Gauge-invariant Lagrangian Research Articles

Binned top quark spin correlation and polarization observables for the LHC at 13.6 TeV

We consider top-antitop quark (tt¯) production at the Large Hadron Collider (LHC) with subsequent decays into dileptonic final states. We use and investigate a set of leptonic angular correlations and distributions with which all the independent coefficient functions of the top-spin-dependent parts of the tt¯ production spin density matrices can be experimentally probed. We compute these observables for the LHC center-of-mass energy 13.6 TeV within the Standard Model at next-to-leading order in the QCD coupling including the mixed QCD weak corrections. We determine also the tt¯ charge asymmetry where we take in addition also the mixed QCD-QED corrections into account. In addition we analyze and compute possible new physics (NP) effects on these observables within effective field theory in terms of a gauge-invariant effective Lagrangian that contains the operators up to mass dimension six that are relevant for hadronic tt¯ production. First, we compute our observables inclusive in phase space. Then, in order to investigate which region in phase space has, for a specific observable, a high NP sensitivity, we determine our observables also in two-dimensional (Mtt¯,cosθt*) bins, where Mtt¯ denotes the tt¯-invariant mass and θt* is the top quark scattering angle in the tt¯ zero-momentum frame. Published by the American Physical Society 2024

Axion-electrodynamics and the Poynting theorem

Abstract In a recent study, we proposed an axion-electrodynamics model that consistently incorporates a lepton Dirac field into the gauge-invariant Lagrangian of a closed physical system. Our investigation delved toward potential applications of the model, with a focus on its implications in the realm of Dark Matter axions interacting with leptons in a nonlinear electrodynamics background. In the present work, we introduce an extended axion-electrodynamics model wherein the Bianchi identities are modified by the axion field. This leads to a modification of the energy conservation law for the fields: the Poynting theorem in a source-free region, in which the axion field is involved. By implementing a quantization scheme, our model can offer a novel approach for addressing the problem of axion production/conversion in the presence of electromagnetic and Dirac fields.

Gauge invariance of radiative jet functions in the position-space formulation of SCET

In subleading powers of soft-collinear effective theory (SCET), the Lagrangian contains couplings between soft quarks and hard-collinear quarks. Matrix elements of the hard-collinear parts of these couplings are radiative jet functions. In the position-space formulation of SCET, the Lagrangians are constructed from operators that appear to be gauge invariant. Nevertheless, we find violations of gauge invariance arise in the hard-collinear sector because gauge transformations can shift the momentum of a hard-collinear quark field from the hard-collinear sector to the soft sector, where the hard-collinear fields, by definition, have no support. The violations of gauge invariance are manifested in perturbation theory in the hard-collinear sector through the absence of certain Feynman diagrams that would be present in full QCD. A consequence of the absence of these diagrams is that the radiative jet functions that follow directly from the position-space Lagrangians are not gauge invariant, and we demonstrate this through explicit calculations in lower-order perturbation theory. We obtain gauge-invariant Lagrangians by adding to existing position-space Lagrangians terms that are proportional to the soft-quark equation of motion. These gauge-invariant Lagrangians are valid for nonzero, as well as zero, quark masses. We also remark briefly on the gauge invariance of certain Lagrangians that have been constructed in the label-momentum formulation of SCET. Published by the American Physical Society 2024

Conformal Yang-Mills field in arbitrary dimensions

Lagrangian of a classical conformal Yang-Mills field in the flat space of even dimension greater than or equal to six involves higher derivatives. We study Lagrangian formulation of the classical conformal Yang-Mills field by using ordinary-derivative (second-derivative) approach. In the framework of the ordinary-derivative approach, a field content, in addition to generic Yang-Mills field, consists of auxiliary vector fields and Stueckelberg scalar fields. For such field content, we obtain a gauge invariant Lagrangian with the conventional second-derivative kinetic terms and the corresponding gauge transformations. The Lagrangian is built in terms of non-abelian field strengths. Structure of a gauge algebra entering gauge symmetries of the conformal Yang-Mills field is described. FFF-vertex of the conformal Yang-Mills field which involves three derivatives is also obtained. For six, eight, and ten dimensions, eliminating the auxiliary vector fields and gauging away the Stueckelberg scalar fields, we obtain a higher-derivative Lagrangian of the conformal Yang-Mills field. For arbitrary dimensions, we demonstrate that all auxiliary fields can be integrated out at non-linear level leading just to a local higher-derivative action which is expressed only in terms of the generic Yang-Mills field.

