Primary Observables for Indirect Searches at Colliders

TL;DR

This paper identifies the fundamental set of collider observables that indicate new heavy physics effects, focusing on primary operators and their relevance to Higgs signals, with methods for their determination and phenomenological implications.

Contribution

It explicitly determines all 3 and 4-point primary operators relevant for Higgs signals at colliders using a new analytical method and Hilbert series validation.

Findings

Identified a finite set of primary operators for collider deviations from the Standard Model.

Developed a new analytical method for determining independent operators.

Provided estimates of the importance of these operators for Higgs decays at the HL-LHC.

Abstract

We consider the complete set of observables for collider searches for indirect effects of new heavy physics. They consist of $SU(3)_{\rm C}\times U(1)_{\rm EM}$ invariant interaction terms/operators that parameterize deviations from the Standard Model. We show that, under very general assumptions, the leading deviations from the Standard Model are given by a finite number of `primary' operators, with the remaining operators given by `Mandelstam descendants' whose effects are suppressed by powers of Mandelstam variables divided by the mass scale $M$ of the heavy physics. We explicitly determine all 3 and 4-point primary operators relevant for Higgs signals at colliders by using the correspondence between on-shell amplitudes and independent operators. We give a detailed discussion of the methods used to obtain this result, including a new analytical method for determining the independent operators. The results are checked using the Hilbert series that counts independent operators. We also give a rough sketch of the phenomenology, including unitarity bounds on the interaction strengths and rough estimates of their importance for Higgs decays at the HL-LHC. These results motivate further exploration of Higgs decays to $Z\bar{f}f$, $W\bar{f}f'$, $\gamma \bar{f}f$, and $Z\gamma\gamma$.