Improvements on dipole shower colour
Jack Holguin, Jeffrey R. Forshaw, Simom Plätzer
Abstract
Abstract The dipole formalism provides a powerful framework from which parton showers can be constructed. In a recent paper (Forshaw et al. 2020), we proposed a dipole shower with improved colour accuracy and in this paper we show how it can be further improved. After an explicit check at $${\mathcal {O}}(\alpha _{\mathrm {s}}^{2})$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>O</mml:mi> <mml:mo>(</mml:mo> <mml:msubsup> <mml:mi>α</mml:mi> <mml:mrow> <mml:mi>s</mml:mi> </mml:mrow> <mml:mn>2</mml:mn> </mml:msubsup> <mml:mo>)</mml:mo> </mml:mrow> </mml:math> we confirm that our original shower performs as it was designed to, i.e. inheriting its handling of angular-ordered radiation from a coherent branching algorithm. We also show how other dipole shower algorithms fail to achieve this. Nevertheless, there is an $${\mathcal {O}}(\alpha _{\mathrm {s}}^{2})$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>O</mml:mi> <mml:mo>(</mml:mo> <mml:msubsup> <mml:mi>α</mml:mi> <mml:mrow> <mml:mi>s</mml:mi> </mml:mrow> <mml:mn>2</mml:mn> </mml:msubsup> <mml:mo>)</mml:mo> </mml:mrow> </mml:math> topology where it differs at sub-leading $$N_{\mathrm {c}}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>N</mml:mi> <mml:mi>c</mml:mi> </mml:msub> </mml:math> from a coherent branching algorithm. This erroneous topology can contribute a leading logarithm to some observables and corresponds to emissions that are ordered in $$k_t$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>k</mml:mi> <mml:mi>t</mml:mi> </mml:msub> </mml:math> but not angle. We propose a simple, computationally efficient way to correct this and assign colour factors in accordance with the coherence properties of QCD to all orders in $$\alpha _{\mathrm {s}}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>α</mml:mi> <mml:mi>s</mml:mi> </mml:msub> </mml:math> .