Testing lepton flavor universality at future Z factories

As one of the hypothetical principles in the Standard Model (SM), lepton flavor universality (LFU) should be tested with a precision as high as possible such that the physics violating this principle can be fully examined. The run of a <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mi>Z</a:mi></a:math> factory at a future <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"><c:msup><c:mi>e</c:mi><c:mo>+</c:mo></c:msup><c:msup><c:mi>e</c:mi><c:mo>−</c:mo></c:msup></c:math> collider, such as the Circular Electron-Positron Collider or Future Circular Collider (electron/positron), provides a great opportunity to perform this task because of the large statistics and high reconstruction efficiencies for <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"><e:mi>b</e:mi></e:math> hadrons at the <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"><g:mi>Z</g:mi></g:math> pole. In this paper, we present a systematic study on the LFU test in future <i:math xmlns:i="http://www.w3.org/1998/Math/MathML" display="inline"><i:mi>Z</i:mi></i:math> factories. The goal is threefold. First, we study the sensitivities of measuring the LFU-violating observables of <k:math xmlns:k="http://www.w3.org/1998/Math/MathML" display="inline"><k:mi>b</k:mi><k:mo stretchy="false">→</k:mo><k:mi>c</k:mi><k:mi>τ</k:mi><k:mi>ν</k:mi></k:math>, i.e., <n:math xmlns:n="http://www.w3.org/1998/Math/MathML" display="inline"><n:mrow><n:msub><n:mrow><n:mi>R</n:mi></n:mrow><n:mrow><n:mi>J</n:mi><n:mo>/</n:mo><n:mi>ψ</n:mi></n:mrow></n:msub></n:mrow></n:math>, <p:math xmlns:p="http://www.w3.org/1998/Math/MathML" display="inline"><p:mrow><p:msub><p:mrow><p:mi>R</p:mi></p:mrow><p:mrow><p:msub><p:mrow><p:mi>D</p:mi></p:mrow><p:mrow><p:mi>s</p:mi></p:mrow></p:msub></p:mrow></p:msub></p:mrow></p:math>, <r:math xmlns:r="http://www.w3.org/1998/Math/MathML" display="inline"><r:mrow><r:msub><r:mrow><r:mi>R</r:mi></r:mrow><r:mrow><r:msubsup><r:mrow><r:mi>D</r:mi></r:mrow><r:mrow><r:mi>s</r:mi></r:mrow><r:mrow><r:mo>*</r:mo></r:mrow></r:msubsup></r:mrow></r:msub></r:mrow></r:math>, and <t:math xmlns:t="http://www.w3.org/1998/Math/MathML" display="inline"><t:msub><t:mi>R</t:mi><t:msub><t:mi mathvariant="normal">Λ</t:mi><t:mi>c</t:mi></t:msub></t:msub></t:math>, where <w:math xmlns:w="http://www.w3.org/1998/Math/MathML" display="inline"><w:mi>τ</w:mi></w:math> decays muonically. For this purpose, we develop the strategies for event reconstruction, based on the track information significantly. Second, we explore the sensitivity robustness against detector performance and its potential improvement with the message of event shape or beyond the <y:math xmlns:y="http://www.w3.org/1998/Math/MathML" display="inline"><y:mi>b</y:mi></y:math>-hadron decays. A picture is drawn on the variation of analysis sensitivities with the detector tracking resolution and soft photon detectability, and the impact of Fox-Wolfram moments is studied on the measurement of relevant flavor events. Finally, we interpret the projected sensitivities in the SM effective field theory, by combining the LFU tests of <ab:math xmlns:ab="http://www.w3.org/1998/Math/MathML" display="inline"><ab:mi>b</ab:mi><ab:mo stretchy="false">→</ab:mo><ab:mi>c</ab:mi><ab:mi>τ</ab:mi><ab:mi>ν</ab:mi></ab:math> and the measurements of <db:math xmlns:db="http://www.w3.org/1998/Math/MathML" display="inline"><db:mrow><db:mi>b</db:mi><db:mo stretchy="false">→</db:mo><db:mi>s</db:mi><db:msup><db:mrow><db:mi>τ</db:mi></db:mrow><db:mrow><db:mo>+</db:mo></db:mrow></db:msup><db:msup><db:mrow><db:mi>τ</db:mi></db:mrow><db:mrow><db:mo>−</db:mo></db:mrow></db:msup></db:mrow></db:math> and <gb:math xmlns:gb="http://www.w3.org/1998/Math/MathML" display="inline"><gb:mi>b</gb:mi><gb:mo stretchy="false">→</gb:mo><gb:mi>s</gb:mi><gb:mover accent="true"><gb:mi>ν</gb:mi><gb:mo stretchy="false">¯</gb:mo></gb:mover><gb:mi>ν</gb:mi></gb:math>. We show that the limits on the LFU-violating energy scale can be pushed up to <lb:math xmlns:lb="http://www.w3.org/1998/Math/MathML" display="inline"><lb:mrow><lb:mo>∼</lb:mo><lb:mi mathvariant="script">O</lb:mi><lb:mo stretchy="false">(</lb:mo><lb:mn>10</lb:mn><lb:mo stretchy="false">)</lb:mo><lb:mtext> </lb:mtext><lb:mtext> </lb:mtext><lb:mi>TeV</lb:mi></lb:mrow></lb:math> for <qb:math xmlns:qb="http://www.w3.org/1998/Math/MathML" display="inline"><qb:mrow><qb:mo>≲</qb:mo><qb:mi mathvariant="script">O</qb:mi><qb:mo stretchy="false">(</qb:mo><qb:mn>1</qb:mn><qb:mo stretchy="false">)</qb:mo></qb:mrow></qb:math> Wilson coefficients at Tera-<vb:math xmlns:vb="http://www.w3.org/1998/Math/MathML" display="inline"><vb:mi>Z</vb:mi></vb:math>. Published by the American Physical Society 2024