Abstract
We present a complete and independent off-shell Green’s basis of the dimension 8 operators in the Standard Model effective field theory (SMEFT). We propose an off-shell amplitude formalism such that this new kind of amplitude has a one-to-one correspondence to general operators carrying all kinds of redundancies. The advantage of such formalism is that all kinds of redundancies can be formulated explicitly in terms of the off-shell spinors and thus be removed systematically from the exhaustive list of the general off-shell amplitudes. Following such procedures, redundant operators can be reduced to the ones with the only redundancy from the equation of motion kept, the Green’s basis. We find there are (993+1649) independent (on-shell + off-shell) operators for one generation of fermions and (44807+66197) ones for three generations at dimension 8. This systematic method can be applied to obtain the Green’s basis at any mass dimension for general EFTs.
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Acknowledgments
We thank Ming-Lei Xiao, Hao-Lin Li and Yi-Ning Wang for valuable discussions, and Jose Santiago for valuable suggestions and communications. Z. R. and J.-H.Y. are supported by the National Science Foundation of China under Grants No. 12022514, No. 11875003 and No. 12047503, and National Key Research and Development Program of China Grant No. 2020YFC2201501, No. 2021YFA0718304, and CAS Project for Young Scientists in Basic Research YSBR-006, the Key Research Program of the CAS Grant No. XDPB15.
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Ren, Z., Yu, JH. A complete set of the dimension-8 Green’s basis operators in the Standard Model effective field theory. J. High Energ. Phys. 2024, 134 (2024). https://doi.org/10.1007/JHEP02(2024)134
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DOI: https://doi.org/10.1007/JHEP02(2024)134