146 research outputs found
Nonperturbative contributions to the quark form factor at high energy
The analysis of nonperturbative effects in high energy asymptotics of the
electomagnetic quark form factor is presented. It is shown that the
nonperturbative effects determine the initial value for the perturbative
evolution of the quark form factor and find their general structure with
respect to the high energy asymptotics. Within the Wilson integral formalism
which is natural for investigation of the soft, IR sensitive, part of the
factorized form factor, the structure of the instanton induced effects in the
evolution equation is discussed. It is demonstrated that the instanton
contributions result in the finite renormalization of the subleading
perturbative result and numerically are characterized by small factor
reflecting the diluteness of the QCD vacuum within the instanton liquid model.
The relevance of the IR renormalon induced effects in high energy asymptotic
behaviour is discussed. The consequences of the various analytization
procedures of the strong coupling constant in the IR domain are considered.Comment: REVTeX, 12 pages, 1 figure. Important references and discussions
added, misprints corrected, minor changes in tex
Deep Inelastic Scattering in Conformal QCD
We consider the Regge limit of a CFT correlation function of two vector and
two scalar operators, as appropriate to study small-x deep inelastic scattering
in N=4 SYM or in QCD assuming approximate conformal symmetry. After clarifying
the nature of the Regge limit for a CFT correlator, we use its conformal
partial wave expansion to obtain an impact parameter representation encoding
the exchange of a spin j Reggeon for any value of the coupling constant. The
CFT impact parameter space is the three-dimensional hyperbolic space H3, which
is the impact parameter space for high energy scattering in the dual AdS space.
We determine the small-x structure functions associated to the exchange of a
Reggeon. We discuss unitarization from the point of view of scattering in AdS
and comment on the validity of the eikonal approximation.
We then focus on the weak coupling limit of the theory where the amplitude is
dominated by the exchange of the BFKL pomeron. Conformal invariance fixes the
form of the vector impact factor and its decomposition in transverse spin 0 and
spin 2 components. Our formalism reproduces exactly the general results predict
by the Regge theory, both for a scalar target and for gamma*-gamma* scattering.
We compute current impact factors for the specific examples of N=4 SYM and QCD,
obtaining very simple results. In the case of the R-current of N=4 SYM, we show
that the transverse spin 2 component vanishes. We conjecture that the impact
factors of all chiral primary operators of N=4 SYM only have components with 0
transverse spin.Comment: 44+16 pages, 7 figures. Some correction
Non-linear evolution in CCFM: The interplay between coherence and saturation
We solve the CCFM equation numerically in the presence of a boundary
condition which effectively incorporates the non-linear dynamics. We retain the
full dependence of the unintegrated gluon distribution on the coherence scale,
and extract the saturation momentum. The resulting saturation scale is a
function of both rapidity and the coherence momentum. In Deep Inelastic
Scattering this will lead to a dependence of the saturation scale on the photon
virtuality in addition to the usual x-Bjorken dependence. At asymptotic
energies the interplay between the perturbative non-linear physics, and that of
the QCD coherence, leads to an interesting and novel dynamics where the
saturation momentum itself eventually saturates. We also investigate various
implementations of the "non-Sudakov" form factor. It is shown that the
non-linear dynamics leads to almost identical results for different form
factors. Finally, different choices of the scale of the running coupling are
analyzed and implications for the phenomenology are discussed.Comment: 37 pages, 21 figure
Renormalisation of heavy-light light ray operators
We calculate the renormalisation of different light ray operators with one
light degree of freedom and a static heavy quark. Both - and
-kernels are considered. A comparison with the light-light case suggests
that the mixing with three-particle operators is solely governed by the light
degrees of freedom. Additionally we show that conformal symmetry is already
broken at the level of the one loop counterterms due to the additional
UV-renormalisation of a cusp in the two contributing Wilson-lines. This general
feature can be used to fix the -renormalisation kernels up to a
constant. Some examples for applications of our results are given.Comment: 23 pages, 5 figures; v2: changed some wording, added a few references
and one appendix concerning some subtleties related to gauge fixing and ghost
terms; v3: clarified calculation in section 3.2., added an explicit
calculation in section 5.2, corrected a few typos and one figure, added a few
comments, results unchanged, except for typesetting matches version to appear
in JHE
Wrapping corrections, reciprocity and BFKL beyond the sl(2) subsector in N=4 SYM
We consider N=4 SYM and a class of spin N, length-3, twist operators beyond
the well studied sl(2) subsector. They can be identified at one-loop with three
gluon operators. At strong coupling, they are associated with spinning strings
with two spins in AdS5. We exploit the Y-system to compute the leading
weak-coupling four loop wrapping correction to their anomalous dimension. The
result is written in closed form as a function of the spin N. We combine the
wrapping correction with the known four-loop asymptotic Bethe Ansatz
contribution and analyze special limits in the spin N. In particular, at large
N, we prove that a generalized Gribov-Lipatov reciprocity holds. At negative
unphysical spin, we present a simple BFKL-like equation predicting the
rightmost leading poles.Comment: 18 page
Operator product expansion in QCD in off-forward kinematics: Separation of kinematic and dynamical contributions
We develop a general approach to the calculation of target mass and finite
t=(p'-p)^2 corrections in hard processes which can be studied in the framework
of the operator product expansion and involve momentum transfer from the
initial to the final hadron state. Such corrections, which are usually referred
to as kinematic, can be defined as contributions of operators of all twists
that can be reduced to total derivatives of the leading twist operators. As the
principal result, we provide a set of projection operators that pick up the
"kinematic" part of an arbitrary flavor-nonsinglet twist-four operator in QCD.
A complete expression is derived for the time-ordered product of two
electromagnetic currents that includes all kinematic corrections to twist-four
accuracy. The results are immediately applicable to the studies of
deeply-virtual Compton scattering, transition gamma^*-> M gamma form factors
and related processes. As a byproduct of this study, we find a series of
"genuine" twist-four flavor-nonsinglet quark-antiquark-gluon operators which
have the same anomalous dimensions as the leading twist quark-antiquark
operators.Comment: 68 pages, 2 figures. Misprints in Eq.(5.64) and several equations in
Sec.6 are corrected. For readers' convenience all corrections are marked in
re
- …