Regge-like relation and a universal description of heavy–light systems

Kan Chen; Yubing Dong; Xiang Liu; Qi-Fang Lü; Takayuki Matsuki

doi:10.1140/epjc/s10052-017-5512-3

2023 Impact factor 4.2

Particles and Fields

Open Access

Eur. Phys. J. C (2018) 78: 20
https://doi.org/10.1140/epjc/s10052-017-5512-3

Regular Article - Theoretical Physics

Regge-like relation and a universal description of heavy–light systems

Kan Chen¹^,2, Yubing Dong³^,4^,5, Xiang Liu¹^,2, Qi-Fang Lü³^,6 and Takayuki Matsuki⁷^,8^*

¹ School of Physical Science and Technology, Lanzhou University, Lanzhou, 730000, China
² Research Center for Hadron and CSR Physics, Institute of Modern Physics of CAS, Lanzhou University, Lanzhou, 730000, China
³ Institute of High Energy Physics, CAS, Beijing, 100049, China
⁴ Theoretical Physics Center for Science Facilities (TPCSF), CAS, Beijing, China
⁵ School of Physical Sciences, University of Chinese Academy of Sciences, Beijing, 101408, China
⁶ Synergetic Innovation Center for Quantum Effects and Applications (SICQEA), Hunan Normal University, Changsha, 410081, China
⁷ Tokyo Kasei University, 1-18-1 Kaga, Itabashi, Tokyo, 173-8602, Japan
⁸ Theoretical Research Division, Nishina Center, RIKEN, Wako, Saitama, 351-0198, Japan

^* e-mail: matsuki@tokyo-kasei.ac.jp

Received: 26 October 2017
Accepted: 28 December 2017
Published online: 12 January 2018

Abstract

Using the Regge-like formula $(M-m_Q)^2=\pi \sigma L$ between hadron mass M and angular momentum L with a heavy quark mass $$m_Q$$ and a string tension $\sigma$ , we analyze all the heavy–light systems, i.e., $$D/D_s/B/B_s$$ mesons and charmed and bottom baryons. Numerical plots are obtained for all the heavy–light mesons of experimental data whose slope becomes nearly equal to 1/2 of that for light hadrons. Assuming that charmed and bottom baryons consist of one heavy quark and one light cluster of two light quarks (diquark), we apply the formula to all the heavy–light baryons including the recently discovered $\Omega _c$ and find that these baryons experimentally measured satisfy the above formula. We predict the average mass values of B, $$B_s$$ , $\Lambda _b$ , $\Sigma _c$ , $\Xi _c$ , and $\Omega _c$ with $$L=2$$ to be 6.01, 6.13, 6.15, 3.05, 3.07, and 3.34 GeV, respectively. Our results on baryons suggest that these baryons can be safely regarded as heavy quark–light cluster configuration. We also find a universal description for all the heavy–light mesons as well as baryons, i.e., one unique line is enough to describe both of charmed and bottom heavy–light systems. Our results suggest that instead of mass itself, gluon flux energy is essential to obtain a linear trajectory. Our method gives a straight line for $$B_c$$ although the curved parent Regge trajectory was suggested before.