# A New Contribution To The Proton Spin Crisis: Non-Zero Boundary Surface Term Due To Confinement in QCD

## TL;DR

This paper identifies a new non-zero boundary surface term in QCD that contributes to the proton spin, arising from confinement effects, and provides a formula for its calculation via lattice QCD.

## Contribution

It introduces a novel boundary surface term in the proton spin sum rule, derived non-perturbatively for lattice QCD computation.

## Key findings

- Boundary surface term is non-zero due to confinement.
- New contribution affects the proton spin sum rule.
- Formula for lattice QCD calculation provided.

## Abstract

The proton spin crisis still remains an unsolved problem in particle physics. It is suggested in the literature that the gauge invariant spin and orbital angular momentum of the quark and the gauge invariant total angular momentum of the gluon contribute to the proton spin. However, in this paper we find a new contribution to the proton spin. This new contribution is due to the boundary surface term in the total angular momentum conservation equation in QCD which is non-zero due to the confinement of the quarks and gluons inside the finite size proton. We derive the non-perturbative formula of this new contribution to the proton spin which can be calculated by using the lattice QCD method.