773 research outputs found
Odderon in the Color Glass Condensate
We discuss the definition and the energy evolution of scattering amplitudes
with -odd ("odderon") quantum numbers within the effective theory for the
Color Glass Condensate (CGC) endowed with the functional, JIMWLK, evolution
equation. We explicitly construct gauge-invariant amplitudes describing
multiple odderon exchanges in the scattering between the CGC and two types of
projectiles: a color--singlet quark--antiquark pair (or `color dipole') and a
system of three quarks in a colorless state. We deduce the energy evolution of
these amplitudes from the general JIMWLK equation, which for this purpose is
recast in a more synthetic form, which is manifestly infrared finite. For the
dipole odderon, we confirm and extend the non--linear evolution equations
recently proposed by Kovchegov, Szymanowski and Wallon, which couple the
evolution of the odderon to that of the pomeron, and predict the rapid
suppression of the odderon exchanges in the saturation regime at high energy.
For the 3--quark system, we focus on the linear regime at relatively low
energy, where our general equations are shown to reduce to the
Bartels--Kwiecinski--Praszalowicz equation. Our gauge--invariant amplitudes,
and the associated evolution equations, stay explicitly outside the M\"obius
representation, which is the Hilbert space where the BFKL Hamiltonian exhibits
holomorphic separability.Comment: 43 pages, 1 figur
JIMWLK evolution in the Gaussian approximation
We demonstrate that the Balitsky-JIMWLK equations describing the high-energy
evolution of the n-point functions of the Wilson lines (the QCD scattering
amplitudes in the eikonal approximation) admit a controlled mean field
approximation of the Gaussian type, for any value of the number of colors Nc.
This approximation is strictly correct in the weak scattering regime at
relatively large transverse momenta, where it reproduces the BFKL dynamics, and
in the strong scattering regime deeply at saturation, where it properly
describes the evolution of the scattering amplitudes towards the respective
black disk limits. The approximation scheme is fully specified by giving the
2-point function (the S-matrix for a color dipole), which in turn can be
related to the solution to the Balitsky-Kovchegov equation, including at finite
Nc. Any higher n-point function with n greater than or equal to 4 can be
computed in terms of the dipole S-matrix by solving a closed system of
evolution equations (a simplified version of the respective Balitsky-JIMWLK
equations) which are local in the transverse coordinates. For simple
configurations of the projectile in the transverse plane, our new results for
the 4-point and the 6-point functions coincide with the high-energy
extrapolations of the respective results in the McLerran-Venugopalan model. One
cornerstone of our construction is a symmetry property of the JIMWLK evolution,
that we notice here for the first time: the fact that, with increasing energy,
a hadron is expanding its longitudinal support symmetrically around the
light-cone. This corresponds to invariance under time reversal for the
scattering amplitudes.Comment: v2: 45 pages, 4 figures, various corrections, section 4.4 updated, to
appear in JHE
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
Gluon Saturation Effects at the Nuclear Surface: Inelastic Cross Section of Proton-Nucleus at Ultra High Energy Cosmic Ray domain
Considering the high-energy limit of the QCD gluon distribution inside a
nucleus, we calculate the proton-nucleus total inelastic cross section using a
simplified dipole model. We show that, if gluon saturation occurs in the
nuclear surface region, the total cross section of proton-nucleus collisions
increases more rapidly as a function of the incident energy compared to that of
a Glauber-type estimate. We discuss the implications of this with respect to
recent ultra-high-energy cosmic ray experiments.Comment: Published in Nuclear Physics A, 29 pages, 5 figures, 1 tabl
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