Bottom baryon2021


Chiaki Itoh
Meijigakuin University, Totsuka, Yokohama 244-8539, Japan

Discussing quark distances, our computed values of 41 baryon masses fit to the experimental values within }8.3 MeV.
PACS numbers: 14.20.Mr, 14.20.Lq, 12.40.Qq

There are 10 bottom baryon masses with reasonable experimental accuracies [1] and wonderful agreement with our computed values of 1994 [2]. There were no reliable experimental values of bottom baryon masses at that time. So we used values of parameters in Ref. [3]; quark masses mu, md, ms, mc, the gluon coupling constant s, the harmonic oscilator constand K, quark distance modifieing constant ȁ@and a constant energy E0. As for the bottom quark mass mb, we used the value given by the meson spectroscopy [4]. Including experimental values of bottom baryons in our parameter fit, we can get more reasonable computed values.

As given in Refs. [2, 3 and 5], we modify the wave functions of the exact solutions of the three-body Schrödinger equations of the harmonic-oscillator potential by the forces caused of the Fermi-Breit terms and compute the baryon masses as the expectation values of the Hamiltonian which contain the relativistic kinetic terms.

As given in the following Table I, our computed values of masses of 16 light baryons, 15 charmed baryons, and 10 bottom baryons fit to the experimental values within }8.3 MeV. The experimental data are those of Ref. [1]. The fit was }9.0 MeV for 22 particles in Ref. [3], }8.5 MeV for 30 particles in Ref. [5], and now, }8.3 MeV for 41 particles, owing to improved experiments. We expect farther improvements. The computer program baryon2021.cpp, Visual C++:: Console Program, is here. We can use C++ in the Visual Studio [6].

As we discussed in Ref. [2],

b > b.

It is crucial to discuss quark distances to get this result; spin-spin interactions dippend on qubic inverse of quark distances [3].

As for b-, it is important to find a from

b-{bss} -> b-b{ss} + .



[1] P. A. Zyla et al. (Particle Data Group), Prog. Theor. Exp. Pys. 2020, o83C01(2020) and 2021 update.

[2] Chiaki Itoh et al., Nuovo Cimento A, 107, 263(1994).

[3] Chiaki Itoh et al., Physical Review D 40, 3660(1989).

[4] Chiaki Itoh et al., Nuovo Cimento A, 105, 1539(1992).

[5] Chiaki Itoh et al., Physical Review D 61, 057502(2000).

[6] Visual Studio 2022 Preview, Microsoft(2021).





TABLE I. Baryon masses 2021, computed and experimental, in units of MeV. Quarks in { } and [ ] are flavor symmetric and antisymmetric, respectively. The values of the parameters are mu =443.013 MeV, md =449.177 MeV, ms =697.812 MeV, mc=1969.391 MeV, mb=5344.023 MeV, s=0.459809, K=5.23375x107 MeV3, =0.210407x10-8 MeV-3, and E0=-1295.89.

  p n + 0 - 0 -
Quarks d{uu} u{dd} s[du] s{uu} s{du} s{dd} u{ss} d{ss}
M(comp) 943.5   945.0   1114.9   1183.9  1187.1   1193.0   1320.8  1328.5 
M(expt) 938.272 939.565 1115.683
}0.006
1189.37
}0.06
1192.642
}0.024
1197.449
}0.030
1314.86
}0.2 
1321.71
}0.07
  ++ + 0 - *+ *0 *- *0
Quarks {uuu} {duu} {udd} {ddd} {suu} {sdu} {sdd} {uss}
M(comp) 1226.7 1225.5 1227.3 1231.9 1381.5 1383.0 1387.3 1527.8 
M(expt) 1230.55
}0.2
  1233.3
}0.4
  1382.8
}0.35
1383.7
}1.0
1387.2
}0.5
1531.80
}0.32
  *- - c+ c++ c+ c0 c+ c0
Quarks {dss} {sss} c[du] c{uu} c{du} c{dd} c[su] c[sd]
M(comp) 1531.8 1665.2  2281.7  2448.4  2445.7 2445.7  2473.3 2476.2
M(expt) 1535.0
}0.6
1672.45
}0.29
2286.46
}0.14
2453.97
}0.14
2452.9
}0.4
2453.75
}0.14
2467.89
}0.4
2470.99
}0.4
  c+ c0 c0 c*++ c*+ c*0 c*+ c*0
Quarks c{su} c{sd} c{ss} {cuu} {cdu} {cdd} {csu} {csd}
M(comp) 2575.0 2574.7 2692.9 2524.4 2522.3 2522.9 2647.8 2648.1
M(expt) 2578.2
}0.5
2578.7
}0.5
2695.2
}1.7
2518.41
}0.2
2517.5
}2.3
2518.48
}0.2
2645.10
}0.30
2646.16
}0.25
  c0 b0 b+ b0 b- b0 b- b0
Quarks {css} b[du] b{uu} b{du} b{dd} b[su] b[sd] b{su}
M(comp) 2762.2 5611.3 5808.3 5809.1 5812.52 5791.5 5797.3 5923.8/TD>
M(expt) 2765.9
}2.0
5619.60
}0.17
5810.56
}0.25
  5815.64
}2.7
5791.9
}0.5
5797.0
}0.9
 
  b- b- b*+ b*0 b*- b*0 b*- b-
Quarks b{sd} b{ss} {buu} {bdu} {bdd} {bsu} {bsd} {bss}
M(comp) 5926.9 6030.9 5838.6 5839.2 5842.5 5953.3 5956.3 6059.4
M(expt) 5935.02
}0.07
  5830.32
}0.27
  5834.74
}0.30
5952.3
}0.6
5955.33
}0.17