Abstract
We present a complete and independent list of the dimension 9 operator basis in the Standard Model effective field theory by an automatic algorithm based on the amplitude-operator correspondence. A complete basis (y-basis) is first constructed by enumerating Young tableau of an auxiliary $SU(N)$ group and the gauge groups, with the equation-of-motion and integration-by-part redundancies all removed. In the presence of repeated fields, another basis (p-basis) with explicit flavor symmetries among them is derived from the y-basis, which further induces a basis of independent monomial operators through a systematic process called de-symmetrization. Our form of operators have advantages over the traditional way of presenting operators constrained by flavor relations, in the simplicity of both eliminating flavor redundancies and identifying independent flavor-specified operators. We list the 90456 (560) operators for three (one) generations of fermions, all of which violate baryon number or lepton number conservation; among them we find new violation patterns as $\Delta B = 2$ and $\Delta L = 3$, which only appear at the dimensions $d \ge 9$.
Highlights
Being the most successful theory of particle physics to date, the standard model (SM) still leaves many questions about the nature of matter unanswered, which motivates direct and indirect experimental searches on new physics (NP)
We present a complete and independent list of the dimension-nine operator basis in the Standard Model effective field theory by an automatic algorithm based on the amplitude-operator correspondence
We provided the full result of the independent dimension-nine operator basis in the Standard Model effective field theory (SMEFT)
Summary
Being the most successful theory of particle physics to date, the standard model (SM) still leaves many questions about the nature of matter unanswered, which motivates direct and indirect experimental searches on new physics (NP). The resulting operator basis we obtain with the above method is listed in terms of various levels of categories: (i) Class: A (Lorentz) class includes types of operators with a given number of fields under each Lorentz irreducible representation (irrep) and the same number of covariant derivatives, such that they may share the same Lorentz structures. It is different from the concept of operator “class” in other literature, because we distinguish the chiralities of the fields as their corresponding particles have definite helicities. In Appendix A, we list useful formulas transforming operators between two- and four-component spinor notations, and in Appendix B we provide a list of subclasses up to dimension nine
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
