Pomeron-Odderon interactions in a Reggeon field theory

In this paper we extend our recent nonperturbative functional renormalization group analysis of Reggeon field theory to the interactions of Pomeron and Odderon fields. We establish the existence of a fixed point and its universal properties, which exhibits a novel symmetry structure in the space of Odderon-Pomeron interactions. As in our previous analysis, this part of our program aims at the investigation of the IR limit of Reggeon field theory (the limit of high energies and large transverse distances). It should be seen in the broader context of trying to connect the nonperturbative infrared region (large transverse distances) with the UV region of small transverse distances where the high energy limit of perturbative QCD applies. We briefly discuss the implications of our findings for the existence of an Odderon in high energy scattering.

Figure 1

Values of the parameters of the fixed point solution of the LPA truncations for different orders $n$ of the polynomial ($3\le n\le 9$). The masses (which equal intercept minus 1) ${\mu }_P$ (red curve) and ${\mu }_O$ (blue dotted curve) for the Pomeron and Odderon fields are in the left panel. The first nonzero couplings $\lambda ,{\lambda }_2,{\lambda }_{41},{\lambda }_{42},{\lambda }_{43},{\lambda }_{46},{\lambda }_{47},r$ are reported on the right panel.

Figure 2

Values of the critical exponents of the fixed point solution of the LPA truncations for different orders $n$ of the polynomial ($3\le n\le 9$). The two negative leading eigenvalues define the two critical exponents ${\nu }_P$ (red curve) and ${\nu }_O$ (blue dotted curve) for the Pomeron and Odderon fields (left panel). We report also the value of a third negative eigenvalue found in our approximation (right panel).

Figure 3

Values of the critical exponent ${\nu }_P(D)$ of the pure Pomeron critical theory obtained from two different polynomial expansions (left panel). The values of ${\nu }_P$ and ${\nu }_O$ at the fixed point obtained from the cubic truncation around the origin for $0<D<4$ (right panel). In the neighborhood of $D=4$ these curves are tangent to those associated to the $\epsilon$-expansion, according to Eq. (62).

Figure 4

Values of the anomalous dimension ${\eta }_P(D)$ of the pure Pomeron critical theory obtained from two different polynomial expansions (left panel). Values of ${\eta }_P$ (red curve) and ${\eta }_O$ (blue dotted curve) (center panel) and of ${\zeta }_P={\zeta }_O$ (right panel) at the fixed point obtained with a cubic truncation for $0<D<4$. In the neighborhood of $D=4$ these curves are tangent to those associated to the $\epsilon$-expansion, according to Eq. (61).