Factorization at next-to-leading power and endpoint divergences in gg → h production
Ze Long Liu, Matthias Neubert, Marvin Schnubel, Xing Wang
Abstract
A bstract We derive a factorization theorem for the Higgs-boson production amplitude in gluon-gluon fusion induced by a light-quark loop, working at next-to-leading power in soft-collinear effective theory. The factorization is structurally similar to that obtained for the h → γγ decay amplitude induced by a light-quark loop, but additional complications arise because of external color charges. We show how the refactorization-based subtraction scheme developed in previous work leads to a factorization theorem free of endpoint divergences. We use renormalization-group techniques to predict the logarithmically enhanced terms in the three-loop gg → h form factor of order $$ {\alpha}_s^3{\ln}^k\left(-{M}_h^2/{m}_b^2\right) $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msubsup> <mml:mi>α</mml:mi> <mml:mi>s</mml:mi> <mml:mn>3</mml:mn> </mml:msubsup> <mml:msup> <mml:mo>ln</mml:mo> <mml:mi>k</mml:mi> </mml:msup> <mml:mfenced> <mml:mrow> <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:msubsup> <mml:mi>m</mml:mi> <mml:mi>b</mml:mi> <mml:mn>2</mml:mn> </mml:msubsup> </mml:mrow> </mml:mfenced> </mml:math> with k = 6, 5, 4, 3. We also resum the first three towers of leading logarithms, $$ {\alpha}_s^n{\ln}^{2n-k}\left(-{M}_h^2/{m}_b^2\right) $$ <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:mi>k</mml:mi> </mml:mrow> </mml:msup> <mml:mfenced> <mml:mrow> <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:msubsup> <mml:mi>m</mml:mi> <mml:mi>b</mml:mi> <mml:mn>2</mml:mn> </mml:msubsup> </mml:mrow> </mml:mfenced> </mml:math> with k = 0, 1, 2, to all orders of perturbation theory.