A bstract We perform a precise calculation of the transverse momentum ( q → T ) distribution of the boson+jet system in boson production events. The boson can be either a photon, W , Z or Higgs boson with mass m V , and q → T is the sum of the transverse momenta of the boson and the leading jet with magnitude q T = | q → T | . Using renormalization group techniques and soft-collinear effective theory, we resum logarithms log ( Q/q T ) and log R at next-to- leading logarithmic accuracy including the non-global logarithms, where Q and R are respectively the hard scattering energy and the radius of the jet. Specifically, we investigate two scenarios of p T J ≲ m V or p T J ≳ m V in Z +jet events, and we examine the q T distributions with different jet radii and study the effect of non-global logarithms. In the end we compare our theoretical calculations with Monte Carlo simulations and data from the LHC.