Primary observables for gauge boson collider signals

In this paper, we determine a basis for the on-shell four-point amplitudes <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mi>V</a:mi><a:mi>V</a:mi><a:mi>V</a:mi><a:mi>V</a:mi></a:math> for Standard Model gauge bosons <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"><c:mi>V</c:mi><c:mo>=</c:mo><c:msup><c:mi>W</c:mi><c:mo>±</c:mo></c:msup><c:mo>,</c:mo><c:mi>Z</c:mi><c:mo>,</c:mo><c:mi>γ</c:mi><c:mo>,</c:mo><c:mi>g</c:mi></c:math>. Following previous work, this completes the analysis of three- and four-point amplitudes for the Standard Model and could be used for model-independent searches for beyond the Standard Model physics at colliders. Our results include a Lagrangian parametrization for the “primary” amplitudes, where including additional derivatives leads to the Mandelstam “descendant” amplitudes, and upper bounds on the coupling constants from imposing unitarity. We also perform an estimate for the sensitivity for new <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"><e:mi>Z</e:mi></e:math> decays at the High-Luminosity LHC, finding that <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"><g:mi>Z</g:mi><g:mo stretchy="false">→</g:mo><g:mi>γ</g:mi><g:mover accent="true"><g:mo>ℓ</g:mo><g:mo stretchy="true">¯</g:mo></g:mover><g:mo>ℓ</g:mo></g:math> could be searched for, but that other decay modes, like <l:math xmlns:l="http://www.w3.org/1998/Math/MathML" display="inline"><l:mi>Z</l:mi><l:mo stretchy="false">→</l:mo><l:mo stretchy="false">(</l:mo><l:mi>γ</l:mi><l:mi>γ</l:mi><l:mi>γ</l:mi><l:mo>,</l:mo><l:mi>γ</l:mi><l:mi>g</l:mi><l:mi>g</l:mi><l:mo stretchy="false">)</l:mo></l:math>, are too small to be discovered after imposing unitarity constraints.