Mass spectra and wave functions of the doubly heavy baryons with JP=1+ heavy diquark cores *

Qiang Li; Chao-Hsi Chang; Si-Xue Qin; Guo-Li Wang

doi:10.1088/1674-1137/44/1/013102

Chinese Physics C, Volume. 44, Issue 1, (2020)

Mass spectra and wave functions of the doubly heavy baryons with JP=1+ heavy diquark cores *

Qiang Li^1,2、*, Chao-Hsi Chang^1,2,3、*, Si-Xue Qin^1、*, and Guo-Li Wang^1、*

Author Affiliations

¹Department of Physics, Chongqing University5Department of Physics, Chongqing University, Chongqing 401331, China

¹Department of Physics, Hebei University6Department of Physics, Hebei University, Baoding 071002, China

¹Institute of Theoretical Physics, Chinese Academy of Sciences2Institute of Theoretical Physics, Chinese Academy of Sciences, Beijing 100190, China

¹School of Physical Science and Technology, Northwestern Polytechnical University1School of Physical Science and Technology, Northwestern Polytechnical University, Xi'an 710072, China

²Institute of Theoretical Physics, Chinese Academy of Sciences2Institute of Theoretical Physics, Chinese Academy of Sciences, Beijing 100190, China

²School of Physical Sciences, University of Chinese Academy of Sciences, 19A Yuquan Road3School of Physical Sciences, University of Chinese Academy of Sciences, 19A Yuquan Road, Beijing 100049, China

³CCAST (World Laboratory)4CCAST (World Laboratory), P.O. Box 8730, Beijing 100190, China

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Figures & Tables(14)

Fig. 1. (color online) BSE of a meson and a diquark. denotes the bound state momentum, and , where is the bound system mass; and are the quark (antiquark) momenta. The blue roman letters denote the Dirac indices.

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Fig. 2. (color online) Radial wave functions of the diquark core with .

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Fig. 3. (color online) The vertex diagram of the diquark core coupling to a gluon.

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Fig. 4. (color online) Form factor of the diquark core coupling to a gluon.

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Fig. 5. (color online) The Bethe-Salpeter equation for a baryon based on the diquark model. The Greek (red) letters are the Lorentz indices; the Roman (blue) letters are the Dirac indices. denote the momenta of the baryon, heavy diquark and the third light quark, respectively.

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Fig. 6. (color online) BS radial wave functions of with the energy levels ; and correspond to the and components, and corresponds to the -wave; is the number of the node plus one. Almost every state contains the -, - and -wave components.

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Fig. 7. (color online) BS radial wave functions of with the energy levels ; , and correspond to the , and components, and correspond to the and -wave. Almost every baryon state contains all , and components.

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Table 1. The parameter (in GeV), for and mesons.
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Table 1. The parameter (in GeV), for and mesons.
0.512 0.509 0.489 0.341 0.322
0.378 0.376 0.352 0.296 0.275

Table 1. Mass spectra of color anti-triplet diquark cores , and , in units of GeV.
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Table 1. Mass spectra of color anti-triplet diquark cores , and , in units of GeV.
3.303 3.651 3.702 3.882
6.594 6.924 6.980 7.142
9.830 10.154 10.217 10.361

Table 2. Wave functions at the origin for the ground states of diquark cores , and (in GeV²).
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Table 2. Wave functions at the origin for the ground states of diquark cores , and (in GeV²).
diquark cores
0.155 0.299 0.618
−0.144 −0.287 −0.600

Table 3. The parameter (in GeV) determined by the spin-weighted average method.
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Table 3. The parameter (in GeV) determined by the spin-weighted average method.
baryons
baryons

Table 4. Mass spectra of the doubly heavy baryons, in units of MeV. Symbols used to label the baryon states are: denotes the radial quantum number of the doubly heavy diquark core inside the baryon; the orbital angular momentum of the diquark; the radial number of the baryon; the baryon spin multiplicity; the orbital angular momentum quantum number between the diquark core and the light quark; and finally the total baryon angular momentum.
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Table 4. Mass spectra of the doubly heavy baryons, in units of MeV. Symbols used to label the baryon states are: denotes the radial quantum number of the doubly heavy diquark core inside the baryon; the orbital angular momentum of the diquark; the radial number of the baryon; the baryon spin multiplicity; the orbital angular momentum quantum number between the diquark core and the light quark; and finally the total baryon angular momentum.
1
2
3
4
1
1

