Letter
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Measurement of the $C P$ asymmetry in $D^{+} \to π^{+} π^{0}$ decays at Belle II

I. Adachi , L. Aggarwal , H. Ahmed , H. Aihara , N. Akopov , S. Alghamdi , M. Alhakami , A. Aloisio , K. Amos et al. (Belle II Collaboration)

K. Amos , M. Angelsmark , N. Anh Ky , C. Antonioli , D. M. Asner , H. Atmacan , V. Aushev , M. Aversano , R. Ayad , V. Babu , H. Bae , N. K. Baghel , P. Bambade , Sw. Banerjee , S. Bansal , M. Barrett , M. Bartl , J. Baudot , A. Baur , A. Beaubien , F. Becherer , J. Becker , J. V. Bennett , F. U. Bernlochner , V. Bertacchi , M. Bertemes , E. Bertholet , M. Bessner , S. Bettarini , V. Bhardwaj , B. Bhuyan , F. Bianchi , D. Biswas , A. Bobrov , D. Bodrov , A. Bondar , G. Bonvicini , J. Borah , A. Boschetti , A. Bozek , M. Bračko , P. Branchini , R. A. Briere , T. E. Browder , A. Budano , S. Bussino , Q. Campagna , M. Campajola , L. Cao , G. Casarosa , C. Cecchi , M.-C. Chang , P. Cheema , L. Chen , B. G. Cheon , K. Chilikin , J. Chin , K. Chirapatpimol , H.-E. Cho , K. Cho , S.-J. Cho , S.-K. Choi , S. Choudhury , I. Consigny , L. Corona , J. X. Cui , S. Das , E. De La Cruz-Burelo , S. A. De La Motte , G. De Pietro , R. de Sangro , M. Destefanis , A. Di Canto , Z. Doležal , I. Domínguez Jiménez , T. V. Dong , X. Dong , M. Dorigo , K. Dugic , G. Dujany , P. Ecker , D. Epifanov , J. Eppelt , R. Farkas , P. Feichtinger , T. Ferber , T. Fillinger , C. Finck , G. Finocchiaro , F. Forti , A. Frey , B. G. Fulsom , A. Gabrielli , A. Gale , E. Ganiev , M. Garcia-Hernandez , R. Garg , G. Gaudino , V. Gaur , V. Gautam , A. Gaz , A. Gellrich , D. Ghosh , H. Ghumaryan , G. Giakoustidis , R. Giordano , A. Giri , P. Gironella Gironell , B. Gobbo , R. Godang , O. Gogota , P. Goldenzweig , W. Gradl , E. Graziani , D. Greenwald , Y. Guan , K. Gudkova , I. Haide , H. Hayashii , S. Hazra , C. Hearty , M. T. Hedges , A. Heidelbach , G. Heine , I. Heredia de la Cruz , M. Hernández Villanueva , T. Higuchi , M. Hoek , M. Hohmann , R. Hoppe , P. Horak , C.-L. Hsu , T. Humair , T. Iijima , K. Inami , G. Inguglia , N. Ipsita , A. Ishikawa , R. Itoh , M. Iwasaki , D. Jacobi , W. W. Jacobs , D. E. Jaffe , E.-J. Jang , Q. P. Ji , S. Jia , Y. Jin , A. Johnson , K. K. Joo , J. Kandra , K. H. Kang , G. Karyan , T. Kawasaki , F. Keil , C. Ketter , C. Kiesling , C.-H. Kim , D. Y. Kim , J.-Y. Kim , K.-H. Kim , Y.-K. Kim , H. Kindo , K. Kinoshita , P. Kodyš , T. Koga , S. Kohani , K. Kojima , A. Korobov , S. Korpar , E. Kovalenko , R. Kowalewski , P. Križan , P. Krokovny , Y. Kulii , R. Kumar , K. Kumara , T. Kunigo , A. Kuzmin , Y.-J. Kwon , K. Lalwani , T. Lam , L. Lanceri , J. S. Lange , T. S. Lau , M. Laurenza , R. Leboucher , F. R. Le Diberder , M. J. Lee , C. Lemettais , P. Leo , P. M. Lewis , C. Li , H.