Soft gluon evolution and non-global logarithms

Abstract

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.

Exponentiating virtual imaginary contributions in a parton shower

“…The accuracy of leading order parton shower programs could be enhanced by improving the treatment of QCD color [2,[4][5][6][7]. We have worked to make our program, Deductor, more accurate with respect to color [1,3,8,9].…”

Resummed predictions for jet-resolution scales in multijet production in e+e− annihilation

“…This is of particular interest for example in the context of recent and ongoing developments to systematically include such corrections into parton-shower event generators, see e.g. [48,49,50,51,52,53,54]. To assess the effect of subleading colour contributions, we redo our calculation in the t'Hooft large-N C limit, defined by taking N C → ∞ while keeping α s N C fixed [55].…”

A Monte-Carlo simulation of double parton scattering

“…The flavour k is uniquely determined by the flavours i and j for LO QCD splittings so no sum is needed. If there is no flavour k such that the branching k → i + j is allowed 16 , then the input for the pair (i, j) should be set equal to zero. The small-y expression involves the unregularised splitting kernel P k→i+j (z) and the sPDF of parton k, which gives the probability of probing such a flavour k at this scale.…”

“…The physics is not changed since b 0 is of the order of unity. 16 Because of colour or flavour considerations. counting between DPS and SPS.…”

“…In order to improve the simulation of the underlying event, one can try to implement new parton showers that would include more aspects such as spin correlations, subleading-colour effects, new choices of kinematics, next-to-leading-order (NLO) splitting kernels, transverse-momentum-dependent parton distributions (TMD), amplitude-level evolutions, etc... Many efforts have been made in those directions recently [11][12][13][14][15][16][17][18][19][20][21][22][23][24].…”