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A Complete Set of the Dimension-8 Green's Basis Operators in the Standard Model Effective Field Theory

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arxiv 2211.01420 v2 pith:PV5KRYFC submitted 2022-11-02 hep-ph hep-th

Zhe Ren , Jiang-Hao Yu This is my paper · ORCID
classification hep-phhep-th
keywords off-shelloperatorsbasisgreendimensiongeneralamplitudescomplete
verification ladder T0 review T1 audit T2 compute T3 formal
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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 amplitudes 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 procedure, 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 the 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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Cited by 3 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Chiral Effective Field Theories for Strong and Weak Dynamics

    hep-ph 2025-01 conditional novelty 7.0 of 10

    The paper constructs complete and minimal relativistic operator bases for nucleon-nucleon, pion-nucleon-nucleon, and three-nucleon sectors up to p6, and a spurion-based leptonic sector up to p4, using Hilbert series a...

  2. Massive Helicity-Chirality Spinor Formalism from Massless Amplitudes with On-shell Mass Insertion

    hep-ph 2025-01 conditional novelty 7.0 of 10

    A new helicity-chirality spinor basis with a 'transversality' charge claims a one-to-one UV-IR correspondence between massive amplitudes and massless amplitudes with Higgs insertions, and reproduces pion decay, top de...

  3. Fingerprinting New Physics with Effective Field Theories

    hep-ph 2025-01 conditional novelty 2.0 of 10

    A thesis compiling published SMEFT global fits, automated UV-model constraints, and ML-based unbinned observables, with projections for HL-LHC, FCC-ee, and CEPC.

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