The thrust distribution at NNLO+NNLL in Higgs decays to quarks and gluons

A bstract We present a calculation of the thrust distribution in Higgs decays to quarks and gluons, $$ H\to b\overline{b} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>H</mml:mi> <mml:mo>→</mml:mo> <mml:mi>b</mml:mi> <mml:mover> <mml:mi>b</mml:mi> <mml:mo>¯</mml:mo> </mml:mover> </mml:math> , $$ H\to c\overline{c} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>H</mml:mi> <mml:mo>→</mml:mo> <mml:mi>c</mml:mi> <mml:mover> <mml:mi>c</mml:mi> <mml:mo>¯</mml:mo> </mml:mover> </mml:math> , and H → gg , including the resummation of large logarithmic corrections that arise in the two-particle limit at next-to-next-to-leading logarithmic (NNLL) accuracy, and match it to fixed-order results for three-particle decays at next-to-next-to-leading order (NNLO) in the strong coupling. The resummation is performed analytically within the A res framework and combined with the fixed-order results using the logR matching technique. The fixed-order calculation is carried out numerically with the NNLO jet parton-level event generator, using the antenna subtraction method. We perform detailed cross-validation in the two-particle region, demonstrating that the expansion of the NNLL resummed result correctly reproduces the logarithmic structure of the fixed-order calculation to $$ \mathcal{O}\left({\alpha}_{\textrm{s}}^3\right) $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>O</mml:mi> <mml:mfenced> <mml:msubsup> <mml:mi>α</mml:mi> <mml:mi>s</mml:mi> <mml:mn>3</mml:mn> </mml:msubsup> </mml:mfenced> </mml:math> , up to a predictable N 3 LL term at $$ \mathcal{O}\left({\alpha}_{\textrm{s}}^3L\right) $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>O</mml:mi> <mml:mfenced> <mml:mrow> <mml:msubsup> <mml:mi>α</mml:mi> <mml:mi>s</mml:mi> <mml:mn>3</mml:mn> </mml:msubsup> <mml:mi>L</mml:mi> </mml:mrow> </mml:mfenced> </mml:math> . In addition to providing the first NNLO+NNLL accurate predictions for the thrust distribution in Higgs decays to quarks and gluons, we analytically extract the $$ \mathcal{O}\left({\alpha}_{\textrm{s}}^2\right) $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>O</mml:mi> <mml:mfenced> <mml:msubsup> <mml:mi>α</mml:mi> <mml:mi>s</mml:mi> <mml:mn>2</mml:mn> </mml:msubsup> </mml:mfenced> </mml:math> hard-virtual correction c 2 and the $$ {\alpha}_{\textrm{s}}^3L $$ <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:mi>L</mml:mi> </mml:math> term G 31 in both the $$ H\to q\overline{q} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>H</mml:mi> <mml:mo>→</mml:mo> <mml:mi>q</mml:mi> <mml:mover> <mml:mi>q</mml:mi> <mml:mo>¯</mml:mo> </mml:mover> </mml:math> ( q = b , c ) and H → gg decay channels.