Dipole momenta and compositeness of the τ lepton at Belle II

The large number of <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mrow><a:mi>τ</a:mi></a:mrow></a:math> leptons available at the Belle II experiment makes it possible to study their properties and the extent of their compositeness. We propose a strategy that relies on three observables defined in terms of elements of the polarization density matrix of the produced <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"><c:mi>τ</c:mi></c:math> pairs, which we obtain via quantum tomography. We find that these observables can explore values of the magnetic dipole moment down to <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"><e:mn>6.3</e:mn><e:mo>×</e:mo><e:msup><e:mn>10</e:mn><e:mrow><e:mo>−</e:mo><e:mn>4</e:mn></e:mrow></e:msup></e:math>, which is 2 orders of magnitude better than the current experimental limit, constrain the electromagnetic radius below <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"><g:mn>4.3</g:mn><g:mo>×</g:mo><g:msup><g:mn>10</g:mn><g:mrow><g:mo>−</g:mo><g:mn>3</g:mn></g:mrow></g:msup><g:mtext> </g:mtext><g:mtext> </g:mtext><g:mi>fm</g:mi></g:math>, and exclude an electric dipole moment larger than <i:math xmlns:i="http://www.w3.org/1998/Math/MathML" display="inline"><i:mrow><i:mn>1.7</i:mn><i:mo>×</i:mo><i:msup><i:mrow><i:mn>10</i:mn></i:mrow><i:mrow><i:mo>−</i:mo><i:mn>17</i:mn></i:mrow></i:msup><i:mtext> </i:mtext><i:mtext> </i:mtext><i:mi mathvariant="normal">e</i:mi><i:mtext> </i:mtext><i:mi>cm</i:mi></i:mrow></i:math>. The quoted limits are at the 95% confidence level (CL) and are obtained for a benchmark integrated luminosity of <l:math xmlns:l="http://www.w3.org/1998/Math/MathML" display="inline"><l:mrow><l:mn>1</l:mn><l:mtext> </l:mtext><l:mtext> </l:mtext><l:msup><l:mrow><l:mi>ab</l:mi></l:mrow><l:mrow><l:mo>−</l:mo><l:mn>1</l:mn></l:mrow></l:msup></l:mrow></l:math> and a Monte Carlo estimate of the statistical sensitivity. Published by the American Physical Society 2024