multi-Regge Region Research Articles

The two-loop symbol of all multi-Regge regions

We study the symbol of the two-loop n-gluon MHV amplitude for all Mandelstam regions in multi-Regge kinematics in N=4 super Yang-Mills theory. While the number of distinct Mandelstam regions grows exponentially with n, the increase of independent symbols turns out to be merely quadratic. We uncover how to construct the symbols for any number of external gluons from just two building blocks which are naturally associated with the six- and seven-gluon amplitude, respectively. The second building block is entirely new, and in addition to its symbol, we also construct a prototype function that correctly reproduces all terms of maximal functional transcendentality.

Heptagon amplitude in the multi-Regge regime

As we have shown in previous work, the high energy limit of scattering amplitudes in N=4 supersymmetric Yang-Mills theory corresponds to the infrared limit of the 1-dimensional quantum integrable system that solves minimal area problems in AdS5. This insight can be developed into a systematic algorithm to compute the strong coupling limit of amplitudes in the multi-Regge regime through the solution of auxiliary Bethe Ansatz equations. We apply this procedure to compute the scattering amplitude for n=7 external gluons in different multi-Regge regions at infinite 't Hooft coupling. Our formulas are remarkably consistent with the expected form of 7-gluon Regge cut contributions in perturbative gauge theory. A full description of the general algorithm and a derivation of results will be given in a forthcoming paper.

Multi-Regge limit of the n-gluon bubble ansatz

Abstract We investigate n-gluon scattering amplitudes in the multi-Regge region of $ \mathcal{N}=4 $ supersymmetric Yang-Mills theory at strong coupling. Through a careful analysis of the thermodynamic bubble ansatz (TBA) for surfaces in AdS 5 with n-g(lu)on boundary conditions we demonstrate that the multi-Regge limit probes the large volume regime of the TBA. In reaching the multi-Regge regime we encounter wall-crossing in the TBA for all n > 6. Our results imply that, in this limit, amplitudes at strong coupling can be calculated through an auxiliary system of algebraic Bethe ansatz equations. Their solutions are expected to determine the strong coupling analogue of Regge cut contributions to the amplitude.

SCATTERING MECHANISM OF HIGH ENERGY STRONG INTERACTION SOFT PROCESSES

Starting from the viewpoint that the constituent quark has its own structure and incorporating the hypothesis of maximum nonperturbative strong interaction reaction (MNSIR), which should be obeyed in high energy strong soft processes, we modified the field theory for soft Pomeron (ℙ) of Landshoff and Nachtmann and proposed a new structure model for the soft Pomeron ℙ and Reggeon ℝ. In this model a pair of constituent quarks coming from colliding hadron in strong soft processes are first disaggregated into a valance quark with a nonperturbative gluon cloud G wrapped about, or, according to the case, into a nonperturbative gluon wrapped by spinor cloud. Corresponding to such mechanism, the relevant structure of soft Pomeron ℙ or Region ℝ is represented by the sum of a series of cut ladder diagrams. In the multi-Regge region, where the energy of the system is very large and the momentum transfer |t| is very small, and in the approximation where only the leading order of log s is preserved, we calculated the [Formula: see text] scattering amplitude and its total cross-section from the sum of such ladder diagrams. The Regge-behavior factor in the form of an exponential power law of s does arise. We also get compact formulas for the trajectories of soft ℙ and ℝ. As example of application, an alternative mechanism of J/Ψ nonquarkonic-hadron decay is proposed.

QCD coherence in the structure function and associated distributions at small x★

We recall the origin of angular ordering in soft parton emission and show that at small x this coherent structure is masked in the structure function while it can be detected in the associated distributions. This is due to the fact that collinear singularities cancel completely in the structure function at fixed transverse momentum for x → 0. In this limit the dependence on the hard scale is lost, the angular ordered region becomes equivalent to the multi-Regge region in which all transverse momenta are of the same order, and one derives the BFKL equation. For the associated distributions at small x such a complete cancellation of collinear singularities does not hold in general, thus large singular contributions are neglected if angular ordering is replaced by multi-Regge phase space. The deduction of these features requires an analysis without any collinear approximations which is done by extending to small x the soft gluon factorization techniques typically used in the region of large x. Since the coherent structure of parton emission is the same in the small and large x regions, one can formulate a unified evolution equation for the structure function, a unified coherent branching and jet algorithm which allows the calculation of associated distributions in all x regions. Such a unified formulation, valid for all x, is presented and compared with usual treatments.

Study of multiparticle production in Reggeon field theory

The concept of Reggeon field theory (RFT) is applied to particle production in the multi-Regge region. For processes with repeated Pomeron ($\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{P}$) exchange we calculate the high-energy behavior of the production cross sections ${\ensuremath{\sigma}}_{n}(s)$ and find that ${\ensuremath{\sigma}}_{n}(s)\ensuremath{\sim}{\ensuremath{\sigma}}_{\mathrm{el}}(s)\ensuremath{\sim}{(\mathrm{ln}s)}^{\ensuremath{-}\frac{5}{6}}$ for every $n$. It is then shown that $s$-channel unitarity constraints are respected: in the absence of $\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{P}$ cuts these processes are known to violate the Froissart bound (Finkelstein-Kajantie problem). We show that the inclusion of $\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{P}$ cuts in our RFT model solves this problem, provided the $\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{P}$-particle-$\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{P}$ vertex is not large. Furthermore, we demonstrate that the way in which $s$-channel unitarity is restored does not lead to decoupling problems. Finally, particle production with a secondary Reggeon exchange is considered. We find that the ${\ensuremath{\sigma}}_{n}(s)$ have qualitatively the same behavior as in the absence of $\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{P}$ cuts.

Unitary Multiperipheral Models

The method of constructing unitary $S$ matrices developed in a recent paper is generalized and applied to two versions of the multiperipheral model. In these models the standard perturbation expansion of the $S$ matrix diverges, so an alternative expansion with improved convergence properties is developed. It is shown that the unitarity condition generates a new type of cut in the angular momentum plane which is dynamical in origin in contrast to the essentially kinematical Mandelstam cuts. This new type of cut ensures that the Froissart bound on the total cross section is obeyed. In an exactly solvable model it is shown that the contribution of the multi-Regge region of phase space to the total cross section always decreases as a power of the energy if the input Regge trajectory is unity or less. It is argued that the qualitative features of the models discussed here will hold for a wide class of multiperipheral-like models.