In this contribution, I discuss the possibilities offered by double parton scattering (DPS) processes initiated by photon-proton interactions. In fact, the DPS cross section depends on the double parton distribution functions (dPDFs) of hadrons. These new quantities encode new informations on the 3D partonic structure of the proton, complementary to TMDs and GPDs. In fact, dPDFs are sensitive to unknown double parton correlations in hadrons which cannot be accessed through, e.g., GPDs. However, dPDFs are almost unknown and, in particular, their dependence on the transverse distance of partons. In our analyses [1, 2, 3, 4] we discussed the impact of both perturbative and non perturbative double parton correlations in dPDFs. In addition, our collaboration studied the impact

of these effects on the experimental observable called effective cross section, $\sigma_{eff}$ [5, 6]. However, as proved in Refs. [7, 8] in proton-proton collisions, e.g. at the LHC, only limited information on the partonic proton structure can be extracted from data due to the lack of information on dPDFs. Therefore, in Ref. [12], we proposse to consider DPS initiated by quasireal photons. In this case, the offshellness of the photons is controlled by measuring leptons, proton or ions from the impinging beam scattered at low angle. At such low virtualities, the photon can fluctuate in a $q − \bar q$ pair which then initiates the double parton scattering with the proton. In this scenario, the photon transverse size could be almost controlled by measuring the virtuality ($Q^2$) and, in turn, the interaction rate in the DPS mechanism. Such a condition leads to the extraction of information on the transverse proton structure from the dependence on $Q^2$ on $\sigma_{eff}^{\gamma p}(Q^2)$. The latter quantity has been calculated, for the first time by using different models for the proton and the photon splitting mechanism. These results have been then used to estimate the DPS cross section for the four jets production via DPS for the HERA kinematics. In fact, the ZEUS collaboration reported significant MPI effects in this channel for the four jets cross sections, and exposed in their analyses possible contamination of the DPS processes. By estimating the expected number of events at given integrated luminosity, we conclude that DPS process in photoproduction gives a significant fraction of the four jet production cross section if cuts on transverse momenta of the jets are low enough.

References

[1] M. Rinaldi, S. Scopetta and V. Vento, Phys. Rev. D 87, 114021 (2013)

[2] M. Rinaldi, S. Scopetta, M. Traini and V. Vento, JHEP 1412, 028 (2014)

[3] M. Rinaldi, S. Scopetta, M. C. Traini and V. Vento, JHEP 1610, 063 (2016)

[4] M. Rinaldi and F. A. Ceccopieri, Phys. Rev. D 95, no. 3, 034040 (2017)

[5] F. A. Ceccopieri, M. Rinaldi and S. Scopetta, Phys. Rev. D 95, no. 11, 114030 (2017)

[6] M. Rinaldi, S. Scopetta, M. Traini and V. Vento, Phys. Lett. B 752, 40 (2016)

[7] M. Rinaldi and F. A. Ceccopieri, JHEP 1909, 097 (2019)

[8] M. Rinaldi and F. A. Ceccopieri, Phys. Rev. D 97, no. 7, 071501 (2018)

[9] G. S. Bali et al., JHEP 1812, 061 (2018)

[10] M. Rinaldi, S. Scopetta, M. Traini and V. Vento, Eur. Phys. J. C 78, no. 9, 781

(2018)

[11] M. Rinaldi, Eur. Phys. J. C 80, no. 7, 678 (2020)

[12] M. Rinaldi and F. A. Ceccopieri, arXiv:2103.13480.