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, un der 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 $Z\overline{f}f$, $W\overline{f}f'$, $γ\overline{f}f$, and $Zγγ$.