The transverse momentum distribution of the toverline{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}_{toverline{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}_{toverline{t}}/textrm{d}mid {overrightarrow{q}}_{textrm{T}}mid . In the context of the effective field theories, SCETII and HQET, we will demonstrate that in spite of the {q}_{tau_{perp }} integrations, the leading asymptotic terms of textrm{d}{sigma}_{toverline{t}}/textrm{d}{q}_{tau } still observe the factorisation pattern in terms of the hard, beam, and soft functions in the vicinity of qτ = 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}_{toverline{t}}/d{q}_{textrm{T},textrm{in}},textrm{d}{sigma}_{toverline{t}}/textrm{d}{q}_{textrm{T},textrm{out}} , and textrm{d}{sigma}_{toverline{t}}/dDelta {phi}_{toverline{t}} , within the domain {M}_{toverline{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}_{toverline{t}} of the toverline{t} pair is evaluated through its kinematical connection to qT,out. This is the first time the azimuthal spectrum Delta {phi}_{toverline{t}} is appraised at or beyond the N2LL level including a consistent treatment of both beam collinear and soft radiation.
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