Gauge Dependence Research Articles

Spin‐charge rotating local reference frames: a unified U(2) = U(1) ⊗ SU(2) approach to the interacting electrons

AbstractA spin‐charge unifying description for the Hubbard model based on the time dependent local gauge transformations is developed. The collective variables for charge and spin are isolated in the form of the space‐time fluctuating U(1) phase field and rotating spin quantization axis governed by the SU(2) symmetry, respectively. As a result interacting electrons appear as a composite objects consisting of bare fermions with attached U(1) and SU(2) gauge fields. We elaborate on the microscopic origins of the effective action with the Coulomb interaction that contain topological theta terms. Furthermore, we unravel the link between non‐trivial multiply‐connected topological structure of the U(2) = U(1) ⊗ SU(2) configurational space for gauge fields and the instanton contribution to the statistical sum. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

New results for light gravitinos at hadron colliders: Fermilab Tevatron limits and CERN LHC perspectives

We derive Feynman rules for the interactions of a single gravitino with (s)quarks and gluons/gluinos from an effective supergravity Lagrangian in nonderivative form and use them to calculate the hadroproduction cross sections and decay widths of single gravitinos. We confirm the results obtained previously with a derivative Lagrangian as well as those obtained with the nonderivative Lagrangian in the high-energy limit and elaborate on the connection between gauge independence and the presence of quartic vertices. We perform extensive numerical studies of branching ratios, total cross sections, and transverse-momentum spectra at the Fermilab Tevatron and the CERN LHC. From the latest CDF monojet cross section limit, we derive a new and robust exclusion contour in the gravitino-squark/gluino mass plane, implying that gravitinos with masses below $2\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}5}$ to $1\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}5}\text{ }\text{ }\mathrm{eV}$ are excluded for squark/gluino masses below 200 and 500 GeV, respectively. These limits are complementary to the one obtained by the CDF Collaboration, $1.1\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}5}\text{ }\text{ }\mathrm{eV}$, under the assumption of infinitely heavy squarks and gluinos. For the LHC, we conclude that supersymmetric scenarios with light gravitinos will lead to a striking monojet signal very quickly after its startup.

Bias adjustment and long‐term verification of radar‐based precipitation estimates

AbstractQuantitative precipitation estimates (QPE) based on weather radar observations are used more and more for water management, in numerical weather prediction models, and for monitoring of severe weather. A straightforward method for bias adjustment of radar‐based and hourly‐updated precipitation accumulations is described. In addition a long‐term verification of the bias‐adjusted composites over a six year period using dependent and independent gauge data is presented. It is found that the adjustment scheme effectively removes the mean‐field bias from the raw accumulations. The adjustment method cannot correct for a range‐dependent bias and therefore it is recommended to also use a simple vertical profile of reflectivity (VPR) adjustment procedure. Copyright © 2007 Royal Meteorological Society

Gauge dependence of the critical dynamics at the superconducting phase transition

The critical dynamics of superconductors in the charged regime is reconsidered within field-theory. For the dynamics the Ginzburg-Landau model with complex order parameter coupled to the gauge field suggested earlier [Lannert et al. Phys. Rev. Lett. 92, 097004 (2004)] is used. Assuming relaxational dynamics for both quantities the renormalization group functions within one loop approximation are recalculated for different choices of the gauge. A gauge independent result for the divergence of the measurable electric conductivity is obtained only at the weak scaling fixed point unstable in one loop order where the time scales of the order parameter and the gauge field are different.

Bilepton effects on theWWV*vertex in the 331 model with right-handed neutrinos via aSUL(2)×UY(1)covariant quantization scheme

In a recent paper [J. Montano, F. Ram\'{\i}rez-Zavaleta, G. Tavares-Velasco, and J. J. Toscano, Phys. Rev. D 72, 055023 (2005).], we investigated the effects of the massive charged gauge bosons (bileptons) predicted by the minimal 331 model on the off-shell vertex $WW{V}^{*}$ ($V=\ensuremath{\gamma}$, $Z$) using a $S{U}_{L}(2)\ifmmode\times\else\texttimes\fi{}{U}_{Y}(1)$ covariant gauge-fixing term for the bileptons. We proceed along the same lines and calculate the effects of the gauge bosons predicted by the 331 model with right-handed neutrinos. It is found that the bilepton effects on the $WW{V}^{*}$ vertex are of the same order of magnitude as those arising from the standard model and several of its extensions, provided that the bilepton mass is of the order of a few hundred of GeVs. For heavier bileptons, their effects on the $WW{V}^{*}$ vertex are negligible. The behavior of the form factors at high energies is also discussed as it is a reflection of the gauge invariance and gauge independence of the $WW{V}^{*}$ Green function obtained via our quantization method.

