Letter
Open Access

Normalization of partial wave $C P$ asymmetries in three-body decays of heavy hadrons

Jing-Juan Qi ^1,2,*, Zhen-Yang Wang ^2,†, Zhen-Hua Zhang ^3,‡, and Xin-Heng Guo ^4,§

¹College of Information and Intelligence Engineering, Zhejiang Wanli University, Zhejiang 315101, China
²Physics Department, Ningbo University, Zhejiang 315211, China
³School of Nuclear Science and Technology, University of South China, Hengyang, 421001, Hunan, China
⁴School of Physics Science and Technology, Kunming University, Kunming 650214, China

^*Contact author: jjqi@mail.bnu.edu.cn
^†Contact author: wangzhenyang@nbu.edu.cn
^‡Contact author: zhangzh@usc.edu.cn
^§Contact author: xhguo@bnu.edu.cn

Phys. Rev. D 113, L111301 – Published 15 June, 2026

DOI: https://doi.org/10.1103/662d-xs1l

Abstract

$C P$ violation in hadronic multibody decays has been extensively studied, and the experimental breakthrough in the heavy baryon sector was made recently. Partial-wave $C P$ asymmetries (PWCPAs) in multibody decays of heavy hadrons, which although provide us with more interference information, suffer from the normalization problem, as is pointed out in this paper. We propose a novel solution to this problem. We introduce a set of extra factors to rescale the PWCPAs to the proper sizes. Instead of determining the set of factors according to the normalization requirement, we demand that all the PWCPAs have the same statistical errors. In this way, we obtain a set of quasi-normalized PWCPAs, in the sense that they are close to the ideal normalized ones. As an application, we perform an analysis of PWCPAs in the decay channel $B^{\pm} \to π^{+} π^{-} π^{\pm}$ . We focus on the phase space region where the invariant mass of the $π^{+} π^{-}$ pair varies around the vector resonance $ρ^{0} (1450)$ . Based on the data of the LHCb Collaboration, the interference patterns among the resonances $ρ^{0} (1450)$ , $f_{2} (1270)$ , and $f_{0} (1500)$ and their contributions to the quasinormalized PWCPAs are analyzed. The analysis indicates that the quasi-normalized PWCPAs can avoid potential misleading or distorted results comparing with some other alternatively defined ones.

Physics Subject Headings (PhySH)

CP violation

Article Text

Supplemental Material

References (31)

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See Supplemental Material at http://link.aps.org/supplemental/10.1103/662d-xs1l for the detailed fitting results and additional comparisons of alternatively defined PWCPAs.

Phys. Rev. D 113, L111301– Published 15 June, 2026

Vol. 113, Iss. 11 — 1 June 2026

Received 28 February 2026
Accepted 19 May 2026

DOI: https://doi.org/10.1103/662d-xs1l

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP³.

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Normalization of partial wave $C P$ asymmetries in three-body decays of heavy hadrons

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Normalization of partial wave CP asymmetries in three-body decays of heavy hadrons

Abstract

Physics Subject Headings (PhySH)

Article Text

Supplemental Material

References (31)

Normalization of partial wave $C P$ asymmetries in three-body decays of heavy hadrons