A Gauge-Invariant Lagrangian Determined by the n-Point Probability Density Function of a Vorticity Field of Wave Optical Turbulence

A Gauge-Invariant Lagrangian Determined by the n-Point Probability Density Function of a Vorticity Field of Wave Optical Turbulence

Generic Behavior of Electromagnetic Fields of Regular Rotating Electrically Charged Compact Objects in Nonlinear Electrodynamics Minimally Coupled to Gravity

Regular rotating electrically charged compact objects are described by nonlinear electrodynamics minimally coupled to gravity in a self-consistent way and without additional assumptions on the relation between the electromagnetic field and gravity. The electromagnetic fields obey the system of four source-free nonlinear equations for the electromagnetic tensor Fμν, with only two independent components due to spacetime symmetry determined by the algebraic structure of electromagnetic stress–energy tensors (pr=−ρ). In this paper, we present, for an arbitrary gauge-invariant Lagrangian, the general regular solution and generic behavior of electromagnetic fields, including the generic features of the Lagrange dynamics, for regular rotating electrically charged black holes and electromagnetic spinning solitons.

Formulation of axion-electrodynamics with Dirac fields

Abstract We propose a straightforward generalization of axion-electrodynamics (AED) for the case in which a lepton Dirac field is present in the U 1 EM ${\left(1\right)}_{\text{EM}}$ gauge-invariant Lagrangian of the closed system. In the associated differential equations of motion we find that variations in the axion field give rise to modifications in the electric current and in the divergence of the axial current. In light of this, we interpret some possible Dark Matter (DM) phenomena. In particular, we discuss on general grounds (i) AED and DM, and (ii) DM axions interacting with leptons in a nonlinear electrodynamics background. We briefly comment on the conceivable application of this model beyond the subject of DM axions realized in condensed-matter physics.

Gauge-invariant formulation of axion-electrodynamics

In this paper, we propose a simple generalization of axion-electrodynamics (AED) for the general case in which Dirac fermion fields and scalar/pseudoscalar axion-like fields are present in the local [Formula: see text]([Formula: see text])[Formula: see text] gauge-invariant Lagrangian of the system. Our primary goal (which is not explored here) is to understand and predict novel phenomena that have no counterpart in standard (pseudoscalar) AED. With this end in view, we discuss on very general grounds, possible processes in which a Dirac field is coupled to axionic fields via the electromagnetic (EM) field.

The tunable 0−π qubit: Dynamics and relaxation

In this paper, we present a systematic treatment of a [Formula: see text] qubit in the presence of a time-dependent external flux. A gauge-invariant Lagrangian and the corresponding Hamiltonian are obtained. The effect of the flux noise on the qubit relaxation is obtained using the perturbation theory. Under a time-dependent drive of sinusoidal form, the survival probability, and transition probabilities have been studied for different strengths and frequencies. The driven qubit is shown to possess coherent oscillations among two distinct states for a weak to moderate strength close to resonant frequencies of the unperturbed qubit. The parameters can be chosen to prepare the system in its ground state. This feature paves the way to prolong the lifetime by combining ideas from weak measurement and quantum Zeno effect. We believe that this is an important variation of a topologically protected qubit which is tunable.

Charged lepton flavor violation in light of the muon magnetic moment anomaly and colliders

Any observation of charged lepton flavor violation (CLFV) implies the existence of new physics beyond the SM in charged lepton sector. CLFV interactions may also contribute to the muon magnetic moment and explain the discrepancy between the SM prediction and the recent muon g-2 precision measurement at Fermilab. We consider the most general SM gauge invariant Lagrangian of Delta L=0 bileptons with CLFV couplings and investigate the interplay of low-energy precision experiments and colliders in light of the muon magnetic moment anomaly. We go beyond previous work by demonstrating the sensitivity of the LHC, the MACE experiment, a proposed muonium-antimuonium conversion experiment, and a muon collider. Currently-available LHC data is already able to probe unexplored parameter space via the CLFV process pprightarrow gamma ^*/Z^*rightarrow ell _1^pm ell _1^pm ell _2^mp ell _2^mp .

Teleparallel gravity coupled to matter content from nonlinear electrodynamics with dyonic configuration

This paper considers a static, spherically symmetric spacetime in the context of teleparallel equivalent of General Relativity coupled to the matter content from nonlinear electrodynamics (NED) supported by gauge-invariant Lagrangians, seeking the feasibility of achieving nonsingular solutions. In this setup, the well-known NED solutions, i.e., the Bardeen and Hayward black holes (BHs) are first examined. Then, some specific dyonic configurations, involving both radial electric and magnetic fields, in the teleparallel gravity framework are analysed. For the special case of a Born-Infeld NED theory, a generalized dyonic Reissner–Nordstrom (RN) solution is obtained in terms of the radial coordinate which exhibits a singular behavior at the origin. Nonetheless, the appearance of a naked singularity is impossible in the adopted Born-Infeld (BI) spacetime. The location and size of horizons depend on the BI parameter, leading to the concept of a hairy BH. However, at infinity it is not distinguishable from a dyonic RNBH characterized only by global charges such as ADM mass, electric and magnetic charges.

