Communications in Theoretical Physics ›› 2022, Vol. 74 ›› Issue (7): 075201. doi: 10.1088/1572-9494/ac738a
• Particle Physics and Quantum Field Theory • Previous Articles Next Articles
Received:
2022-03-09
Revised:
2022-05-17
Accepted:
2022-05-26
Published:
2022-07-01
Contact:
Xin-Yu Liu
E-mail:sunbx@bjut.edu.cn;liuxinyu@emails.bjut.edu.cn
Bao-Xi Sun, Xin-Yu Liu, Commun. Theor. Phys. 74 (2022) 075201.
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Table 1.
The coefficients ${C}_{ij}$ in the pseudoscalar meson and baryon octet interaction with strangeness $S=-2$ and charge $Q=0,$ ${C}_{ji}={C}_{ij}.$"
${C}_{ij}$ | ${\pi }^{+}{{\rm{\Xi }}}^{-}$ | ${\pi }^{0}{{\rm{\Xi }}}^{0}$ | ${\bar{K}}^{0}{\rm{\Lambda }}$ | ${K}^{-}{{\rm{\Sigma }}}^{+}$ | ${\bar{K}}^{0}{{\rm{\Sigma }}}^{0}$ | $\eta {{\rm{\Xi }}}^{0}$ |
---|---|---|---|---|---|---|
${\pi }^{+}{{\rm{\Xi }}}^{-}$ | $1$ | $-\sqrt{2}$ | $-\sqrt{\displaystyle \frac{3}{2}}$ | $0$ | $-\displaystyle \frac{1}{\sqrt{2}}$ | $0$ |
${\pi }^{0}{{\rm{\Xi }}}^{0}$ | $0$ | $\displaystyle \frac{\sqrt{3}}{2}$ | $-\displaystyle \frac{1}{\sqrt{2}}$ | $-\displaystyle \frac{1}{2}$ | $0$ | |
${\bar{K}}^{0}{\rm{\Lambda }}$ | $0$ | $0$ | $0$ | $-\displaystyle \frac{3}{2}$ | ||
${K}^{-}{{\rm{\Sigma }}}^{+}$ | $1$ | $-\sqrt{2}$ | $-\sqrt{\displaystyle \frac{3}{2}}$ | |||
${\bar{K}}^{0}{{\rm{\Sigma }}}^{0}$ | $0$ | $\displaystyle \frac{\sqrt{3}}{2}$ | ||||
$\eta {{\rm{\Xi }}}^{0}$ | $0$ |
Table 2.
The coefficients ${C}_{ij}$ in the pseudoscalar meson and baryon octet interaction with strangeness $S=-2$ and isospin $I=1/2,$ ${C}_{ji}={C}_{ij}.$"
${C}_{ij}$ | $\pi {\rm{\Xi }}$ | $\bar{K}{\rm{\Lambda }}$ | $\bar{K}{\rm{\Sigma }}$ | $\eta {\rm{\Xi }}$ |
---|---|---|---|---|
$\pi {\rm{\Xi }}$ | $2$ | $-\displaystyle \frac{3}{2}$ | $-\displaystyle \frac{1}{2}$ | $0$ |
$\bar{K}{\rm{\Lambda }}$ | $0$ | $0$ | $-\displaystyle \frac{3}{2}$ | |
$\bar{K}{\rm{\Sigma }}$ | $2$ | $\displaystyle \frac{3}{2}$ | ||
$\eta {\rm{\Xi }}$ | $0$ |
Table 3.
The subtraction constants ${a}_{ij}$ used in the calculation, where the regularization scale takes the value of 630 MeV, i.e. $\mu =630\,$MeV."
${a}_{\pi {\rm{\Xi }}}$ | ${a}_{\bar{K}{\rm{\Lambda }}}$ | ${a}_{\bar{K}{\rm{\Sigma }}}$ | ${a}_{\eta {\rm{\Xi }}}$ | |
---|---|---|---|---|
Set 1 | −2.0 | −2.0 | −2.0 | −2.0 |
Set 2 | −2.2 | −2.0 | −2.0 | −2.0 |
Set 3 | −2.0 | −2.2 | −2.0 | −2.0 |
Set 4 | −2.5 | −1.6 | −2.0 | −2.0 |
Set 5 | −3.1 | −1.0 | −2.0 | −2.0 |
Table 4.
The pole position and corresponding coupling constants ${g}_{i}$ for different parameter sets calculated with the loop function in equation (10), where the pole position in the complex energy plane is in units of MeV."
Set 1 | Set 2 | Set 3 | Set 4 | Set 5 | |
---|---|---|---|---|---|
Pole position | 1566-i119 | 1557-i99 | 1558-i113 | 1558-i83 | 1553-i60 |
${g}_{\pi {\rm{\Xi }}}$ | 2.2-i1.5 | 2.2-i1.3 | 2.1-i1.5 | 2.2-i2.4 | 2.1-i0.8 |
${g}_{\bar{K}{\rm{\Lambda }}}$ | −1.8+i0.6 | −1.8+i0.5 | −1.7+i0.6 | −1.9+i0.5 | −2.1+i0.4 |
${g}_{\bar{K}{\rm{\Sigma }}}$ | −0.5+i0.3 | −0.5+i0.3 | −0.5+i0.3 | −0.6+i0.3 | −0.7+i0.2 |
${g}_{\eta {\rm{\Xi }}}$ | 0.1-i0.3 | 0.1-i0.3 | 0.2-i0.3 | −0.0-i0.1 | −0.3-i0 |
Table 5.
The pole position and corresponding coupling constants ${g}_{i}$ for different parameter sets calculated with the loop function in equation (11), where the pole position in the complex energy plane is in units of MeV."
Set 1 | Set 2 | Set 3 | Set 4 | Set 5 | |
---|---|---|---|---|---|
Pole position | 1557-i104 | 1550-i89 | 1552-i100 | 1551-i78 | 1546-i60 |
${g}_{\pi {\rm{\Xi }}}$ | 2.2-i1.4 | 2.2-i1.2 | 2.1-i1.4 | 2.2-i1.0 | 2.1-i1.0 |
${g}_{\bar{K}{\rm{\Lambda }}}$ | −1.7+i0.5 | −1.7+i0.5 | −1.7+i0.5 | −1.8+i0.5 | −2.0+i0.4 |
${g}_{\bar{K}{\rm{\Sigma }}}$ | −0.5+i0.3 | −0.5+i0.3 | −0.5+i0.3 | −0.6+i0.3 | −0.6+i0.2 |
${g}_{\eta {\rm{\Xi }}}$ | 0.1-i0.3 | 0.1-i0.2 | 0.2-i0.3 | 0.0-i0.1 | −0.2-i0.0 |
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