2016/06/13 by Craig D. Roberts · 1 citation
Physics and Astronomy · #Amplitude #Anomaly (physics) #Bound state #Covariant transformation #Hadron #High-Energy Particle Collisions Research #Massless particle #Mathematical physics #Meson #Observable #Particle physics #Particle physics theoretical and experimental studies #Physics #Pion #Pseudoscalar #Pseudoscalar meson #Quantum Chromodynamics and Particle Interactions #Quantum chromodynamics #Quantum mechanics #Scattering amplitude #Theoretical physics #hep-lat #hep-ph #nucl-ex #nucl-th
paper · pdf · doi:10.1007/s00601-016-1168-z
12 pages, 2 figures. Contribution to a Topical Issue of Few Body Systems, celebrating the journal's 30th birthday
arxiv created 2016/06/13 · openalex publication_date 2016/12/09 · arxiv updated 2017/01/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
The energy-momentum tensor in chiral QCD, Tμν, exhibits an anomaly, viz. Θ0 :=Tμμ ≠ 0. Measured in the proton, this anomaly yields mp2, where mp is the proton's mass; but, at the same time, when computed in the pion, the answer is mπ2=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 Poincaré-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 Tμν because a massless particle does not possess a rest-frame. On the other hand, the dynamical chiral symmetry breaking (DCSB) paradigm, connected with a Poincaré-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, ⟨ π| Θ0 |π⟩ =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.