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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2404.14152 |
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| _version_ | 1866914764661194752 |
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| author | Li, Xuan-He Sun, Hao Tang, Feng-Jie Yu, Jiang-Hao |
| author_facet | Li, Xuan-He Sun, Hao Tang, Feng-Jie Yu, Jiang-Hao |
| contents | Chiral perturbation theory systematically describes the low energy dynamics of meson and baryons using nonlinear Nambu-Goldstone fields. Using the Young tensor technique, we construct the pure mesonic effective operators up to $p^8$-order, one-to-one corresponding to contact amplitudes with the on-shell Adler zero condition. The off-shell external sources, non-vanishing under equation-of-motion conditions, are also added to the operator bases. We also show the invariant tensor bases using the Young tableau is equivalent to the trace bases with Cayley-Hamilton relations. Separated into different $CP$ eigenstates, at $\mathcal{O}(p^8)$ we obtain the operator lists of the 567 $C$+$P$+ operators, 483 $C$+$P$- operators, 376 $C$-$P$+ operators, and 408 $C$-$P$- operators for $SU(2)$ case, while there are 1959 $C$+$P$+ operators, 1809 $C$+$P$- operators, 1520 $C$-$P$+ operators, and 1594 $C$-$P$- operators for $SU(3)$ case, consistent with results using the Hilbert series. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_14152 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Complete $CP$ Eigen-bases of Mesonic Chiral Lagrangian up to $p^8$-order Li, Xuan-He Sun, Hao Tang, Feng-Jie Yu, Jiang-Hao High Energy Physics - Phenomenology Chiral perturbation theory systematically describes the low energy dynamics of meson and baryons using nonlinear Nambu-Goldstone fields. Using the Young tensor technique, we construct the pure mesonic effective operators up to $p^8$-order, one-to-one corresponding to contact amplitudes with the on-shell Adler zero condition. The off-shell external sources, non-vanishing under equation-of-motion conditions, are also added to the operator bases. We also show the invariant tensor bases using the Young tableau is equivalent to the trace bases with Cayley-Hamilton relations. Separated into different $CP$ eigenstates, at $\mathcal{O}(p^8)$ we obtain the operator lists of the 567 $C$+$P$+ operators, 483 $C$+$P$- operators, 376 $C$-$P$+ operators, and 408 $C$-$P$- operators for $SU(2)$ case, while there are 1959 $C$+$P$+ operators, 1809 $C$+$P$- operators, 1520 $C$-$P$+ operators, and 1594 $C$-$P$- operators for $SU(3)$ case, consistent with results using the Hilbert series. |
| title | Complete $CP$ Eigen-bases of Mesonic Chiral Lagrangian up to $p^8$-order |
| topic | High Energy Physics - Phenomenology |
| url | https://arxiv.org/abs/2404.14152 |