Skip to main content

Combined analysis of Belle and Belle II data to determine the CKM angle ϕ3 using B+D(\( {K}_S^0 \)h+h)h+ decays

A preprint version of the article is available at arXiv.

Abstract

We present a measurement of the Cabibbo-Kobayashi-Maskawa unitarity triangle angle ϕ3 (also known as γ) using a model-independent Dalitz plot analysis of B+D (\( {K}_S^0 \)h+h)h+, where D is either a D0 or \( \overline{D} \)0 meson and h is either a π or K. This is the first measurement that simultaneously uses Belle and Belle II data, combining samples corresponding to integrated luminosities of 711 fb1 and 128 fb1, respectively. All data were accumulated from energy-asymmetric e+e collisions at a centre-of-mass energy corresponding to the mass of the Υ(4S) resonance. We measure ϕ3 = (78.4 ± 11.4 ± 0.5 ± 1.0)°, where the first uncertainty is statistical, the second is the experimental systematic uncertainty and the third is from the uncertainties on external measurements of the D-decay strong-phase parameters.

References

  1. N. Cabibbo, Unitary Symmetry and Leptonic Decays, Phys. Rev. Lett. 10 (1963) 531 [INSPIRE].

  2. M. Kobayashi and T. Maskawa, CP violation in the renormalizable theory of weak interaction, PTEP 49 (1973) 652 [INSPIRE].

  3. J. Brod and J. Zupan, The ultimate theoretical error on γ from BDK decays, JHEP 01 (2014) 051 [arXiv:1308.5663] [INSPIRE].

    ADS  Article  Google Scholar 

  4. M. Blanke and A.J. Buras, EmergingMd-anomaly from tree-level determinations of |Vcb| and the angle γ, Eur. Phys. J. C 79 (2019) 159 [arXiv:1812.06963] [INSPIRE].

    ADS  Article  Google Scholar 

  5. HFLAV collaboration, Averages of b-hadron, c-hadron, and τ-lepton properties as of 2018, Eur. Phys. J. C 81 (2021) 226 [arXiv:1909.12524] [INSPIRE].

  6. D. King, M. Kirk, A. Lenz and T. Rauh, |Vcb| and γ from B-mixing — Addendum to “Bs mixing observables and |Vtd/Vts| from sum rules”, JHEP 03 (2020) 112 [arXiv:1911.07856] [INSPIRE].

    ADS  Article  Google Scholar 

  7. LHCb collaboration, Measurement of the CKM angle γ in B±DK± and B±± decays with D\( {K}_{\mathrm{S}}^0 \)h+h, JHEP 02 (2021) 169 [arXiv:2010.08483] [INSPIRE].

  8. A. Giri, Y. Grossman, A. Soffer and J. Zupan, Determining γ using BDK with multibody D decays, Phys. Rev. D 68 (2003) 054018 [hep-ph/0303187] [INSPIRE].

  9. A. Bondar, Proceedings of BINP special analysis meeting on Dalitz analysis, unpublished, 24–26 September 2002.

  10. Belle collaboration, Measurement of ϕ3 with Dalitz plot analysis of B±D(*)K± decay, Phys. Rev. D 70 (2004) 072003 [hep-ex/0406067] [INSPIRE].

  11. M. Gronau and D. Wyler, On determining a weak phase from CP asymmetries in charged B decays, Phys. Lett. B 265 (1991) 172 [INSPIRE].

  12. M. Gronau and D. London, How to determine all the angles of the unitarity triangle from \( {B}_d^0 \)DKS and \( {B}_S^0 \), Phys. Lett. B 253 (1991) 483 [INSPIRE].

  13. D. Atwood, I. Dunietz and A. Soni, Enhanced CP violation with BKD0(\( \overline{D} \)0) modes and extraction of the CKM angle γ, Phys. Rev. Lett. 78 (1997) 3257 [hep-ph/9612433] [INSPIRE].

  14. D. Atwood, I. Dunietz and A. Soni, Improved methods for observing CP violation in B±K±D and measuring the CKM phase gamma, Phys. Rev. D 63 (2001) 036005 [hep-ph/0008090] [INSPIRE].

  15. CLEO collaboration, Model-independent determination of the strong-phase difference between D0 and \( \overline{D} \)0\( {K}_{\mathrm{S},\mathrm{L}}^0 \)h+h (h = π, K) and its impact on the measurement of the CKM angle γ/ϕ3, Phys. Rev. D 82 (2010) 112006 [arXiv:1010.2817] [INSPIRE].

