Role of angular observables in probing nonstandard <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mi>H</mml:mi> <mml:mi>Z</mml:mi> <mml:mi>Z</mml:mi> </mml:math> couplings at an electron-proton collider

In this study, we explore various lab-frame angular observables at the Large Hadron-electron Collider (LHeC) to test their sensitivity to the most general structure of the Higgs ( <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"> <a:mi>H</a:mi> </a:math> ) to neutral weak boson ( <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"> <c:mi>Z</c:mi> </c:math> ) coupling ( <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"> <e:mi>H</e:mi> <e:mi>Z</e:mi> <e:mi>Z</e:mi> </e:math> ) via the process <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"> <g:msup> <g:mi>e</g:mi> <g:mo>−</g:mo> </g:msup> <g:mi>p</g:mi> <g:mo stretchy="false">→</g:mo> <g:msup> <g:mi>e</g:mi> <g:mo>−</g:mo> </g:msup> <g:mi>H</g:mi> <g:mi>j</g:mi> </g:math> at the center of mass energy <j:math xmlns:j="http://www.w3.org/1998/Math/MathML" display="inline"> <j:msqrt> <j:mi>s</j:mi> </j:msqrt> <j:mo>≈</j:mo> <j:mn>1.3</j:mn> <j:mtext> </j:mtext> <j:mtext> </j:mtext> <j:mi>TeV</j:mi> </j:math> . The most general Lorentz structure of the <l:math xmlns:l="http://www.w3.org/1998/Math/MathML" display="inline"> <l:mi>H</l:mi> <l:mi>Z</l:mi> <l:mi>Z</l:mi> </l:math> coupling beyond the standard model is composed of two <n:math xmlns:n="http://www.w3.org/1998/Math/MathML" display="inline"> <n:mrow> <n:mi>C</n:mi> <n:mi>P</n:mi> </n:mrow> </n:math> -even ( <p:math xmlns:p="http://www.w3.org/1998/Math/MathML" display="inline"> <p:msub> <p:mi>λ</p:mi> <p:mrow> <p:mn>1</p:mn> <p:mi>Z</p:mi> </p:mrow> </p:msub> </p:math> and <r:math xmlns:r="http://www.w3.org/1998/Math/MathML" display="inline"> <r:msub> <r:mi>λ</r:mi> <r:mrow> <r:mn>2</r:mn> <r:mi>Z</r:mi> </r:mrow> </r:msub> </r:math> ) and one <t:math xmlns:t="http://www.w3.org/1998/Math/MathML" display="inline"> <t:mrow> <t:mi>C</t:mi> <t:mi>P</t:mi> </t:mrow> </t:math> -odd ( <v:math xmlns:v="http://www.w3.org/1998/Math/MathML" display="inline"> <v:msub> <v:mover accent="true"> <v:mi>λ</v:mi> <v:mo stretchy="false">˜</v:mo> </v:mover> <v:mi>Z</v:mi> </v:msub> </v:math> ) component. In a previous study, we investigated the absolute value of azimuthal correlation ( <z:math xmlns:z="http://www.w3.org/1998/Math/MathML" display="inline"> <z:mo stretchy="false">|</z:mo> <z:mi mathvariant="normal">Δ</z:mi> <z:mi>ϕ</z:mi> <z:mo stretchy="false">|</z:mo> </z:math> ) between the final state electron and the jet to derive constraints on the nonstandard <eb:math xmlns:eb="http://www.w3.org/1998/Math/MathML" display="inline"> <eb:mi>H</eb:mi> <eb:mi>Z</eb:mi> <eb:mi>Z</eb:mi> </eb:math> couplings. This choice of observable is motivated by its potential to discriminate between <gb:math xmlns:gb="http://www.w3.org/1998/Math/MathML" display="inline"> <gb:mrow> <gb:mi>C</gb:mi> <gb:mi>P</gb:mi> </gb:mrow> </gb:math> -odd and <ib:math xmlns:ib="http://www.w3.org/1998/Math/MathML" display="inline"> <ib:mrow> <ib:mi>C</ib:mi> <ib:mi>P</ib:mi> </ib:mrow> </ib:math> -even couplings in the <kb:math xmlns:kb="http://www.w3.org/1998/Math/MathML" display="inline"> <kb:msup> <kb:mi>e</kb:mi> <kb:mo>−</kb:mo> </kb:msup> <kb:mi>p</kb:mi> <kb:mo stretchy="false">→</kb:mo> <kb:msub> <kb:mi>ν</kb:mi> <kb:mi>e</kb:mi> </kb:msub> <kb:mi>H</kb:mi> <kb:mi>j</kb:mi> </kb:math> process. Since the process <nb:math xmlns:nb="http://www.w3.org/1998/Math/MathML" display="inline"> <nb:msup> <nb:mi>e</nb:mi> <nb:mo>−</nb:mo> </nb:msup> <nb:mi>p</nb:mi> <nb:mo stretchy="false">→</nb:mo> <nb:msup> <nb:mi>e</nb:mi> <nb:mo>−</nb:mo> </nb:msup> <nb:mi>H</nb:mi> <nb:mi>j</nb:mi> </nb:math> has an electron in the final state, one can construct more angular observables. In addition to <qb:math xmlns:qb="http://www.w3.org/1998/Math/MathML" display="inline"> <qb:mo stretchy="false">|</qb:mo> <qb:mi mathvariant="normal">Δ</qb:mi> <qb:mi>ϕ</qb:mi> <qb:mo stretchy="false">|</qb:mo> </qb:math> , we identify new angular observables: the sign-sensitive azimuthal correlation ( <vb:math xmlns:vb="http://www.w3.org/1998/Math/MathML" display="inline"> <vb:mi mathvariant="normal">Δ</vb:mi> <vb:mi>ϕ</vb:mi> </vb:math> ) and the polar angle of the final state electron ( <yb:math xmlns:yb="http://www.w3.org/1998/Math/MathML" display="inline"> <yb:mi>θ</yb:mi> </yb:math> ), which are suitable for constraining nonstandard <ac:math xmlns:ac="http://www.w3.org/1998/Math/MathML" display="inline"> <ac:mi>H</ac:mi> <ac:mi>Z</ac:mi> <ac:mi>Z</ac:mi> </ac:math> coupling. Our analysis shows that these new angles improve the constraints on <cc:math xmlns:cc="http://www.w3.org/1998/Math/MathML" display="inline"> <cc:msub> <cc:mi>λ</cc:mi> <cc:mrow> <cc:mn>2</cc:mn> <cc:mi>Z</cc:mi> </cc:mrow> </cc:msub> </cc:math> and <ec:math xmlns:ec="http://www.w3.org/1998/Math/MathML" display="inline"> <ec:msub> <ec:mover accent="true"> <ec:mi>λ</ec:mi> <ec:mo stretchy="false">˜</ec:mo> </ec:mover> <ec:mi>Z</ec:mi> </ec:msub> </ec:math> in the range of 48%–67%. We also study the potential of the asymmetry in <ic:math xmlns:ic="http://www.w3.org/1998/Math/MathML" display="inline"> <ic:mi mathvariant="normal">Δ</ic:mi> <ic:mi>ϕ</ic:mi> </ic:math> to constrain the parameters corresponding to the <lc:math xmlns:lc="http://www.w3.org/1998/Math/MathML" display="inline"> <lc:mrow> <lc:mi>C</lc:mi> <lc:mi>P</lc:mi> </lc:mrow> </lc:math> -odd coupling.