Gauge Dependence Research Articles

On the relationship between gauge dependence and IR divergences in the \u210f-expansion of the effective potential

Perturbative calculations of the effective potential evaluated at a broken minimum, Vmin, are plagued by difficulties. It is hard to get a finite and gauge invariant result for Vmin. In fact, the methods proposed to deal with gauge dependence and ir divergences are orthogonal in their approaches. Gauge dependence is dealt with through the ℏ-expansion, which establishes and maintains a strict loop-order separation of terms. On the other hand, ir divergences seem to require a resummation that mixes the different loop orders. In this paper we test these methods on Fermi gauge Abelian Higgs at two loops. We find that the resummation procedure is not capable of removing all divergences. Surprisingly, the ℏ-expansion seems to be able to deal with both the divergences and the gauge dependence. In order to isolate the physical part of Vmin, we are guided by the separation of scales that motivated the resummation procedure; the key result is that only hard momentum modes contribute to Vmin.

Quark mass function from a one-gluon-exchange-type interaction in Minkowski space

We present first results for the quark mass function in Minkowski space in both the spacelike and timelike regions calculated from the same quark-antiquark interaction kernel used in the latest meson calculations using the Gross equation. This kernel consists of a Lorentz vector effective one-gluon-exchange-type interaction, a vector constant, and a mixed scalar-pseudoscalar covariant linear confining interaction that does not contribute to the mass function. We analyze the gauge dependence of our results, prove the gauge independence of the constituent quark mass and mass gap equation, and identify the Yennie gauge as the appropriate gauge to be used in CST calculations. We compare our results in the spacelike region to lattice QCD data and find good agreement.

Canonical energy and Hertz potentials for perturbations of Schwarzschild spacetime

Canonical energy is a valuable tool for analyzing the linear stability of black hole spacetimes; positivity of canonical energy for all perturbations implies mode stability, whereas the failure of positivity for any perturbation implies instability. Nevertheless, even in the case of 4D Schwarzschild spacetime—which is known to be stable—manifest positivity of the canonical energy is difficult to establish, due to the presence of constraints on the initial data as well as the gauge dependence of the canonical energy integrand. Consideration of perturbations generated by a Hertz potential would appear to be a promising way to improve this situation, since the constraints and gauge dependence are eliminated when the canonical energy is expressed in terms of the Hertz potential. We prove that the canonical energy of a metric perturbation of Schwarzschild that is generated by a Hertz potential is positive. We relate the energy quantity arising in the linear stability proof of Dafermos, Holzegel and Rodnianski (DHR) to the canonical energy of an associated metric perturbation generated by a Hertz potential. We also relate the Regge–Wheeler variable of DHR to the ordinary Regge–Wheeler and twist potential variables of the associated perturbation. Since the Hertz potential formalism can be generalized to a Kerr black hole, our results may be useful for the analysis of the linear stability of Kerr.

Gauge invariance and origin independence of electronic charge density and current density induced by optical fields.

Expressions for the first-order polarization charge density ρ (1) and current density J (1) induced in a molecule by a monochromatic plane wave, obtained by time-dependent quantum mechanical perturbation theory, have been investigated to assess their gauge invariance and independence of the coordinate system in passive and active translations. The conditions arrived at show that, within the (long wavelengths) dipole approximation, only the electric contributions to these densities are needed to rationalize the phenomenology. To the next higher quadrupole approximation, assuming that the magnetic field and the electric field gradient are uniform over the molecular dimensions, corresponding contributions to ρ (1) and J (1) are considered. It has been found that total densities are independent of the origin, whereas the contributions from electric and magnetic fields are not separately invariant. A magnetic contribution to J (1), which is by itself origin independent, can be defined by means of an approach based on continuous translation of the origin of the coordinate system.

Gauge dependence of the one-loop divergences in 6D, [formula omitted] abelian theory

We study the gauge dependence of the one-loop effective action for the abelian 6D, N=(1,0) supersymmetric gauge theory formulated in harmonic superspace. We introduce the superfield ξ-gauge, construct the corresponding gauge superfield propagator, and calculate the one-loop two- and three-point Green functions with two external hypermultiplet legs. We demonstrate that in the general ξ-gauge the two-point Green function of the hypermultiplet is divergent, as opposed to the Feynman gauge ξ=1. The three-point Green function with two external hypermultiplet legs and one leg of the gauge superfield is also divergent. We verified that the Green functions considered satisfy the Ward identity formulated in N=(1,0) harmonic superspace and that their gauge dependence vanishes on shell. Using the result for the two- and three-point Green functions and arguments based on the gauge invariance, we present the complete divergent part of the one-loop effective action in the general ξ-gauge.

