Abstract
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 p8-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 \( \mathcal{O}\left({p}^8\right) \) 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.
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Acknowledgments
We would like to express our gratitude to Chuan-Qiang Song for the valuable assistance provided and for the insightful discussions throughout the course of this work. This work is supported by the National Science Foundation of China under Grants No. 12347105, No. 12375099 and No. 12047503, and the National Key Research and Development Program of China Grant No. 2020YFC2201501, No. 2021YFA0718304.
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Li, XH., Sun, H., Tang, FJ. et al. Complete CP eigen-bases of mesonic chiral Lagrangian up to p8-order. J. High Energ. Phys. 2024, 189 (2024). https://doi.org/10.1007/JHEP08(2024)189
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DOI: https://doi.org/10.1007/JHEP08(2024)189