Skip to main content

Measurement of CP observables in B± → D(*)K± and B± → D(*)π± decays using two-body D final states

A preprint version of the article is available at arXiv.


Measurements of CP observables in B±D(*)K± and B±D(*)π± decays are presented, where D(∗) indicates a neutral D or D meson that is an admixture of meson and anti-meson states. Decays of the D(∗) meson to the 0 and final states are partially reconstructed without inclusion of the neutral pion or photon. Decays of the D meson are reconstructed in the K±π, K+K, and π+π final states. The analysis uses a sample of charged B mesons produced in proton-proton collisions and collected with the LHCb experiment, corresponding to integrated luminosities of 2.0, 1.0, and 5.7 fb1 taken at centre-of-mass energies of 7, 8, and 13 TeV, respectively. The measurements of partially reconstructed B±D(*)K± and B±D(∗)π± with DKπ± decays are the first of their kind, and a first observation of the B±\( {\left(D{\pi}^0\right)}_{D^{\ast }}{\pi}^{\pm } \) decay is made with a significance of 6.1 standard deviations. All CP observables are measured with world-best precision, and in combination with other LHCb results will provide strong constraints on the CKM angle γ.


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

    Article  ADS  Google Scholar 

  2. M. Kobayashi and T. Maskawa, CP Violation in the Renormalizable Theory of Weak Interaction, Prog. Theor. Phys. 49 (1973) 652 [INSPIRE].

    Article  ADS  Google Scholar 

  3. LHCb collaboration, Update of the LHCb combination of the CKM angle γ, LHCb-CONF-2018-002 [CERN-LHCb-CONF-2018-002] (2018).

  4. HFLAV collaboration, Averages of b-hadron, c-hadron, and τ-lepton properties as of 2018, arXiv:1909.12524 [INSPIRE].

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

  6. CKMfitter Group, CP violation and the CKM matrix: Assessing the impact of the asymmetric B factories, Eur. Phys. J. C 41 (2005) 1 [hep-ph/0406184] [INSPIRE].

  7. UTfit collaboration, The Unitarity Triangle Fit in the Standard Model and Hadronic Parameters from Lattice QCD: A Reappraisal after the Measurements ofms and BR(Bτντ), JHEP 10 (2006) 081 [hep-ph/0606167] [INSPIRE].

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

    Article  ADS  Google Scholar 

  9. A. Bondar and T. Gershon, On ϕ3 measurements using BDK decays, Phys. Rev. D 70 (2004) 091503 [hep-ph/0409281] [INSPIRE].

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

    Article  Google Scholar 

  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].

    Article  ADS  Google Scholar 

  12. 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].

  13. LHCb collaboration, Measurement of CP observables in B±D(*)K± and B±D(∗)π± decays, Phys. Lett. B 777 (2018) 16 [LHCb-PAPER-2017-021] [CERN-EP-2017-195] [arXiv:1708.06370] [INSPIRE].

  14. LHCb collaboration, Measurement of CP observables in B±DK± and B±± with two- and four-body D decays, Phys. Lett. B 760 (2016) 117 [arXiv:1603.08993] [INSPIRE].

  15. LHCb collaboration, LHCb Detector Performance, Int. J. Mod. Phys. A 30 (2015) 1530022 [arXiv:1412.6352] [INSPIRE].

  16. M. Rama, Effect of D − \( \overline{D} \) mixing in the extraction of γ with BD0K and BD0π decays, Phys. Rev. D 89 (2014) 014021 [arXiv:1307.4384] [INSPIRE].

    Article  Google Scholar 

  17. LHCb collaboration, The LHCb Detector at the LHC, 2008 JINST 3 S08005 [INSPIRE].

  18. V.V. Gligorov and M. Williams, Efficient, reliable and fast high-level triggering using a bonsai boosted decision tree, 2013 JINST 8 P02013 [arXiv:1210.6861] [INSPIRE].

  19. 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].

  20. T. Sjöstrand, S. Mrenna and P.Z. Skands, PYTHIA 6.4 Physics and Manual, JHEP 05 (2006) 026 [hep-ph/0603175] [INSPIRE].

  21. I. Belyaev et al., Handling of the generation of primary events in Gauss, the LHCb simulation framework, J. Phys. Conf. Ser. 331 (2011) 032047 [INSPIRE].

    Article  Google Scholar 

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

    Article  ADS  Google Scholar 

  23. P. Golonka and Z. Was, PHOTOS Monte Carlo: A Precision tool for QED corrections in Z and W decays, Eur. Phys. J. C 45 (2006) 97 [hep-ph/0506026] [INSPIRE].

  24. J. Allison et al., GEANT4 developments and applications, IEEE Trans. Nucl. Sci. 53 (2006) 270 [INSPIRE].

    Article  ADS  Google Scholar 

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

  26. M. Clemencic et al., The LHCb simulation application, Gauss: Design, evolution and experience, J. Phys. Conf. Ser. 331 (2011) 032023 [INSPIRE].

    Article  Google Scholar 

  27. G.A. Cowan, D.C. Craik and M.D. Needham, RapidSim: an application for the fast simulation of heavy-quark hadron decays, Comput. Phys. Commun. 214 (2017) 239 [arXiv:1612.07489] [INSPIRE].

