Experimental tests for theories of chiral-symmetry breaking
196912 pages
Published in:
- Phys.Rev. 188 (1969) 2330-2341
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Abstract: (APS)
Assuming a picture of the strong interactions in which the Hamiltonian is the sum of an SU(3)⊗SU(3)-symmetric piece H0 plus a small symmetry-breaking term εH1, we show how to calculate relations among the corrections of order ε to the symmetry limit. Our techniques are purely group-theoretic and involve no extraneous dynamical assumptions, so that our results provide direct experimental tests for various symmetry-breaking schemes. For example, we show that if εH1 belongs to the (3, 3¯)⊗(3¯, 3) representation of SU(3)⊗SU(3), then there is one sum rule satisfied by the corrections to the generalized Goldberger-Treiman relations for the three decays n→p+e+ν, Σ→N+e+ν, and Λ→N+e+ν. We also show that the so-called Σ terms, which are closely related to εH1, can be obtained from on-the-mass-shell scattering amplitudes (albeit at an unphysical energy point) if terms of order ε2 can be neglected in comparison to terms of order ε. The question of whether or not lowest-order calculations of symmetry breaking are meaningful is discussed in some detail.- symmetry: chiral
- symmetry: broken
- symmetry: su(3) x su(3)
- group theory
- sum rule
- n: decay
- decay: n
- final state
- p: electron: neutrino
- sigma: decay
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