The direct coupling of light quarks to heavy di-quarks

Journal Article · 06 November 2018 · Physics Letters B

DOI: https://doi.org/10.1016/j.physletb.2018.11.004 · OSTI ID:1481037

An, Haipeng ^[1]; Wise, Mark B. ^[2]

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1. Tsinghua Univ., Beijing (China); Perimeter Inst. for Theoretical Physics, Waterloo, ON (Canada)
2. California Inst. of Technology (CalTech), Pasadena, CA (United States). Walter Burke Inst. for Theoretical Physics

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.

• Research Organization: California Institute of Technology (CalTech), Pasadena, CA (United States)
• Sponsoring Organization: USDOE Office of Science (SC), High Energy Physics (HEP)
• Grant/Contract Number: SC0011632
• OSTI ID: 1481037
• Alternate ID(s): OSTI ID: 1597478
• Journal Information: Physics Letters B, Vol. 788, Issue C; ISSN 0370-2693
• Publisher: ElsevierCopyright Statement
• Country of Publication: United States
• Language: English