# Testing the standard model with $D_{(s)} \to K_1 (\to K\pi\pi) \gamma$ decays

## TL;DR

This paper proposes a method to test the standard model by measuring photon polarization in charm decays involving $K_1$ mesons, which could reveal new physics through asymmetry analysis.

## Contribution

It introduces a novel approach to extract photon polarization in $D_{(s)}$ decays using up-down asymmetry, enabling tests of the standard model and potential new physics.

## Key findings

- Proportionality factor in asymmetry can be sizable, up to a few 10%.
- Method applicable to both $D^+$ and $D_s$ decays, sensitive to new physics.
- Null test does not require precise knowledge of hadronic factors.

## Abstract

The photon polarization in $D_{(s)} \to K_1 (\to K\pi\pi) \gamma$ decays can be extracted from an up-down asymmetry in the $K \pi \pi$ system, along the lines of the method known to $B \to K_1 (\to K\pi\pi) \gamma$ decays. Charm physics is advantageous as partner decays exist: $D^+ \to K_1^+ (\to K\pi\pi) \gamma$, which is standard model-like, and $D_s \to K_1^+ (\to K\pi\pi) \gamma$, which is sensitive to physics beyond the standard model in $|\Delta c| =|\Delta u|=1$ transitions. The standard model predicts their photon polarizations to be equal up to U-spin breaking corrections, while new physics in the dipole operators can split them apart at order one level. We estimate the proportionality factor in the asymmetry multiplying the polarization parameter from axial vectors $K_1(1270)$ and $K_1(1400)$ to be sizable, up to the few ${\cal{O}}(10)\%$ range. The actual value of the hadronic factor matters for the experimental sensitivity, but is not needed as an input to perform the null test.