Physics with Positron Beams at Jefferson Lab 12 GeV.

Positronbeams, both polarized and unpolarized, are identified as essential ingredients for the experimental program at the next generation of lepton accelerators. In the context of the Hadronic Physics program at the Jefferson Laboratory (JLab), positronbeams are complementary, even essential, tools for a precise understanding of the electromagnetic structure of the nucleon, in both the elastic and the deep-inelastic regimes. For instance, elastic scattering of (un)polarized electrons and positronsoff the nucleonallows for a model independent determination of the electromagnetic formfactors of the nucleon. Also, the deeply virtual Compton scatteringof (un)polarized electrons and positronsallows us to separate unambiguously the different contributions to the cross section of the lepto-production of photons, enabling an accurate determination of the nucleonGeneralized Parton Distributions (GPDs), and providing an access to its Gravitational Form Factors. Furthermore, positronbeams offer the possibility of alternative tests of the Standard Model through the search of a dark photonor the precise measurement of electroweak couplings. This letter proposes to develop an experimental positronprogram at JLab to perform unique high impact measurements with respect to the two-photon exchange problem, the determination of the proton and the neutron GPDs, and the search for the $A^{\prime}$ dark photon.