-J. Li , L. K. Li , S. X. Li , W. Z. Li , Y. Li , Y. B. Li , Y. P. Liao , J. Libby , J. Lin , S. Lin , M. H. Liu , Q. Y. Liu , Y. Liu , Z. Liu , D. Liventsev , S. Longo , A. Lozar , T. Lueck , C. Lyu , Y. Ma , M. Maggiora , S. P. Maharana , R. Maiti , G. Mancinelli , R. Manfredi , E. Manoni , M. Mantovano , D. Marcantonio , S. Marcello , C. Marinas , C. Martellini , A. Martens , T. Martinov , L. Massaccesi , M. Masuda , D. Matvienko , S. K. Maurya , M. Maushart , J. A. McKenna , Z. Mediankin Gruberová , R. Mehta , F. Meier , D. Meleshko , M. Merola , C. Miller , M. Mirra , S. Mitra , K. Miyabayashi , G. B. Mohanty , S. Mondal , S. Moneta , A. L. Moreira de Carvalho , H.-G. Moser , R. Mussa , I. Nakamura , M. Nakao , Y. Nakazawa , M. Naruki , Z. Natkaniec , A. Natochii , M. Nayak , M. Neu , S. Nishida , R. Okubo , H. Ono , Y. Onuki , E. R. Oxford , G. Pakhlova , S. Pardi , K. Parham , H. Park , J. Park , S.-H. Park , B. Paschen , A. Passeri , S. Patra , S. Paul , T. K. Pedlar , I. Peruzzi , R. Pestotnik , L. E. Piilonen , P. L. M. Podesta-Lerma , T. Podobnik , A. Prakash , C. Praz , S. Prell , E. Prencipe , M. T. Prim , S. Privalov , H. Purwar , P. Rados , G. Raeuber , S. Raiz , V. Raj , K. Ravindran , J. U. Rehman , M. Reif , S. Reiter , M. Remnev , L. Reuter , D. Ricalde Herrmann , I. Ripp-Baudot , G. Rizzo , S. H. Robertson , J. M. Roney , A. Rostomyan , N. Rout , D. A. Sanders , S. Sandilya , L. Santelj , C. Santos , V. Savinov , B. Scavino , C. Schmitt , M. Schnepf , K. Schoenning , C. Schwanda , A. J. Schwartz , Y. Seino , A. Selce , K. Senyo , J. Serrano , M. E. Sevior , C. Sfienti , W. Shan , G. Sharma , X. D. Shi , T. Shillington , T. Shimasaki , J.-G. Shiu , D. Shtol , B. Shwartz , A. Sibidanov , F. Simon , J. Skorupa , R. J. Sobie , M. Sobotzik , A. Soffer , A. Sokolov , E. Solovieva , S. Spataro , B. Spruck , M. Starič , P. Stavroulakis , S. Stefkova , L. Stoetzer , R. Stroili , M. Sumihama , H. Svidras , M. Takizawa , S. S. Tang , K. Tanida , F. Tenchini , F. Testa , O. Tittel , R. Tiwary , D. Tonelli , E. Torassa , K. Trabelsi , F. F. Trantou , I. Tsaklidis , M. Uchida , I. Ueda , T. Uglov , K. Unger , Y. Unno , K. Uno , S. Uno , P. Urquijo , Y. Ushiroda , S. E. Vahsen , R. van Tonder , K. E. Varvell , M. Veronesi , V. S. Vismaya , L. Vitale , R. Volpe , M. Wakai , S. Wallner , M.-Z. Wang , X. L. Wang , A. Warburton , S. Watanuki , C. Wessel , E. Won , B. D. Yabsley , S. Yamada , W. Yan , S. B. Yang , J. Yelton , K. Yi , J. H. Yin , K. Yoshihara , J. Yuan , Y. Yusa , L. Zani , F. Zeng , M. Zeyrek , B. Zhang , V. Zhilich , J. S. Zhou , Q. D. Zhou , L. Zhu , and R. Žlebčík (Belle II Collaboration)

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Phys. Rev. D 112, L031101 – Published 8 August, 2025

