Scalar and spin-two energy-momentum-tensor structure in near-threshold charmonium probes of the proton

Abstract

I analyze the energy-momentum-tensor (EMT) content of the chromoelectric operator that governs the leading interaction of compact charmonium with soft gluonic fields. In the renormalized MS operator basis this interaction separates into a scalar anomaly/sigma branch and a traceless spin-two branch. The forward light-front spin-two term is fixed by partonic plus-momentum fractions and gives a controlled correction to scalar dominance. Off forward, however, the chromoelectric spin-two contraction is not governed by $A_i(t)$ alone; it also contains the combination $3B_i(t)-D_i(t)$, equivalently $6J_i(t)-3A_i(t)-D_i(t)$. This identifies which EMT structures charmonium can access in forward and differential observables, without interpreting the measured slope as a model-independent static three-dimensional mass radius.

Comments: 14 pages, 3 figures