Tests of BSM Higgs interactions by the combination <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mo stretchy="false">(</mml:mo> <mml:msubsup> <mml:mi>κ</mml:mi> <mml:mi>V</mml:mi> <mml:mn>2</mml:mn> </mml:msubsup> <m

In this work, we study the potential of analyzing the particular combination of <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"> <a:mi>κ</a:mi> </a:math> modifiers given by <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"> <c:msubsup> <c:mi>κ</c:mi> <c:mi>V</c:mi> <c:mn>2</c:mn> </c:msubsup> <c:mo>−</c:mo> <c:msub> <c:mi>κ</c:mi> <c:mrow> <c:mn>2</c:mn> <c:mi>V</c:mi> </c:mrow> </c:msub> </c:math> to disentangle beyond Standard Model Higgs signals in double Higgs production with two extra light jets at LHC. We use the Higgs effective field theory approach, HEFT, for the gauge invariant description of these two <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"> <e:msub> <e:mi>κ</e:mi> <e:mi>V</e:mi> </e:msub> </e:math> and <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"> <g:msub> <g:mi>κ</g:mi> <g:mrow> <g:mn>2</g:mn> <g:mi>V</g:mi> </g:mrow> </g:msub> </g:math> parameters representing the BSM interactions of the Higgs particle with the electroweak gauge bosons, <i:math xmlns:i="http://www.w3.org/1998/Math/MathML" display="inline"> <i:mi>H</i:mi> <i:mi>V</i:mi> <i:mi>V</i:mi> </i:math> and <k:math xmlns:k="http://www.w3.org/1998/Math/MathML" display="inline"> <k:mi>H</k:mi> <k:mi>H</k:mi> <k:mi>V</k:mi> <k:mi>V</k:mi> </k:math> , respectively. We illustrate the bonus of studying this particular combination <m:math xmlns:m="http://www.w3.org/1998/Math/MathML" display="inline"> <m:msubsup> <m:mi>κ</m:mi> <m:mi>V</m:mi> <m:mn>2</m:mn> </m:msubsup> <m:mo>−</m:mo> <m:msub> <m:mi>κ</m:mi> <m:mrow> <m:mn>2</m:mn> <m:mi>V</m:mi> </m:mrow> </m:msub> </m:math> focusing in just one process, <o:math xmlns:o="http://www.w3.org/1998/Math/MathML" display="inline"> <o:mi>H</o:mi> <o:mi>H</o:mi> <o:mi>j</o:mi> <o:mi>j</o:mi> </o:math> , instead of studying <q:math xmlns:q="http://www.w3.org/1998/Math/MathML" display="inline"> <q:msub> <q:mi>κ</q:mi> <q:mi>V</q:mi> </q:msub> </q:math> and <s:math xmlns:s="http://www.w3.org/1998/Math/MathML" display="inline"> <s:msub> <s:mi>κ</s:mi> <s:mrow> <s:mn>2</s:mn> <s:mi>V</s:mi> </s:mrow> </s:msub> </s:math> separately using various processes. For the detailed analysis here, we focus on the particular final state <u:math xmlns:u="http://www.w3.org/1998/Math/MathML" display="inline"> <u:mi>H</u:mi> <u:mo stretchy="false">(</u:mo> <u:mo stretchy="false">→</u:mo> <u:mi>γ</u:mi> <u:mi>γ</u:mi> <u:mo stretchy="false">)</u:mo> <u:mi>H</u:mi> <u:mo stretchy="false">(</u:mo> <u:mo stretchy="false">→</u:mo> <u:mi>b</u:mi> <u:mover accent="true"> <u:mi>b</u:mi> <u:mo stretchy="false">¯</u:mo> </u:mover> <u:mo stretchy="false">)</u:mo> <u:mi>j</u:mi> <u:msup> <u:mi>j</u:mi> <u:mo>′</u:mo> </u:msup> </u:math> , with two photons, two b-jets and two light jets, which we analyze fully including parton showering, fragmentation, hadronization and detector effects, in both signal and main background. We find that the sensitivity to <eb:math xmlns:eb="http://www.w3.org/1998/Math/MathML" display="inline"> <eb:msubsup> <eb:mi>κ</eb:mi> <eb:mi>V</eb:mi> <eb:mn>2</eb:mn> </eb:msubsup> <eb:mo>−</eb:mo> <eb:msub> <eb:mi>κ</eb:mi> <eb:mrow> <eb:mn>2</eb:mn> <eb:mi>V</eb:mi> </eb:mrow> </eb:msub> </eb:math> could be notably improved at the HL-LHC by the proper cuts on the final state <gb:math xmlns:gb="http://www.w3.org/1998/Math/MathML" display="inline"> <gb:mi>b</gb:mi> <gb:mover accent="true"> <gb:mi>b</gb:mi> <gb:mo stretchy="false">¯</gb:mo> </gb:mover> <gb:mi>γ</gb:mi> <gb:mi>γ</gb:mi> <gb:mi>j</gb:mi> <gb:msup> <gb:mi>j</gb:mi> <gb:mo>′</gb:mo> </gb:msup> </gb:math> that select optimally the events with VBF-topology and <kb:math xmlns:kb="http://www.w3.org/1998/Math/MathML" display="inline"> <kb:mi>H</kb:mi> <kb:mi>H</kb:mi> </kb:math> -topology. In particular, we propose strategies based on a good isolation of <mb:math xmlns:mb="http://www.w3.org/1998/Math/MathML" display="inline"> <mb:mi>γ</mb:mi> <mb:mi>γ</mb:mi> </mb:math> and b-jet pairs, and focus specially on specific variables like <ob:math xmlns:ob="http://www.w3.org/1998/Math/MathML" display="inline"> <ob:msub> <ob:mi>η</ob:mi> <ob:mrow> <ob:mi>γ</ob:mi> <ob:mi>γ</ob:mi> </ob:mrow> </ob:msub> </ob:math> and <qb:math xmlns:qb="http://www.w3.org/1998/Math/MathML" display="inline"> <qb:msubsup> <qb:mi>P</qb:mi> <qb:mrow> <qb:mi>γ</qb:mi> <qb:mi>γ</qb:mi> </qb:mrow> <qb:mi>T</qb:mi> </qb:msubsup> </qb:math> where the signal events distributions may efficiently discriminate between BSM signal versus SM background. We will show here how the high transversality of these two pairs in the signal (inherited from the high transversality of the <sb:math xmlns:sb="http://www.w3.org/1998/Math/MathML" display="inline"> <sb:mi>H</sb:mi> </sb:math> ’s) is correlated with the nonvanishing value of this <ub:math xmlns:ub="http://www.w3.org/1998/Math/MathML" display="inline"> <ub:mo stretchy="false">(</ub:mo> <ub:msubsup> <ub:mi>κ</ub:mi> <ub:mi>V</ub:mi> <ub:mn>2</ub:mn> </ub:msubsup> <ub:mo>−</ub:mo> <ub:msub> <ub:mi>κ</ub:mi> <ub:mrow> <ub:mn>2</ub:mn> <ub:mi>V</ub:mi> </ub:mrow> </ub:msub> <ub:mo stretchy="false">)</ub:mo> </ub:math> combination.