A basic ingredient of the master formula for the dijet spectrum is the S matrix for color-singlet multiparton states, and here we report on an important technical progress, the evaluation of the four-gluon color-dipole cross section operator. We investigate the breakdown of collinear factorization for non-inclusive Copyright © 2020 Elsevier B.V. or its licensors or contributors. The third advantage of signal flow-two port analytical methods is its ability to simplify the analysis of dual loop feedback architectures. Symbol the result also admits a crossing symmetry $\alpha_{ij}\to The color structure needed for resummation of all colored 2 -> 3 processes is calculated using multiplet inspired s-channel bases. multiple pole terms in each diagram reduce to sums of products of lower-loop The O(αs2) mixing of four-quark into semileptonic operators is instead a new result and represents one of the last missing ingredients of the next-to-next-to-leading-order analysis of rare semileptonic B meson decays. Rev. D61 (2000) 014004, hep-ph/9903240. In the Standard Model of particle physics,the theory of the strong interaction, Quantum Chromodynamics (QCD), is a gauge theory of symmetry group SU (Nc) with respect to the color quantum number. Here, we exhibit one-loop mixing matrices for the full list of 2 → 2 reactions involving light quarks and gluons. It also supports the definition of color vectors They noted a weird symmetry that it possesses under interchange of internal (colour group) and external (scattering angle) degrees of freedom and speculated that this may be related to an embedding into a context that correlates internal and external variables such as string theory. treat the photoproduction cross section of two high transverse momentum jets This study should provide the necessary tools to address nuclear broadening of n-parton systems in phenomenology while highlighting the color structure of the process. The resulting predictions agree well with H1 data. In this way the resulting matrices, describing the color structure, are guaranteed to obey simplifying symmetries. We compute the complete O(αs2) anomalous dimension matrix relevant for the b→sγ, b→sgand b→sℓ+ℓ−transitions in the standard model and some of its extensions. The first advantage is its amenability to a straightforward application of the stability theories and compensation strategies discussed in Part I. A general discussion is presented of the single logarithmic soft factor that appears in two scale QCD observables in processes involving four partons. Wilson lines, and their subsequent finite anomalous dimension. The second definition indicates, however, Join ResearchGate to discover and stay up-to-date with the latest research from leading experts in, Access scientific knowledge from anywhere. In the limit of low gap energy, good agreement with experiment is additional radiation in the gap in Herwig++. implementation, Rapidity gap physics at contemporary colliders, Super-leading logarithms in non-global observables in QCD: Colour basis independent calculation. exponentiation in multiparton scattering amplitudes, where the exponent is infrared and collinear safety. The latter simplifies in the ‘compact pair expansion’ which singles out the global charges (Casimirs) of the pair color states. It is more prosaic, but equally unexpected, and may also point to the fact that colour evolution might be understood in some deeper theoretical framework. regulator. with a large intermediate rapidity region as a factorizable quantity in We have large class of final-state resummations, in a range of processes. The eight-by-eight anomalous dimension matrix for gluon-gluon scattering shows a simplified structure in the basis corresponding to definite color exchange in the t-channel. in this class of webs the Symbol alphabet is restricted to$\alpha_{ij}\$ and The first entry above implies that the purpose of a computer is to perform operations, with a strong hint that these operations are likely to be mathematical in nature. Relevant singularities of multi-eikonal amplitudes up to three loops In a previous paper we reported the discovery of super-leading logarithmic terms in a non-global QCD observable. this article we derive NLL resummed results for generic observables. We examine these The momentum spectra for dijets in all possible color representations are reported in the form of explicit quadratures in terms of the collective nuclear unintegrated glue. highlight and discuss the conditions that the observable should satisfy for the We present a detailed discussion of both. (c) 2005 Elsevier B.V. All rights reserved. The origin of the breaking of conventional linear k{sub perpendicular} factorization for hard processes in a nuclear environment is by now well established. some unphysical behaviour for wide-angle gluon emission in QCD 2 to 2 In a recent paper, Dokshitzer and Marchesini rederived the anomalous dimension matrix for colour evolution of gg→gg scattering, first derived by Kidonakis, Oderda and Sterman. Logarithmically enhanced effects due to radiation of soft gluons at large angles in 2 -> 2 QCD scattering processes are treated in terms of the "fifth form factor" that accompanies the four collinear singular Sudakov form factors attached to incoming and outgoing hard partons. framework to that of webs, we derive renormalization constraints expressing all Indeed, compute is a synonym for ‘calculate’, and the initial development of the modern computer in the 1940s and 1950s was as a device for speeding up lengthy and complex calculations. In this short update we recalculate the first super-leading logarithmic contribution to the 'gaps between jets' cross-section using a colour basis independent notation. of all possible orthonormal bases, but that this subset is the natural