The paper delivers the first complete non-redundant dimension-six operator basis for SMEFT at finite temperature using the Hilbert series on R^3 x S^1.
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Dimension-Six Terms in the Standard Model Lagrangian
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abstract
When the Standard Model is considered as an effective low-energy theory, higher dimensional interaction terms appear in the Lagrangian. Dimension-six terms have been enumerated in the classical article by Buchmueller and Wyler [3]. Although redundance of some of those operators has been already noted in the literature, no updated complete list has been published to date. Here we perform their classification once again from the outset. Assuming baryon number conservation, we find 15 + 19 + 25 = 59 independent operators (barring flavour structure and Hermitian conjugations), as compared to 16 + 35 + 29 = 80 in Ref.[3]. The three summed numbers refer to operators containing 0, 2 and 4 fermion fields. If the assumption of baryon number conservation is relaxed, 4 new operators arise in the four-fermion sector.
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Finite-temperature operator basis on $\mathbb{R}^3 \times S^1$ for SMEFT
The paper delivers the first complete non-redundant dimension-six operator basis for SMEFT at finite temperature using the Hilbert series on R^3 x S^1.