Leading-logarithmic threshold resummation of Higgs production in gluon fusion at next-to-leading power
Martin Beneke, Mathias Garny, Sebastian Jaskiewicz, Robert Szafron, Leonardo Vernazza, Jian Wang
Abstract
A bstract We sum the leading logarithms $$ {\alpha}_s^n{\ln}^{2n-1}\left(1-z\right) $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msubsup> <mml:mi>α</mml:mi> <mml:mi>s</mml:mi> <mml:mi>n</mml:mi> </mml:msubsup> <mml:msup> <mml:mo>ln</mml:mo> <mml:mrow> <mml:mn>2</mml:mn> <mml:mi>n</mml:mi> <mml:mo>−</mml:mo> <mml:mn>1</mml:mn> </mml:mrow> </mml:msup> <mml:mfenced> <mml:mrow> <mml:mn>1</mml:mn> <mml:mo>−</mml:mo> <mml:mi>z</mml:mi> </mml:mrow> </mml:mfenced> </mml:math> , n = 1 , 2 , . . . , near the kinematic threshold $$ z={m}_H^2/\hat{s}\to 1 $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>z</mml:mi> <mml:mo>=</mml:mo> <mml:msubsup> <mml:mi>m</mml:mi> <mml:mi>H</mml:mi> <mml:mn>2</mml:mn> </mml:msubsup> <mml:mo>/</mml:mo> <mml:mover> <mml:mi>s</mml:mi> <mml:mo>̂</mml:mo> </mml:mover> <mml:mo>→</mml:mo> <mml:mn>1</mml:mn> </mml:math> at next-to-leading power in the expansion in (1 − z ) for Higgs production in gluon fusion. We highlight the new contributions compared to Drell-Yan production in quark-antiquark annihilation and show that the final result can be obtained to all orders by the substitution of the colour factor C F → C A , confirming previous fixed-order results. We also provide a numerical analysis of the next-to-leading power leading logarithms, which indicates that they are numerically relevant.