Projected transverse momentum resummation in top-antitop pair production at LHC

Abstract

The transverse momentum distribution of the $t\overline{t}$ system is of both experimental and theoretical interest. In the presence of azimuthally asymmetric divergences, pursuing resummation at high logarithmic precision is rather demanding in general. In this paper, we propose the projected transverse momentum spectrum $\textrm{d}{\sigma}_{t\overline{t}}/\textrm{d}{q}_{\tau }$, which is derived from the classical ${\overrightarrow{q}}_{\textrm{T}}$ spectrum by integrating out the rejection component ${q}_{\tau_{\perp }}$ with respect to a reference unit vector $\overrightarrow{\tau}$, to serve as an alternative solution to remove these asymmetric divergences, in addition to the azimuthally averaged case $\textrm{d}{\sigma}_{t\overline{t}}/\textrm{d}\mid {\overrightarrow{q}}_{\textrm{T}}\mid$. In the context of the effective field theories, SCET_II and HQET, we will demonstrate that in spite of the ${q}_{\tau_{\perp }}$ integrations, the leading asymptotic terms of $\textrm{d}{\sigma}_{t\overline{t}}/\textrm{d}{q}_{\tau }$ still observe the factorisation pattern in terms of the hard, beam, and soft functions in the vicinity of q_τ = 0 GeV. Then, with the help of the renormalisation group equation techniques, we carry out the resummation at NLL+NLO, N²LL+N²LO, and approximate N²LL′+N²LO accuracy on three observables of interest, $\textrm{d}{\sigma}_{t\overline{t}}/d{q}_{\textrm{T},\textrm{in}},\textrm{d}{\sigma}_{t\overline{t}}/\textrm{d}{q}_{\textrm{T},\textrm{out}}$, and $\textrm{d}{\sigma}_{t\overline{t}}/d\Delta {\phi}_{t\overline{t}}$, within the domain ${M}_{t\overline{t}}$ ≥ 400 GeV. The first two cases are obtained by choosing $\overrightarrow{\tau}$ parallel and perpendicular to the top quark transverse momentum, respectively. The azimuthal de-correlation $\Delta {\phi}_{t\overline{t}}$ of the $t\overline{t}$ pair is evaluated through its kinematical connection to q_T,out. This is the first time the azimuthal spectrum $\Delta {\phi}_{t\overline{t}}$ is appraised at or beyond the N²LL level including a consistent treatment of both beam collinear and soft radiation.