NNLL$^\prime$ resummation of azimuthal decorrelation for boosted top quark pair production at the LHC

TL;DR

This work develops a transverse-momentum dependent (TMD) factorization and resummation framework for boosted top-quark pair production in the back-to-back limit, addressing the dual challenges of heavy-quark mass effects and soft radiation. A two-step matching procedure—QCD to SCET+HQET and then to SCET+bHQET— enables simultaneous resummation of logarithms associated with the top mass and azimuthal decorrelation, culminating in NNLL' accuracy. A central achievement is the first extraction of the two-loop ultra-collinear function from refactorizing the fully differential massive soft function, completing the perturbative set needed for NNLL' predictions. Numerical results at 13 TeV demonstrate reduced scale uncertainties and finite predictions in the back-to-back region, providing a robust benchmark for heavy-quark TMD resummation and paving the way for N^3LL extensions and applications to boosted bottom quarks or proton-nucleus collisions.

Abstract

The precision program of the Large Hadron Collider (LHC) increasingly relies on the boosted regime, where top quark properties are probed at the TeV scale. However, the simultaneous presence of heavy quark mass effects and large logarithmic corrections from soft radiation poses a significant challenge for theoretical predictions. In this work, we develop a transverse momentum dependent (TMD) factorization and resummation framework for boosted top quark pair production in the back-to-back limit at the LHC. By employing a two step matching procedure, matching QCD through $\mathrm{SCET}\,+\,\mathrm{HQET}$ onto $\mathrm{SCET}\,+\,\mathrm{bHQET}$, we systematically resum large logarithms associated with both the top quark mass and the azimuthal decorrelation. A key component of our formalism is the first extraction of the two-loop ultra-collinear function, obtained via the refactorization of the fully differential massive soft function. This result completes the set of perturbative ingredients required to achieve $\mathrm{NNLL}^\prime$ accuracy for the azimuthal decorrelation distribution. Our framework establishes a new benchmark for heavy-quark TMD resummation in the boosted limit at hadron colliders.

Figures (2)

• Figure 1: A schematic illustration of the two-step factorization procedure. First, full QCD is matched onto a hybrid SCET and HQET description, where $\boldsymbol{H}^m$ denotes the massive hard function, $\boldsymbol{S}^m$ the massive TMD soft function, and $f$ the standard transverse-momentum-dependent parton distribution functions. Second, in the boosted limit, the HQET sector is matched onto bHQET, introducing the massless hard function $\boldsymbol{H}$, the massive jet function $\mathcal{J}_m$, the massive soft function $\mathcal{S}_m$, the massless TMD soft function $\boldsymbol{S}$, and the ultra-collinear function $S^{\text{uc}}$.
• Figure 2: Azimuthal $\delta\phi$ distribution in $pp$ collisions at NLL (blue), NNLL (green) and NNLL$^\prime$ (orange) accuracy. The uncertainty estimates are shown for variations in the renormalization scales $\mu_h$ and $\mu_j$ and $\mu_{b_{*}}$, where each scale is varied up and down by a factor of two.