2, 84, 30, 993, 560, 15456, 11962, 261485, . . .: higher dimension operators in the SM EFT

Abstract

In a companion paper [1], we show that operator bases for general effective field theories are controlled by the conformal algebra. Equations of motion and integration by parts identities can be systematically treated by organizing operators into irreducible representations of the conformal group. In the present work, we use this result to study the standard model effective field theory (SM EFT), determining the content and number of higher dimension operators up to dimension 12, for an arbitrary number of fermion generations. We find additional operators to those that have appeared in the literature at dimension 7 (specifically in the case of more than one fermion generation) and at dimension 8. (The title sequence is the total number of independent operators in the SM EFT with one fermion generation, including hermitian conjugates, ordered in mass dimension, starting at dimension 5.)

Multiboson interactions at the LHC

“…At ∆ i = 6 there are already 59 operators in the SM (Buchmuller and Wyler, 1986;Grzadkowski et al, 2010), while for ∆ i = 8 an exhaustive list of 535 operators was finally classified in (Lehman and Martin, 2016). While there are slight differences in number of operators at a fixed dimension in the literature depending on what assumptions are chosen, the operator basis has now been extended through ∆ i = 12 in the SM using more sophisticated mathematical techniques (Henning et al, 2015). However, the important and simple to understand point is that as ∆ i increases the number of operators greatly…”

On HQET and NRQCD operators of dimension 8 and above

“…As research progresses, higher dimensional operators are receiving more and more attention. For example, the construction of higher dimension operators in the Standard Model Effective Field Theory (SM EFT) was shown recently be simpler than one might expect [38]. In this paper we investigated the question of constructing higher dimensional operators for the HQET and NRQCD (NRQED) Lagrangians.…”

The Z decay width in the SMEFT: y t and λ corrections at one loop

“…7 The Class 7 operators contribute directly to Z →b L b L at one loop with the finite terms 22) and through Higgs tadpoles as…”

“…The number of non redundant operators in L (5) , L (6) , L (7) and L (8) is known [1][2][3][4][5][6][7] and a general algorithm to determine operator bases at higher orders has been established in refs. [6][7][8][9], making the SMEFT, in principle, defined to all orders in the expansion in local operators.…”

“…[6][7][8][9], making the SMEFT, in principle, defined to all orders in the expansion in local operators. In this work, we use a naive power counting in mass dimension so that the operators Q (k) i will be suppressed by k − 4 powers of the cutoff scale Λ, where the C (k) i are the Wilson coefficients.…”