Linearly polarized photon fusion as a precision probe of the tau lepton dipole moments at lepton colliders

We present a comprehensive investigation into the anomalous magnetic dipole moment ( <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"> <a:msub> <a:mi>a</a:mi> <a:mi>τ</a:mi> </a:msub> </a:math> ) and electric dipole moment ( <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"> <c:msub> <c:mi>d</c:mi> <c:mi>τ</c:mi> </c:msub> </c:math> ) of the <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"> <e:mi>τ</e:mi> </e:math> lepton using the <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"> <g:mi>γ</g:mi> <g:mi>γ</g:mi> <g:mo stretchy="false">→</g:mo> <g:msup> <g:mi>τ</g:mi> <g:mo>+</g:mo> </g:msup> <g:msup> <g:mi>τ</g:mi> <g:mo>−</g:mo> </g:msup> </g:math> process at future lepton colliders, with the Super Tau-Charm Facility serving as a benchmark. By employing transverse-momentum-dependent factorization, we introduce novel observables derived from <j:math xmlns:j="http://www.w3.org/1998/Math/MathML" display="inline"> <j:mi>cos</j:mi> <j:mn>2</j:mn> <j:mi>ϕ</j:mi> </j:math> , <l:math xmlns:l="http://www.w3.org/1998/Math/MathML" display="inline"> <l:mi>sin</l:mi> <l:mn>2</l:mn> <l:mi>ϕ</l:mi> </l:math> , and <n:math xmlns:n="http://www.w3.org/1998/Math/MathML" display="inline"> <n:mi>cos</n:mi> <n:mn>4</n:mn> <n:mi>ϕ</n:mi> </n:math> azimuthal asymmetries to precisely probe the <p:math xmlns:p="http://www.w3.org/1998/Math/MathML" display="inline"> <p:mi>τ</p:mi> </p:math> lepton’s electromagnetic structure. Our analysis significantly enhances the precision of <r:math xmlns:r="http://www.w3.org/1998/Math/MathML" display="inline"> <r:msub> <r:mi>a</r:mi> <r:mi>τ</r:mi> </r:msub> </r:math> constraints within the photon-photon fusion process, yielding <t:math xmlns:t="http://www.w3.org/1998/Math/MathML" display="inline"> <t:mi>Re</t:mi> <t:mo stretchy="false">(</t:mo> <t:msub> <t:mi>a</t:mi> <t:mi>τ</t:mi> </t:msub> <t:mo stretchy="false">)</t:mo> <t:mo>∈</t:mo> <t:mo stretchy="false">[</t:mo> <t:mo>−</t:mo> <t:mn>4.6</t:mn> <t:mo>,</t:mo> <t:mn>7.0</t:mn> <t:mo stretchy="false">]</t:mo> <t:mo>×</t:mo> <t:msup> <t:mn>10</t:mn> <t:mrow> <t:mo>−</t:mo> <t:mn>3</t:mn> </t:mrow> </t:msup> </t:math> at the <z:math xmlns:z="http://www.w3.org/1998/Math/MathML" display="inline"> <z:mn>2</z:mn> <z:mi>σ</z:mi> </z:math> confidence level, which approaches the precision of the Standard Model prediction. These findings highlight the considerable potential of azimuthal asymmetry measurements for high-precision determinations of fundamental particle properties at future lepton colliders.