Abstract
A binned Dalitz plot analysis of B± → DK± decays, with D → K 0S π+π− and D → K 0S K+K−, is used to perform a measurement of the CP-violating observables x± and y±, which are sensitive to the Cabibbo-Kobayashi-Maskawa angle γ. The analysis is performed without assuming any D decay model, through the use of information on the strong-phase variation over the Dalitz plot from the CLEO collaboration. Using a sample of proton-proton collision data collected with the LHCb experiment in 2015 and 2016, and corresponding to an integrated luminosity of 2.0 fb−1, the values of the CP violation parameters are found to be x− = (9.0 ± 1.7 ± 0.7 ± 0.4) × 10−2, y− = (2.1 ± 2.2 ± 0.5 ± 1.1) × 10−2, x+ = (−7.7 ± 1.9 ± 0.7 ± 0.4) × 10−2, and y+ = (−1.0 ± 1.9 ± 0.4 ± 0.9) × 10−2. The first uncertainty is statistical, the second is systematic, and the third is due to the uncertainty (on the strong-phase measurements. These values are used to obtain γ = (87 + 11− 12 )∘, rB = 0.086 + 0.013− 0.014 , and δB = (101±11)°, where rB is the ratio between the suppressed and favoured B-decay amplitudes and δB is the corresponding strong-interaction phase difference. This measurement is combined with the result obtained using 2011 and 2012 data collected with the LHCb experiment, to give γ = (80 + 10− 9 )∘, rB = 0.080 ± 0.011, and δB = (110 ± 10)°.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
Change history
16 October 2018
The B+ and B? labels of the confidence regions in figure 10 of the original paper [1] were erroneously swapped. The corrected figure is shown in figure 10.
16 October 2018
The B+ and B? labels of the confidence regions in figure 10 of the original paper [1] were erroneously swapped. The corrected figure is shown in figure 10.
16 October 2018
The B+ and B? labels of the confidence regions in figure 10 of the original paper [1] were erroneously swapped. The corrected figure is shown in figure 10.
References
N. Cabibbo, Unitary symmetry and leptonic decays, Phys. Rev. Lett. 10 (1963) 531 [INSPIRE].
M. Kobayashi and T. Maskawa, CP violation in the renormalizable theory of weak interaction, Prog. Theor. Phys. 49 (1973) 652 [INSPIRE].
J. Brod and J. Zupan, The ultimate theoretical error on γ from B → DK decays, JHEP 01 (2014) 051 [arXiv:1308.5663] [INSPIRE].
HFLAV collaboration, Y. Amhis et al., Averages of b-hadron, c-hadron and τ-lepton properties as of summer 2016, Eur. Phys. J. C 77 (2017) 895 [arXiv:1612.07233] [INSPIRE].
D. Atwood, I. Dunietz and A. Soni, Improved methods for observing CP-violation in B ± → KD and measuring the CKM phase gamma, Phys. Rev. D 63 (2001) 036005 [hep-ph/0008090] [INSPIRE].
A. Giri, Y. Grossman, A. Soffer and J. Zupan, Determining gamma using B ± → DK ± with multibody D decays, Phys. Rev. D 68 (2003) 054018 [hep-ph/0303187] [INSPIRE].
A. Bondar, Proceedings of BINP special analysis meeting on Dalitz analysis, September 24–26 (2002), unpublished.
LHCb collaboration, A study of CP-violation in B ± → DK ± and B ± → Dπ ± decays with D → K 0 S K ± π ∓ final states, Phys. Lett. B 733 (2014) 36 [arXiv:1402.2982] [INSPIRE].
LHCb collaboration, Measurement of the CKM angle γ using B ± → DK ± with D → K 0S π + π −, K 0S K + K − decays, JHEP 10 (2014) 097 [arXiv:1408.2748] [INSPIRE].
LHCb collaboration, A study of CP violation in B ∓ → Dh ∓ (h = K, π) with the modes D → K ∓ π ± π 0 , D → π + π − π 0 and D → K + K − π 0, Phys. Rev. D 91 (2015) 112014 [arXiv:1504.05442] [INSPIRE].
LHCb collaboration, Measurement of CP observables in B ± → DK ± and B ± → Dπ ± with two- and four-body D decays, Phys. Lett. B 760 (2016) 117 [arXiv:1603.08993] [INSPIRE].
