Selection rules and quark correlations in the N* resonance spectrum

Abstract

Abstract. A "Λ selection rule" for N * resonances in the presence of QCD mixing effects is identified. Due to the QCD mixing, excitations of 20-plets are possible in SU(6). We show that this selection rule is useful for classifying PDG states at N = 2, and for clarifying whether strongly correlated diquarks survive for L > 0.PACS. 12.39.-x phenomenological quark models -13.60.-r Photon and charged-lepton interactions with hadrons Quark model and selection rulesAlthough it has been about forty years since the quark model was first applied to the problem of baryon resonances, it is still not well established whether three constituent quarks or a quark-diquark effective degrees of freedom are needed in the description of the baryon spectrum. In the recent years, significant progresses on the photo-nuclear reactions as a probe for the internal structure of nucleon and nucleon resonance have been made in experiment, which provide not only stringent constraints on theoretical phenomenologies but also novel insights into the strong QCD dynamics in this challenging regime.A standard and phenomenologically successful assumption common to a large number of papers in the quark model is that photon transitions are additive in the constituent quarks [1,2,3]. This assumption also underlies models of hadronic production and decay in the sense that when q 1 q 2 q 3 → [q 1 q 2 q i ] + [q 3qi ], the quark pair q 1 q 2 are effectively spectators and only q 3 is involved in driving the transition. Such approximations lead to well known selection rules, which have proved useful in classifying resonances [1]. We adopt this approximation as a first step and show that within it there is a further selection rule that appears to have been overlooked in the literature. We shall refer to this as the "Λ selection rule" and show how it may help classify N * resonances [4]. The standard SU(6)⊗O(3) wavefunction can be constructed from three fundamental representations of group S 3 : SU (6) : 6 ⊗ 6 ⊗ 6 = 56 s + 70 ρ + 70 λ + 20 a , (1) where the subscripts denote the corresponding S 3 basis for each representation, and the bold numbers denote the dimension of the corresponding representation. The spinflavor wavefunctions can be expressed as |N 6 , 2S+1 N 3 , where N 6 (=56, 70 or 20) and N 3 (=8, 10, or 1) denote the SU(6) and SU(3) representation and S stands for the total spin. The SU(6)⊗O(3) (symmetric) wavefunction is