are prohibited except for spinor fields, and hence the other fields are auxiliary. Their kinetic terms, including those of the LL gauge field and the vierbein, are induced by spinor loops simultaneously with the LL gauge field mass. The LL symmetry is necessarily broken spontaneously and hence is nothing but a hidden local symmetry, from which gravity is emergent.

Large field excursions from dimensional (de)construction

An inflation model based on dimensional (de)construction of a massive gauge theory is proposed. The inflaton in this model is the “zero-mode” of a component of the massive gauge field in the (de)constructed extra dimensions. The inflaton potential originates from the gauge invariant Stueckelberg potential. At low energy, the field range of the inflaton is enhanced by a factor Nd/2 compared to the field range of the original fields in the model, where d is the number of the (de)constructed extra dimensions and N is the number of the lattice points in each (de)constructed dimension. This enhancement of the field range is used to achieve a trans-Planckian inflaton field excursion. The extension of the mechanism “excursions through KK modes” to the case of (de)constructed extra dimensions is also studied. The burst of particle productions by this mechanism may have observable consequences in a region of the model parameter space.

Emergent vortex–electron interaction from dualization

We consider the Abelian Higgs model in 3+1 dimensions with vortex lines, into which charged fermions are introduced. This could be viewed as a model of a type-II superconductor with unpaired electrons (or holes), analogous to the boson–fermion model of high-Tc superconductors but one in which the bosons and fermions interact only through the electromagnetic gauge field. We investigate the dual formulation of this model, which is in terms of a massive antisymmetric tensor gauge field Bμν mediating the interaction of the vortex lines. This field couples to the fermions through a nonlocal spin-gauge interaction term. We then calculate the quantum correction due to the fermions at one loop and show that due to the presence of this new nonlocal term a topological B∧F interaction is induced in the effective action, leading to an increase in the mass of both the photon and the tensor gauge field. Additionally, we find a Coulomb potential between the electrons, but with a large dielectric constant generated by the one-loop effects.

Fakeons, unitarity, massive gravitons, and the cosmological constant

We give a simple proof of perturbative unitarity in gauge theories and quantum gravity using a special gauge that allows us to separate the physical poles of the free propagators, which are quantized by means of the Feynman prescription, from the poles that belong to the gauge-trivial sector, which are quantized by means of the fakeon prescription. The proof applies to renormalizable theories, including the ultraviolet complete theory of quantum gravity with fakeons formulated recently, as well as low-energy (nonrenormalizable) theories. We clarify a number of subtleties related to the study of scattering processes in the presence of a cosmological constant Λ. The scattering ampli- tudes, defined by expanding the metric around flat space, obey the optical theorem up to corrections due to Λ, which are negligible for all practical purposes. Problems of interpretation would arise if such corrections became important. In passing, we obtain local, unitary (and “almost” renormalizable) theories of massive gravitons and gauge fields, which violate gauge invariance and general covariance explicitly.

Massive dual gauge field and confinement in Minkowski space: Electric charge

SU(2) gauge theory in the nonlinear gauge of the Curci-Ferrari type is studied in low-energy region. We give a classical solution that connects color electric charges. Its dual solution, which has a configuration of monopole, is also presented. Due to the gluon condensation subsequent to the ghost condensation, these classical fields become massive. The massive Lagrangian with the classical solution and that with the dual solution are derived. We show that these Lagrangians produce a linear potential between a quark and an antiquark. This is the mechanism of quark confinement that is different from the magnetic monopole condensation.

Spontaneous breaking of Weyl quadratic gravity to Einstein action and Higgs potential

We consider the (gauged) Weyl gravity action, quadratic in the scalar curvature ( tilde{R} ) and in the Weyl tensor ( {tilde{C}}_{mu nu rho sigma} ) of the Weyl conformal geometry. In the absence of matter fields, this action has spontaneous breaking in which the Weyl gauge field ωμ becomes massive (mass mω ∼ Planck scale) after “eating” the dilaton in the tilde{R} 2 term, in a Stueckelberg mechanism. As a result, one recovers the Einstein-Hilbert action with a positive cosmological constant and the Proca action for the massive Weyl gauge field ωμ. Below mω this field decouples and Weyl geometry becomes Riemannian. The Einstein-Hilbert action is then just a “low-energy” limit of Weyl quadratic gravity which thus avoids its previous, long-held criticisms. In the presence of matter scalar field ϕ1 (Higgs-like), with couplings allowed by Weyl gauge symmetry, after its spontaneous breaking one obtains in addition, at low scales, a Higgs potential with spontaneous electroweak symmetry breaking. This is induced by the non-minimal coupling {xi}_1{phi}_1^2tilde{R} to Weyl geometry, with Higgs mass ∝ ξ1/ξ0 (ξ0 is the coefficient of the tilde{R} 2 term). In realistic models ξ1 must be classically tuned ξ1 ≪ ξ0. We comment on the quantum stability of this value.

Gauge-independent approach to resonant dark matter annihilation

In spontaneously broken gauge theories, transition amplitudes describing dark-matter (DM) annihilation processes through a resonance may become highly inaccurate close to a production threshold, if a Breit-Wigner (BW) ansatz with a constant width is used. To partially overcome this problem, the BW propagator needs to be modified by including a momentum dependent decay width. However, such an approach to resonant transition amplitudes generically suffers from gauge artefacts that may also give rise to a bad or ambiguous high-energy behaviour for such amplitudes. We address the two problems of gauge dependence and high-energy unitarity within a gauge-independent framework of resummation implemented by the so-called Pinch Technique. We study DM annihilation via scalar resonances in a gauged U(1)X complex-scalar extension of the Standard Model that features a massive stable gauge field which can play the role of the DM. We find that the predictions for the DM abundance may vary significantly from previous studies based on the naive BW ansatz and propose an alternative simple approximation which leads to the correct DM phenomenology. In particular, our results do not depend on the gauge-fixing parameter and are consistent with considerations from high-energy unitarity.