[Paper Review] Effective Operators for Dark Matter Interactions

Mateusz Duch|arXiv (Cornell University)|Oct 16, 2014

Particle physics theoretical and experimental studies8 references3 citations

TL;DR

This thesis classifies effective operators up to dimension 6 that mediate interactions between the Standard Model (including right-handed neutrinos) and a dark matter sector composed of gauge singlet scalar, left- and right-chiral fermions, and a vector boson. It identifies which operators are renormalizable, which can be generated at tree level, and which require loop corrections, under stability symmetries for dark matter fields, providing a comprehensive framework for dark matter phenomenology beyond the Standard Model.

ABSTRACT

The aim of this thesis is to determine possible interactions between the Standard Model with right-chiral neutrinos and a sector of dark matter composed of a real scalar, left- and right-chiral fermion and a vector particle, which are singlets of the Standard Model gauge group. In the introductory chapters we review the evidence for dark matter and methods of its detection. In the main part, we present the complete list of gauge singlet operators of dimension not greater than 4, that consist of the standard sector fields. We obtain also an analogous list for the dark matter particles. Using both of them, we find the possible interactions between the two sectors, firstly for the renormalizable theories, then within the effective theory framework with operators up to dimension 6, imposing the stability symmetry condition on each dark matter field. We consider the problem of generation for the effective operators in underlying, renormalizable gauge theory that includes the Standard Model. It is shown, which of the operators can be generated in tree-level approximation and which require a loop.

Motivation & Objective

• To systematically classify all gauge singlet operators of dimension ≤6 involving Standard Model fields and dark matter fields.
• To identify viable interactions between the Standard Model (including right-chiral neutrinos) and a dark sector composed of scalar, fermionic, and vector dark matter candidates.
• To determine which effective operators can be generated in a UV-complete, renormalizable theory, distinguishing between tree-level and loop-induced generation.
• To impose stability symmetries on dark matter fields and analyze their impact on allowed interaction structures.
• To provide a foundation for phenomenological studies of dark matter by mapping the complete set of possible low-energy interactions.

Proposed method

• Construct a complete list of gauge singlet operators of dimension ≤6 using the Standard Model fields, including right-handed neutrinos.
• Generate a parallel list of operators involving only dark matter fields, respecting their quantum numbers and stability symmetries.
• Combine both lists to identify all possible interaction terms between the visible and dark sectors.
• Analyze the UV origin of each effective operator by considering their generation in an underlying renormalizable gauge theory.
• Use group-theoretic and symmetry-based methods to classify operators under the Standard Model gauge group and dark matter stability symmetries.
• Determine whether each interaction can be generated at tree level or requires loop corrections in the UV theory.

Experimental results

Research questions

• RQ1 Which effective operators of dimension ≤6 mediate interactions between the Standard Model and a dark matter sector of gauge singlet particles?
• RQ2 Which of these operators can be generated in a UV-complete, renormalizable theory at tree level?
• RQ3 Which operators require loop corrections for their generation in the UV theory?
• RQ4 How do stability symmetries on individual dark matter fields constrain the allowed interaction structures?
• RQ5 What is the complete classification of possible low-energy interactions between the Standard Model and a minimal dark matter sector?

Key findings

• A complete list of all gauge singlet operators of dimension ≤6 involving Standard Model fields, including right-handed neutrinos, has been systematically derived.
• A corresponding list of operators involving only dark matter fields—scalar, left- and right-chiral fermions, and a vector particle—has been constructed under stability symmetry constraints.
• The intersection of both lists yields all possible renormalizable and effective interactions between the Standard Model and the dark matter sector.
• It is determined that some effective operators can be generated at tree level in the UV theory, while others require loop-level dynamics for their emergence.
• The classification includes the role of the Stueckelberg mechanism and Higgs portal interactions in mediating dark matter couplings.
• The framework provides a complete basis for phenomenological studies of dark matter beyond the Standard Model, including direct and indirect detection signals.