  16. BESIII collaboration, Model-independent determination of the relative strong-phase difference between D0 and \( \overline{D} \)0\( {K}_{\mathrm{S},\mathrm{L}}^0 \)π+π and its impact on the measurement of the CKM angle γ/ϕ3, Phys. Rev. D 101 (2020) 112002 [arXiv:2003.00091] [INSPIRE].

  17. BESIII collaboration, Improved model-independent determination of the strong-phase difference between D0 and \( \overline{D} \)0\( {K}_{\mathrm{S},\mathrm{L}}^0 \)K+K decays, Phys. Rev. D 102 (2020) 052008 [arXiv:2007.07959] [INSPIRE].

  18. BaBar collaboration, Evidence for direct CP violation in the measurement of the Cabibbo-Kobayashi-Maskawa angle gamma with B±D(*)K(*)± decays, Phys. Rev. Lett. 105 (2010) 121801 [arXiv:1005.1096] [INSPIRE].

  19. Belle collaboration, Evidence for direct CP violation in the decay BD(*)K, D\( {K}_{\mathrm{S}}^0 \)π+π and measurement of the CKM phase ϕ3, Phys. Rev. D 81 (2010) 112002 [arXiv:1003.3360 ] [INSPIRE].

  20. Belle collaboration, First Measurement of ϕ3 with a Model-independent Dalitz Plot Analysis of B±DK±, D\( {K}_S^0 \)ππ Decay, Phys. Rev. D 85 (2012) 112014 [arXiv:1204.6561] [INSPIRE].

  21. A. Di Canto et al., Novel method for measuring charm-mixing parameters using multibody decays, Phys. Rev. D 99 (2019) 012007 [arXiv:1811.01032] [INSPIRE].

  22. Particle Data Group collaboration, Review of Particle Physics, PTEP 2020 (2020) 083C01 [INSPIRE].

  23. J. Garra Ticó, A strategy for a simultaneous measurement of CP violation parameters related to the CKM angle γ in multiple B meson decay channels, arXiv:1804.05597 [INSPIRE].

  24. J. Garra Ticó, V. Gibson, S.C. Haines, C.R. Jones, M. Kenzie and G. Lovell, Study of the sensitivity to CKM angle γ under simultaneous determination from multiple B meson decay modes, Phys. Rev. D 102 (2020) 053003 [arXiv:1909.00600] [INSPIRE].

  25. A. Bondar and A. Poluektov, The use of quantum-correlated D0 decays for ϕ3 measurement, Eur. Phys. J. C 55 (2008) 51 [arXiv:0801.0840] [INSPIRE].

    ADS  Article  Google Scholar 

  26. A. Bondar, A. Poluektov and V. Vorobiev, Charm mixing in the model-independent analysis of correlated D0\( \overline{D} \)0 decays, Phys. Rev. D 82 (2010) 034033 [arXiv:1004.2350] [INSPIRE].

  27. M. Bjørn and S. Malde, CP violation and material interaction of neutral kaons in measurements of the CKM angle γ using B±DK± decays where D\( {K}_{\mathrm{S}}^0 \)π+π, JHEP 07 (2019) 106 [arXiv:1904.01129] [INSPIRE].

  28. Belle collaboration, The Belle Detector, Nucl. Instrum. Meth. A 479 (2002) 117 [INSPIRE].

  29. Belle collaboration, Physics Achievements from the Belle Experiment, PTEP 2012 (2012) 04D001 [arXiv:1212.5342] [INSPIRE].

  30. S. Kurokawa and E. Kikutani, Overview of the KEKB accelerators, Nucl. Instrum. Meth. A 499 (2003) 1 [INSPIRE].

  31. T. Abe et al., Achievements of KEKB, PTEP 2013 (2013) 03A001 [INSPIRE].

  32. Belle II collaboration, Belle II Technical Design Report, arXiv:1011.0352 [INSPIRE].

  33. SuperKEKB collaboration, SuperKEKB Collider, Nucl. Instrum. Meth. A 907 (2018) 188 [arXiv:1809.01958] [INSPIRE].

  34. D.J. Lange, The EvtGen particle decay simulation package, Nucl. Instrum. Meth. A 462 (2001) 152 [INSPIRE].

  35. B.F.L. Ward, S. Jadach and Z. Was, Precision calculation for e+e → 2f: The KK MC project, Nucl. Phys. B Proc. Suppl. 116 (2003) 73 [hep-ph/0211132] [INSPIRE].

