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.
Low-derivative operators of the Standard Model effective field theory via Hilbert series methods
6 Pith papers cite this work. Polarity classification is still indexing.
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abstract
In this work, we explore an extension of Hilbert series techniques to count operators that include derivatives. For sufficiently low-derivative operators, we find an algorithm that gives the number of invariant operators, properly accounting for redundancies due to the equations of motion and integration by parts. Specifically, the technique can be applied whenever there is only one Lorentz invariant for a given partitioning of derivatives among the fields. At higher numbers of derivatives, equation of motion redundancies can be removed, but the increased number of Lorentz contractions spoils the subtraction of integration by parts redundancies. While restricted, this technique is sufficient to automatically generate the complete set of invariant operators of the Standard Model effective field theory for dimensions 6 and 7 (for arbitrary numbers of flavors). At dimension 8, the algorithm does not automatically generate the complete operator set; however, it suffices for all but five classes of operators. For these remaining classes, there is a well defined procedure to manually determine the number of invariants. Using these methods, we thereby derive the set of 535 dimension-8 $N_f = 1$ operators.
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A modular assembly method constructs D-dimensional higher-derivative four-point amplitudes involving fermions from gauge-invariant blocks, color factors, and permutation-invariant scalar polynomials.
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.
In a toy qubit model of quarks, baryons are fortuitous with exponential counting and super-exponential complexity while mesons are monotone with polynomial counting and power-law complexity.
Reviews advances toward global SMEFT fits across top, Higgs, and electroweak sectors including NLO QCD effects and multi-sector combinations.
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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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$D$-Dimensional Modular Assembly of Higher-Derivative Four-Point Contact Amplitudes Involving Fermions
A modular assembly method constructs D-dimensional higher-derivative four-point amplitudes involving fermions from gauge-invariant blocks, color factors, and permutation-invariant scalar polynomials.
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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.
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Fortuity and Complexity in a Simple Quark Model
In a toy qubit model of quarks, baryons are fortuitous with exponential counting and super-exponential complexity while mesons are monotone with polynomial counting and power-law complexity.
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Towards global fits in EFT's and New Physics implications
Reviews advances toward global SMEFT fits across top, Higgs, and electroweak sectors including NLO QCD effects and multi-sector combinations.