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

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.)

MINIMAL EXTENDED FLAVOR GROUPS, MATTER FIELDS CHIRAL REPRESENTATIONS, AND THE FLAVOR QUESTION

We show the specific unusual features on chiral gauge anomalies cancellation in the minimal, necessarily 3-3-1, and the largest 3-4-1 weak isospin chiral gauge semisimple group leptoquark–bilepton extensions of the 3-2-1 conventional standard model of nuclear and electromagnetic interactions. In such models a natural answer for the fundamental question of fermion generation replication arises directly from the self-consistency of a local gauge quantum field theory, which constrains the number of the QFD fermion families to the QCD color charges.

INFLATIONARY COSMOLOGY FROM NONCOMMUTATIVE GEOMETRY

In the framework of the Connes-Lott model based on noncommutative geometry, the basic features of a gauge theory in the presence of gravity are reviewed, in order to show the possible physical relevance of this scheme for inflationary cosmology. These models naturally contain at least two scalar fields, interacting with each other whenever more than one fermion generation is assumed. In this paper we propose to investigate the behavior of these two fields (one of which represents the distance between the copies of a two-sheeted space-time) in the early stages of the universe evolution. In particular the simplest Abelian model, which preserves the main characteristics of more complicate gauge theories, is considered and the corresponding inflationary dynamics is studied. We find that a chaotic inflation is naturally favored, leading to a field configuration in which no symmetry breaking occurs and the final distance between the two sheets of space-time is smaller the greater the number of e fold in each sheet.