Theory of CP angles measurement

TL;DR

This paper reviews methods for directly measuring the unitarity angles of the CKM matrix, discusses current experimental capabilities, and highlights the importance of lattice QCD in constraining the unitarity triangle and supporting CP violation theory.

Contribution

It provides an overview of the status and prospects of direct measurements of the unitarity angles, emphasizing experimental strategies and lattice QCD inputs for the unitarity triangle.

Findings

Belle-II's potential to improve $oldsymbol{ heta_3}$ measurement with $D^0$ Dalitz decays

Progress in lattice QCD constraining the unitarity triangle

Compatibility of lattice constraints with direct measurements

Abstract

In the early 80's Sanda-san and collaborators wrote key papers on the direct and clean determination of the unitarity angle $\phi_1$ ($\beta$). This motivated many of us for analogously coming up with ways for direct and clean determinations of the other two unitarity angles, $\phi_2 (\alpha)$ and $\phi_3 (\gamma)$. Current status of these direct determinations as well as our expectations for when Belle-II has 50 $ab^{-1}$ of luminosity and LHCb with some upgrades, will be given. In particular, it is emphasized that for direct determination of $\phi_3$, Belle-II should be able to handle final states in $D^0$ or $\bar D^0$ Dalitz decays, that contain one $\pi^0$ (which are difficult for LHCb) then they may make further inroads in improving the accuracy of $\phi_3$ determination. Early lattice inputs for constraining the unitarity triangle (UT) are briefly recalled. Its crucial role in supporting the Kobayashi-Maskawa theory of CP violation is emphasized. Over the years lattice methods have made significant progress and latest constraints from these for the UT will be discussed as well as compatibility with current direct determinations and some comments on future outlook will be made.