Regularization of the fermion selfenergy and the electromagnetic vertex in the Yukawa model within lightfront dynamics
Abstract
In lightfront dynamics, the regularization of amplitudes by traditional cutoffs imposed on the transverse and longitudinal components of particle momenta corresponds to restricting the integration volume by a nonrotationally invariant domain. The result depends not only on the size of this domain (i.e., on the cutoff values), but also on its orientation determined by the position of the lightfront plane. Explicitly covariant formulation of lightfront dynamics allows us to parametrize the latter dependence in a very transparent form. If we decompose the regularized amplitude in terms of independent invariant amplitudes, extra (nonphysical) terms should appear, with spin structures which explicitly depend on the orientation of the lightfront plane. The number of form factors, i.e., the coefficients of this decomposition, therefore also increases. The spin1/2 fermion selfenergy is determined by three scalar functions, instead of the two standard ones, while for the elastic electromagnetic vertex the number of form factors increases from two to five. In the present paper we calculate perturbatively all these form factors in the Yukawa model. Then we compare the results obtained in the two following ways: (i) by using the lightfront dynamics graph technique rules directly; (ii) by integrating the corresponding Feynman amplitudes in terms ofmore »
 Authors:
 Lebedev Physical Institute, Leninsky Prospekt 53, 119991 Moscow (Russian Federation)
 Laboratoire de Physique Corpusculaire, Universite BlaisePascal, CNRS/IN2P3, 24 avenue des Landais, F63177 Aubiere Cedex (France)
 Publication Date:
 OSTI Identifier:
 21011105
 Resource Type:
 Journal Article
 Resource Relation:
 Journal Name: Physical Review. D, Particles Fields; Journal Volume: 75; Journal Issue: 4; Other Information: DOI: 10.1103/PhysRevD.75.045012; (c) 2007 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA)
 Country of Publication:
 United States
 Language:
 English
 Subject:
 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; AMPLITUDES; COMPARATIVE EVALUATIONS; ELECTROMAGNETISM; FERMIONS; FORM FACTORS; ORIENTATION; QUANTUM FIELD THEORY; SCALARS; SELFENERGY; SPIN
Citation Formats
Karmanov, V. A., Smirnov, A. V., and Mathiot, J.F. Regularization of the fermion selfenergy and the electromagnetic vertex in the Yukawa model within lightfront dynamics. United States: N. p., 2007.
Web. doi:10.1103/PHYSREVD.75.045012.
Karmanov, V. A., Smirnov, A. V., & Mathiot, J.F. Regularization of the fermion selfenergy and the electromagnetic vertex in the Yukawa model within lightfront dynamics. United States. doi:10.1103/PHYSREVD.75.045012.
Karmanov, V. A., Smirnov, A. V., and Mathiot, J.F. Thu .
"Regularization of the fermion selfenergy and the electromagnetic vertex in the Yukawa model within lightfront dynamics". United States.
doi:10.1103/PHYSREVD.75.045012.
