Seeking a possible approach to understanding the origin of the proton mass using twist-4 contributions in inclusive reactions

Most of the mass of the visible universe originates from the strong interaction. Quantitatively reproducing the origin of the nucleon mass is one of the important challenges in fundamental science. Since the next-generation Electron-Ion Collider has identified resolving this problem as one of its major goals, further theoretical studies are needed to develop approaches to investigating the origin experimentally. In this paper, we explore the possibility of evaluating the ``gluon condensate term’’ which is particularly difficult to determine among the contributions to the nucleon mass, using high-energy scattering experiments. We first express the gluon condensate term in terms of experimentally accessible twist-4 lightcone matrix elements. We then derive, for the first time, analytic formulas for the cross section including all twist-4 contributions from pure quark, quark-gluon, and pure gluon matrix elements in $ep$ collisions, and show how these contributions can be related to the gluon condensate term.