The evolution equations for Green functions of the Reggeon Field Theory (RFT) are equivalent to those of the inclusive distributions for the reaction-diffusion system of classical particles. We use this equivalence to obtain numerically Green functions and amplitudes of the RFT with all loop contributions included. The numerical realization of the approach is described and some important applications including total and elastic proton--proton cross sections are studied. It is shown that the loop diagram contribution is essential but can be imitated in the eikonal cross section description by changing the Pomeron intercept. A role of the quartic Pomeron coupling which is an inherent part of the stochastic model is shown to be negligible for available energies.
We review recent progress on the calculation of scattering amplitudes in the high-energy limit. We start by illustrating the shockwave formalism, which allows one to calculate amplitudes as iterated solutions of rapidity evolution equations. We then focus on our recent results regarding $2\to 2$ parton scattering. We present the calculation of the imaginary part of the amplitude, at next-to-leading logarithmic accuracy in the high-energy logarithms, formally to all orders, and in practice to 13 loops. We then discuss the computation of the real part of the amplitude at next-to-next-to-leading …
Using an iterative solution of rapidity evolution equations, we compute partonic $2\to 2$ gauge theory amplitudes at four loops in full colour up to the Next-to-Next-to-Leading Logarithms (NNLL) in the Regge limit. By contrasting the resulting amplitude with the exponentiation properties of soft singularities we determine the four-loop correction to the soft anomalous dimension at this logarithmic accuracy, which universally holds in any gauge theory. We find that the latter features quartic Casimir contributions beyond those appearing in the cusp anomalous dimension. Finally, in the case of $…
We test the consistency of the data on the nucleon structure functions with analyticity and the Regge asymptotics of the virtual Compton amplitude. By solving a functional extremal problem, we derive an optimal lower bound on the maximum difference between the exact amplitude and the dominant Reggeon contribution for energies $ν$ above a certain high value $ν_h(Q^2)$. Considering in particular the difference of the amplitudes $T_1^\inel(ν, Q^2)$ for the proton and neutron, we find that the lower bound decreases in an impressive way when $ν_h(Q^2)$ is increased, and represents a very small frac…
The unitarity corrections to the propagator of reggeized gluons calculated in the framework of QCD RFT require a knowledge of the expressions for Reggeon propagator and vertices of interaction of three reggeized gluons (Reggeons) to one QCD loop precision, see \cite{Our6}. In this paper we calculate the vertex of interactions of $A_+ A_+ A_-$ Reggeon fields, i.e. vertex of transition of $A_-$ Reggeon field to $A_+ A_+$ fields, to this precision. We demonstrate, that all loop leading logarithmic order contributions to the vertex can be summed through the integro-differential equation similarly …
Using rapidity evolution equations we study two-to-two gauge-theory scattering amplitudes in the Regge limit. We carry out explicit computations at next-to-next-to-leading logarithmic accuracy through four loops and present new results for both infrared-singular and finite contributions to the amplitude. New techniques are devised in order to derive the colour structure stemming from three-Reggeon exchange diagrams in terms of commutators of channel operators, obtaining results that are valid for any gauge group, and apply to scattered particles in any colour representation. We also elucidate …
We study two-to-two parton scattering amplitudes in the high-energy limit of perturbative QCD by iteratively solving the BFKL equation. This allows us to predict the imaginary part of the amplitude to leading-logarithmic order for arbitrary $t$-channel colour exchange. The corrections we compute correspond to ladder diagrams with any number of rungs formed between two Reggeized gluons. Our approach exploits a separation of the two-Reggeon wavefunction, performed directly in momentum space, between a soft region and a generic (hard) region. The former component of the wavefunction leads to infr…
The Cottingham formula expresses the leading contribution of the electromagnetic interaction to the proton-neutron mass difference as an integral over the forward Compton amplitude. Since quarks and gluons reggeize, the dispersive representation of this amplitude requires a subtraction. We assume that the asymptotic behaviour is dominated by Reggeon exchange. This leads to a sum rule that expresses the subtraction function in terms of measurable quantities. The evaluation of this sum rule leads to $m_{QED}^{p-n}=0.58\pm 0.16\,\mbox{MeV}$.
We introduce a method to extract the symbol of the coefficient of $(2πi)^2$ of MHV remainder functions in planar N=4 Super Yang-Mills in multi-Regge kinematics region directly from the symbol in full kinematics. At two loops this symbol can be uplifted to the full function in a unique way, without any beyond-the-symbol ambiguities. We can therefore determine all two-loop MHV amplitudes at function level in all kinematic regions with different energy signs in multi-Regge kinematics. We analyse our results and we observe that they are consistent with the hypothesis of a contribution from the exc…
