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Register a new userRenormalization group analysis of reggeon field theory: flow equations
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Can large distance high energy QCD be described by Reggeon Field Theory as an effective emergent theory? We start to investigate the issue employing functional renormalisation group techniques.
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In this paper we consider the complete momentum-independent quartic order truncation for the effective average action of a real Abelian rank 3 tensorial group field theory. This complete truncation includes non-melonic as well as double-trace interactions. In the usual functional renormalization group perspective, the inclusion of more operators that belong to the underlying theory space corresponds to an improvement of the truncation of the effective average action. We show that the inclusion of non-melonic and double-trace operators in the truncation brings subtleties. In particular, we discuss the assignment of scaling dimensions to the non-melonic sector and how the inclusion of double-trace operators considerably changes the results for critical exponents when they are not included. We argue that this is not a particular problem of the present model by comparing the results with a pure tensor model. We discuss how these issues should be investigated in future work.
We explore the influence of the current quark mass on observables in the low energy regime of hadronic interactions within a renormalization group analysis of the Nambu-Jona-Lasinio model in its bosonized form. We derive current quark mass expansions for the pion decay constant and the pion mass, and we recover analytically the universal logarithmic dependence. A numerical solution of the renormalization group flow equations enables us to determine effective low energy constants from the model. We find values consistent with the phenomenological estimates used in chiral perturbation theory.
The gradient flow bears a close resemblance to the coarse graining, the guiding principle of the renormalization group (RG). In the case of scalar field theory, a precise connection has been made between the gradient flow and the RG flow of the Wilson action in the exact renormalization group (ERG) formalism. By imitating the structure of this connection, we propose an ERG differential equation that preserves manifest gauge invariance in Yang--Mills theory. Our construction in continuum theory can be extended to lattice gauge theory.
In this paper we extend our recent non perturbative 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.
Reggeon field theory (RFT), originally developed in the context of high energy diffraction scattering, has a much wider applicability, describing, for example, the universal critical behavior of stochastic population models as well as probabilistic geometric problems such as directed percolation. In 1975 Suranyi and others developed cut RFT, which can incorporate the cutting rules of Abramovskii, Gribov and Kancheli for how each diagram contributes to inclusive cross-sections. In this note we describe the corresponding probabilistic interpretations of cut RFT: as a population model of two genotypes, which can reproduce both asexually and sexually; and as a kind of bicolor directed percolation problem. In both cases the AGK rules correspond to simple limiting cases of these problems.
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