The direct coupling of light quarks to heavy di-quarks

Haipeng An,Mark B Wise

doi:10.1016/j.physletb.2018.11.004

Abstract

In the limit mQ>mQvrel>mQvrel2≫ΛQCD hadronic states with two heavy quarks Q should 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 (Sv†Sv)(q¯γμvμq) that couples this color anti-triplet di-quark field Sv (with four-velocity v) directly to the light quarks q in the low energy effective theory. It is O(1/(αs(mQvrel)mQ2)). While our work is mostly of pedagogical value we make an estimate of the contribution of this operator to the masses of Ξbbq baryon and TQQq¯q¯ tetraquark using the non-relativistic constituent quark model.

Highlights

The lowest lying1 Q Q q baryons containing two heavy quarks are stable with respect to the strong interactions
Q C D when the heavy diquark is in a color 3 ̄ configuration, because of the attractive one gluon color Coulombic potential the di-quark has a large binding energy and a small size
One could still write an effective theory [17,24] for the lowest lying baryons containing two heavy quarks interacting with low momentum photons and pions, or an effective theory containing the possible di-quark configurations but matching the latter to an effective field theory just containing the lowest lying di-quark configuration and the Q C D gluon and light quark degrees of freedom would not be justified

Summary

Introduction

The lowest lying Q Q q baryons containing two heavy quarks are stable with respect to the strong interactions. Q C D when the heavy diquark is in a color 3 ̄ configuration, because of the attractive one gluon color Coulombic potential the di-quark has a large binding energy (compared with Q C D ) and a small size (compared with 1/ Q C D ). In this case one can match full QCD directly onto an HQET like theory at a scale μ which we take to be μ = mQ vrel In this limit the color six Q Q configurations and Coulombic excitations above the lowest lying color anti-triplet di-quark state (described by principal quantum numbers n > 1) are much heavier than the ground state and can be integrated out of the theory. The latter is physically more appropriate so we will use it for any quantitative estimates we make using these formulae going forward

Matching

Running

A non-relativistic constituent quark model estimate

Concluding remarks