<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mi>V</mml:mi> </mml:math> -associated production and vector boson fusion as an LHC signature of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline">

We investigate the role of vector boson fusion (VBF) and associated production with an electroweak boson ( <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"> <a:mi>V</a:mi> </a:math> -AP) of beyond-the-Standard-Model Higgs bosons at the LHC in probing <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"> <c:mi>C</c:mi> <c:mi>P</c:mi> </c:math> violation in extended Higgs sectors. Resonant production of a new Higgs boson through <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"> <e:mi>V</e:mi> </e:math> -AP and VBF subsequently decaying into a <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"> <g:mi>Z</g:mi> </g:math> boson and a 125 GeV Higgs boson <i:math xmlns:i="http://www.w3.org/1998/Math/MathML" display="inline"> <i:mi>h</i:mi> </i:math> would be a robust sign of <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> violation, since <m:math xmlns:m="http://www.w3.org/1998/Math/MathML" display="inline"> <m:mi>h</m:mi> </m:math> has been measured to be (predominantly) a <o:math xmlns:o="http://www.w3.org/1998/Math/MathML" display="inline"> <o:mi>C</o:mi> <o:mi>P</o:mi> </o:math> -even state. After identifying this and other sets of signatures which rely on <q:math xmlns:q="http://www.w3.org/1998/Math/MathML" display="inline"> <q:mi>V</q:mi> </q:math> -AP and VBF to jointly uncover <s:math xmlns:s="http://www.w3.org/1998/Math/MathML" display="inline"> <s:mi>C</s:mi> <s:mi>P</s:mi> </s:math> violation, we analyze the prospects to measure <u:math xmlns:u="http://www.w3.org/1998/Math/MathML" display="inline"> <u:mi>C</u:mi> <u:mi>P</u:mi> </u:math> violation in this way for the complex two-Higgs-doublet model at the High-Luminosity LHC.