@article{osti_21011105,
title = {Regularization of the fermion selfenergy and the electromagnetic vertex in the Yukawa model within lightfront dynamics},
author = {Karmanov, V. A. and Smirnov, A. V. and Mathiot, J.F.},
abstractNote = {In lightfront dynamics, the regularization of amplitudes by traditional cutoffs imposed on the transverse and longitudinal components of particle momenta corresponds to restricting the integration volume by a nonrotationally invariant domain. The result depends not only on the size of this domain (i.e., on the cutoff values), but also on its orientation determined by the position of the lightfront plane. Explicitly covariant formulation of lightfront dynamics allows us to parametrize the latter dependence in a very transparent form. If we decompose the regularized amplitude in terms of independent invariant amplitudes, extra (nonphysical) terms should appear, with spin structures which explicitly depend on the orientation of the lightfront plane. The number of form factors, i.e., the coefficients of this decomposition, therefore also increases. The spin1/2 fermion selfenergy is determined by three scalar functions, instead of the two standard ones, while for the elastic electromagnetic vertex the number of form factors increases from two to five. In the present paper we calculate perturbatively all these form factors in the Yukawa model. Then we compare the results obtained in the two following ways: (i) by using the lightfront dynamics graph technique rules directly; (ii) by integrating the corresponding Feynman amplitudes in terms of the lightfront variables. For each of these methods, we use two types of regularization: the transverse and longitudinal cutoffs, and the PauliVillars regularization. In the latter case, the dependence of amplitudes on the lightfront plane orientation vanishes completely provided enough PauliVillars subtractions are made.},
doi = {10.1103/PHYSREVD.75.045012},
journal = {Physical Review. D, Particles Fields},
number = 4,
volume = 75,
place = {United States},
year = {Thu Feb 15 00:00:00 EST 2007},
month = {Thu Feb 15 00:00:00 EST 2007}
}

We consider the ground state in a model with scalar nucleons and a meson using the formalism of lightfront dynamics. Lightfront potentials for twonucleon bound states are calculated using two approaches. First, lightfront timeordered perturbation theory is used to calculate one and twomesonexchange potentials. These potentials give results that agree well with the ladder and ladder plus crossed box BetheSalpeter spectra. Secondly, approximations that incorporate nonperturbative physics are used to calculate alternative onemesonexchange potentials. These nonperturbative potentials give better agreement with the spectra of the full nonperturbative groundstate calculation of our restricted model than the perturbative potentials. For lightly boundmore »

Spacelike and timelike pion electromagnetic form factor and Fock state components within the lightfront dynamics
The simultaneous investigation of the pion electromagnetic form factor in the space and timelike regions within a lightfront model allows one to address the issue of nonvalence components of the pion and photon wave functions. Our relativistic approach is based on a microscopic vectormesondominance model for the dressed vertex where a photon decays in a quarkantiquark pair, and on a simple parametrization for the emission or absorption of a pion by a quark. The results show an excellent agreement in the space like region up to 10 (GeV/c){sup 2}, while in timelike region the model produces reasonable results up tomore » 
Relativistic boundstate problem in the lightfront Yukawa model
We study the renormalization problem on the light front for the twofermion bound state in the (3+1)dimensional Yukawa model, working within the lowestorder TammDancoff approximation. In addition to traditional mass and wavefunction renormalization, new types of counterterms are required. These are nonlocal and involve arbitrary functions of the longitudinal momenta. Their appearance is consistent with general powercounting arguments on the light front. We estimate the arbitrary function'' in two ways: (1) by using perturbation theory as a guide and (2) by considering the asymptotic large transverse momentum behavior of the kernel in the boundstate equations. The latter method, as itmore » 
Lowestorder mass corrections for a (1+1)dimensional Yukawa model in lightfront perturbation theory
In this work we {ital explicitly} demonstrate the equivalence of covariant (Feynman) perturbation theory with noncovariant lightfront perturbation theory (LFPT) for lowestorder selfenergy corrections in the (1+1)dimensional Yukawa model. We also perform calculations in oldfashioned perturbation theory in the infinitemomentum frame (OFPT{sub {infinity}}) to elucidate the differences between LFPT and OFPT{sub {infinity}}. 
Yukawa radiative corrections to the triple selfcouplings of neutral CPeven Higgs bosons and to the H {sup {yields}} hh decay rate within the minimal supersymmetric standard model
Within the minimal supersymmetric standard model, four selfcouplings, {lambda}{sub hhh}, {lambda}{sub hhH}, {lambda}{sub hHH}, and {lambda}{sub HHH}, and the decay rate {gamma}(H {sup {yields}} hh) are calculated with allowance for oneloop corrections induced by the contribution of the t, b, and c quarks, the {tau} lepton, and the corresponding superpartners and with the aid of the onshell renormalization scheme. An analysis of the dependences of these features on tan{beta} and the mass of the A Higgs boson, M{sub A}, shows that, in a specific region of the modelparameter space, the calculated corrections can make a significant contribution to the couplingsmore »