Abstract
Different decompositions of the nucleon mass, in terms of the masses and energies of the underlying constituents, have been proposed in the literature. We explore the corresponding sum rules in quantum electrodynamics for an electron at one-loop order in perturbation theory. To this aim we compute the form factors of the energy-momentum tensor, by paying particular attention to the renormalization of ultraviolet divergences, operator mixing and scheme dependence. We clarify the expressions of all the proposed sum rules in the electron rest frame in terms of renormalized operators. Furthermore, we consider the same sum rules in a moving frame, where they become energy decompositions. Finally, we discuss some implications of our study on the mass sum rules for the nucleon.
Highlights
A lot of work has already been done for what concerns the spin decomposition of the nucleon, as well as the pressure and shear distributions
The paper is organized as follows: in Section 2, we review the basic properties of the EMT and give the parametrization of the EMT matrix elements in terms of form factors, while in Section 3 we discuss the renormalization procedure leading to the renormalized EMT form factors
We discussed in detail the forward matrix elements of the EMT for an electron state by performing the calculation at order O(α) in quantum electrodynamics (QED)
Summary
The “canonical” EMT is defined as the Noether current associated with the space-time translational invariance of the Lagrangian, and it satisfies the continuity equation. This corresponds to the Belinfante-Rosenfeld [46,47,48] procedure that allows one to incorporate specific properties into the EMT, such as the symmetry in the Lorentz indices and the gauge invariance. The space-time point at which the EMT is evaluated is irrelevant thanks to the translational invariance of the forward matrix element. Since the total EMT is renormalized with the standard Lagrangian renormalization and we are just considering the matrix elements for an electron state, the vertex counterterm coincides with the counterterm for the electron field. V1,2 are the diagrams associated with the interaction term present in Teμν, whereas V3 is the one-loop electron vertex correction that arises from the derivative term in Teμν. V4 is the one-loop vertex correction with the photon coupled directly to the external operator
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
