This paper employs the <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mi>H</a:mi><a:mo>+</a:mo><a:mi>b</a:mi><a:mo>+</a:mo><a:mtext>jets</a:mtext></a:math> signature in proton-proton collisions to explore the structure of the <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"><c:mi>H</c:mi><c:mi>b</c:mi><c:mover accent="true"><c:mi>b</c:mi><c:mo stretchy="false">¯</c:mo></c:mover></c:math> couplings. The focus of the analysis lies in the decay of the Higgs boson into a photon pair, taking into account both reducible and irreducible backgrounds and a realistic simulation of the detector effects. To enhance the discrimination between signal and background, a multivariate analysis is employed to analyze the kinematic variables and optimise the signal-to-background ratio. The results indicate that the <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"><g:mi>H</g:mi><g:mo>+</g:mo><g:mi>b</g:mi><g:mo>+</g:mo><g:mtext>jets</g:mtext></g:math> process can significantly contribute to the precise measurement of <i:math xmlns:i="http://www.w3.org/1998/Math/MathML" display="inline"><i:mi>C</i:mi><i:mi>P</i:mi></i:math>-even and <k:math xmlns:k="http://www.w3.org/1998/Math/MathML" display="inline"><k:mi>C</k:mi><k:mi>P</k:mi></k:math>-odd couplings between the bottom quark and the Higgs boson at the LHC and FCC-hh. Finally, a novel asymmetry is introduced for the purpose of probing <m:math xmlns:m="http://www.w3.org/1998/Math/MathML" display="inline"><m:mi>C</m:mi><m:mi>P</m:mi></m:math> violation within the <o:math xmlns:o="http://www.w3.org/1998/Math/MathML" display="inline"><o:mi>H</o:mi><o:mi>b</o:mi><o:mover accent="true"><o:mi>b</o:mi><o:mo stretchy="false">¯</o:mo></o:mover></o:math> coupling, formulated exclusively based on lab-frame momenta. Published by the American Physical Society 2024
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