Gauge dependence of the strong-field approximation: Theory vs. experiment for photodetachment of F −

The dependence of the strong-field approximation on the gauge used for the description of the driving laser field is reviewed in connection with the choice of the initial bound state of the unperturbed atom or ion. Electron energy spectra are calculated for the various combinations of gauge and wave function and compared with experimental data for photodetachment of F − by a circularly polarized laser field [B. Bergues, Y. Ni, H. Helm, I. Yu. Kiyan, Phys. Rev. Lett. 95 (2005) 263002]. If the laser intensity is considered a fitting parameter, then our length-gauge results reproduce the experimental results very well. In contrast, in velocity gauge no satisfactory fit can be obtained for any intensity.

Gauge Covariance and the Chiral Condenate in QED3

The ambiguities associated with the lack of gauge invariance in the non-perturbative truncations of Schwinger-Dyson equations (SDEs) are a challenging problem which has not yet been resolved in a decisive fashion. Pursuing this aim, we study dynamical chiral symmetry breaking in quantum electrodynamics in three space-time dimensions (QED3). We investigate the gauge dependence of the chiral condensate both in the quenched and the unquenched versions of the theory and emphasize the importance of taking into account the gauge covariance properties of the fermion propagator as dictated by its Landau-Khalatnikov-Fradkin transformation (LKFT). We present numerical solutions of the SDE of the fermion propagator which respect Ward-Green-Takahashi identities (WGTI) and LKFT simultaneously. As a striking consequence, we obtain a practically gauge independent chiral condensate.

Relativistic many-body calculations of electric-dipole lifetimes, rates and oscillator strengths of Δn = 0 transitions between 3l−14l′ states in Ni-like ions

Transition rates, oscillator strengths and line strengths are calculated for electric-dipole (E1) transitions between odd-parity 3s23p63d94l1, 3s23p53d104l2 and 3s3p63d104l1 states and even-parity 3s23p63d94l2, 3s23p53d104l1 and 3s3p63d104l2 (with 4l1 = 4p, 4f and 4l2 = 4s, 4d) in Ni-like ions with the nuclear charges ranging from Z = 34 to 100. Relativistic many-body perturbation theory (RMBPT), including the Breit interaction, is used to evaluate retarded E1 matrix elements in length and velocity forms. The calculations start from a 1s22s22p63s23p63d10 Dirac–Fock potential. First-order RMBPT is used to obtain intermediate coupling coefficients and second-order RMBPT is used to calculate transition matrix elements. Contributions from negative-energy states are included in the second-order E1 matrix elements to ensure the gauge independence of transition amplitudes. Transition energies used in the calculation of oscillator strengths and transition rates are from second-order RMBPT. Lifetimes of the 3s23p63d94d levels are given for Z = 34–100. These atomic data are important in modelling of M-shell radiation spectra of heavy ions generated in electron beam ion trap experiments and in M-shell diagnostics of plasmas.

UNDERLYING GAUGE SYMMETRIES OF SECOND-CLASS CONSTRAINTS SYSTEMS

Gauge-invariant systems in unconstrained configuration and phase spaces, equivalent to second-class constraints systems upon a gauge-fixing, are discussed. A mathematical pendulum on an (n-1)-dimensional sphere Sn-1 as an example of a mechanical second-class constraints system and the O(n) nonlinear sigma model as an example of a field theory under second-class constraints are discussed in details and quantized using the existence of underlying dilatation gauge symmetry and by solving the constraint equations explicitly. The underlying gauge symmetries involve, in general, velocity dependent gauge transformations and new auxiliary variables in extended configuration space. Systems under second-class holonomic constraints have gauge-invariant counterparts within original configuration and phase spaces. The Dirac's supplementary conditions for wave functions of first-class constraints systems are formulated in terms of the Wigner functions which admit, as we show, a broad set of physically equivalent supplementary conditions. Their concrete form depends on the manner the Wigner functions are extrapolated from the constraint submanifolds into the whole phase space.

