Search for the pseudoscalar Higgs boson <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:msub> <mml:mi>A</mml:mi> <mml:mn>0</mml:mn> </mml:msub> </mml:math> of the bestest little Higgs model at the LHC and FCC-hh

We analyze the sensitivity of the Large Hadron Collider (LHC) and the Future Circular Collider-hadron-hadron (FCC-hh) to the existence of pseudoscalar Higgs boson <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"> <a:msub> <a:mi>A</a:mi> <a:mn>0</a:mn> </a:msub> </a:math> predicted by the bestest little Higgs model. We study the tree-level (two and three body) and one-loop decays of the pseudoscalar, <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"> <c:mrow> <c:msub> <c:mrow> <c:mi>A</c:mi> </c:mrow> <c:mn>0</c:mn> </c:msub> <c:mo stretchy="false">→</c:mo> <c:mi>b</c:mi> <c:mover accent="true"> <c:mrow> <c:mi>b</c:mi> </c:mrow> <c:mrow> <c:mo stretchy="false">¯</c:mo> </c:mrow> </c:mover> <c:mo>,</c:mo> <c:mi>t</c:mi> <c:mover accent="true"> <c:mrow> <c:mi>t</c:mi> </c:mrow> <c:mrow> <c:mo stretchy="false">¯</c:mo> </c:mrow> </c:mover> <c:mo>,</c:mo> <c:mi>γ</c:mi> <c:mi>t</c:mi> <c:mover accent="true"> <c:mrow> <c:mi>t</c:mi> </c:mrow> <c:mrow> <c:mo stretchy="false">¯</c:mo> </c:mrow> </c:mover> <c:mo>,</c:mo> <c:mi>γ</c:mi> <c:mi>b</c:mi> <c:mover accent="true"> <c:mrow> <c:mi>b</c:mi> </c:mrow> <c:mrow> <c:mo stretchy="false">¯</c:mo> </c:mrow> </c:mover> <c:mo>,</c:mo> <c:mi>Z</c:mi> <c:mi>t</c:mi> <c:mover accent="true"> <c:mrow> <c:mi>t</c:mi> </c:mrow> <c:mrow> <c:mo stretchy="false">¯</c:mo> </c:mrow> </c:mover> <c:mo>,</c:mo> <c:mi>Z</c:mi> <c:mi>b</c:mi> <c:mover accent="true"> <c:mrow> <c:mi>b</c:mi> </c:mrow> <c:mrow> <c:mo stretchy="false">¯</c:mo> </c:mrow> </c:mover> <c:mo>,</c:mo> <c:mi>W</c:mi> <c:mi>t</c:mi> <c:mover accent="true"> <c:mrow> <c:mi>b</c:mi> </c:mrow> <c:mrow> <c:mo stretchy="false">¯</c:mo> </c:mrow> </c:mover> <c:mo>,</c:mo> <c:msub> <c:mrow> <c:mi>h</c:mi> </c:mrow> <c:mn>0</c:mn> </c:msub> <c:mi>t</c:mi> <c:mover accent="true"> <c:mrow> <c:mi>t</c:mi> </c:mrow> <c:mrow> <c:mo stretchy="false">¯</c:mo> </c:mrow> </c:mover> <c:mo>,</c:mo> <c:msub> <c:mrow> <c:mi>h</c:mi> </c:mrow> <c:mn>0</c:mn> </c:msub> <c:mi>b</c:mi> <c:mover accent="true"> <c:mrow> <c:mi>b</c:mi> </c:mrow> <c:mrow> <c:mo stretchy="false">¯</c:mo> </c:mrow> </c:mover> </c:mrow> </c:math> , and <x:math xmlns:x="http://www.w3.org/1998/Math/MathML" display="inline"> <x:mrow> <x:msub> <x:mrow> <x:mi>A</x:mi> </x:mrow> <x:mrow> <x:mn>0</x:mn> </x:mrow> </x:msub> <x:mo stretchy="false">→</x:mo> <x:mi>γ</x:mi> <x:mi>γ</x:mi> <x:mo>,</x:mo> <x:mi>γ</x:mi> <x:mi>Z</x:mi> <x:mo>,</x:mo> <x:mi>Z</x:mi> <x:mi>Z</x:mi> <x:mo>,</x:mo> <x:mi>g</x:mi> <x:mi>g</x:mi> <x:mo>,</x:mo> <x:mi>W</x:mi> <x:mi>W</x:mi> </x:mrow> </x:math> , respectively. In addition, we perform a phenomenological study of the production of the pseudoscalar <ab:math xmlns:ab="http://www.w3.org/1998/Math/MathML" display="inline"> <ab:msub> <ab:mi>A</ab:mi> <ab:mn>0</ab:mn> </ab:msub> </ab:math> via gluon-fusion <cb:math xmlns:cb="http://www.w3.org/1998/Math/MathML" display="inline"> <cb:mi>g</cb:mi> <cb:mi>g</cb:mi> <cb:mo stretchy="false">→</cb:mo> <cb:msub> <cb:mi>A</cb:mi> <cb:mn>0</cb:mn> </cb:msub> <cb:mo stretchy="false">→</cb:mo> <cb:mi>Y</cb:mi> </cb:math> processes, where <gb:math xmlns:gb="http://www.w3.org/1998/Math/MathML" display="inline"> <gb:mi>Y</gb:mi> <gb:mo>≡</gb:mo> <gb:mi>b</gb:mi> <gb:mover accent="true"> <gb:mi>b</gb:mi> <gb:mo stretchy="false">¯</gb:mo> </gb:mover> <gb:mo>,</gb:mo> <gb:mi>t</gb:mi> <gb:mover accent="true"> <gb:mi>t</gb:mi> <gb:mo stretchy="false">¯</gb:mo> </gb:mover> <gb:mo>,</gb:mo> <gb:mi>γ</gb:mi> <gb:mi>γ</gb:mi> <gb:mo>,</gb:mo> <gb:mi>γ</gb:mi> <gb:mi>Z</gb:mi> <gb:mo>,</gb:mo> <gb:mi>Z</gb:mi> <gb:mi>Z</gb:mi> <gb:mo>,</gb:mo> <gb:mi>g</gb:mi> <gb:mi>g</gb:mi> <gb:mo>,</gb:mo> <gb:mi>W</gb:mi> <gb:mi>W</gb:mi> </gb:math> . From the cross section of the processes of interest and the expected integrated luminosity of the LHC and FCC-hh, we determined the number of events that could be produced in both colliders.