DOI: https://doi.org/10.1103/3kqk-ldm4

Abstract

We measure the $C P$ asymmetry in $D^{+} \to π^{+} π^{0}$ decays reconstructed in $e^{+} e^{-}$ collisions at the Belle II experiment using a dataset corresponding to an integrated luminosity of $428 {fb}^{- 1}$ . A control sample of $D^{+} \to π^{+} K_{S}^{0}$ decays is used to correct for detection and production asymmetries. The result $A_{C P} (D^{+} \to π^{+} π^{0}) = (- 1.8 \pm 0.9 \pm 0.1) %$ , where the first uncertainty is statistical and the second systematic, is the most precise determination to date. It agrees with the prediction of $C P$ symmetry from the standard model and with results of previous measurements.

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Article Text

References (63)

N. Cabibbo, Unitary symmetry and leptonic decays, Phys. Rev. Lett. 10, 531 (1963).
M. Kobayashi and T. Maskawa, $C P$ -violation in the renormalizable theory of weak interaction, Prog. Theor. Phys. 49, 652 (1973).
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).
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).
V. Fanti et al. (NA48 Collaboration), A new measurement of direct $C P$ violation in two pion decays of the neutral kaon, Phys. Lett. B 465, 335 (1999).
B. Aubert et al. (BABAR Collaboration), Measurement of the $C P$ asymmetry amplitude $\sin 2 β$ with $B^{0}$ mesons, Phys. Rev. Lett. 89, 201802 (2002).
K. Abe et al. (Belle Collaboration), An Improved measurement of mixing induced $C P$ violation in the neutral $B$ meson system, Phys. Rev. D 66, 071102 (2002).
B. Aubert et al. (BABAR Collaboration), Direct $C P$ violating asymmetry in $B^{0} \to K^{+} π^{-}$ decays, Phys. Rev. Lett. 93, 131801 (2004).
Y. Chao et al. (Belle Collaboration), Evidence for direct $C P$ violation in $B^{0} \to K^{+} π^{-}$ decays, Phys. Rev. Lett. 93, 191802 (2004).
R. Aaij et al. (LHCb Collaboration), Observation of $C P$ violation in $B^{\pm} \to D K^{\pm}$ decays, Phys. Lett. B 712, 203 (2012); 713, 351(E) (2012).
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).
S. L. Glashow, J. Iliopoulos, and L. Maiani, Weak interactions with lepton-hadron symmetry, Phys. Rev. D 2, 1285 (1970).
M. Golden and B. Grinstein, Enhanced $C P$ violations in hadronic charm decays, Phys. Lett. B 222, 501 (1989).
F. Buccella, M. Lusignoli, G. Miele, A. Pugliese, and P. Santorelli, Nonleptonic weak decays of charmed mesons, Phys. Rev. D 51, 3478 (1995).
S. Bianco, F. L. Fabbri, D. Benson, and I. Bigi, A Cicerone for the physics of charm, Riv. Nuovo Cimento 26N7, 1 (2003).
Y. Grossman, A. L. Kagan, and Y. Nir, New physics and $C P$ violation in singly Cabibbo suppressed $D$ decays, Phys. Rev. D 75, 036008 (2007).
M. Artuso, B. Meadows, and A. A. Petrov, Charm meson decays, Annu. Rev. Nucl. Part. Sci. 58, 249 (2008).
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), Measurement of the time-integrated $C P$ asymmetry in $D^{0} \to K^{+} K^{-}$ decays, Phys. Rev. Lett. 131, 091802 (2023).
M. Chala, A. Lenz, A. V. Rusov, and J. Scholtz, $Δ A_{C P}$ within the standard model and beyond, J. High Energy Phys. 07 (2019) 161.
A. Dery and Y. Nir, Implications of the LHCb discovery of $C P$ violation in charm decays, J. High Energy Phys. 12 (2019) 104.
L. Calibbi, T. Li, Y. Li, and B. Zhu, Simple model for large $C P$ violation in charm decays, $B$ -physics anomalies, muon $g - 2$ and dark matter, J. High Energy Phys. 10 (2020) 070.