Polarization tensor in de Sitter gauge gravity

The gauge theory of the de Sitter group, [Formula: see text], in the ambient space formalism has been considered in this paper. This method is important to construction of the de Sitter super-conformal gravity and Quantum gravity. [Formula: see text] gauge vector fields are needed which correspond to [Formula: see text] generators of the de Sitter group. Using the gauge-invariant Lagrangian, the field equations of these vector fields have been obtained. The gauge vector field solutions are recalled. By using these solutions, the spin-[Formula: see text] gauge potentials has been constructed. There are two possibilities for presenting this tensor field: rank-[Formula: see text] symmetric and mixed symmetry rank-[Formula: see text] tensor fields. To preserve the conformal transformation, a spin-[Formula: see text] field must be represented by a mixed symmetry rank-[Formula: see text] tensor field, [Formula: see text]. This tensor field has been rewritten in terms of a generalized polarization tensor field and a de Sitter plane wave. This generalized polarization tensor field has been calculated as a combination of vector polarization, [Formula: see text], and tensor polarization of rank-2, [Formula: see text], which can be used in the gravitational wave consideration. There is a certain extent of arbitrariness in the choice of this tensor and we fix it in such a way that, in the limit, [Formula: see text], one obtains the polarization tensor in Minkowski spacetime. It has been shown that under some simple conditions, the spin-[Formula: see text] mixed symmetry rank-[Formula: see text] tensor field can be simultaneously transformed by unitary irreducible representation of de Sitter and conformal groups ([Formula: see text]).

Revealing hidden symmetries and gauge invariance of the massive Carroll-Field-Jackiw model

In this paper we have analyzed the improved version of the Gauge Unfixing (GU) formalism of the massive Carroll-Field-Jackiw model, which breaks both the Lorentz and gauge invariances, to disclose hidden symmetries to obtain gauge invariance, the key stone of the Standard Model. In this process, as usual, we have converted this second-class system into a first-class one and we have obtained two gauge invariant models. We have verified that the Poisson brackets involving the gauge invariant variables, obtained through the GU formalism, coincide with the Dirac brackets between the original second-class variables of the phase space. Finally, we have obtained two gauge invariant Lagrangians where one of them represents the Stückelberg form.

Conformal Totally Symmetric Arbitrary Spin Fermionic Fields

Conformal totally symmetric arbitrary spin fermionic fields propagating in the flat space-time of even dimension d ≥ 4 are investigated. A first-derivative metric-like formulation involving the Fang-Fronsdal kinetic operator for such fields is developed. A gauge invariant Lagrangian and the corresponding gauge transformations are obtained. The gauge symmetries of the Lagrangian are realized by using auxiliary fields and the Stückelberg fields. A realization of the conformal algebra symmetries on the space of conformal gauge fermionic fields is obtained. The on-shell degrees of freedom of the fermionic arbitrary spin conformal fields are also studied.

Variational formulation of compressible hydrodynamics in curved spacetime and symmetry of stress tensor

Hydrodynamics of the non-relativistic compressible fluid in the curved spacetime is derived using the generalized framework of the stochastic variational method (SVM) for continuum medium. The fluid-stress tensor of the resultant equation becomes asymmetric for the exchange of the indices, different from the standard Euclidean one. Its incompressible limit suggests that the viscous term should be represented with the Bochner Laplacian. Moreover the modified Navier–Stokes–Fourier equation proposed by Brenner can be considered even in the curved spacetime. To confirm the compatibility with the symmetry principle, SVM is applied to the gauge-invariant Lagrangian of a charged compressible fluid and then the Lorentz force is reproduced as the interaction between the Abelian gauge fields and the viscous charged fluid.