LHCb collaboration, Measurement of CP-violation parameters in B 0 → DK *0 decays, Phys. Rev. D 90 (2014) 112002 [arXiv:1407.8136] [INSPIRE].
LHCb collaboration, Measurement of CP asymmetry in B 0 s → D ∓ s K ± decays, JHEP 11 (2014) 060 [arXiv:1407.6127] [INSPIRE].
LHCb collaboration, Study of B − → DK − π + π − and B − → Dπ − π + π − decays and determination of the CKM angle γ, Phys. Rev. D 92 (2015) 112005 [arXiv:1505.07044] [INSPIRE].
LHCb collaboration, Constraints on the unitarity triangle angle γ from Dalitz plot analysis of B 0 → DK + π − decays, Phys. Rev. D 93 (2016) 112018 [arXiv:1602.03455] [INSPIRE].
A. Bondar and A. Poluektov, Feasibility study of model-independent approach to ϕ 3 measurement using Dalitz plot analysis, Eur. Phys. J. C 47 (2006) 347 [hep-ph/0510246] [INSPIRE].
A. Bondar and A. Poluektov, The Use of quantum-correlated D 0 decays for ϕ 3 measurement, Eur. Phys. J. C 55 (2008) 51 [arXiv:0801.0840] [INSPIRE].
CLEO collaboration, J. Libby et al., Model-independent determination of the strong-phase difference between D 0 and \( {\overline{D}}^0\to {K}_{S,L}^0{h}^{+}{h}^{-}\left(h=\pi, K\right) \) and its impact on the measurement of the CKM angle γ/ϕ 3, Phys. Rev. D 82 (2010) 112006 [arXiv:1010.2817] [INSPIRE].
Belle collaboration, H. Aihara et al., First Measurement of ϕ 3 with a model-independent Dalitz plot analysis of B → DK, D → K 0 S π + π − decay, Phys. Rev. D 85 (2012) 112014 [arXiv:1204.6561] [INSPIRE].
Belle collaboration, K. Negishi et al., First model-independent Dalitz analysis of B 0 → DK *0 , D → K 0 S π + π − decay, PTEP 2016 (2016) 043C01 [arXiv:1509.01098] [INSPIRE].
LHCb collaboration, Model-independent measurement of the CKM angle γ using B 0 → DK *0 decays with D → K 0 S π + π − and K 0 S K + K −, JHEP 06 (2016) 131 [arXiv:1604.01525] [INSPIRE].
BaBar collaboration, B. Aubert et al., Measurement of γ in B ∓ → D (*) K ∓ decays with a Dalitz analysis of D → K 0 S π − π +, Phys. Rev. Lett. 95 (2005) 121802 [hep-ex/0504039] [INSPIRE].
BaBar collaboration, B. Aubert et al., Improved measurement of the CKM angle γ in B ∓ → D (*) K (*∓) decays with a Dalitz plot analysis of D decays to K 0 S π + π − and K 0 S K + K −, Phys. Rev. D 78 (2008) 034023 [arXiv:0804.2089] [INSPIRE].
BaBar collaboration, P. del Amo Sanchez et al., 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].
Belle collaboration, A. Poluektov et al., Measurement of ϕ 3 with Dalitz plot analysis of B ± → D (*) K ± decay, Phys. Rev. D 70 (2004) 072003 [hep-ex/0406067] [INSPIRE].
Belle collaboration, A. Poluektov et al., Measurement of ϕ 3 with Dalitz plot analysis of B + → D (*) K (*)+ decay, Phys. Rev. D 73 (2006) 112009 [hep-ex/0604054] [INSPIRE].
Belle collaboration, A. Poluektov et al., Evidence for direct CP-violation in the decay B → D (*) K ± , D → K 0 S π + π − and measurement of the CKM phase ϕ 3, Phys. Rev. D 81 (2010) 112002 [arXiv:1003.3360] [INSPIRE].
LHCb collaboration, Measurement of CP violation and constraints on the CKM angle γ in B ± → DK ± with D → K 0 S π + π − decays, Nucl. Phys. B 888 (2014) 169 [arXiv:1407.6211] [INSPIRE].
M. Battaglieri et al., Analysis tools for next-generation hadron spectroscopy experiments, Acta Phys. Polon. B 46 (2015) 257 [arXiv:1412.6393] [INSPIRE].