Gauge dependence of tadpole and mass renormalization for a seesaw extended 2HDM

We study the gauge dependence of the neutrino mass renormalization in a two Higgs doublet model, that is extended with one singlet seesaw neutrino. This model gives only one light neutrino a mass at tree level, while the second light mass is generated at loop level via the interaction with the second Higgs doublet. At one loop level, one neutrino stays massless. We use multiplicative renormalization constants to define counterterms. The renormalized mass parameters are defined as the complex poles of the propagators, using the complex mass scheme for mass renormalization. With this setup, we analytically get the expressions for the neutrino mass counterterms and isolate the gauge dependent part. We show, how relating this gauge dependent part with the tadpole renormalization leads to gauge independent counterterm definitions, hence gauge independent bare masses for neutrinos.

Localization of the Standard Model via the Higgs mechanism and a finite electroweak monopole from non-compact five dimensions

We propose a minimal and self-contained model in non-compact flat five dimensions which localizes the Standard Model (SM) on a domain wall. Localization of gauge fields is achieved by the condensation of Higgs field via a Higgs dependent gauge kinetic term in five-dimensional Lagrangian. The domain wall connecting vacua with unbroken gauge symmetry drives the Higgs condensation which provides both electroweak symmetry breaking and gauge field localization at the same time. Our model predicts higher-dimensional interactions $|H|^{2n}(F_{\mu\nu})^2$ in the low-energy effective theory. This leads to two expectations: The one is a new tree-level contribution to $H \to \gamma\gamma$ ($H \to gg$) decay whose signature is testable in future LHC experiment. The other is a finite electroweak monopole which may be accessible to the MoEDAL experiment. Interactions of translational Nambu-Goldstone boson is shown to satisfy a low-energy theorem.

One-loop renormalized Higgs boson vertices in the Georgi-Machacek model

We compute renormalized vertices of the 125 GeV Higgs boson $h$ with the weak gauge bosons ($hVV$), fermions ($hf\bar{f}$) and itself ($hhh$) in the Georgi-Machacek model at one-loop level. The renormalization is performed based on the on-shell scheme with the use of the minimal subtraction scheme only for the $hhh$ vertex. We explicitly show the gauge dependence in the counterterms of the scalar mixing parameters in the general $R_\xi$ gauge, and that the dependence can be removed by using the pinch technique in physical scattering processes. We then discuss the possible allowed deviations in these one-loop corrected Higgs couplings from the standard model predictions by scanning model parameters under the constraints of perturbative unitarity and vacuum stability as well as those from experimental data.

H-COUP: A program for one-loop corrected Higgs boson couplings in non-minimal Higgs sectors

We describe a numerical calculation tool H-COUP33The webpage of H-COUP is given in http://www-het.phys.sci.osaka-u.ac.jp/~kanemu/HCOUP_HP1013/HCOUP_HP.html, where one can download the set of source files of H-COUP_1.0. written in Fortran, which provides one-loop electroweak corrected vertices for the discovered Higgs boson h(125) in various Higgs sectors. The renormalization is based on the improved on-shell scheme without gauge dependence. In the first version H-COUP_1.0, the following models are included, namely, the Higgs singlet model, four types (Type-I, Type-II, Type-X, Type-Y) of two Higgs doublet models with a softly-broken Z2 symmetry and the inert doublet model. We first briefly introduce these models and then explain how to install and run this tool in an individual machine. A sample of numerical outputs is provided for user information. Program summaryProgram title: H-COUPProgram Files doi: http://dx.doi.org/10.17632/f88szmrj5x.1Licensing provisions: GPLv3Programming language: Fortran90Nature of problem: One-loop electroweak corrected vertices for the discovered Higgs boson h(125) are numerically calculated in the Higgs singlet model, four types (Type-I, Type-II, Type-X, Type-Y) of two Higgs doublet models with a softly-broken Z2 symmetry and the inert doublet model. The renormalization is based on the improved on-shell scheme without gauge dependence. Loop induced decay rates, i.e., h→γγ, h→Zγ and h→gg are also computed in these extended Higgs sectors at leading order.Solution method: All one-loop integrals for one-, two- and three-point functions are analytically expressed by using Passarino–Veltman functions in a systematic way, and their numerical values are calculated through the LoopTools. One-loop corrected h(125) vertices are then numerically provided in terms of form factors which are obtained by decomposing their Lorentz structure.Additional comments including restrictions and unusual features: In the version 1.0, QCD corrections are not included in the calculation of the h(125) vertices as well as the loop induced decay rates. In addition, the total width, decay branching ratios and cross sections are not outputted automatically. Details of these issues are described in Sec. VII of this manual.

