357 research outputs found
The Three-point Function in Split Dimensional Regularization in the Coulomb Gauge
We use a gauge-invariant regularization procedure, called ``split dimensional
regularization'', to evaluate the quark self-energy and
quark-quark-gluon vertex function in the Coulomb
gauge, . The technique of split
dimensional regularization was designed to regulate Coulomb-gauge Feynman
integrals in non-Abelian theories. The technique which is based on two complex
regulating parameters, and , is shown to generate a
well-defined set of Coulomb-gauge integrals. A major component of this project
deals with the evaluation of four-propagator and five-propagator Coulomb
integrals, some of which are nonlocal. It is further argued that the standard
one-loop BRST identity relating and , should by rights be
replaced by a more general BRST identity which contains two additional
contributions from ghost vertex diagrams. Despite the appearance of nonlocal
Coulomb integrals, both and are local functions which
satisfy the appropriate BRST identity. Application of split dimensional
regularization to two-loop energy integrals is briefly discussed.Comment: Latex, 17 pages, 4 figures, uses epsf.sty, epsfig.sty; to appear in
Nuc. Phys.
Split dimensional regularization for the Coulomb gauge at two loops
We evaluate the coefficients of the leading poles of the complete two-loop
quark self-energy \Sigma(p) in the Coulomb gauge. Working in the framework of
split dimensional regularization, with complex regulating parameters \sigma and
n/2-\sigma for the energy and space components of the loop momentum,
respectively, we find that split dimensional regularization leads to
well-defined two-loop integrals, and that the overall coefficient of the
leading pole term for \Sigma(p) is strictly local. Extensive tables showing the
pole parts of one- and two-loop Coulomb integrals are given. We also comment on
some general implications of split dimensional regularization, discussing in
particular the limit \sigma \to 1/2 and the subleading terms in the
epsilon-expansion of noncovariant integrals.Comment: 32 pages Latex; figures replaced, text unchange
The light-cone gauge and the calculation of the two-loop splitting functions
We present calculations of next-to-leading order QCD splitting functions,
employing the light-cone gauge method of Curci, Furmanski, and Petronzio (CFP).
In contrast to the `principal-value' prescription used in the original CFP
paper for dealing with the poles of the light-cone gauge gluon propagator, we
adopt the Mandelstam-Leibbrandt prescription which is known to have a solid
field-theoretical foundation. We find that indeed the calculation using this
prescription is conceptionally clear and avoids the somewhat dubious
manipulations of the spurious poles required when the principal-value method is
applied. We reproduce the well-known results for the flavour non-singlet
splitting function and the N_C^2 part of the gluon-to-gluon singlet splitting
function, which are the most complicated ones, and which provide an exhaustive
test of the ML prescription. We also discuss in some detail the x=1 endpoint
contributions to the splitting functions.Comment: 41 Pages, LaTeX, 8 figures and tables as eps file
Scattering of Glue by Glue on the Light-cone Worldsheet II: Helicity Conserving Amplitudes
This is the second of a pair of articles on scattering of glue by glue, in
which we give the light-cone gauge calculation of the one-loop on-shell
helicity conserving scattering amplitudes for gluon-gluon scattering
(neglecting quark loops). The 1/p^+ factors in the gluon propagator are
regulated by replacing p^+ integrals with discretized sums omitting the p^+=0
terms in each sum. We also employ a novel ultraviolet regulator that is
convenient for the light-cone worldsheet description of planar Feynman
diagrams. The helicity conserving scattering amplitudes are divergent in the
infra-red. The infrared divergences in the elastic one-loop amplitude are shown
to cancel, in their contribution to cross sections, against ones in the cross
section for unseen bremsstrahlung gluons. We include here the explicit
calculation of the latter, because it assumes an unfamiliar form due to the
peculiar way discretization of p^+ regulates infrared divergences. In resolving
the infrared divergences we employ a covariant definition of jets, which allows
a transparent demonstration of the Lorentz invariance of our final results.
Because we use an explicit cutoff of the ultraviolet divergences in exactly 4
space-time dimensions, we must introduce explicit counterterms to achieve this
final covariant result. These counter-terms are polynomials in the external
momenta of the precise order dictated by power-counting. We discuss the
modifications they entail for the light-cone worldsheet action that reproduces
the ``bare'' planar diagrams of the gluonic sector of QCD. The simplest way to
do this is to interpret the QCD string as moving in six space-time dimensions.Comment: 56 pages, 21 figures, references added, minor typos correcte
Next-to-leading order Calculation of a Fragmentation Function in a Light-Cone Gauge
The short-distance coefficients for the color-octet ^3S_1 term in the
fragmentation function for a gluon to split into polarized heavy quarkonium
states are re-calculated to order alpha_s^2. The light-cone gauge remarkably
simplifies the calculation by eliminating many Feynman diagrams at the expense
of introducing spurious poles in loop integrals. We do not use any conventional
prescriptions for spurious pole. Instead, we only use gauge invariance with the
aid of Collins-Soper definition of the fragmentation function. Our result
agrees with a previous calculation of Braaten and Lee in the Feynman gauge, but
disagrees with another previous calculation.Comment: 16 pages, 4 figures, version published in Physical Review
Perturbation theory for the two-dimensional abelian Higgs model in the unitary gauge
In the unitary gauge the unphysical degrees of freedom of spontaneously
broken gauge theories are eliminated. The Feynman rules are simpler than in
other gauges, but it is non-renormalizable by the rules of power counting. On
the other hand, it is formally equal to the limit of the
renormalizable R-gauge. We consider perturbation theory to one-loop
order in the R-gauge and in the unitary gauge for the case of the
two-dimensional abelian Higgs model. An apparent conflict between the unitary
gauge and the limit of the R-gauge is resolved, and it is
demonstrated that results for physical quantities can be obtained in the
unitary gauge.Comment: 15 pages, LaTeX2e, uses the feynmf package, formulations correcte
- …