ar X iv : h ep - p h / 99 04 45 9 v 2 2 2 Ju n 19 99 Chiral quarks , chiral limit , nonanalytic terms and baryon spectroscopy

It is shown that the principal pattern in baryon spectroscopy, which is associated with the flavor-spin hyperfine interactins, is due to the spontaneous breaking of chiral symmetry in QCD and persists in the chiral limit. All corrections , which are associated with a finite quark (Goldstone boson) mass are suppressed by the factor (µ/Λ χ) 2 and higher. In a recent work [1] Thomas and Krein questioned the foundations of the description of the baryon spectrum with a chiral constituent quark model [2,3]. They claim that " ...the leading nonanalytic (LNA) contributions are incorrect in such approaches. The failure to implement the correct chiral behaviour of QCD results in incorrect systematics for the corrections to the masses. " The argument made was that the splitting pattern implied by the short-range Goldstone boson exchange (GBE) 1 operator − τ i · τ j σ i · σ j , (1) should be inconsistent with chiral symmetry because it is inconsistent with the leading non-analytic contribution to baryon mass predicted by heavy baryon chiral perturbation theory (HBChPT) [4]. I here show that the HBChPT has no bearing on this issue. It is shown by Jenkins and Manohar [4] that the nonanalytic contributions to octet and decuplet masses, such as µ 3 , µ 2 ln µ 2 , ..., where µ stands for a Goldstone boson mass, within the HBChPT in the chiral limit arise only from the loop diagrams a) and b) of Fig. 1, where only diagonal octet-octet or decuplet-decuplet vertices with respect to baryon field contribute, and there is no contribution from the diagrams c) and d) of Fig. 1, where the intermediate baryon belongs to a different SU(3) multiplet. This argument was used by Thomas and Krein, but it was not emphasized that this statement is valid only in the chiral limit. In this limit the ∆ and N (decuplet-octet) are well split and all the infrared divergences of the diagrams c) and d) disappear. Since it is infrared contributions which are an 1 Through the whole paper I use pion-exchange. The transition to the whole GBE exchange within the SU (3) F limit implies a substitution of the SU (2) flavor matrices by the SU (3) ones.