Table 5. Mass spectra (in MeV) of the doubly heavy baryons.
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Table 5. Mass spectra (in MeV) of the doubly heavy baryons.
1
2
3
4
1
1

Table 6. Comparison of the predictions of the ground state masses (in GeV) of the doubly heavy baryons. The results in the third [21] and forth [66,67] columns are from the lattice QCD calculations. Note that here , denote the baryons with diquark core.

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Table 6. Comparison of the predictions of the ground state masses (in GeV) of the doubly heavy baryons. The results in the third [21] and forth [66,67] columns are from the lattice QCD calculations. Note that here , denote the baryons with diquark core.

This	[21]	[66,67]	[22,68]	[9]	[69]	[70]	[71]	[72]
3.601	3.610	−	3.627	3.620	3.612	3.547	3.633	3.606
3.703	3.692	−	3.690	3.727	3.706	3.719	3.696	3.675
3.710	3.738	3.712	3.692	3.778	3.702	3.648	3.732	3.715
3.814	3.822	3.788	3.756	3.872	3.783	3.770	3.802	3.772
6.931	6.959	6.945	6.933	6.933	6.919	6.904	6.948	−
6.997	6.985	6.989	6.969	6.980	6.986	6.936	6.973	−
7.033	7.032	6.994	6.984	7.088	6.986	6.994	7.047	−
7.101	7.059	7.056	−	7.130	7.046	7.017	7.066	−
10.182	10.143	−	10.162	10.202	10.197	10.185	10.169	10.138
10.214	10.178	−	10.184	10.237	10.236	10.216	10.189	10.169
10.276	10.273	−	10.208	10.359	10.260	10.271	10.259	10.230
10.309	10.308	−	−	10.389	10.297	10.289	10.268	10.258

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Qiang Li, Chao-Hsi Chang, Si-Xue Qin, Guo-Li Wang. Mass spectra and wave functions of the doubly heavy baryons with JP=1+ heavy diquark cores *[J]. Chinese Physics C, 2020, 44(1):

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Paper Information

Category: Particles and fields

Received: Sep. 13, 2019

Accepted: --

Published Online: Sep. 29, 2020

The Author Email: Li Qiang (liruo@nwpu.edu.cn), Chang Chao-Hsi (zhangzx@itp.ac.cn), Qin Si-Xue (sqin@cqu.edu.cn), Wang Guo-Li (gl_wang@hit.edu.cn)

DOI:10.1088/1674-1137/44/1/013102

Topics

Nuclear physics

Particles and fields

Particle and nuclear astrophysics and cosmology

Table 1. The parameter (in GeV), for and mesons.

Table 1. The parameter (in GeV), for and mesons.

Table 1. Mass spectra of color anti-triplet diquark cores , and , in units of GeV.

Table 1. Mass spectra of color anti-triplet diquark cores , and , in units of GeV.

Table 2. Wave functions at the origin for the ground states of diquark cores , and (in GeV2).

Table 2. Wave functions at the origin for the ground states of diquark cores , and (in GeV2).

Table 3. The parameter (in GeV) determined by the spin-weighted average method.

Table 3. The parameter (in GeV) determined by the spin-weighted average method.

Table 5. Mass spectra (in MeV) of the doubly heavy baryons.

Table 5. Mass spectra (in MeV) of the doubly heavy baryons.

Table 6. Comparison of the predictions of the ground state masses (in GeV) of the doubly heavy baryons. The results in the third [21] and forth [66,67] columns are from the lattice QCD calculations. Note that here , denote the baryons with diquark core.

Table 6. Comparison of the predictions of the ground state masses (in GeV) of the doubly heavy baryons. The results in the third [21] and forth [66,67] columns are from the lattice QCD calculations. Note that here , denote the baryons with diquark core.

Table 2. Wave functions at the origin for the ground states of diquark cores , and (in GeV²).

Table 2. Wave functions at the origin for the ground states of diquark cores , and (in GeV²).