22 research outputs found
Momentum sum rule and factorization of double parton distributions
We show that the momentum sum rule is a necessary condition for factorization
of double parton distributions into a product of two single parton
distributions for small values of the parton momentum fractions x and large
enough values of the evolution scale Q. This is a somewhat surprising result
since the momentum sum rule involves integration over all values of the
momentum fraction. In essence, the momentum sum rule provides a proper relation
between the double and single parton distributions, which is necessary for the
small x factorization at large .Comment: 11 pages, 4 figures, version published in Phys. Rev.
Numerical solution of the nonlinear evolution equation at small x with impact parameter and beyond the LL approximation
Nonlinear evolution equation at small x with impact parameter dependence is
analyzed numerically. Saturation scales and the radius of expansion in impact
parameter are extracted as functions of rapidity. Running coupling is included
in this evolution, and it is found that the solution is sensitive to the
infrared regularization. Kinematical effects beyond leading logarithmic
approximation are taken partially into account by modifying the kernel which
includes the rapidity dependent cuts. While the local nonlinear evolution is
not very sensitive to these effects, the kinematical constraints cannot be
neglected in the evolution with impact parameter.Comment: 22 pages, 37 figures, RevTe
Small x nonlinear evolution with impact parameter and the structure function data
The nonlinear Balitsky-Kovchegov equation at small x is solved numerically,
incorporating impact parameter dependence. Confinement is modeled by including
effective gluon mass in the dipole evolution kernel, which regulates the
splitting of dipoles with large sizes. It is shown, that the solution is
sensitive to different implementations of the mass in the kernel. In addition,
running coupling effects are taken into account in this analysis. Finally, a
comparison of the calculations using the dipole framework with the inclusive
data from HERA on the structure functions F2 and FL is performed.Comment: 19 pages, 11 figures. Minor revision. One reference added, two
figures update
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
Exact kinematics in the small x evolution of the color dipole and gluon cascade
The problem of kinematic effects in the gluon and color dipole cascades is
addressed in the large N_c limit of SU(N_c) Yang--Mills theory. We investigate
the tree level multi-gluon components of the gluon light cone wave functions in
the light cone gauge keeping the exact kinematics of the gluon emissions. We
focus on the components with all helicities identical to the helicity of the
incoming gluon. The recurrence relations for the gluon wave functions are
derived. In the case when the virtuality of the incoming gluon is neglected the
exact form of the multi-gluon wave function is obtained. Furthermore, we
propose an approximate scheme to treat the kinematic effects in the color
dipole evolution kernel. The new kernel entangles longitudinal and transverse
degrees of freedom and leads to a reduced diffusion in the impact parameter.
When evaluated in the next-to-leading logarithmic (NLL) accuracy, the kernel
reproduces the correct form of the double logarithmic terms of the dipole size
ratios present in the exact NLL dipole kernel. Finally, we analyze the
scattering of the incoming gluon light cone components off a gluon target and
the fragmentation of the scattered state into the final state. The equivalence
of the resulting amplitudes and the maximally-helicity-violating amplitudes is
demonstrated in the special case when the target gluon is far in rapidity from
the evolved gluon wave function.Comment: 37 pages, 13 figure
Physics of ultrahigh energy neutrinos
Ultrahigh energy neutrinos can provide important information about the
distant astronomical objects and the origin of the Universe. Precise knowledge
about their interactions and production rates is essential for estimating
background, expected fluxes and detection probabilities. In this paper we
review the applications of the high energy QCD to the calculations of the
interaction cross sections of the neutrinos. We also study the production of
the ultrahigh energy neutrinos in the atmosphere due to the charm and beauty
decays.Comment: 27 pages, 11 Figure
Evolution equations for the double parton distributions. Initial conditions and transverse momentum dependence
In the first part of this contribution we discuss the problem of the initial conditions for the evolution of double parton distribution functions (PDFs). We show that one can construct a framework based on the expansion in terms of the Dirichlet functions in which both single and double PDFs satisfy momentum sum rules. In the second part, we propose how to include the transverse momentum dependence for the double parton distribution functions using the extension of the Kimber-Martin-Ryskin framework previously applied to the single PDFs
Evolution equations for the double parton distributions. Initial conditions and transverse momentum dependence
In the first part of this contribution we discuss the problem of the initial conditions for the evolution of double parton distribution functions (PDFs). We show that one can construct a framework based on the expansion in terms of the Dirichlet functions in which both single and double PDFs satisfy momentum sum rules. In the second part, we propose how to include the transverse momentum dependence for the double parton distribution functions using the extension of the Kimber-Martin-Ryskin framework previously applied to the single PDFs