Background: It has been proposed that the azimuthal distributions of heavy flavor quark-antiquark pairs may be modified in the medium of a heavy-ion collision. Purpose: This work tests this proposition through next-to-leading order (NLO) calculations of the azimuthal distribution, $dsigma/dphi$, including transverse momentum broadening, employing $<k_T^2>$ and fragmentation in exclusive $Q bar Q$ pair production. While these studies were done for $p+p$, $p + bar p$ and $p+$Pb collisions, understanding azimuthal angle correlations between heavy quarks in these smaller, colder systems is important for their interpretation in heavy-ion collisions. Methods: First, single inclusive $p_T$ distributions calculated with the exclusive HVQMNR code are compared to those calculated in the fixed-order next-to-leading logarithm approach. Next the azimuthal distributions are calculated and sensitivities to $<k_T^2>$, $p_T$ cut, and rapidity are studied at $sqrt{s} = 7$ TeV. Finally, calculations are compared to $Q bar Q$ data in elementary $p+p$ and $p + bar p$ collisions at $sqrt{s} = 7$ TeV and 1.96 TeV as well as to the nuclear modification factor $R_{p {rm Pb}}(p_T)$ in $p+$Pb collisions at $sqrt{s_{NN}} = 5.02$ TeV measured by ALICE. Results: The low $p_T$ ($p_T < 10$ GeV) azimuthal distributions are very sensitive to the $k_T$ broadening and rather insensitive to the fragmentation function. The NLO contributions can result in an enhancement at $phi sim 0$ absent any other effects. Agreement with the data was found to be good. Conclusions: The NLO calculations, assuming collinear factorization and introducing $k_T$ broadening, result in significant modifications of the azimuthal distribution at low $p_T$ which must be taken into account in calculations of these distributions in heavy-ion collisions.
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