Determination of the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>D</mml:mi><mml:mo stretchy="false">→</mml:mo><mml:mi>π</mml:mi><mml:mi>π</mml:mi></mml:math> ratio of penguin over tree diagrams

Abstract

We study the penguin over tree ratio in <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mi>D</a:mi><a:mo stretchy="false">→</a:mo><a:mi>π</a:mi><a:mi>π</a:mi></a:math> decays. This ratio can serve as a probe for rescattering effects. Assuming the Standard Model and in the isospin limit, we derive expressions that relate both the magnitude and the phase of this ratio to direct <d:math xmlns:d="http://www.w3.org/1998/Math/MathML" display="inline"><d:mi>C</d:mi><d:mi>P</d:mi></d:math> asymmetries and branching fractions. We find that the current data suggest that rescattering is large. A dedicated experimental analysis with current and future data will be able to significantly reduce the errors on these determinations, and enable us to check if indeed there is significant rescattering in <f:math xmlns:f="http://www.w3.org/1998/Math/MathML" display="inline"><f:mi>D</f:mi><f:mo stretchy="false">→</f:mo><f:mi>π</f:mi><f:mi>π</f:mi></f:math> decays. Published by the American Physical Society 2024