Odderon in the Color Glass Condensate

Abstract

We discuss the definition and the energy evolution of scattering amplitudes with $C$-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 Möbius representation, which is the Hilbert space where the BFKL Hamiltonian exhibits holomorphic separability.

43 pages, 1 figure

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