Pion transverse momentum dependent parton distributions in a light-front constituent approach, and the Boer-Mulders effect in the pion-induced Drell-Yan process

At leading twist the transverse momentum dependent parton distributions of the pion consist of two functions, the unpolarized ${f}_{1,\ensuremath{\pi}}(x,{\mathbit{k}}_{\ensuremath{\perp}}^{2})$ and the Boer-Mulders function ${h}_{1,\ensuremath{\pi}}^{\ensuremath{\perp}}(x,{\mathbit{k}}_{\ensuremath{\perp}}^{2})$. We study both functions within a light-front constituent model of the pion, comparing the results with different pion models and the corresponding nucleon distributions from a light-front constituent model. After evolution from the model scale to the relevant experimental scales, the results for the collinear pion valence parton distribution function ${f}_{1,\ensuremath{\pi}}(x)$ are in very good agreement with available parametrizations. Using the light-front constituent model results for the Boer-Mulders functions of the pion and nucleon, we calculate the coefficient $\ensuremath{\nu}$ in the angular distribution of Drell-Yan dileptons produced in pion-nucleus scattering, which is responsible for the violation of the Lam-Tung relation. We find a good agreement with the data, and carefully discuss the range of applicability of our approach.