The Direct Coupling of Light Quarks to Heavy Di-quarks

Abstract

In the limit m_Q > m_Q v_(rel) > m_Q v_(rel)^2 ≫ Λ_(QCD) hadronic states with two heavy quarks Qshould be describable by a version of HQET where the heavy quark is replaced by a di-quark degree of freedom. In this limit the di-quark is a small (compared with 1/ΛQCD) color anti-triplet, bound primarily by a color Coulomb potential. The excited Coulombic states and color six states are much heavier than the color anti-triplet ground state. The low lying spectrum of hadrons containing two heavy quarks is then determined by the coupling of the light quarks and gluons with momentum of order ΛQCD to this ground state di-quark. In this short paper we calculate the coefficient of leading local operator (S_v^†S_v)(qγ^μv_μq) that couples this color anti-triplet di-quark field S_v (with four-velocity v) directly to the light quarks q in the low energy effective theory. It is O(1/(α_s(m_Qv_(rel))m_Q^2)). While our work is mostly of pedagogical value we make an estimate of the contribution of this operator to the masses of Ξ_(bbq) baryon and T_(QQqq) tetraquark using the non-relativistic constituent quark model.