Title: The direct coupling of light quarks to heavy di-quarks

Abstract

In the limit $m_Q>m_Q{v}_{\mathrm{rel}}>m_Q{v_{\mathrm{rel}}}^2>>{\mathrm{\Lambda }}_{QCD}$ 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 $1/{\mathrm{\Lambda }}_{QCD}$) 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 ${\mathrm{\Lambda }}_{QCD}$ to this ground state di-quark. In this short paper we calculate the coefficient of leading local operator $\left(S_v^{\mathrm{†}}{S}_v\right)\left(\overline{q}{\gamma }^{\mu }{v}_{\mu }q\right)$ 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 $\mathcal{O}(1/({\alpha }_s\left(m_Q{v}_{\mathrm{rel}}\right)m_Q^2\left)\right)$. While our work is mostly of pedagogical value we make an estimate of the contribution of this operator to the masses of ${\mathrm{\Xi }}_{bbq}$ baryon and $T_{QQ\overline{q}\overline{q}}$ tetraquark using the non-relativistic constituent quark model.

Authors:

An, Haipeng; Wise, Mark B.

Publication Date:

2019-01-01

Research Org.:

California Institute of Technology (CalTech), Pasadena, CA (United States)

Sponsoring Org.:

USDOE Office of Science (SC), High Energy Physics (HEP)

OSTI Identifier:

1481037

Alternate Identifier(s):

OSTI ID: 1597478

Grant/Contract Number:  

SC0011632

Resource Type:

Published Article

Journal Name:

Physics Letters B

Additional Journal Information:

Journal Name: Physics Letters B Journal Volume: 788 Journal Issue: C; Journal ID: ISSN 0370-2693

Publisher:

Elsevier

Country of Publication:

Netherlands

Language:

English

Subject:

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS