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.
Hilbert Series for Constructing Lagrangians: expanding the phenomenologist's toolbox
4 Pith papers cite this work. Polarity classification is still indexing.
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abstract
This note presents the Hilbert series technique to a wider audience in the context of constructing group-invariant Lagrangians. This technique provides a fast way to calculate the number of operators of a specified mass dimension for a given field content, and is a useful cross check on more well-known group theoretical methods. In addition, at least when restricted to invariants without derivatives, the Hilbert series technique supplies a robust way of counting invariants in scenarios which, due to the large number of fields involved or to high dimensional group representations, are intractable by traditional methods. We work out several practical examples.
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A group-theoretic construction yields complete form factor bases for scalar, vector, and tensor operators on spin-1/2 to spin-2 particles, with new P and T structures for higher spins and identification of a redundant conserved structure for spin-2 in existing literature.
A minimal basis with fewer terms and simpler contractions is given for non-derivative baryon-number-violating operators in SMEFT up to mass dimension 11.
citing papers explorer
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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.
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Covariant Construction of Generalized Form Factors
A group-theoretic construction yields complete form factor bases for scalar, vector, and tensor operators on spin-1/2 to spin-2 particles, with new P and T structures for higher spins and identification of a redundant conserved structure for spin-2 in existing literature.
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Basis for non-derivative baryon-number-violating operators
A minimal basis with fewer terms and simpler contractions is given for non-derivative baryon-number-violating operators in SMEFT up to mass dimension 11.
- Fortuity and Complexity in a Simple Quark Model