    Article  ADS  Google Scholar 

  28. Particle Data collaboration, Review of Particle Physics, Prog. Theor. Exp. Phys. 2020 (2020) 083C01 [INSPIRE].

  29. W.D. Hulsbergen, Decay chain fitting with a Kalman filter, Nucl. Instrum. Meth. A 552 (2005) 566 [physics/0503191] [INSPIRE].

  30. B.P. Roe, H.-J. Yang, J. Zhu, Y. Liu, I. Stancu and G. McGregor, Boosted decision trees, an alternative to artificial neural networks, Nucl. Instrum. Meth. A 543 (2005) 577 [physics/0408124] [INSPIRE].

  31. F. Pedregosa et al., Scikit-learn: Machine Learning in Python, J. Mach. Learn. Res. 12 (2011) 2825 [arXiv:1201.0490] [INSPIRE].

    MathSciNet  MATH  Google Scholar 

  32. M. Adinolfi et al., Performance of the LHCb RICH detector at the LHC, Eur. Phys. J. C 73 (2013) 2431 [arXiv:1211.6759] [INSPIRE].

    Article  ADS  Google Scholar 

  33. R. Aaij et al., Selection and processing of calibration samples to measure the particle identification performance of the LHCb experiment in Run 2, Eur. Phys. J. Tech. Instrum. 6 (2019) 1 [arXiv:1803.00824] [INSPIRE].

    Google Scholar 

  34. D. Martínez Santos and F. Dupertuis, Mass distributions marginalized over per-event errors, Nucl. Instrum. Meth. A 764 (2014) 150 [arXiv:1312.5000] [INSPIRE].

    Article  ADS  Google Scholar 

  35. N.L. Johnson, Systems of frequency curves generated by methods of translation, Biometrika 36 (1949) 149 [INSPIRE].

    MathSciNet  Article  Google Scholar 

  36. T. Skwarnicki, A study of the radiative cascade transitions between the Upsilon-prime and Upsilon resonances, Ph.D. Thesis, Institute of Nuclear Physics, Krakow Poland (1986).

  37. T. Latham, The Laura++ Dalitz plot fitter, AIP Conf. Proc. 1735 (2016) 070001 [arXiv:1603.00752] [INSPIRE].

    Article  Google Scholar 

  38. LHCb collaboration, Dalitz plot analysis of B0\( \overline{D} \)0π+π decays, Phys. Rev. D 92 (2015) 032002 [LHCb-PAPER-2014-070] [CERN-PH-EP-2015-110] [arXiv:1505.01710] [INSPIRE].

  39. LHCb collaboration, Amplitude analysis of B0\( \overline{D} \)0K+π decays, Phys. Rev. D 92 (2015) 012012 [LHCb-PAPER-2015-017] [CERN-PH-EP-2015-107] [arXiv:1505.01505] [INSPIRE].

  40. LHCb collaboration, Study of the D0p amplitude in \( {\Lambda}_b^0 \)D0 decays, JHEP 05 (2017) 030 [LHCb-PAPER-2016-061] [CERN-EP-2017-007] [arXiv:1701.07873] [INSPIRE].

  41. LHCb collaboration, Measurement of b-hadron production fractions in 7 TeV pp collisions, Phys. Rev. D 85 (2012) 032008 [CERN-PH-EP-2011-172] [LHCb-PAPER-2011-018] [arXiv:1111.2357] [INSPIRE].

  42. LHCb collaboration, Dalitz plot analysis of \( {B}_s^0 \)\( \overline{D} \)0Kπ+ decays, Phys. Rev. D 90 (2014) 072003 [LHCb-PAPER-2014-036] [CERN-PH-EP-2014-184] [arXiv:1407.7712] [INSPIRE].

  43. BaBar collaboration, Measurement of the branching fraction and polarization for the decay BD0*K*−, Phys. Rev. Lett. 92 (2004) 141801 [hep-ex/0308057] [INSPIRE].

  44. LHCb collaboration, First observation of the decays \( \overline{B} \)0D+Kπ+π and BD0Kπ+π, Phys. Rev. Lett. 108 (2012) 161801 [LHCb-PAPER-2011-040] [CERN-EP-PH-EP-2011-229] [arXiv:1201.4402] [INSPIRE].

  45. LHCb collaboration, Measurement of the B± production asymmetry and the CP asymmetry in B±J/ψK± decays, Phys. Rev. D 95 (2017) 052005 [LHCb-PAPER-2016-054] [CERN-EP-2016-325] [arXiv:1701.05501] [INSPIRE].

  46. BaBar collaboration, Search for bu transitions in BDK and DK Decays, Phys. Rev. D 82 (2010) 072006 [arXiv:1006.4241] [INSPIRE].

  47. LHCb collaboration, Measurement of the CKM angle γ from a combination of LHCb results, JHEP 12 (2016) 087 [LHCb-PAPER-2016-032] [CERN-EP-2016-270] [arXiv:1611.03076] [INSPIRE].

  48. BaBar collaboration, Observation of direct CP-violation in the measurement of the Cabibbo-Kobayashi-Maskawa angle gamma with B±D(*)K(*)± decays, Phys. Rev. D 87 (2013) 052015 [arXiv:1301.1029] [INSPIRE].

Download references

Author information