26 research outputs found
A Gribov equation for the photon Green's function
We present a derivation of the Gribov equation for the gluon/photon Green's
function D(q). Our derivation is based on the second derivative of the
gauge-invariant quantity Tr ln D(q), which we interpret as the gauge-boson
`self-loop'. By considering the higher-order corrections to this quantity, we
are able to obtain a Gribov equation which sums the logarithmically enhanced
corrections. By solving this equation, we obtain the non-perturbative running
coupling in both QCD and QED. In the case of QCD, alpha_S has a singularity in
the space-like region corresponding to super-criticality, which is argued to be
resolved in Gribov's light-quark confinement scenario. For the QED coupling in
the UV limit, we obtain a \propto Q^2 behaviour for space-like Q^2=-q^2. This
implies the decoupling of the photon and an NJLVL-type effective theory in the
UV limit.Comment: 12 pages, 5 figures; version to be published in Eur. Phys. J.
Impact of double-logarithmic electroweak radiative corrections on the non-singlet structure functions at small x
In the QCD context, the non-singlet structure functions of u and d -quarks
are identical, save the initial quark densities. Electroweak radiative
corrections, being flavor-dependent, bring further difference between the
non-singlets. This difference is calculated in the double-logarithmic
approximation and the impact of the electroweak corrections on the non-singlet
intercepts is estimated numerically.Comment: 17 pages, no figure
Critical Exponents from AdS/CFT with Flavor
We use the AdS/CFT correspondence to study the thermodynamics of massive N=2
supersymmetric hypermultiplet flavor fields coupled to N=4 supersymmetric
SU(Nc) Yang-Mills theory, formulated on curved four-manifolds, in the limits of
large Nc and large 't Hooft coupling. The gravitational duals are probe
D-branes in global thermal AdS. These D-branes may undergo a topology-changing
transition in the bulk. The D-brane embeddings near the point of the topology
change exhibit a scaling symmetry. The associated scaling exponents can be
either real- or complex-valued. Which regime applies depends on the
dimensionality of a collapsing submanifold in the critical embedding. When the
scaling exponents are complex-valued, a first-order transition associated with
the flavor fields appears in the dual field theory. Real scaling exponents are
expected to be associated with a continuous transition in the dual field
theory. For one example with real exponents, the D7-brane, we study the
transition in detail. We find two field theory observables that diverge at the
critical point, and we compute the associated critical exponents. We also
present analytic and numerical evidence that the transition expresses itself in
the meson spectrum as a non-analyticity at the critical point. We argue that
the transition we study is a true phase transition only when the 't Hooft
coupling is strictly infinite.Comment: 31 pages, 21 eps files in 12 figures; v2 added one reference and one
footnote, version published in JHE
Dirac sheets and gauge fixing in lattice gauge theory
Photon correlators in pure gauge theory for different lattice
actions are considered under the Lorentz gauge condition. They are shown to
depend strongly on the gauge fixing ambiguity and on the corresponding
existence of Dirac sheets. For the Coulomb phase a gauge fixing algorithm is
proposed which avoids Dirac sheets and allows to find the global extremum of
the non-local gauge condition. Sorry, figures are not included and can be sent
by ordinary mail.Comment: 11 pages preprint HU Berlin--IEP--93/2, June 199
Matching NLO parton shower matrix element with exact phase space: case of W -> l nu (gamma) and gamma^* -> pi^+pi^-(gamma)
The PHOTOS Monte Carlo is often used for simulation of QED effects in decay
of intermediate particles and resonances. Momenta are generated in such a way
that samples of events cover the whole bremsstrahlung phase space. With the
help of selection cuts, experimental acceptance can be then taken into account.
