We present recent studies on the effects of different kind of correlations in double parton distribution functions (dPDFs). These quantities have been calculated in Ref. [1], within the Light-Front fully Poincar\'e covariant approach and in a constituent quark model framework. This first analysis shows how dynamical correlations, induced by the used model, prevent the factorization of dPDFs in terms of standard parton distribution function (PDFs). Furthermore, in order to give useful predictions for experimental analyses, in Ref. [2], the so called ``effective cross section'', $\sigma_{eff}$, fundamental ingredient for the comprehension of the role of double parton scattering in proton-proton collisions, has been evaluated by means of the dPDFs calculated in Ref. \cite{rinaldi1}. In addition, radiatively generated sea quarks and gluons have been included in this analysis, through the dPDF pQCD evolution. The obtained $\sigma_{eff}$ shows, in particular, a strong $x$ dependence in the valence region, a feature not yet observed in the experimental determination of $\sigma_{eff}$, given the present accuracy of the experimental analyses. In two subsequent papers of ours, Refs. [3,4], we have pursued the study of different kind of correlation effects on dPDFs. In the first one, the authors show the important role of perturbative and non perturbative correlations in the $x_1$ and $x_2$ (longitudinal momentum fraction carried by two partons in a proton) dependence of dPDFs also at low values $x$ and at higher scales including, for the first time, gluons and sea quarks non perturbatively generated. In the second contribution [4], elaborating on the results presented in Ref. \cite{rinaldi1}, the impact of model independent correlations, induced by the correct treatment of relativity in the evaluation of dPDFs, has been assessed, with particular emphasis on factorization of the
$(x_1, ~x_2)-b_\perp$ dependence, being $b_\perp$ the transverse distance between the two partons.

References

[1] M. Rinaldi, S. Scopetta, M. Traini and V. Vento, JHEP 12, 028 (2014) [arXiv:1409.1500 [hep-ph]].

[2] M. Rinaldi, S. Scopetta, M. Traini and V. Vento, Phys. Lett. B 752, 40 (2016) doi:10.1016/j.physletb.2015.11.031 [arXiv:1506.05742 [hep-ph]].

[3] M. Rinaldi, S. Scopetta, M. C. Traini and V. Vento, arXiv:1608.02521 [hep-ph].

[4] M. Rinaldi, F. A. Ceccopieri in preparation. 2