Asuming a U boson wich is masive and neutral as a dark matter particles are analyzed. This work is a first step to study the interactions between ultra high energy cosmic rays with a hypothetical dark matter particle background, composed by U bosons and investigate possible signals of new physics in the highest energy cosmic rays spectrum. In order to do this, a framework of pyisics beyond the Standard Model is assumed where the interactions between the U boson and elemental particles occur through a Compton effect. Afterwards, We estimate the differential cross section between the U boson and a fermion with spin 1/2 with our formulas, in the limit where the U boson is massless and the fermion is an electron. Finally, the results are analyzed and validated by reproducing the behavior of classical Compton effect.