Y. Grossman and S. Schacht, The emergence of the $Δ U = 0$ rule in charm physics, J. High Energy Phys. 07 (2019) 020.
H.-Y. Cheng and C.-W. Chiang, Revisiting $C P$ violation in $D \to P P$ and $V P$ decays, Phys. Rev. D 100, 093002 (2019).
A. J. Buras, P. Colangelo, F. De Fazio, and F. Loparco, The charm of 331, J. High Energy Phys. 10 (2021) 021.
S. Schacht and A. Soni, Enhancement of charm $C P$ violation due to nearby resonances, Phys. Lett. B 825, 136855 (2022).
I. Bediaga, T. Frederico, and P. C. Magalhães, Enhanced charm $C P$ asymmetries from final state interactions, Phys. Rev. Lett. 131, 051802 (2023).
R. Bause, H. Gisbert, G. Hiller, T. Höhne, D. F. Litim, and T. Steudtner, $U$ -spin- $C P$ anomaly in charm, Phys. Rev. D 108, 035005 (2023).
S. Schacht, A $U$ -spin anomaly in charm $C P$ violation, J. High Energy Phys. 03 (2023) 205.
A. Pich, E. Solomonidi, and L. Vale Silva, Final-state interactions in the $C P$ asymmetries of charm-meson two-body decays, Phys. Rev. D 108, 036026 (2023).
M. Gavrilova, Y. Grossman, and S. Schacht, Determination of the $D \to π π$ ratio of penguin over tree diagrams, Phys. Rev. D 109, 033011 (2024).
Y. Grossman, A. L. Kagan, and J. Zupan, Testing for new physics in singly Cabibbo suppressed $D$ decays, Phys. Rev. D 85, 114036 (2012).
G. Hiller, M. Jung, and S. Schacht, $S U (3)$ -flavor anatomy of nonleptonic charm decays, Phys. Rev. D 87, 014024 (2013).
F. Buccella, A. Paul, and P. Santorelli, $S U (3)_{F}$ breaking through final state interactions and $C P$ asymmetries in $D \to P P$ decays, Phys. Rev. D 99, 113001 (2019).
F. Buccella, M. Lusignoli, G. Mangano, G. Miele, A. Pugliese, and P. Santorelli, $C P$ Violating asymmetries in charged $D$ meson decays, Phys. Lett. B 302, 319 (1993).
H. Mendez et al. (CLEO Collaboration), Measurements of $D$ meson decays to two pseudoscalar mesons, Phys. Rev. D 81, 052013 (2010).
V. Babu et al. (Belle Collaboration), Search for $C P$ violation in the $D^{+} \to π^{+} π^{0}$ decay at Belle, Phys. Rev. D 97, 011101 (2018).
R. Aaij et al. (LHCb Collaboration), Search for $C P$ violation in $D_{(s)}^{+} \to h^{+} π^{0}$ and $D_{(s)}^{+} \to h^{+} η$ decays, J. High Energy Phys. 06 (2021) 019.
I. Adachi et al. (Belle II Collaboration), Measurement of the integrated luminosity of data samples collected during 2019-2022 by the Belle II experiment, Chin. Phys. C 49, 013001 (2025).
F. A. Berends, K. J. F. Gaemers, and R. Gastmans, $α^{3}$ contribution to the angular asymmetry in $e^{+} e^{-} \to μ^{+} μ^{-}$ , Nucl. Phys. B63, 381 (1973).
R. W. Brown, K. O. Mikaelian, V. K. Cung, and E. A. Paschos, Electromagnetic background in the search for neutral weak currents via $e^{+} e^{-} \to μ^{+} μ^{-}$ , Phys. Lett. 43B, 403 (1973).
R. J. Cashmore, C. M. Hawkes, B. W. Lynn, and R. G. Stuart, The forward-backward asymmetry in $e^{+} e^{-} \to μ^{+} μ^{-}$ comparisons between the theoretical calculations at the one loop level in the Standard Model and with the experimental measurements, Z. Phys. C 30, 125 (1986).
T. Abe et al. (Belle II Collaboration), Belle II technical design report, arXiv:1011.0352.
W. Altmannshofer et al., The Belle II physics book, Prog. Theor. Exp. Phys. 2019, 123C01 (2019); 2020, 029201(E) (2020).
K. Akai, K. Furukawa, and H. Koiso, SuperKEKB collider, Nucl. Instrum. Methods Phys. Res., Sect. A 907, 188 (2018).
