28 research outputs found
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
Fully Unintegrated Parton Correlation Functions and Factorization in Lowest Order Hard Scattering
Motivated by the need to correct the potentially large kinematic errors in
approximations used in the standard formulation of perturbative QCD, we
reformulate deeply inelastic lepton-proton scattering in terms of gauge
invariant, universal parton correlation functions which depend on all
components of parton four-momentum. Currently, different hard QCD processes are
described by very different perturbative formalisms, each relying on its own
set of kinematical approximations. In this paper we show how to set up
formalism that avoids approximations on final-state momenta, and thus has a
very general domain of applicability. The use of exact kinematics introduces a
number of significant conceptual shifts already at leading order, and tightly
constrains the formalism. We show how to define parton correlation functions
that generalize the concepts of parton density, fragmentation function, and
soft factor. After setting up a general subtraction formalism, we obtain a
factorization theorem. To avoid complications with Ward identities the full
derivation is restricted to abelian gauge theories; even so the resulting
structure is highly suggestive of a similar treatment for non-abelian gauge
theories.Comment: 44 pages, 69 figures typos fixed, clarifications and second appendix
adde
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
Traveling wave fronts and the transition to saturation
We propose a general method to study the solutions to nonlinear QCD evolution
equations, based on a deep analogy with the physics of traveling waves. In
particular, we show that the transition to the saturation regime of high energy
QCD is identical to the formation of the front of a traveling wave. Within this
physical picture, we provide the expressions for the saturation scale and the
gluon density profile as a function of the total rapidity and the transverse
momentum. The application to the Balitsky-Kovchegov equation for both fixed and
running coupling constants confirms the effectiveness of this method.Comment: 9 pages, 3 figures, references adde
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
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
Next-to-leading and resummed BFKL evolution with saturation boundary
We investigate the effects of the saturation boundary on small-x evolution at
the next-to-leading order accuracy and beyond. We demonstrate that the
instabilities of the next-to-leading order BFKL evolution are not cured by the
presence of the nonlinear saturation effects, and a resummation of the higher
order corrections is therefore needed for the nonlinear evolution. The
renormalization group improved resummed equation in the presence of the
saturation boundary is investigated, and the corresponding saturation scale is
extracted. A significant reduction of the saturation scale is found, and we
observe that the onset of the saturation corrections is delayed to higher
rapidities. This seems to be related to the characteristic feature of the
resummed splitting function which at moderately small values of x possesses a
minimum.Comment: 34 page
Limiting fragmentation in hadron-hadron collisions at high energies
Limiting fragmentation in proton-proton, deuteron-nucleus and nucleus-nucleus
collisions is analyzed in the framework of the Balitsky-Kovchegov equation in
high energy QCD. Good agreement with experimental data is obtained for a wide
range of energies. Further detailed tests of limiting fragmentation at RHIC and
the LHC will provide insight into the evolution equations for high energy QCD.Comment: 28 pages, 10 figures (2 new figures, text slightly expanded, and some
additional references
Non-linear QCD dynamics and exclusive production in collisions
The exclusive processes in electron-proton () interactions are an
important tool to investigate the QCD dynamics at high energies as they are in
general driven by the gluon content of proton which is strongly subject to
parton saturation effects. In this paper we compute the cross sections for the
exclusive vector meson production as well as the deeply virtual Compton
scattering (DVCS) relying on the color dipole approach and considering the
numerical solution of the Balitsky-Kovchegov equation including running
coupling corrections. We show that the small- evolution given by this
evolution equation is able to describe the DESY-HERA data and is relevant for
the physics of the exclusive observables in future electron-proton colliders
and in photoproduction processes to be measured in coherent interactions at the
LHC.Comment: 6 pages, 4 figure
HE-LHC: The High-Energy Large Hadron Collider – Future Circular Collider Conceptual Design Report Volume 4
In response to the 2013 Update of the European Strategy for Particle Physics (EPPSU), the Future Circular Collider (FCC) study was launched as a world-wide international collaboration hosted by CERN. The FCC study covered an energy-frontier hadron collider (FCC-hh), a highest-luminosity high-energy lepton collider (FCC-ee), the corresponding 100 km tunnel infrastructure, as well as the physics opportunities of these two colliders, and a high-energy LHC, based on FCC-hh technology. This document constitutes the third volume of the FCC Conceptual Design Report, devoted to the hadron collider FCC-hh. It summarizes the FCC-hh physics discovery opportunities, presents the FCC-hh accelerator design, performance reach, and staged operation plan, discusses the underlying technologies, the civil engineering and technical infrastructure, and also sketches a possible implementation. Combining ingredients from the Large Hadron Collider (LHC), the high-luminosity LHC upgrade and adding novel technologies and approaches, the FCC-hh design aims at significantly extending the energy frontier to 100 TeV. Its unprecedented centre-of-mass collision energy will make the FCC-hh a unique instrument to explore physics beyond the Standard Model, offering great direct sensitivity to new physics and discoveries