A Solution of the Odderon Problem

Abstract

The intercept of the odderon trajectory is derived, by finding the spectrum of the second integral of motion of the three reggeon system in high energy QCD. When combined with earlier solution of the appropriate Baxter equation, this leads to the determination of the low lying states of that system. In particular, the energy of the lowest state gives the intercept of the odderon α O (0) = 1 − 0.2472α s N c /π.

New representation for the odderon wave function

“…Perturbative QCD predicts also an existence of the object with the same quantum numbers except of the C parity -the odderon [2,3,4], which controls the energy behavior of the difference of the cross-sections, σ tot pp − σ tot pp ∼ s α O −1 , with α O being the odderon intercept. Contrary to the BFKL pomeron, the intercept of the odderon trajectory has been calculated only recently [5,6] which generated renewed interest in the subject [7,8,9]. In this letter we present an alternative derivation of the odderon wave function.…”

Supersymmetric Yang-Mills Quantum Mechanics

“…Simplified (i.e. quenched, D=4) systems were also studied by lattice Monte Carlo methods for intermediate size groups [14]. The asymptotic behavior in N was observed and a possible evidence for the two phase structure was found.…”

Pomeron fan diagrams in perturbative QCD

“…First, our analysis contains the pomeron → two odderon vertex (see the discussion in section 3, after (3.10)). This vertex was found as early as in 1999, when only the Janik-Wosiek solution (JW) for the odderon [20,21] was known, describing a C-odd bound state of three reggeized gluons. Soon afterwards a new solution with intercept one was found in [19] (the BLV odderon).…”

“…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.…”

“…Below this vertex, the two triplet states, in the large-N c approximation, evolve separately and do not mix. Each of them forms an QCD odderon state, as described for example, in [19][20][21].…”