Zero-jettiness resummation for top-quark pair production at the LHC
Simone Alioli, Alessandro Broggio, Matthew A. Lim
Abstract
A bstract We study the resummation of the 0-jettiness resolution variable $$ \mathcal{T} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>T</mml:mi> </mml:math> 0 for the top-quark pair production process in hadronic collisions. Starting from an effective theory framework we derive a factorisation formula for this observable which allows its resummation at any logarithmic order in the $$ \mathcal{T} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>T</mml:mi> </mml:math> 0 → 0 limit. We then calculate the $$ \mathcal{O} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>O</mml:mi> </mml:math> ( α s ) corrections to the soft function matrices and, by employing renormalisation group equation methods, we obtain the ingredients for the resummation formula up to next-to-next-to-leading logarithmic (NNLL) accuracy. We study the impact of these corrections to the 0-jettiness distribution by comparing predictions at different accuracy orders: NLL, NLL′, NNLL and approximate NNLL′ ( $$ {\mathrm{NNLL}}_{\mathrm{a}}^{\prime } $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msubsup> <mml:mtext>NNLL</mml:mtext> <mml:mi>a</mml:mi> <mml:mo>′</mml:mo> </mml:msubsup> </mml:math> ). We match these results to the corresponding fixed order calculations both at leading order and next-to-leading order for the t $$ \overline{t} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mover> <mml:mi>t</mml:mi> <mml:mo>¯</mml:mo> </mml:mover> </mml:math> +jet production process, obtaining the most accurate prediction of the 0-jettiness distribution for the top-quark pair production process at $$ {\mathrm{NNLL}}_{\mathrm{a}}^{\prime } $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msubsup> <mml:mtext>NNLL</mml:mtext> <mml:mi>a</mml:mi> <mml:mo>′</mml:mo> </mml:msubsup> </mml:math> +NLO accuracy.