Radiatively induced neutrino mass model with flavor dependent gauge symmetry

We study a radiative seesaw model at one-loop level with a flavor dependent gauge symmetry U(1)μ−τ, in which we consider bosonic dark matter. We also analyze the constraints from lepton flavor violations, muon g−2, relic density of dark matter, and collider physics, and carry out numerical analysis to search for allowed parameter region which satisfy all the constraints and to investigate some predictions. Furthermore we find that a simple but adhoc hypothesis induces specific two zero texture with inverse mass matrix, which provides us several predictions such as a specific pattern of Dirac CP phase.

A survey of inkjet-printed low-cost sensors

Abstract Inkjet-printers from the company Epson and others can be used to fabricate low-cost sensors on coated PET films. By using nanoparticle-based dispersions resistive temperature dependent sensors, strain gauges, thermocouples and pressure sensors can be fabricated. For these purposes the gauge factors, Seebeck coefficients and temperature coefficients of resistance for Ag, Carbon Black and PEDOT:PSS dispersions on Mitsubishi® and Pelikan® PET substrates are characterized. Furthermore, piezoresistive effects in transverse and longitudinal strain directions are discussed. Additionally, a printed sensor system for measuring strains within a surface is presented. Finally, an injection-moulding process and a lamination process are used to improve the mechanical scratching of those sensors.

Artificial magnetic-field quenches in synthetic dimensions

Recent cold atom experiments have realized models where each hyperfine state at an optical lattice site can be regarded as a separate site in a synthetic dimension. In such synthetic ribbon configurations, manipulation of the transitions between the hyperfine levels provide direct control of the hopping in the synthetic dimension. This effect was used to simulate a magnetic field through the ribbon. Precise control over the hopping matrix elements in the synthetic dimension makes it possible to change this artificial magnetic field much faster than the time scales associated with atomic motion in the lattice. In this paper, we consider such a magnetic flux quench scenario in synthetic dimensions. Sudden changes have not been considered for real magnetic fields as such changes in a conducting system would result in large induced currents. Hence, we first study the difference between a time varying real magnetic field and an artificial magnetic field using a minimal six site model. This minimal model clearly shows the connection between gauge dependence and the lack of on site induced scalar potential terms. We then investigate the dynamics of a wavepacket in an infinite two or three leg ladder following a flux quench and find that the gauge choice has a dramatic effect on the packet dynamics. Specifically, a wavepacket splits into a number of smaller packets. Both the weights and the number of packets depend on the implemented gauge. If an initial packet, prepared under zero flux in a n--leg ladder, is quenched to Hamiltonian with a vector potential parallel to the ladder; it splits into at most $n$ smaller wavepackets. The same initial packet splits up to $n^2$ packets if the vector potential is implemented to be along the rungs. Finally, we show that edge states in a thick ribbon are robust under the quench only when the same gap supports an edge state for the final Hamiltonian.

Renormalization scheme and gauge (in)dependence of the generalized Crewther relation: what are the real grounds of the \u03b2-factorization property?

The problem of scheme and gauge dependence of the factorization property of the renormalization group β-function in the SU(Nc) QCD generalized Crewther relation (GCR), which connects the flavor non-singlet contributions to the Adler and Bjorken polarized sum rule functions, is investigated at the mathcal{O}left({a}_s^4right) level of perturbation theory. It is known that in the gauge-invariant renormalization overline{mathrm{MS}} -scheme this property holds in the QCD GCR at least at this order. To study whether this factorization property is true in all gauge-invariant schemes, we consider the MS-like schemes in QCD and the QED-limit of the GCR in the overline{mathrm{MS}} -scheme and in two other gauge-independent subtraction schemes, namely in the momentum MOM and the on-shell OS schemes. In these schemes we confirm the existence of the β-function factorization in the QCD and QED variants of the GCR. The problem of the possible β-factorization in the gauge-dependent renormalization schemes in QCD is studied. To investigate this problem we consider the gauge non-invariant mMOM and MOMgggg-schemes. We demonstrate that in the mMOM scheme at the mathcal{O}left({a}_s^3right) level the β-factorization is valid for three values of the gauge parameter ξ only, namely for ξ = −3, −1 and ξ = 0. In the mathcal{O}left({a}_s^4right) order of PT it remains valid only for case of the Landau gauge ξ = 0. The consideration of these two gauge-dependent schemes for the QCD GCR allows us to conclude that the factorization of RG β-function will always be implemented in any MOM-like renormalization schemes with linear covariant gauge at ξ = 0 and ξ = −3 at the mathcal{O}left({a}_s^3right) approximation. It is demonstrated that if factorization property for the MS-like schemes is true in all orders of PT, as theoretically indicated in the several works on the subject, then the factorization will also occur in the arbitrary MOM-like scheme in the Landau gauge in all orders of perturbation theory as well.

