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Intrinsic Transverse Motion of the Pion’s Valence Quarks


Shi, Chao; Cloet, Ian


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 vertical bar l(z)vertical bar = 1 leading Fock-state light-front wave functions (LFWFs) [labeled by psi 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 LF\VFs, 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,14) dependence and in general do not factorize into separate functions of each variable. For k(T)(2) < 1 GeV2 the k(T)(2) dependence of the LFWFs is well described by a Gaussian; however for 14 > 10 GeV2 these LFWFs behave as psi(0) proportional to x(1 - x)/k(T)(2) and psi(1) proportional to x(1 - x)/k(T)(2) 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 zeta prescriptions which allows a qualitative comparison with Drell-Yan data.



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