Nucleon gravitational form factors from instantons: forces between quark and gluon subsystems

Abstract

Using the instanton picture of the QCD vacuum we compute the nucleon $\bar c^Q(t)$ form factor of the quark part of the energy momentum tensor (EMT). This form factor describes the non-conservation of the quark part of EMT and contributes to the quark pressure distribution inside the nucleon. Also it can be interpreted in terms of forces between quark and gluon subsystems inside the nucleon. We show that this form factor is parametrically small in the instanton packing fraction. Numerically we obtain for the nucleon EMT a small value of $\bar c^Q(0)\simeq 1.4\cdot 10^{-2}$ at the low normalisation point of $\sim 0.4$ GeV$^2$. This smallness implies interesting physics picture - the forces between quark and gluon mechanical subsystems are smaller than the forces inside each subsystem. The forces from side of gluon subsystem squeeze the quark subsystem - they are compression forces. Additionally, the smallness of $\bar c^Q(t)$ might justify Teryaev's equipartition conjecture. We estimate that the contribution of $\bar c^Q (t)$ to the pressure distribution inside the nucleon is in the range of 1 -20 % relative to the contribution of the quark $D$-term.