Gauge and parametrization ambiguity in quantum gravity

The gauge and parametrization dependence is discussed in quantum gravity in an arbitrary dimension $D$. Explicit one-loop calculations are performed within the most general parametrization of quantum metric with seven arbitrary parameters. On the other hand, some of the gauge fixing parameters are fixed to make the calculations relatively simple. We confirm the general theorem stating that the on-shell local terms in the one-loop effective action are independent on the gauge and parametrization ambiguity.

Two-probe versus van der Pauw method in studying the piezoresistivity of single-wall carbon nanotube thin films

The use of the van der Pauw (VDP) method for characterizing and evaluating the piezoresistive behavior of carbon nanomaterial enabled piezoresistive sensors have not been systematically studied. By using single-wall carbon nanotube (SWCNT) thin films as a model system, herein we report a coupled electrical-mechanical experimental study in conjunction with a multiphysics finite element simulation as well as an analytic analysis to compare the two-probe and VDP testing configuration in evaluating the piezoresistive behavior of carbon nanomaterial enabled piezoresistive sensors. The key features regarding the sample aspect ratio dependent piezoresistive sensitivity or gauge factor were identified for the VDP testing configuration. It was found that the VDP test configuration offers consistently higher piezoresistive sensitivity than the two-probe testing method.

On gauge dependence of gravitational waves from a first-order phase transition in classical scale-invariant U(1)′ models

We study gauge dependence of gravitational waves produced from a first-order phase transition in classical scale-invariant U(1)′ models. Accidental gauge independence of the one-loop effective potential in this class of models is spoiled by including thermal resummation. The gauge artifact in the resummed effective potential propagates to the gravitational wave spectrum and results in one order of magnitude uncertainties in the prediction under a specific gauge choice.

Emergence of electromotive force by time dependent gauge fields in monolayer graphene

We propose a valley-dependent electromotive force in a graphene device based on a deformed graphene in the presence of magnetic field. The coexistence of the strain and magnetic field in the presented mechanism leads to a valley dependent electromotive force in zero Fermi energy. In the non-zero Fermi energies strain alone could induce a valley dependent electromotive force while the magnetic field alone could not induce any electromotive force in zero and any level of Fermi energy. The calculations are based on the Berry curvature approaches.

Composite operators in functional renormalization group approach

The gauge dependence problem of the effective action for general gauge theories in the framework of a modified functional renormalization group approach proposed recently is studied. It is shown that the effective action remains gauge-dependent on-shell.

Renormalization schemes for the Two-Higgs-Doublet Model and applications to h \u2192 WW/ZZ \u2192 4 fermions

We perform the renormalization of different types of Two-Higgs-Doublet Models for the calculation of observables at next-to-leading order. In detail, we suggest four different renormalization schemes based on on-shell renormalization conditions as far as possible and on overline{mathrm{MS}} prescriptions for the remaining field-mixing parameters where no distinguished on-shell condition exists and make contact to existing schemes in the literature. In particular, we treat the tadpole diagrams in different ways and discuss issues of gauge independence and perturbative stability in the considered schemes. The renormalization group equations for the overline{mathrm{MS}} parameters are solved in each scheme, so that a consistent renormalization scale variation can be performed. We have implemented all Feynman rules including counterterms and the renormalization conditions into a FeynArts model file, so that amplitudes and squared matrix elements can be generated automatically. As an application we compute the decay of the light, CP-even Higgs boson of the Two-Higgs-Doublet Model into four fermions at next-to-leading order. The comparison of different schemes and the investigation of the renormalization scale dependence allows us to test the perturbative consistency in each of the renormalization schemes, and to get a better estimate of the theoretical uncertainty that arises due to the truncation of the perturbation series.

Gauge invariant one-loop corrections to Higgs boson couplings in nonminimal Higgs models

We comprehensively evaluate renormalized Higgs boson couplings at one-loop level in non-minimal Higgs models such as the Higgs Singlet Model (HSM) and the four types of Two Higgs Doublet Models (THDMs) with a softly-broken $Z_2$ symmetry. The renormalization calculation is performed in the on-shell scheme improved by using the pinch technique to eliminate the gauge dependence in the renormalized couplings. We first review the pinch technique for scalar boson two-point functions in the Standard Model (SM), the HSM and the THDMs. We then discuss the difference in the results of the renormalized Higgs boson couplings between the improved on-shell scheme and the ordinal one with a gauge dependence appearing in mixing parameters of scalar bosons. Finally, we widely investigate how we can identify the HSM and the THDMs focusing on the pattern of deviations in the renormalized Higgs boson couplings from predictions in the SM.