Search for Associated Production of a Higgs Boson and Two Vector Bosons via Vector-Boson Scattering at <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mrow> <mml:msqrt> <mml:mrow> <mml:mi>s</mml:mi> </mml:mrow> </mml:msqrt> <mml:mo>=</mml:mo> <mml:mn>13</mml:mn> <mml:mtext> </mml:mtext> <mml:mtext> </mml:mtext> <mml:mi>TeV</mml:mi> </mml:mrow> </mml:math>

<jats:p> A search for Higgs boson ( <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"> <a:mi>H</a:mi> </a:math> ) production in association with two vector bosons ( <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"> <c:mi>V</c:mi> <c:mo>=</c:mo> <c:mi>W</c:mi> </c:math> , <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"> <e:mi>Z</e:mi> </e:math> ) via vector-boson scattering (VBS) is presented using proton-proton collision data collected at <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"> <g:msqrt> <g:mi>s</g:mi> </g:msqrt> <g:mo>=</g:mo> <g:mn>13</g:mn> <g:mtext> </g:mtext> <g:mtext> </g:mtext> <g:mi>TeV</g:mi> </g:math> by the CMS experiment, corresponding to an integrated luminosity of <i:math xmlns:i="http://www.w3.org/1998/Math/MathML" display="inline"> <i:mn>138</i:mn> <i:mtext> </i:mtext> <i:mtext> </i:mtext> <i:msup> <i:mi>fb</i:mi> <i:mrow> <i:mo>−</i:mo> <i:mn>1</i:mn> </i:mrow> </i:msup> </i:math> . Events containing two forward jets consistent with VBS, a large-radius jet from the decay of a boosted <k:math xmlns:k="http://www.w3.org/1998/Math/MathML" display="inline"> <k:mi>H</k:mi> </k:math> to a pair of <m:math xmlns:m="http://www.w3.org/1998/Math/MathML" display="inline"> <m:mi>b</m:mi> </m:math> quarks, and zero, one, or two charged leptons coming from <o:math xmlns:o="http://www.w3.org/1998/Math/MathML" display="inline"> <o:mi>V</o:mi> </o:math> decays are selected. The process is excluded at 95% confidence level for observed (expected) values of the <q:math xmlns:q="http://www.w3.org/1998/Math/MathML" display="inline"> <q:mi>V</q:mi> <q:mi>V</q:mi> <q:mi>H</q:mi> <q:mi>H</q:mi> </q:math> coupling modifier <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> outside the interval <u:math xmlns:u="http://www.w3.org/1998/Math/MathML" display="inline"> <u:mn>0.40</u:mn> <u:mo>&lt;</u:mo> <u:msub> <u:mi>κ</u:mi> <u:mrow> <u:mn>2</u:mn> <u:mi>V</u:mi> </u:mrow> </u:msub> <u:mo>&lt;</u:mo> <u:mn>1.60</u:mn> </u:math> ( <w:math xmlns:w="http://www.w3.org/1998/Math/MathML" display="inline"> <w:mn>0.34</w:mn> <w:mo>&lt;</w:mo> <w:msub> <w:mi>κ</w:mi> <w:mrow> <w:mn>2</w:mn> <w:mi>V</w:mi> </w:mrow> </w:msub> <w:mo>&lt;</w:mo> <w:mn>1.66</w:mn> </w:math> ), assuming standard model values for all other couplings, thus establishing a novel probe of the <y:math xmlns:y="http://www.w3.org/1998/Math/MathML" display="inline"> <y:mi>V</y:mi> <y:mi>V</y:mi> <y:mi>H</y:mi> <y:mi>H</y:mi> </y:math> interaction. Constraints are also set on the individual <ab:math xmlns:ab="http://www.w3.org/1998/Math/MathML" display="inline"> <ab:msub> <ab:mi>κ</ab:mi> <ab:mrow> <ab:mn>2</ab:mn> <ab:mi>W</ab:mi> </ab:mrow> </ab:msub> </ab:math> and <cb:math xmlns:cb="http://www.w3.org/1998/Math/MathML" display="inline"> <cb:msub> <cb:mi>κ</cb:mi> <cb:mrow> <cb:mn>2</cb:mn> <cb:mi>Z</cb:mi> </cb:mrow> </cb:msub> </cb:math> coupling modifiers and on the allowed region in the <eb:math xmlns:eb="http://www.w3.org/1998/Math/MathML" display="inline"> <eb:mrow> <eb:msub> <eb:mrow> <eb:mi>κ</eb:mi> </eb:mrow> <eb:mrow> <eb:mn>2</eb:mn> <eb:mi>W</eb:mi> </eb:mrow> </eb:msub> <eb:mtext>−</eb:mtext> <eb:msub> <eb:mrow> <eb:mi>κ</eb:mi> </eb:mrow> <eb:mrow> <eb:mn>2</eb:mn> <eb:mi>Z</eb:mi> </eb:mrow> </eb:msub> </eb:mrow> </eb:math> plane. </jats:p>