In this contribution, we present possible new advantages of observing double parton
scattering (DPS) processes initiated by photon-proton interactions. As discussed,
in principle, the observation of DPS processes could lead to access fundamental information
on double parton distribution functions of the protons. These new quantities, appearing in
the DPS cross section, represent a novel and promising tool to access the 3D partonic
structure of the proton, complementary to TMDs and GPDs. In fact, dPDFs encode double
parton correlations in hadrons which cannot be accessed through, e.g., GPDs. Up to date,
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 also investigated how these effects affect an experimental observable called
effective cross section, sigma_eff [5, 6]. However, as proved in Refs. [7, 8] in proton-proton
collisions, the information on the partonic proton structure are quite limited due to the lack
of information on dPDFs and their relative first moment called effective form factor (eff),
the latter entering the definition of sigma_eff. Let us mention that recently lattice data
on the pion moments of dPDFs [9] have been used to extract information on the quark distances
in the meson and to test holographic models of the pion structure [10, 11], Furthermore,
in this contribution we focus on the possibility to observe DPS in processes initiated by
quasireal photons [12]. In such a photoproduction process, 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 will fluctuate hadronically and/or
electro-magnetically in a the q-qbar pair which then initiates a double parton scattering
on the proton. The key idea is that the photon transverse size could be almost controlled by
measuring the virtuality and, in turn, the interaction rate in the DPS mechanism could
appreciated offering information on the transverse proton structure. In our analysis we
prove that the dependence of sigma_eff[gamma proton] on the photon virtuality Q2 could
be quasi-directly related to the mean transverse distance between two partons in the
proton active in the DPS process. Moreover, different models of the photon and proton
effs have been used to calculate, for the first time, sigma_eff[gamma proton](Q2).
These results have been then used to estimate the DPS cross section for the four jets
production via DPS in HERA kinematics, since in this channel collaborations reported
significant MPI effects on 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 processes in photoproduction gives
a significant fraction of the four jet production cross sections, if cuts on transverse
momenta of the jets are low enough. Moreover, also the DPS peculiar dependence on Q2
could be tested against models of the proton structure, with the possibility to consider
even more exotic final state, involving, for example, single or double quarkonia.
Finally in Ref. [12] a procedure to extract mean transverse distance between two
partons in the proton from sigma_eff[gamma proton](Q2) has been developed.
References
[1] M. Rinaldi, S. Scopetta, 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, S. Scopetta, Phys. Rev. D 95, no. 11, 114030 (2017)
[6] M. Rinaldi, S. Scopetta, M. Traini, V. Vento, Phys. Lett. B 752, 40 (2016)
[7] M. Rinaldi, F. A. Ceccopieri, JHEP 1909, 097 (2019)
[8] M. Rinaldi, 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, 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, F. A. Ceccopieri, arXiv:2103.13480.
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