The program is based on an exact multiphoton phase space. Crude matrix element
is obtained by iteration of a universal multidimensional kernel. It ensures
exact distribution in the soft photon region. Algorithm is compatible with
exclusive exponentiation. To evaluate the program's precision, it is necessary
to control the kernel with the help of perturbative results. If available,
kernel is constructed from the exact first order matrix element. This ensures
that all terms necessary for non-leading logarithms are taken into account. In
the present paper we will focus on the W -> l nu and gamma^* -> pi^+ pi^-
decays. The Born level cross sections for both processes approach zero in some
points of the phase space. A process dependent compensating weight is
constructed to incorporate the exact matrix element, but is recommended for use
in tests only. In the hard photon region, where scalar QED is not expected to
be reliable, the compensating weight for gamma^* decay can be large. With
respect to the total rate, the effect remains at the permille level. It is
nonetheless of interest. The terms leading to the effect are analogous to some
terms appearing in QCD. The present paper can be understood either as a
contribution to discussion on how to match two collinear emission chains
resulting from charged sources in a way compatible with the exact and complete
phase space, exclusive exponentiation and the first order matrix element of QED
(scalar QED), or as the practical study of predictions for accelerator
experiments.Comment: 24 page
P-vortices and Drama of Gribov Copies
We present results of the careful study of the Gribov copies problem in SU(2)
lattice gauge theory for the direct maximal center projection widely used in
confinement studies. Applying simulated annealing algorithm we demonstrate that
this problem is more severe than it was thought before. The projected (gauge
noninvariant) string tension is not in the agreement with the physical string
tension. We do not find any indications that P-vortices reproduce the full
SU(2) string tension neither in the infinite volume limit nor in the continuum
limit.Comment: 16 pages, 7 figures, Latex2e, typos correcte
The small x gluon and b\bar{b} production at the LHC
We study open b\bar{b} production at large rapidity at the LHC in an attempt
to pin down the gluon distribution at very low x. For the LHC energy of 7 TeV,
at next-to-leading order (NLO), there is a large factorization scale
uncertainty. We show that the uncertainty can be greatly reduced if events are
selected in which the transverse momenta of the two B-mesons balance each other
to some accuracy, that is |\vec p_{1T}+\vec p_{2T}| < k_0. This will fix the
scale \mu_F \simeq k_0, and will allow the LHCb experiment, in particular, to
study the x-behaviour of gluon distribution down to x ~ 10^{-5}, at rather low
scales, \mu ~ 2 GeV. We evaluate the expected cross sections using, for
illustrative purposes, various recent sets of Parton Distribution Functions.Comment: 13 pages, 5 figure
Renormalizability of a quark-gluon model with soft BRST breaking in the infrared region
We prove the renormalizability of a quark-gluon model with a soft breaking of
the BRST symmetry, which accounts for the modification of the large distance
behavior of the quark and gluon correlation functions. The proof is valid to
all orders of perturbation theory, by making use of softly broken Ward
identities.Comment: 20 pages, no figures. Preprint number added in v2
Small x resummation in collinear factorisation
The summation of the small x-corrections to hard-scattering QCD amplitudes by
collinear factorisation method is reconsidered and the K-factor is derived in
leading ln x approximation with a result differing from the corresponding
expression by Catani and Hautmann (Nucl. Phys. B 427, 475, 1994). The
significance of the difference is demonstrated in the examples of structure
function F_L and of exclusive vector meson electroproduction. The formulation
covers the channels of non-vanishing conformal spin n paving the way for new
applications.Comment: 34 pages, 6 figure
Accessing directly the properties of fundamental scalars in the confinement and Higgs phase
The properties of elementary particles are encoded in their respective
propagators and interaction vertices. For a SU(2) gauge theory coupled to a
doublet of fundamental complex scalars these propagators are determined in both
the Higgs phase and the confinement phase and compared to the Yang-Mills case,
using lattice gauge theory. Since the propagators are gauge-dependent, this is
done in the Landau limit of 't Hooft gauge, permitting to also determine the
ghost propagator. It is found that neither the gauge boson nor the scalar
differ qualitatively in the different cases. In particular, the gauge boson
acquires a screening mass, and the scalar's screening mass is larger than the
renormalized mass. Only the ghost propagator shows a significant change.
Furthermore, indications are found that the consequences of the residual
non-perturbative gauge freedom due to Gribov copies could be different in the
confinement and the Higgs phase.Comment: 11 pages, 6 figures, 1 table; v2: one minor error corrected; v3: one
appendix on systematic uncertainties added and some minor changes, version to
appear in EPJ