By A. W. Thomas (auth.), J. W. Negele, Erich Vogt (eds.)
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Extra resources for Advances in Nuclear Physics: Volume 13
In view of the importance of the axial current in our later development of a chiral-symmetric model of hadronic structure, we shall discuss the calculation of gA in detail. First, we briefly review the standard phenomenological treatment of weak interactions. 20) The hadronic vector and axial vector components have both strangeness conserving (L1S = 0, proportional to cos (Je) and nonconserving 32 A. W. Thomas (LIS = 1, proportional to sin (Je) pieces. For our purposes only the LlS = 0 piece is relevant and we shall effectively set (Je = 0 for pedagogical purposes.
Actually a much more appropriate term would be hidden chiral symmetry because Eq. 54) is invariant under the chiral transformation a-+a-g'!! -+ !! 58) Finally, the conserved vector current associated with Eq. 3. PCAC in the a-Model Having obtained a chiral-symmetric theory with a nucleon mass, all we need to do to make contact with the real world is to introduce a mass for the pion. 62) Chiral Symmetry and the Bag Model 51 in Eq. 65) Because we broke the chiral SU(2) symmetry with the -ca term, the axial current is no longer conserved.
However, such a review would be incomplete without some discussion of the relationship of this phenomenology to QCD. 1 to provide that background. 1. Motivation Finding the solution of QCD, which is widely accepted as the correct theory of strong interactions, poses a very difficult problem (AL 73, MP 78). It is quite likely that some genuine physical insight will be required if we are ever to solve the QCD equations. Symmetry arguments may be of great importance in developing that insight. In the innocent days of 1968, when only three quark flavors were known, Gell-Mann, Oakes, and Renner (GOR) proposed the following scheme (Gel+ 68).