D. J. Lange, The evtgen particle decay simulation package, Nucl. Instrum. Methods Phys. Res., Sect. A 462, 152 (2001).
T. Sjöstrand, S. Ask, J. R. Christiansen, R. Corke, N. Desai, P. Ilten, S. Mrenna, S. Prestel, C. O. Rasmussen, and P. Z. Skands, An Introduction to pythia 8.2, Comput. Phys. Commun. 191, 159 (2015).
S. Jadach, B. F. L. Ward, and Z. Wąs, The precision Monte Carlo event generator KK for two-fermion final states in $e^{+} e^{-}$ collisions, Comput. Phys. Commun. 130, 260 (2000).
E. Barberio, B. van Eijk, and Z. Wąs, photos: A universal Monte Carlo for QED radiative corrections in decays, Comput. Phys. Commun. 66, 115 (1991).
E. Barberio and Z. Wąs, photos: A universal Monte Carlo for QED radiative corrections. Version 2.0, Comput. Phys. Commun. 79, 291 (1994).
S. Agostinelli et al. (geant4 Collaboration), geant4: A simulation toolkit, Nucl. Instrum. Methods Phys. Res., Sect. A 506, 250 (2003).
Belle II Framework Software Group, T. Kuhr et al., The Belle II Core Software, Comput. Software Big Sci. 3, 1 (2019).
Belle II Collaboration, Belle II Analysis Software Framework (basf2), 10.5281/zenodo.5574115 (2025).
I. Adachi et al. (Belle II Collaboration), Charged-hadron identification at Belle II, arXiv:2506.04355.
S. Longo et al., CsI(Tl) pulse shape discrimination with the Belle II electromagnetic calorimeter as a novel method to improve particle identification at electron-positron colliders, Nucl. Instrum. Methods Phys. Res., Sect. A 982, 164562 (2020).
I. Adachi et al. (Belle and Belle II Collaborations), Search for lepton flavor-violating decay modes $B^{0} \to K_{S}^{0} τ^{\pm} ℓ^{\mp}$ ( $ℓ = μ$ , $e$ ) with hadronic $B$ -tagging at Belle and Belle II, Phys. Rev. Lett. 135, 041801 (2025).
S. Navas et al. (Particle Data Group), Review of particle physics, Phys. Rev. D 110, 030001 (2024).
J.-F. Krohn et al. (Belle II Analysis Software Group), Global decay chain vertex fitting at Belle II, Nucl. Instrum. Methods Phys. Res., Sect. A 976, 164269 (2020).
H. Voss, A. Höcker, J. Stelzer, and F. Tegenfeldt, TMVA, the toolkit for multivariate data analysis with ROOT, Proc. Sci. ACAT2007 (2007) 040.
A. Hoecker et al., TMVA—toolkit for multivariate data analysis, arXiv:physics/0703039.
I. Adachi et al. (Belle II Collaboration), Novel method for the identification of the production flavor of neutral charmed mesons, Phys. Rev. D 107, 112010 (2023).
N. L. Johnson, Systems of frequency curves generated by methods of translation, Biometrika 36, 149 (1949).
LHCb, R. Aaij et al., Measurement of $C P$ asymmetry in $D^{0} \to K^{-} K^{+}$ and $D^{0} \to π^{-} π^{+}$ decays, J. High Energy Phys. 07 (2014) 041.

Phys. Rev. D 112, L031101– Published 8 August, 2025

Vol. 112, Iss. 3 — 1 August 2025

Received 9 June 2025
Accepted 29 July 2025

DOI: https://doi.org/10.1103/3kqk-ldm4

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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Measurement of the $C P$ asymmetry in $D^{+} \to π^{+} π^{0}$ decays at Belle II

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Measurement of the CP asymmetry in D+→π+π0 decays at Belle II

Abstract

Physics Subject Headings (PhySH)

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References (63)

Measurement of the $C P$ asymmetry in $D^{+} \to π^{+} π^{0}$ decays at Belle II