Studies of the resonance structure in $D^{0} \to K^\mp \pi^\pm \pi^\pm \pi^\mp$ decays

TL;DR

This paper constructs detailed amplitude models of specific D0 decays to understand their resonance structures, providing precise measurements of resonance parameters and coherence factors, which aid future CP violation and charm mixing studies.

Contribution

It introduces new amplitude models for D0 decays with precise resonance parameter measurements and a quasi model-independent analysis of the K(1460) resonance.

Findings

Resonance contributions from axial states dominate decay amplitudes.

Precise measurements of lineshape parameters for key resonances.

Calculated coherence factor R_{K3π} = 0.459 with detailed uncertainties.

Abstract

Amplitude models are constructed to describe the resonance structure of ${D^{0}\to K^{-}\pi^{+}\pi^{+}\pi^{-}}$ and ${D^{0} \to K^{+}\pi^{-}\pi^{-}\pi^{+}}$ decays using $pp$ collision data collected at centre-of-mass energies of 7 and 8 TeV with the LHCb experiment, corresponding to an integrated luminosity of $3.0\mathrm{fb}^{-1}$. The largest contributions to both decay amplitudes are found to come from axial resonances, with decay modes $D^{0} \to a_1(1260)^{+} K^{-}$ and $D^{0} \to K_1(1270/1400)^{+} \pi^{-}$ being prominent in ${D^{0}\to K^{-}\pi^{+}\pi^{+}\pi^{-}}$ and $D^{0}\to K^{+}\pi^{-}\pi^{-}\pi^{+}$, respectively. Precise measurements of the lineshape parameters and couplings of the $a_1(1260)^{+}$, $K_1(1270)^{-}$ and $K(1460)^{-}$ resonances are made, and a quasi model-independent study of the $K(1460)^{-}$ resonance is performed. The coherence factor of the decays is calculated from the amplitude models to be $R_{K3\pi} = 0.459\pm 0.010\,(\mathrm{stat}) \pm 0.012\,(\mathrm{syst}) \pm 0.020\,(\mathrm{model})$, which is consistent with direct measurements. These models will be useful in future measurements of the unitary-triangle angle $\gamma$ and studies of charm mixing and $C\!P$ violation.