Chiral symmetry breaking and the quark model: Unification of baryon and meson constraints

• Published in: Nuclear physics. B Vol. 123; no. 3; pp. 445 - 492
• Main Authors: Gunion, J.F., McNamee, P.C., Scadron, M.D.
• Format: Journal Article
• Language: English
• Published: United States Elsevier B.V 01.01.1977
• ISSN: 0550-3213; 1873-1562
• DOI: 10.1016/0550-3213(77)90176-6

We review the subject of chiral symmetry breaking and its connection with the quark model. When the light plane SU(3) charges and quark field density matrix elements are transformed back to the usual static basis it becomes clear that expectation values of chiral breaking operators, such as qλ iq , do not necessarily have simple SU(3) transformation properties. Starting with the standard current quark chiral Hamiltonian H′ = m u uu + m d dd + m s ss , we then use current quark light-cone distribution function concepts in combination with constraints from (i) Compton amplitude fixed poles, (ii) baryon octet and decuplet mass differences, (iii) πN and KN σ terms, (iv) G A/ G V, (v) low-energy π photoproduction multipoles, (vi) Goldberger-Treiman discrepancies, (vii) meson mass ratios in PCAC and, (viii) meson mass differences to determine m ̂ = 1 2 (m u + m d) and m s in more than four independent ways. Our results are all mutually consistent and yield the values m ̂ ≈ m π and m s/ m ̂ ≈ 5 . In particular the independent baryon and meson sectors of the theory are completely compatible.