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wilson-eft / wilson

A Python package for the running and matching of Wilson coefficients above and below the electroweak scale
https://wilson-eft.github.io
MIT License
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Redundant operators #72

Closed jackypheno closed 3 years ago

jackypheno commented 3 years ago

I think, since the Wilson coefficient ll_ijji and ll_iijj are related through Fierz, one of them should be removed from the Warsaw basis:

https://github.com/wcxf/wcxf-bases/blob/429bcbf1f2b9fc80f488ffd88b5e497f7dd4a3e2/smeft.warsaw.basis.yml

jasonaebischerGIT commented 3 years ago

Yes, I agree. Thanks for bringing it up!

DavidMStraub commented 3 years ago

But if you Fierz them, you'll have different SU(2) contractions.

DavidMStraub commented 3 years ago

Note: the number of real parameters in this basis has been checked to be 2499. So if there are redundant operators, also https://arxiv.org/pdf/1312.2014.pdf is wrong.

jasonaebischerGIT commented 3 years ago

Yes, David is right; Say we compare ll_1122 and ll_1221 (dropping gamma matrices for simplicity):

1122: (nu_e nu_e)[(nu_mu nu_mu) + (mu mu)] + (e e)[(nu_mu nu_mu) + (mu mu)]

1221: (nu_e nu_mu)[(nu_mu nu_e) + (mu e)] + (e mu)[(nu_mu nu_e) + (mu e)]

One can never bring one in the form of the other using Fierz relations.

jackypheno commented 3 years ago

@DavidMStraub @jasonaebischerGIT Indeed, thanks for the clarification. Closing.

DavidMStraub commented 3 years ago

Glad I could help :slightly_smiling_face: