Bounds on SMEFT affecting multigauge and Higgs-gauge couplings using two and three body spin correlations in <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:

The upcoming electron-positron collider provides an ideal place to probe deviation from the Standard Model predictions with its clean environment, beam polarization, and significant luminosity. We studied anomalous quartic gauge boson couplings ( <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"> <a:mi>V</a:mi> <a:mi>V</a:mi> <a:msup> <a:mi>W</a:mi> <a:mo>−</a:mo> </a:msup> <a:msup> <a:mi>W</a:mi> <a:mo>+</a:mo> </a:msup> <a:mo>,</a:mo> <a:mi>V</a:mi> <a:mo>∈</a:mo> <a:mo stretchy="false">{</a:mo> <a:mi>γ</a:mi> <a:mo>,</a:mo> <a:mi>Z</a:mi> <a:mo stretchy="false">}</a:mo> </a:math> ), triple gauge couplings ( <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"> <e:msup> <e:mi>W</e:mi> <e:mo>−</e:mo> </e:msup> <e:msup> <e:mi>W</e:mi> <e:mo>+</e:mo> </e:msup> <e:mi>γ</e:mi> <e:mo>/</e:mo> <e:mi>Z</e:mi> </e:math> ), and Higgs-gauge couplings <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"> <g:mrow> <g:mo stretchy="false">(</g:mo> <g:mi>H</g:mi> <g:mi>V</g:mi> <g:mi>V</g:mi> <g:mo>,</g:mo> <g:mi>V</g:mi> <g:mo>∈</g:mo> <g:mo stretchy="false">{</g:mo> <g:msup> <g:mrow> <g:mi>W</g:mi> </g:mrow> <g:mrow> <g:mo>±</g:mo> </g:mrow> </g:msup> <g:mo>,</g:mo> <g:mi>Z</g:mi> <g:mo>,</g:mo> <g:mi>γ</g:mi> <g:mo stretchy="false">}</g:mo> <g:mo stretchy="false">)</g:mo> </g:mrow> </g:math> induced by <m:math xmlns:m="http://www.w3.org/1998/Math/MathML" display="inline"> <m:mi>S</m:mi> <m:mi>U</m:mi> <m:mo stretchy="false">(</m:mo> <m:mn>2</m:mn> <m:msub> <m:mo stretchy="false">)</m:mo> <m:mi>L</m:mi> </m:msub> <m:mo>×</m:mo> <m:mi>U</m:mi> <m:mo stretchy="false">(</m:mo> <m:mn>1</m:mn> <m:msub> <m:mo stretchy="false">)</m:mo> <m:mi>Y</m:mi> </m:msub> </m:math> gauge-invariant dimension-6 operators in <s:math xmlns:s="http://www.w3.org/1998/Math/MathML" display="inline"> <s:mrow> <s:mn>2</s:mn> <s:mi>j</s:mi> <s:msup> <s:mrow> <s:mi>e</s:mi> </s:mrow> <s:mrow> <s:mo>−</s:mo> </s:mrow> </s:msup> <s:msup> <s:mrow> <s:mi>e</s:mi> </s:mrow> <s:mrow> <s:mo>+</s:mo> </s:mrow> </s:msup> <s:mi>μ</s:mi> <s:menclose notation="updiagonalstrike" other="updiag1"> <s:mrow> <s:mi>E</s:mi> </s:mrow> </s:menclose> </s:mrow> </s:math> final events with initial beam polarization. The phase space of two prominent amplitudes—i.e., triple gauge boson production ( <w:math xmlns:w="http://www.w3.org/1998/Math/MathML" display="inline"> <w:mi>W</w:mi> <w:mi>W</w:mi> <w:mi>Z</w:mi> </w:math> ) and vector boson scattering subprocesses—are selected with kinematic cuts on <y:math xmlns:y="http://www.w3.org/1998/Math/MathML" display="inline"> <y:msub> <y:mi>m</y:mi> <y:mrow> <y:msup> <y:mi>e</y:mi> <y:mo>−</y:mo> </y:msup> <y:msup> <y:mi>e</y:mi> <y:mo>+</y:mo> </y:msup> </y:mrow> </y:msub> </y:math> . The full quantum states of the diboson system in vector boson scattering (VBS) and the triboson system in <ab:math xmlns:ab="http://www.w3.org/1998/Math/MathML" display="inline"> <ab:mi>W</ab:mi> <ab:mi>W</ab:mi> <ab:mi>Z</ab:mi> </ab:math> are given by 80 and 728 independent parameters (polarizations and spin correlations), respectively, which are obtained in the form of angular asymmetries. Further, the reconstruction of vector polarization asymmetries associated with the <cb:math xmlns:cb="http://www.w3.org/1998/Math/MathML" display="inline"> <cb:mi>W</cb:mi> </cb:math> boson and their correlations requires flavor tagging of light jets and is thus neglected. We provide one-parameter limits at a 95% confidence level, combining cross section and spin-related observables. The projected one-parameter constraints on Wilson coefficients (WCs) are found to be more stringent than the current limits reported by the LHC experiments. A channel study highlights that <eb:math xmlns:eb="http://www.w3.org/1998/Math/MathML" display="inline"> <eb:mi>W</eb:mi> <eb:mi>W</eb:mi> <eb:mi>Z</eb:mi> </eb:math> puts stringent bounds on two <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> -even WCs, viz. <ib:math xmlns:ib="http://www.w3.org/1998/Math/MathML" display="inline"> <ib:msub> <ib:mi>c</ib:mi> <ib:mi>W</ib:mi> </ib:msub> </ib:math> and <kb:math xmlns:kb="http://www.w3.org/1998/Math/MathML" display="inline"> <kb:msub> <kb:mi>c</kb:mi> <kb:mrow> <kb:mi>W</kb:mi> <kb:mi>W</kb:mi> <kb:mi>W</kb:mi> </kb:mrow> </kb:msub> </kb:math> , while VBS topology puts stringent bounds on the remaining seven WCs. Finally, marginalized limits on all nine anomalous couplings are obtained with Markov chain Monte Carlo analysis. The limits are found to be insensitive to systematic errors and dominated by statistics.