Primary observables for indirect searches at colliders

Abstract We consider the complete set of observables for collider searches for indirect effects of new heavy physics. They consist of SU(3)C × U(1)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 f ¯ f $$ Z\overline{f}f $$ , W f ¯ f ′ $$ W\overline{f}{f}^{\prime } $$ , γ f ¯ f $$ \gamma \overline{f}f $$ , and Zγγ.