Gauge Dependence of Gravitational Correction to Running of Gauge Couplings

Recently an interesting idea has been put forward by Robinson and Wilczek that the incorporation of quantized gravity in the framework of Abelian and non-Abelian gauge theories results in a correction to the running of gauge coupling and, as a consequence, increase the grand unification scale and asymptotic freedom. In this Letter it is shown by explicit calculations that this correction depends on the choice of gauge.

REFINEMENTS IN EFFECTIVE POTENTIAL CALCULATIONS IN THE MSSM

The one-loop effective potential is a powerful tool in studying the electroweak symmetry breaking of supersymmetric theories, whose precise calculation may have important phenomenological consequences. In this work, we are correctly treating the contribution of the Higgs sector to the effective potential and refine the radiative corrections to the Higgs mixing parameter μ, which is known to affect greatly the supersymmetric spectrum. Working at the average stop scale to minimize the effect of the stop sector, we find additional corrections which can play a dominant role in the focus point region of the parameter space of the MSSM. The comparison of our results with those of the literature is discussed. We also discuss the gauge dependence of the effective potential and its effect on the μ parameter in analyses where this is determined from the one-loop minimization conditions of the effective potential.

Simple on-shell renormalization framework for the Cabibbo-Kobayashi-Maskawa matrix

We present an explicit on-shell framework to renormalize the Cabibbo-Kobayashi-Maskawa (CKM) quark mixing matrix at the one-loop level. It is based on a novel procedure to separate the external-leg mixing corrections into gauge-independent self-mass (sm) and gauge-dependent wave-function renormalization contributions, and to adjust nondiagonal mass counterterm matrices to cancel all the divergent sm contributions, and also their finite parts subject to constraints imposed by the Hermiticity of the mass matrices. It is also shown that the proof of gauge independence and finiteness of the remaining one-loop corrections to $W\ensuremath{\rightarrow}{q}_{i}+{\overline{q}}_{j}$ reduces to that in the unmixed, single-generation case. Diagonalization of the complete mass matrices leads then to an explicit expression for the CKM counterterm matrix, which is gauge independent, preserves unitarity, and leads to renormalized amplitudes that are nonsingular in the limit in which any two fermions become mass degenerate.

Effective theory of Wilson lines and deconfinement

To study the deconfining phase transition at nonzero temperature, I outline the perturbative construction of an effective theory for straight, thermal Wilson lines. Certain large, time dependent gauge transformations play a central role. They imply the existence of interfaces, which can be used to determine the form of the effective theory as a gauged, nonlinear sigma model of adjoint matrices. Especially near the transition, the Wilson line may undergo a Higgs effect. As an adjoint field, this can generate eigenvalue repulsion in the effective theory.

Form factors and branching ratio for the B→lνγ decay

Form factors parameterizing radiative leptonic decays of heavy mesons (B+→γl+νl) against photon energy are computed in the language of dispersion relations. The states contributing to the absorptive part in the dispersion relation are the multiparticle continuum, estimated by the quark triangle graph, and resonances with quantum numbers 1- and 1+, which includes B* and BA * and their radial excitations, which model the higher state contributions. Constraints provided by the asymptotic behavior of the structure dependent amplitude, Ward identities and gauge invariance are used to provide useful information for the parameters needed. The couplings gBB*γ and fBBA*γ are predicted as we restrict ourselves to the first radial excitation; otherwise using these as an input the radiative decay coupling constants for the radial excitations are predicted. The value of the branching ratio for the process B+→γμ+νμ is found to be in the range 0.5×10-6. A detailed comparison is given with other approaches.

WAVE FUNCTION RENORMALIZATION PRESCRIPTION OF UNSTABLE PARTICLE

We define four Wave function Renormalization Constants (WRCs) for unstable particles under the LSZ reduction formula. By CPT conservation law we obtain a new wave function renormalization condition and determine the four WRCs. By calculating the gauge dependence of the physical amplitudes we demonstrate the consistency of the current wave function renormalization prescription with the gauge theory in standard model. We also prove that the conventional wave function renormalization prescription leads to physical amplitudes of gauge dependent.

