53 research outputs found
Connection between complete and Moebius forms of gauge invariant operators
We study the connection between complete representations of gauge invariant
operators and their Moebius representations acting in a limited space of
functions. The possibility to restore the complete representations from Moebius
forms in the coordinate space is proven and a method of restoration is worked
out. The operators for transition from the standard BFKL kernel to the
quasi-conformal one are found both in Moebius and total representations.Comment: Changed title and a short paragraph in the section "Conclusion";
unchanged results. Version to appear on Nucl. Phys.
NLO inclusive jet production in --factorization
The inclusive production of jets in the central region of rapidity is studied
in -factorization at next-to-leading order (NLO) in QCD perturbation
theory. Calculations are performed in the Regge limit making use of the NLO
BFKL results. A jet cone definition is introduced and a proper phase--space
separation into multi-Regge and quasi-multi-Regge kinematic regions is carried
out. Two situations are discussed: scattering of highly virtual photons, which
requires a symmetric energy scale to separate the impact factors from the gluon
Green's function, and hadron-hadron collisions, where a non--symmetric scale
choice is needed.Comment: 36 pages, 5 figures. Version to be published in JHEP. Some typos
correcte
Dimensional Regularisation and Factorisation Schemes in the BFKL Equation at Subleading Leve
We study the anomalous dimensions and coefficient functions generated by the
BFKL equation in 4+2 epsilon dimensions, by investigating both running coupling
effects, and the inclusion of the full next-to-leading kernel. After
generalising the Fourier representation of the solutions to this case, we
analyse the beta-dependent renormalisation-group factorisation of anomalous
dimension and coefficient contributions to the gluon density. We derive on this
basis the normalisation factor of the Q0-scheme with respect to the
MSbar-scheme, including beta-dependent corrections to it, and we outline the
derivation of the full next-to-leading contributions. We also provide an
expression for the resummed gamma_qg in the MSbar-scheme which exhibits its
universality and is explicit up to quadratures.Comment: 32 pages, 2 figure
Matching of the low-x evolution kernels
We demonstrate that the ambiguity of the low-x evolution kernels in the
next-to-leading order (NLO) permits one to match the Mobius form of the BFKL
kernel and the kernel of the colour dipole model and to construct the Mobius
invariant NLO BFKL kernel in N=4 supersymmetric Yang-Mills theory.Comment: 17 pages, references adde
A matrix formulation for small-x singlet evolution
We propose a matrix evolution equation in (x,kt)-space for flavour singlet,
unintegrated quark and gluon densities, which generalizes DGLAP and BFKL
equations in the relevant limits. The matrix evolution kernel is constructed so
as to satisfy renormalization group constraints in both the ordered and
antiordered regions of exchanged momenta kt, and incorporates the known NLO
anomalous dimensions in the MSbar scheme as well as the NLx BFKL kernel. We
provide a hard Pomeron exponent and effective eigenvalue functions that include
the n_f-dependence, and give also the matrix of resummed DGLAP splitting
functions. The results connect smoothly with those of the single-channel
approach. The novel P_{qa} splitting functions show resummation effects delayed
down to x=0.0001, while both P_{ga} entries show a shallow dip around x=0.001,
similarly to the gluon-gluon single-channel results. We remark that the matrix
formulation poses further constraints on the consistency of a BFKL framework
with the MSbar scheme, which are satisfied at NLO, but marginally violated by
small n_f/N_c^2-suppressed terms at NNLO.Comment: 36 pages, 5 figure
On the coordinate representation of NLO BFKL
The ``non-Abelian'' part of the quark contribution to the BFKL kernel in the
next-to-leading order (NLO) is found in the coordinate representation by direct
transfer of the contribution from the momentum representation where it was
calculated before. The results obtained are used for the examination of
conformal properties of the NLO BFKL kernel and of the relation between the
BFKL and color dipole approaches.Comment: 18 pages; minor misprints remove
The dipole form of the BFKL kernel in supersymmetric Yang--Mills theories
The dipole (M\"{o}bius) representation of the colour singlet BFKL kernel in
the next-to-leading order is found in supersymmetric Yang--Mills theories.
Ambiguities of this form and its conformal properties are discussed.Comment: 11 pages, LaTeX; added references for sections 4 and
Expanding running coupling effects in the hard Pomeron
We study QCD hard processes at scales of order k^2 > Lambda^2 in the limit in
which the beta-function coefficient - b is taken to be small, but alphas(k) is
kept fixed. The (nonperturbative) Pomeron is exponentially suppressed in this
limit, making it possible to define purely perturbative high-energy Green's
functions. The hard Pomeron exponent acquires diffusion and running coupling
corrections which can be expanded in the b parameter and turn out to be
dependent on the effective coupling b alphas^2 Y. We provide a general setup
for this b-expansion and we calculate the first few terms both analytically and
numerically.Comment: 36 pages, 15 figures, additional references adde
The dipole form of the quark part of the BFKL kernel
The dipole form of the ``Abelian'' part of the massless quark contribution to
the BFKL kernel is found in the coordinate representation by direct transfer
from the momentum representation where the contribution was calculated before.
It coincides with the corresponding part of the quark contribution to the
dipole kernel calculated recently by Balitsky and is conformal invariant.Comment: 9 page
Difference between standard and quasi-conformal BFKL kernels
As it was recently shown, the colour singlet BFKL kernel, taken in Moebius
representation in the space of impact parameters, can be written in
quasi-conformal shape, which is unbelievably simple compared with the
conventional form of the BFKL kernel in momentum space. It was also proved that
the total kernel is completely defined by its Moebius representation. In this
paper we calculated the difference between standard and quasi-conformal BFKL
kernels in momentum space and discovered that it is rather simple. Therefore we
come to the conclusion that the simplicity of the quasi-conformal kernel is
caused mainly by using the impact parameter space.Comment: 18 page
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