Odderon in the color glass condensate

Abstract

We discuss the definition and the energy evolution of scattering amplitudes with Codd ("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 colorsinglet 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-KwiecinskiPraszalowicz equation. Our gauge-invariant amplitudes, and the associated evolution equations, stay explicitly outside the Möbius representation, which is the Hilbert space where the BFKL Hamiltonian exhibits holomorphic separability.

A New Mechanism for Generating a Single Transverse Spin Asymmetry

“…(72) is that the spin-dependent cross section falls off with decreasing longitudinal momentum fraction α, which implies that the corresponding STSA decreases with decreasing Feynman-x of the projectile, in qualitative agreement with the experimental data.…”

Color dipoles from Bremsstrahlung in QCD evolution at high energy

“…When the action of H BREM is restricted to such gauge-invariant operators, Eq. (2.7) can be equivalently replaced by [21] 12) with M xyz denoting the dipole kernel [1] : …”

“…[13,21]). Specifically, the Bremsstrahlung and JIMWLK evolutions are known to be dual to each other [9,10], in the sense that the corresponding Hamiltonians and also the respective Poisson brackets get interchanged with each other under the following duality transformations 4 :…”

Pomeron fan diagrams in perturbative QCD

“…For this special odderon solution, the pomeron→two-odderon vertex becomes similar to the triple pomeron vertex. It is this special odderon solution which appears in the generalizations of the BK-equation [15,16]. Our more general version (3.10), on the other hand, allows to inlcude also other three-gluon solutions, such as the one found in [20,21] with intercept slightly below one.…”

“…Since the structure of this odderon is practically identical to the pomeron, it became possible to radically simplify vertices for both pomeron →two odderon and odderon → odderon+pomeron transitions, which actually reduce to the triple pomeron form. This allowed to easily derive the coupled system of evolution of the pomeron and odderon including both transitions [15,16]. This system was analyzed in [26] where the angular dependence introduced by the pomeron→two odderon transition (POO) was drastically simplified.…”