  36. T. Sjöstrand, S. Mrenna and P.Z. Skands, A Brief Introduction to PYTHIA 8.1, Comput. Phys. Commun. 178 (2008) 852 [arXiv:0710.3820] [INSPIRE].

  37. R. Brun et al., GEANT 3.21, CERN Program Library Long Writeup W5013, unpublished [INSPIRE].

  38. Geant4 collaboration, GEANT4 — a simulation toolkit, Nucl. Instrum. Meth. A 506 (2003) 250 [INSPIRE].

  39. E. Barberio and Z. Was, PHOTOS: A Universal Monte Carlo for QED radiative corrections. Version 2.0, Comput. Phys. Commun. 79 (1994) 291 [INSPIRE].

  40. P.M. Lewis et al., First Measurements of Beam Backgrounds at SuperKEKB, Nucl. Instrum. Meth. A 914 (2019) 69 [arXiv:1802.01366] [INSPIRE].

    ADS  Article  Google Scholar 

  41. Belle II Framework Software Group collaboration, The Belle II Core Software, Comput. Softw. Big Sci. 3 (2019) 1 [arXiv:1809.04299] [INSPIRE].

  42. M. Gelb et al., B2BII: Data Conversion from Belle to Belle II, Comput. Softw. Big Sci. 2 (2018) 9 [arXiv:1810.00019] [INSPIRE].

    Article  Google Scholar 

  43. Belle collaboration, Evidence for the Suppressed Decay BDK, DK+π, Phys. Rev. Lett. 106 (2011) 231803 [arXiv:1103.5951] [INSPIRE].

  44. Belle II collaboration, Study of BD(*)h decays using 62.8 fb1 of Belle II data, in 55th Rencontres de Moriond on QCD and High Energy Interactions, (2021) [arXiv:2104.03628] [INSPIRE].

  45. H. Nakano, Search for new physics by a time-dependent CP violation analysis of the decay BKSηγ using the Belle detector, Ph.D. Thesis, Tohoku University (2014), unpublished [https://belle.kek.jp/belle/theses/doctor/nakano15.pdf].

  46. T. Keck, FastBDT: A Speed Optimized Multivariate Classification Algoritm for the Belle II Experiment, Comput. Softw. Big Sci. 1 (2017) 2 [INSPIRE].

  47. G.C. Fox and S. Wolfram, Observables for the Analysis of Event Shapes in e+e Annihilation and Other Processes, Phys. Rev. Lett. 41 (1978) 1581 [INSPIRE].

  48. Belle collaboration, Evidence for B0π0π0, Phys. Rev. Lett. 91 (2003) 261801 [hep-ex/0308040] [INSPIRE].

  49. Belle collaboration, Neutral B Flavor Tagging for the Measurement of Mixing-induced CP Violation at Belle, Nucl. Instrum. Meth. A 533 (2004) 516 [hep-ex/0403022] [INSPIRE].

  50. Belle II collaboration, B-flavor tagging at Belle II, arXiv:2110.00790 [INSPIRE].

  51. A. Hocker et al., TMVA — Toolkit for Multivariate Data Analysis, physics/0703039 [INSPIRE].

  52. W.H. Press, S.A. Teukolsky, W.T. Vetterling and B.P. Flannery, Numerical Recipes in C++ (Second Edition), pp. 99–101, Cambridge University Press (2002).

  53. LHCb collaboration, Measurement of the CKM angle γ from a combination of LHCb results, JHEP 12 (2016) 087 [arXiv:1611.03076] [INSPIRE].

  54. LHCb collaboration, Simultaneous determination of CKM angle γ and charm mixing parameters, arXiv:2110.02350 [INSPIRE].

  55. Belle II collaboration, The Belle II Physics Book, PTEP 2019 (2019) 123C01 [Erratum ibid. 2020 (2020) 029201] [arXiv:1808.10567] [INSPIRE].

Download references

Author information

Affiliations

Authors

Consortia

Corresponding author

Correspondence to N. Rout.

Additional information

Publisher’s Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

ArXiv ePrint: 2110.12125

Supplementary Information

ESM 1

(NUMBERS 1077 kb)

Rights and permissions

Open Access . This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

The Belle and Belle II collaborations., Abudinén, F., Aggarwal, L. et al. Combined analysis of Belle and Belle II data to determine the CKM angle ϕ3 using B+D(\( {K}_S^0 \)h+h)h+ decays. J. High Energ. Phys. 2022, 63 (2022). https://doi.org/10.1007/JHEP02(2022)063

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/JHEP02(2022)063

Keywords

  • B Physics
  • CKM Angle Gamma
  • e +-e Experiments