Exponentiating virtual imaginary contributions in a parton shower

Abstract

The operator in a parton shower algorithm that represents the imaginary part of virtual Feynman graphs has a non-trivial color structure and is large because it is proportional to a factor of 4π. In order to improve the treatment of color in a parton shower, it may help to exponentiate this phase operator. We show that it is possible to do so by exponentiating matrices that are no larger than 14 × 14. Using the example of the probability to have a gap in the rapidity interval between two high transverse momentum jets, we test this exponentiation algorithm by comparing to the result of treating the phase operator perturbatively. We find that the exponentiation works, but that the net effect of the exponentiated phase operator is quite small for this problem, so that one can as well use the perturbative approach.

Colour and logarithmic accuracy in final-state parton showers

“…Two other calculations are based on parton showers at finite α s and a truncation of the 1/N 2 c series: Nagy and Soper examined rapidity gaps between dijets at hadron colliders [6,33], while De Angelis, Forshaw and Plätzer examined the energy in a slice for the Z →qq and H → gg processes [8]. Only the processes examined in that latter paper are within the scope of our work here, but their simulation at finite α s precludes a meaningful direct comparison, because it would be impossible to know whether any differences between their results and ours are associated with subleading-colour effects or instead subleading logarithmic (α n s L n−1 ) effects.…”

Evolution of parton showers and parton distribution functions

“…The first order version of S pert no−split ðμ 2 Þ used in DEDUCTOR is approximate in that it omits the contributions from the imaginary part of virtual graphs. These contributions can be included perturbatively [16] or even in exponentiated form [17], but we find that they are not numerically important [16,17].…”

“…Within the framework of Ref. [8], the shower evolution operator Uðμ 2 s ; μ 2 h Þ is probability preserving thanks to the inclusion of the operator U V ðμ 2 f ; μ 2 Þ in its definition (17). In PYTHIA and other parton shower event generators, the parton shower is probability preserving without the need for U V ðμ 2 f ; μ 2 Þ.…”

“…The theory we use for DEDUCTOR [3,[7][8][9][10][11][12][13][14][15][16][17] uses a vector space, the "statistical space," that describes the momenta, flavors, colors, and spins for all of the partons created in a shower as the shower develops. 2 The shower is then The general theory includes parton spins but DEDUCTOR simply averages over spins.…”

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].…”