Intrinsic Transverse Motion of the Pion's Valence Quarks

Starting with the solution to the Bethe-Salpeter equation for the pion, in a beyond rainbow-ladder truncation to QCD's Dyson-Schwinger equations, we determine the pion's l_{z}=0 and |l_{z}|=1 leading Fock-state light-front wave functions (LFWFs) [labeled by ψ_{l_{z}}(x,k_{T}^{2})]. The leading-twist time-reversal even transverse momentum dependent parton distribution function (TMD) of the pion is then directly obtained using these LFWFs. A key characteristic of the LFWFs, which is driven by dynamical chiral symmetry breaking, is that at typical hadronic scales they are broad functions in the light-cone momentum fraction x. The LFWFs have a nontrivial (x,k_{T}^{2}) dependence and in general do not factorize into separate functions of each variable. For k_{T}^{2}≲1  GeV^{2} the k_{T}^{2} dependence of the LFWFs is well described by a Gaussian; however for k_{T}^{2}≳10  GeV^{2} these LFWFs behave as ψ_{0}∝x(1-x)/k_{T}^{2} and ψ_{1}∝x(1-x)/k_{T}^{4}, and therefore exhibit the power-law behavior predicted by perturbative QCD. The pion's TMD naturally inherits many features from the LFWFs. The TMD evolution of our result is studied using both the b^{*} and ζ prescriptions which allows a qualitative comparison with Drell-Yan data.