Optimal estimation of Higgs-gauge boson couplings at the future <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:msup> <mml:mi>e</mml:mi> <mml:mo>+</mml:mo> </mml:msup> <mml:msup> <mml:mi>e</mml:mi> <mml:mo>−</mml:mo> <

The proposed <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"> <a:msup> <a:mi>e</a:mi> <a:mo>+</a:mo> </a:msup> <a:msup> <a:mi>e</a:mi> <a:mo>−</a:mo> </a:msup> </a:math> collider offers an ideal environment for precise estimation of Higgs boson properties which are of utmost importance to validate the Standard Model of particle physics. We investigate <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"> <c:mi>h</c:mi> <c:mi>V</c:mi> <c:mi>V</c:mi> </c:math> couplings, where <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"> <e:mi>V</e:mi> <e:mo>∈</e:mo> <e:mo stretchy="false">{</e:mo> <e:mi>Z</e:mi> <e:mo>,</e:mo> <e:mi>γ</e:mi> <e:mo stretchy="false">}</e:mo> </e:math> with single Higgs production associated with <i:math xmlns:i="http://www.w3.org/1998/Math/MathML" display="inline"> <i:mi>Z</i:mi> </i:math> boson at the proposed <k:math xmlns:k="http://www.w3.org/1998/Math/MathML" display="inline"> <k:msup> <k:mi>e</k:mi> <k:mo>+</k:mo> </k:msup> <k:msup> <k:mi>e</k:mi> <k:mo>−</k:mo> </k:msup> </k:math> machine with <m:math xmlns:m="http://www.w3.org/1998/Math/MathML" display="inline"> <m:msqrt> <m:mi>s</m:mi> </m:msqrt> <m:mo>=</m:mo> <m:mn>250</m:mn> <m:mtext> </m:mtext> <m:mtext> </m:mtext> <m:mi>GeV</m:mi> </m:math> , within the Standard Model effective field theory framework. We employ the recoil mass of the dilepton system, to select the signal phase space, i.e, <o:math xmlns:o="http://www.w3.org/1998/Math/MathML" display="inline"> <o:mi>Z</o:mi> <o:mi>h</o:mi> <o:mo stretchy="false">→</o:mo> <o:msup> <o:mi>l</o:mi> <o:mo>+</o:mo> </o:msup> <o:msup> <o:mi>l</o:mi> <o:mo>−</o:mo> </o:msup> <o:mi>b</o:mi> <o:mover accent="true"> <o:mi>b</o:mi> <o:mo stretchy="false">¯</o:mo> </o:mover> </o:math> events. The constraints on the Wilson coefficients (WCs) are obtained using the optimal observable technique. On comparison with the current experimental limits at 68% CL with <t:math xmlns:t="http://www.w3.org/1998/Math/MathML" display="inline"> <t:mn>138</t:mn> <t:mtext> </t:mtext> <t:mtext> </t:mtext> <t:msup> <t:mi>fb</t:mi> <t:mrow> <t:mo>−</t:mo> <t:mn>1</t:mn> </t:mrow> </t:msup> </t:math> luminosity, our limits are tighter by a factor ranging from 1.5–10 for <v:math xmlns:v="http://www.w3.org/1998/Math/MathML" display="inline"> <v:mrow> <v:mi>C</v:mi> <v:mi>P</v:mi> </v:mrow> </v:math> -even operators, while <x:math xmlns:x="http://www.w3.org/1998/Math/MathML" display="inline"> <x:mrow> <x:mi>C</x:mi> <x:mi>P</x:mi> </x:mrow> </x:math> -odd WCs shows comparable limits.