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A Strong Constraint on Chiral Symmetry Breaking at Short Distances

Aug, 1974
19 pages
Published in:
  • Nucl.Phys.B 85 (1975) 189-207
  • Published: 1975
DOI:
Report number:
  • CERN-TH-1922
View in:
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19751986199720082018210
Abstract: (Elsevier)
It is shown that if chiral symmetry is broken by a piece of the Hamiltonian density which transforms as a member of a (3, 3 ) + ( 3 ,3) multiplet of SU (3) × SU (3) and has scale dimension d , then it is necessary to have d ⩾ 3 to avoid inconsistency with low energy theorems which follow from spontaneous symmetry breaking. This is demonstrated using previously derived inequalities for K ℓ3 decay, combined with a detailed analysis of the SU (3) × SU (3) structure of the short-distance expansion for products of current divergences. Asymptotically free gauge theories and some theories with an infrared stable hadronic fixed point can survive this constraint, and for the latter the cross section for e + e − annihilation into hadrons should approach its asymptotically scale-invariant behaviour quite slowly. A softened quark-gluon model with d = 3 is excluded.
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