# Disentangling weak and strong interactions in $B\to K^*(\to K\pi)\pi$ Dalitz-plot analyses

## TL;DR

This paper analyzes $B o K^* o K o ext{pi}$ decays through Dalitz plots to disentangle weak and strong phases, constraining CKM parameters and examining hadronic amplitude hierarchies with current and future experimental data.

## Contribution

It introduces a new isospin analysis method for $B o K^* o K ext{pi}$ decays, improving robustness over previous approaches and providing insights into hadronic amplitudes and CKM parameters.

## Key findings

- Current data show multiple solutions inconsistent with theoretical hierarchies.
- A bound on annihilation contributions offers a more reliable method than electroweak penguin bounds.
- Future measurements at LHCb and Belle II could refine these analyses.

## Abstract

Dalitz-plot analyses of $B\rightarrow K\pi\pi$ decays provide direct access to decay amplitudes, and thereby weak and strong phases can be disentangled by resolving the interference patterns in phase space between intermediate resonant states. A phenomenological isospin analysis of $B\rightarrow K^*(\rightarrow K\pi)\pi$ decay amplitudes is presented exploiting available amplitude analyses performed at the Babar, Belle and LHCb experiments. A first application consists in constraining the CKM parameters thanks to an external hadronic input. A method, proposed some time ago by two different groups and relying on a bound on the electroweak penguin contribution, is shown to lack the desired robustness and accuracy, and we propose a more alluring alternative using a bound on the annihilation contribution. A second application consists in extracting information on hadronic amplitudes assuming the values of the CKM parameters from a global fit to quark flavour data. The current data yields several solutions, which do not fully support the hierarchy of hadronic amplitudes usually expected from theoretical arguments (colour suppression, suppression of electroweak penguins), as illustrated from computations within QCD factorisation. Some prospects concerning the impact of future measurements at LHCb and Belle II are also presented. Results are obtained with the CKMfitter analysis package, featuring the frequentist statistical approach and using the Rfit scheme to handle theoretical uncertainties.