Quantum effective action in spacetimes with branes and boundaries: Diffeomorphism invariance

We construct a gauge-fixing procedure in the path integral for gravitational models with branes and boundaries. This procedure incorporates a set of gauge conditions which gauge away effectively decoupled diffeomorphisms acting in the $(d+1)$-dimensional bulk and on the $d$-dimensional brane. The corresponding gauge-fixing factor in the path integral factorizes as a product of the bulk and brane (surface-theory) factors. This factorization underlies a special bulk wavefunction representation of the brane effective action. We develop the semiclassical expansion for this action and explicitly derive it in the one-loop approximation. The one-loop brane effective action can be decomposed into the sum of the gauge-fixed bulk contribution and the contribution of the pseudodifferential operator of the brane-to-brane propagation of quantum gravitational perturbations. The gauge dependence of these contributions is analyzed by the method of Ward identities. By the recently suggested method of the Neumann-Dirichlet reduction the bulk propagator in the semiclassical expansion is converted to the Dirichlet boundary conditions preferable from the calculational viewpoint.

Radiative atomic processes and Galilean and gauge transformations

Radiative atomic processes, in which charged particles moving with velocities much less than the speed of light emit a photon, are normally considered by using the Schrödinger equation. By analysing the transformation properties of the radiative transition amplitudes under the change of a reference frame we establish that the total cross sections and decay rates, calculated with the Schrödinger equation, are Galilean invariant and that this invariance holds irrespective of the accuracy of wavefunctions describing the charged particles. By considering, within the scope of one reference frame, the radiative processes for two identical atomic systems which have different translational (centre-of-mass) velocities we show that the total cross sections and decay rates in general depend on this velocity if approximate wavefunctions are employed and that this is the direct consequence of the problem of gauge dependence. We also present a detailed discussion of the intimate interrelation between Galilean and gauge transformations which, if overlooked, can easily lead to the misinterpretation of the problem of gauge dependence as the ‘problem of Galilean non-invariance’.

Higher-dimensional knotlike topological defects in local non-Abelian topological tensor currents

We present the novel topological tensor currents to describe the infinitesimal thin higher-dimensional topological defects in the local SO(n) gauge theory. The topological quantization of defects and the inner structure of the currents are obtained. As the generalization of Nielsen-Olesen local U(1) field theory for Nambu string, the local SO(n) gauge-invariant Lagrangian and the motion equation of the higher-dimensional topological defects are derived. Moreover, for closed defects, we study their important topological configuration, i.e., the higher-dimensional knotlike structures. Using the topological tensor currents and their preimages, we construct a series of metric independent integrals and prove their gauge independence. Similar to the helicity integral characterizing one-dimensional knotlike vortex filament, these topological invariants are evaluated to the generalized linking numbers of higher-dimensional knotlike defects.

The condensate 〈(A µ 2 )〉 in commutative and noncommutative theories

It is shown that gauge invariance of the operator \int dx tr(A_{\mu}^{2}-\frac{2}{g \xi} x^{\nu} \theta_{\mu\nu} A^{\mu}) in noncommutative gauge theory does not lead to gauge independence of its vacuum condensate. Generalized Ward identities are obtained for Green's functions involving operator \underset{\Omega \to \infty}{lim}\frac{1}{\Omega} \int\limits_{\Omega} dx tr(A_{\mu}^{2}) in noncommutative and commutative gauge theories.

The suppression of neutralino annihilation into Zh

The Indirect Detection of neutralino Dark Matter is most promising through annihilation channels producing a hard energy spectrum for the detected particles, such as the neutralino annihilation into $Zh$. A cancellation however makes this particular annihilation channel generically subdominant in the huge parameter space of supersymmetric models. This cancellation requires non-trivial relations between neutralino mixings and masses, which we derive from gauge independence and unitarity of the MSSM. To show how the cancellation overshoots leaving only a subdominant result, we use a perturbative expansion in powers of the electroweak/supersymmetry breaking ratio $m_{Z}/m_{\chi}$.