Canonical quantization of massive symmetric rank-two tensor in string theory

The canonical quantization of a massive symmetric rank-two tensor in string theory, which contains two Stueckelberg fields, was studied. As a preliminary study, we performed a canonical quantization of the Proca model to describe a massive vector particle that shares common properties with the massive symmetric rank-two tensor model. By performing a canonical analysis of the Lagrangian, which describes the symmetric rank-two tensor, obtained by Siegel and Zwiebach (SZ) from string field theory, we deduced that the Lagrangian possesses only first class constraints that generate local gauge transformation. By explicit calculations, we show that the massive symmetric rank-two tensor theory is gauge invariant only in the critical dimension of open bosonic string theory, i.e., d=26. This emphasizes that the origin of local symmetry is the nilpotency of the Becchi-Rouet-Stora-Tyutin (BRST) operator, which is valid only in the critical dimension. For a particular gauge imposed on the Stueckelberg fields, the gauge-invariant Lagrangian of the SZ model reduces to the Fierz-Pauli Lagrangian of a massive spin-two particle. Thus, the Fierz-Pauli Lagrangian is a gauge-fixed version of the gauge-invariant Lagrangian for a massive symmetric rank-two tensor. By noting that the Fierz-Pauli Lagrangian is not suitable for studying massive spin-two particles with small masses, we propose the transverse-traceless (TT) gauge to quantize the SZ model as an alternative gauge condition. In the TT gauge, the two Stueckelberg fields can be decoupled from the symmetric rank-two tensor and integrated trivially. The massive spin-two particle can be described by the SZ model in the TT gauge, where the propagator of the massive spin-two particle has a well-defined massless limit.

Structure of Gauge-Invariant Lagrangians

The theory of gauge fields in Theoretical Physics poses several mathematical problems of interest in Differential Geometry and in Field Theory. Below, we tackle one of these problems: the existence of a finite system of generators of gauge-invariant Lagrangians and how to compute them. More precisely, if $$p:C\rightarrow M$$ is the bundle of connections on a principal G-bundle $$\pi :P\rightarrow M$$, and G is a semisimple connected Lie group, then a finite number $$L_1,\dotsc ,L_{N^\prime }$$ of gauge-invariant Lagrangians defined on $$J^1C$$ is proved to exist such that for any other gauge-invariant Lagrangian $$L\in C^\infty (J^1C)$$, there exists a function $$F\in C^\infty ({\mathbb {R}}^{N^\prime })$$, such that $$L=F(L_1,\dotsc ,L_{N^\prime })$$. Several examples are dealt with explicitly.

Sensitivity of future lepton colliders and low-energy experiments to charged lepton flavor violation from bileptons

The observation of charged lepton flavor violation is a clear sign of physics beyond the Standard Model (SM). In this work, we investigate the sensitivity of future lepton colliders to charged lepton flavor violation via on-shell production of bileptons, and compare their sensitivity with current constraints and future sensitivities of low-energy experiments. Bileptons couple to two charged leptons with possibly different flavors and are obtained by expanding the general SM gauge invariant Lagrangians with or without lepton number conservation. We find that future lepton colliders will provide complementary sensitivity to the charged-lepton-flavor-violating couplings of bileptons compared with low-energy experiments. The future improvements of muonium-antimuonium conversion, lepton flavor non-universality in leptonic {\tau} decays, electroweak precision observables and the anomalous magnetic moments of charged leptons will also be able to probe similar parameter space.

Violation of the Kluberg-Stern-Zuber theorem in SCET

A classic result, originally due to Kluberg-Stern and Zuber, states that operators that vanish by the classical equation of motion (eom) do not mix into “physical” operators. Here we show that and explain why this result does not hold in soft-collinear effective theory (SCET) for the renormalization of power-suppressed operators. We calculate the non-vanishing mixing of eom operators for the simplest case of N -jet operators with a single collinear field in every direction. The result implies that — for the computation of the anomalous dimension but not for on-shell matrix elements — there exists a preferred set of fields that must be used to reproduce the infrared singularities of QCD scattering amplitudes. We identify these fields and explain their relation to the gauge-invariant SCET Lagrangian. Further checks reveal another generic property of SCET beyond leading power, which will be relevant to resummation at the next-to-leading logarithmic level, the divergence of convolution integrals with the hard matching coefficients. We propose an operator solution that allows to consistently renormalize such divergences.

Massive conformal particles with non-Abelian charges from free U(2N,2N)-twistor dynamics: Quantization and coherent states

The inclusion of non-Abelian U(N) internal charges (other than the electric charge) into Twistor Theory is accomplished through the concept of “colored twistors” (ctwistors for short) transforming under the colored conformal symmetry U(2N,2N). In particular, we are interested in 2N-ctwistors describing colored spinless conformal massive particles with phase space U(2N,2N)∕U(2N)×U(2N). Penrose formulas for incidence relations are generalized to N>1. We propose U(2N)-gauge invariant Lagrangians for 2N-ctwistors and we quantize them through a bosonic representation, interpreting quantum states as particle–hole excitations above the ground state. The connection between the corresponding Hilbert (Fock-like with constraints) space and the carrier space of a discrete series representation of U(2N,2N) is established through a coherent state (holomorphic) representation.