HFLAV $τ$ branching fractions fit and measurements of Vus with $τ$ lepton data

<jats:p>We report the status of the Heavy Flavour Averaging Group (HFLAV) averages of the <jats:inline-formula><jats:alternatives><jats:tex-math>\tau</jats:tex-math><mml:math xmlns:mml="http://www.w3. org/1998/Math/MathML" display="inline"><mml:mi>τ</mml:mi></mml:math></jats:alternatives></jats:inline-formula> lepton measurements We then update the latest published HFLAV global fit of the <jats:inline-formula><jats:alternatives><jats:tex-math>\tau</jats:tex-math><mml:math xmlns:mml="http://www.w3. org/1998/Math/MathML" display="inline"><mml:mi>τ</mml:mi></mml:math></jats:alternatives></jats:inline-formula> lepton branching fractions (Spring 2017) with recent results by . We use the fit results to update the Cabibbo-Kobayashi-Maskawa (CKM) matrix element <jats:inline-formula><jats:alternatives><jats:tex-math>\left|V_{us}\right|</jats:tex-math><mml:math xmlns:mml="http://www.w3. org/1998/Math/MathML" display="inline"><mml:mrow><mml:mo stretchy="true" form="prefix">|</mml:mo><mml:msub><mml:mi>V</mml:mi><mml:mrow><mml:mi>u</mml:mi><mml:mi>s</mml:mi></mml:mrow></mml:msub><mml:mo stretchy="true" form="postfix">|</mml:mo></mml:mrow></mml:math></jats:alternatives></jats:inline-formula> measurements with the <jats:inline-formula><jats:alternatives><jats:tex-math>\tau</jats:tex-math><mml:math xmlns:mml="http://www.w3. org/1998/Math/MathML" display="inline"><mml:mi>τ</mml:mi></mml:math></jats:alternatives></jats:inline-formula> branching fractions. We combine the direct <jats:inline-formula><jats:alternatives><jats:tex-math>\tau</jats:tex-math><mml:math xmlns:mml="http://www.w3. org/1998/Math/MathML" display="inline"><mml:mi>τ</mml:mi></mml:math></jats:alternatives></jats:inline-formula> branching fraction measurements with indirect predictions using kaon branching fractions measurements to improve the determination of <jats:inline-formula><jats:alternatives><jats:tex-math>\left|V_{us}\right|</jats:tex-math><mml:math xmlns:mml="http://www.w3. org/1998/Math/MathML" display="inline"><mml:mrow><mml:mo stretchy="true" form="prefix">|</mml:mo><mml:msub><mml:mi>V</mml:mi><mml:mrow><mml:mi>u</mml:mi><mml:mi>s</mml:mi></mml:mrow></mml:msub><mml:mo stretchy="true" form="postfix">|</mml:mo></mml:mrow></mml:math></jats:alternatives></jats:inline-formula> using <jats:inline-formula><jats:alternatives><jats:tex-math>\tau</jats:tex-math><mml:math xmlns:mml="http://www.w3. org/1998/Math/MathML" display="inline"><mml:mi>τ</mml:mi></mml:math></jats:alternatives></jats:inline-formula> branching fractions. The <jats:inline-formula><jats:alternatives><jats:tex-math>\left|V_{us}\right|</jats:tex-math><mml:math xmlns:mml="http://www.w3. org/1998/Math/MathML" display="inline"><mml:mrow><mml:mo stretchy="true" form="prefix">|</mml:mo><mml:msub><mml:mi>V</mml:mi><mml:mrow><mml:mi>u</mml:mi><mml:mi>s</mml:mi></mml:mrow></mml:msub><mml:mo stretchy="true" form="postfix">|</mml:mo></mml:mrow></mml:math></jats:alternatives></jats:inline-formula> determinations based on the inclusive branching fraction of <jats:inline-formula><jats:alternatives><jats:tex-math>\tau</jats:tex-math><mml:math xmlns:mml="http://www.w3. org/1998/Math/MathML" display="inline"><mml:mi>τ</mml:mi></mml:math></jats:alternatives></jats:inline-formula> to strange final states are about <jats:inline-formula><jats:alternatives><jats:tex-math>3\sigma</jats:tex-math><mml:math xmlns:mml="http://www.w3. org/1998/Math/MathML" display="inline"><mml:mrow><mml:mn>3</mml:mn><mml:mi>σ</mml:mi></mml:mrow></mml:math></jats:alternatives></jats:inline-formula> lower than the <jats:inline-formula><jats:alternatives><jats:tex-math>\left|V_{us}\right|</jats:tex-math><mml:math xmlns:mml="http://www.w3. org/1998/Math/MathML" display="inline"><mml:mrow><mml:mo stretchy="true" form="prefix">|</mml:mo><mml:msub><mml:mi>V</mml:mi><mml:mrow><mml:mi>u</mml:mi><mml:mi>s</mml:mi></mml:mrow></mml:msub><mml:mo stretchy="true" form="postfix">|</mml:mo></mml:mrow></mml:math></jats:alternatives></jats:inline-formula> determination from the CKM matrix unitarity. </jats:p>