Single Pion Transitions of Charmed Baryons

The SU(2Nf ) ⊗ O(3) constituent quark model symmetry of the light diquark system are used to analyze single pion transitions of Swave to S-wave and P-wave to S-wave heavy baryons. We show that the Heavy Quark Symmetry (HQS) coupling factors are given in terms of the three independent couplings gΣQΛQπ, fΛQ1ΣQπ and fΛQ1ΣQπ. Light-Front quark model spin wave functions are, then, employed to calculate these couplings and to predict decay rates of single pion transitions between charm baryon states. A talk given at the MRST ‘98 conference, “ Toward the Theory of Everything ”, May 13-15, 1998. Montréal, Canada. To appear in the proceedings. Heavy Quark Symmetry (HQS) and SU(2Nf )×O(3) light diquark symmetry can be used to construct heavy baryon spin wave functions a la BetheSalpater [1, 2]. These covariant wave functions were employed [3] to analyze current-induced bottom baryon to charm baryon transitions. Similar procedure will be followed here to study heavy baryon S-wave to S-wave and P-wave to S-wave single pion transitions. In single–pion transitions between heavy baryons, the pion is emitted by each of the light quarks while the heavy quark is unaffected. In fact, the heavy baryon velocity will not be changed when emitting the pion since it is infinitely massive and will not recoil. In a heavy baryon, a light diquark system with quantum numbers j couples with a heavy quark with J Q = 1/2 + to form a doublet with J = (j ± 1/2). Heavy quark symmetry allows us to write down a general form for the heavy baryon spin wave functions [4, 3]. Ignoring isospin indices, one has χαβγ = (φμ1···μj )αβψ μ1...μj γ (v) . (1) Here, v = P M is the baryon four velocity, μ1 · · ·μj are Lorentz indices, the spinor indices α and β refer to the light quark system and the index γ refers to the heavy quark. In the heavy quark limit, the χαβγ satisfy the BargmannWigner equation on the heavy quark index ( 6v)′ γ χαβγ′ = χαβγ . (2) In general the light degrees of freedom spin wave functions (φμ1···μj )αβ are written in terms of the two bispinors [χ]αβ and [χ 1 μ]αβ . The matrix [χ ]αβ = [( 6v+1)γ5C]αβ , projects out a spin-0 object, is symmetric when interchanging α and β. However, [χμ]αβ = [( 6v + 1)γ⊥μC]αβ which projects out a spin-1 object is antisymmetric. Here, C is the charge conjugation operator and γ⊥ μ = γμ − 6vvμ. On the other hand the “superfield” ψ μ1...μj γ (v) stands for the two spin wave functions corresponding to the two heavy quark symmetry degenerate states with spins (j ± 1/2). They are generally written in terms of the Dirac spinor u and the Rarita-Schwinger spinor uμ. The S-wave heavy-baryon spin wave functions are given by χ ΛQ αβγ = (χ )αβuγ (3) and χ ΣQ αβγ = (χ )αβ { 1 √ 3 γ⊥ μ γ5u uμ }