Perspective on the origin of hadron masses

Abstract

The energy-momentum tensor in chiral QCD, $T_{\mu\nu}$, exhibits an anomaly, viz. $\Theta_0 :=T_{\mu\mu} \neq 0$. Measured in the proton, this anomaly yields $m_p^2$, where $m_p$ is the proton's mass; but, at the same time, when computed in the pion, the answer is $m_\pi^2=0$. Any attempt to understand the origin and nature of mass, and identify observable expressions thereof, must explain and unify these two apparently contradictory results, which are fundamental to the nature of our Universe. Given the importance of Poincar\'e-invariance in modern physics, the utility of a frame-dependent approach to this problem seems limited. That is especially true of any approach tied to a rest-frame decomposition of $T_{\mu\nu}$ because a massless particle does not possess a rest-frame. On the other hand, the dynamical chiral symmetry breaking (DCSB) paradigm, connected with a Poincar\'e-covariant treatment of the continuum bound-state problem, provides a straightforward, simultaneous explanation of both these identities, and also a diverse array of predictions, testable at existing and proposed facilities. From this perspective, $\langle \pi| \Theta_0 |\pi \rangle =0$ owing to exact, symmetry-driven cancellations which occur between one-body dressing effects and two-body-irreducible binding interactions in any well-defined computation of the forward scattering amplitude that defines this expectation value in the pseudoscalar meson. The cancellation is incomplete in any other hadronic bound state, with a remainder whose scale is set by the size of one-body dressing effects.