Light quark mediated Higgs boson threshold production in the next-to-leading logarithmic approximation
Charalampos Anastasiou, Alexander A. Penin
Abstract
A bstract We study the amplitude of the Higgs boson production in gluon fusion mediated by a light quark loop and evaluate the logarithmically enhanced radiative corrections to the next-to-leading logarithmic approximation which sums up the terms of the form $$ {\alpha}_s^n{\ln}^{2n-1}\left({m}_H/{m}_q\right) $$ <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:msub> <mml:mi>m</mml:mi> <mml:mi>H</mml:mi> </mml:msub> <mml:mo>/</mml:mo> <mml:msub> <mml:mi>m</mml:mi> <mml:mi>q</mml:mi> </mml:msub> </mml:mrow> </mml:mfenced> </mml:math> to all orders in the strong coupling constant. This result is used for the calculation of the process cross section near the production threshold and gives a quantitative estimate of the three and four-loop bottom quark contribution to the Higgs boson production at the Large Hadron Collider.