Stress in static force fields and the sign of the D-term

Abstract

The sign of the D-term is negative for a variety of hadrons, including the proton and pion. Speculation that this is the result of a mechanical stability condition has persisted despite counterexamples, including the positive D-term of the hydrogen atom. In this work, I explore how the sign of the D-term is influenced by the stress carried by static abelian force fields, finding the contributions from spin-even fields to be negative and the contributions from spin-odd fields (such as the electromagnetic field) to be positive. These contributions correlate with the signs of the D-terms of the fields' respective quanta. Since fields with different spin can produce identical potentials---thus resulting in equally-stable composite systems with identical wave functions---the sign of the D-term has nothing to do with stability. Since hadrons are bound by spin-one gluons, their negative D-terms appear atypical and require explanation. I briefly speculate on how color flux confinement could produce a negative hadronic D-term.