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Regge trajectories for the doubly heavy triquarks $((Qq)\bar{Q}')$

Xin-Ru Liu, Qi Liu, He Song, Jiao-Kai Chen

Abstract

We attempt to apply the Regge trajectory approach to the doubly heavy triquarks $((Qq)\bar{Q}^{\prime})$ $(Q,\,Q'=b,\,c; q=u,\,d,\,s)$. We propose the Regge trajectory relations for the doubly heavy triquarks, and then employ them to crudely estimate the spectra of the triquarks $((cu)\bar{c})$, $((cu)\bar{b})$, $((cs)\bar{c})$, $((cs)\bar{b})$, $((bu)\bar{c})$, $((bu)\bar{b})$, $((bs)\bar{c})$, and $((bs)\bar{b})$. The $λ$-trajectories and the $ρ$-trajectories are investigated. The triquark Regge trajectory becomes a new and very simple approach for estimating the spectra of triquarks. It also provides a simple method to investigate the $ρ$-mode and $σ$-mode excitations of pentaquarks and hexaquarks in the triquark picutre. Moreover, the spin-averaged masses of the ground states of pentaquarks $(\bar{c}(cu))(cu)$, $(\bar{b}(bu))(bu)$ and $(\bar{c}(cu))(bu)$ are estimated, which are consistent with other theoretical predictions.

Regge trajectories for the doubly heavy triquarks $((Qq)\bar{Q}')$

Abstract

We attempt to apply the Regge trajectory approach to the doubly heavy triquarks . We propose the Regge trajectory relations for the doubly heavy triquarks, and then employ them to crudely estimate the spectra of the triquarks , , , , , , , and . The -trajectories and the -trajectories are investigated. The triquark Regge trajectory becomes a new and very simple approach for estimating the spectra of triquarks. It also provides a simple method to investigate the -mode and -mode excitations of pentaquarks and hexaquarks in the triquark picutre. Moreover, the spin-averaged masses of the ground states of pentaquarks , and are estimated, which are consistent with other theoretical predictions.
Paper Structure (14 sections, 35 equations, 3 figures, 8 tables)

This paper contains 14 sections, 35 equations, 3 figures, 8 tables.

Table of Contents

  1. Introduction
  2. Regge trajectory relations
  3. Preliminary
  4. Spinless Salpeter equation
  5. Regge trajectory relations for heavy-heavy and heavy-light systems
  6. Regge trajectory relations for the doubly heavy triquarks $((Qq)\bar{Q}')$
  7. Regge trajectories for the doubly heavy triquarks $((Qq)\bar{Q}')$
  8. Parameters
  9. $\rho$-trajectories for the doubly heavy triquarks
  10. $\lambda$-trajectories for the doubly heavy triquarks
  11. Discussions
  12. Conclusions
  13. States of triquarks
  14. List of the Regge trajectory relations

Figures (3)

  • Figure 1: Schematic diagram of the doubly heavy triquark $((Qq)\bar{Q}')$ in the antiquark-diquark picture. The grey part represents the heavy-light diquark $(Qq)$ composed of one heavy quark $Q$ and one light quark $q$. The circle on the right denotes the heavy antiquark $\bar{Q}'$.
  • Figure 2: Radial and orbital $\rho$-trajectories for the doubly heavy triquarks $((cu)\bar{c})$, $((cu)\bar{b})$, $((cs)\bar{c})$, $((cs)\bar{b})$, $((bu)\bar{c})$, $((bu)\bar{b})$, $((bs)\bar{c})$, and $((bs)\bar{b})$. $n^1s_0$ and $1^1l_{l}$ denote the spin singlets of diquarks. $n^3s_1$ and $1^3l_{l+1}$ denote the spin triplets. Circles represent the predicted data and the black lines represent the fitted formulas. Data are listed in Table \ref{['tab:massrho']} and formulas are in Table \ref{['tab:rtbehav']}.
  • Figure 3: Radial and orbital $\lambda$-trajectories for the doubly heavy triquarks $((cu)\bar{c})$, $((cu)\bar{b})$, $((cs)\bar{c})$, $((cs)\bar{b})$, $((bu)\bar{c})$, $((bu)\bar{b})$, $((bs)\bar{c})$, and $((bs)\bar{b})$. $1^1s_0$ and $1^3s_1$ denote the spin singlets and spin triplets of diquarks, respectively. Circles represent the predicted data and the black lines represent the fitted formulas. Data are listed in Tables \ref{['tab:masslambdac']} and the formulas are in Table \ref{['tab:rtbehav']}.