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

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.