Eikonal gluon bremsstrahlung at finite N c beyond two loops

118

We consider soft-gluon evolution at the amplitude level. Our evolution algorithm applies to generic hard-scattering processes involving any number of coloured partons and we present a reformulation of the algorithm in such a way as to make the cancellation of infrared divergences explicit. We also emphasise the special role played by a Lorentzinvariant evolution variable, which coincides with the transverse momentum of the latest emission in a suitably defined dipole zero-momentum frame. Handling large colour matrices presents the most significant challenge to numerical implementations and we present a means to expand systematically about the leading colour approximation. Specifically, we present a systematic procedure to calculate the resulting colour traces, which is based on the colour flow basis. Identifying the leading contribution leads us to re-derive the BanfiMarchesini-Smye equation. However, our formalism is more general and can systematically perform resummation of contributions enhanced by the t'Hooft coupling α s N ∼ 1, along with successive perturbations that are parametrically suppressed by powers of 1/N . We also discuss how our approach relates to earlier work.

Section: Jhep05(2018)044supporting

confidence: 79%

Soft gluon evolution and non-global logarithms

Martinez

Angelis

Forshaw

et al. 2018

118

“…The latter is sufficient to capture all single logarithms α n s L n , with L being the large NGL. As stated in the introduction, we do not show herein explicit formulae for the said squared-amplitudes and refer the reader to our coming paper [39]. Moreover, for the purpose of this paper, we do not consider the role of any jet algorithm, and postpone such work to future publications.…”

Section: Hemisphere Mass Distribution At One and Two-loopsmentioning

confidence: 99%

“…3 Consequently we have been able to analytically calculate all squared amplitudes for the emission of soft energy-ordered gluons (for all possible real, virtual and real-virtual configurations) in the eikonal approximation fully (at finite N c ) up to five-loops. We leave the presentation of these squared-amplitudes and the method of calculation to a forthcoming paper [39].…”

Section: Introductionmentioning

confidence: 99%

Non-global logarithms at finite N c beyond leading order

Khelifa-Kerfa

Delenda

2015

Self Cite

Abstract:We analytically compute non-global logarithms at finite N c fully up to 4 loops and partially at 5 loops, for the hemisphere mass distribution in e + e − → di-jets to leading logarithmic accuracy. Our method of calculation relies solely on integrating the eikonal squared-amplitudes for the emission of soft energy-ordered real-virtual gluons over the appropriate phase space. We show that the series of non-global logarithms in the said distribution exhibits a pattern of exponentiation thus confirming -by means of brute force -previous findings. In the large-N c limit, our results coincide with those recently reported in literature. A comparison of our proposed exponential form with allorders numerical solutions is performed and the phenomenological impact of the finite-N c corrections is discussed.

“…More specifically, we consider triple soft-gluon radiation at the tree level in QCD hard scattering. Partial results on triple soft-gluon radiation are available in the literature [23]- [29] and we comment on them throughout the paper. These results are limited to specific processes and to energy ordering approximations.…”

Section: Introductionmentioning

confidence: 99%

Triple (and quadruple) soft-gluon radiation in QCD hard scattering

Catani

Colferai

Torrini

2020

We consider the radiation of three soft gluons in a generic process for multiparton hard scattering in QCD. In the soft limit the corresponding scattering amplitude has a singular behaviour that is factorized and controlled by a colorful soft current. We compute the tree-level current for triple soft-gluon emission from both massless and massive hard partons. The three-gluon current is expressed in terms of maximally non-abelian irreducible correlations. We compute the soft behaviour of squared amplitudes and the colour correlations produced by the squared current. The radiation of one and two soft gluons leads to colour dipole correlations. Triple soft-gluon radiation produces in addition colour quadrupole correlations between the hard partons. We examine the soft and collinear singularities of the squared current in various energy ordered and angular ordered regions. We discuss some features of soft radiation to all-loop orders for processes with two and three hard partons. Considering triple soft-gluon radiation from three hard partons, colour quadrupole interactions break the Casimir scaling symmetry between quarks and gluons. We also present some results on the radiation of four soft gluons from two hard partons, and we discuss the colour monster contribution and its relation with the violation (and generalization) of Casimir scaling. We also compute the first correction of O(1/N 2 c ) to the eikonal formula for multiple soft-gluon radiation with strong energy ordering from two hard gluons.