LHCb collaboration, A model-independent Dalitz plot analysis of B ± → DK ± with D → K 0S h + h − (h = π, K) decays and constraints on the CKM angle γ, Phys. Lett. B 718 (2012) 43 [arXiv:1209.5869] [INSPIRE].
A. Bondar, A. Poluektov and V. Vorobiev, Charm mixing in the model-independent analysis of correlated \( {D}^0{\overline{D}}^0 \) decays, Phys. Rev. D 82 (2010) 034033 [arXiv:1004.2350] [INSPIRE].
LHCb collaboration, The LHCb detector at the LHC, 2008 JINST 3 S08005 [INSPIRE].
LHCb collaboration, LHCb detector performance, Int. J. Mod. Phys. A 30 (2015) 1530022 [arXiv:1412.6352] [INSPIRE].
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].
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].
T. Sjöstrand, S. Mrenna and P.Z. Skands, PYTHIA 6.4 physics and manual, JHEP 05 (2006) 026 [hep-ph/0603175] [INSPIRE].
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].
D.J. Lange, The EvtGen particle decay simulation package, Nucl. Instrum. Meth. A 462 (2001) 152 [INSPIRE].
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].
Geant4 collaboration, J. Allison et al., GEANT4 developments and applications, IEEE Trans. Nucl. Sci. 53 (2006) 270.
GEANT4 collaboration, S. Agostinelli et al., GEANT4 — a simulation toolkit, Nucl. Instrum. Meth. A 506 (2003) 250 [INSPIRE].
M. Clemencic et al., The LHCb simulation application, Gauss: design, evolution and experience, J. Phys. Conf. Ser. 331 (2011) 032023 [INSPIRE].
W.D. Hulsbergen, Decay chain fitting with a Kalman filter, Nucl. Instrum. Meth. A 552 (2005) 566 [physics/0503191] [INSPIRE].
Particle Data Group collaboration, C. Patrignani et al., Review of particle physics, Chin. Phys. C 40 (2016) 100001 [INSPIRE].
L. Breiman et al., Classification and regression trees, Wadsworth international group, Belmont, California U.S.A. (1984).
Y. Freund and R. E. Schapire, A decision-theoretic generalization of on-line learning and an application to boosting, J. Comput. Syst. Sci. 55 (1997) 119.
T. Skwarnicki, A study of the radiative cascade transitions between the ϒ′ and ϒ resonances, Ph.D. thesis, Institute of Nuclear Physics, Krakow, Poland (1986) [DESY-F31-86-02].
M. Pivk and F.R. Le Diberder, SPlot: a statistical tool to unfold data distributions, Nucl. Instrum. Meth. A 555 (2005) 356 [physics/0402083] [INSPIRE].
LHCb collaboration, Measurement of CP observables in B ± → D (*) K ± and B ± → D (*) π ± decays, Phys. Lett. B 777 (2018) 16 [arXiv:1708.06370] [INSPIRE].
LHCb collaboration, Dalitz plot analysis of \( {B}_s^0\to \overline{D}{}^{\circ}{K}^{-}{\pi}^{+} \) decays, Phys. Rev. D 90 (2014) 072003 [arXiv:1407.7712] [INSPIRE].
T. Gershon, J. Libby and G. Wilkinson, Contributions to the width difference in the neutral D system from hadronic decays, Phys. Lett. B 750 (2015) 338 [arXiv:1506.08594] [INSPIRE].
F. James and M. Winkler, Minuit user’s guide (2004).
F. James and M. Roos, Minuit: a system for function minimization and analysis of the parameter errors and correlations, Comput. Phys. Commun. 10 (1975) 343 [INSPIRE].
LHCb collaboration, Update of the LHCb combination of the CKM angle γ using B → DK decays, LHCb-CONF-2017-004 (2017).
LHCb collaboration, Measurement of CP observables in B ± → DK *± decays using two- and four-body D final states, JHEP 11 (2017) 156 [Erratum ibid. 05 (2018) 067] [arXiv:1709.05855] [INSPIRE].
LHCb collaboration, Measurement of CP asymmetry in D 0 → K − K + and D 0 → π − π + decays, JHEP 07 (2014) 041 [arXiv:1405.2797] [INSPIRE].
Y. Grossman and M. Savastio, Effects of \( {K}^0\hbox{--} {\overline{K}}^0 \) mixing on determining γ from B ± → DK ±, JHEP 03 (2014) 008 [arXiv:1311.3575] [INSPIRE].
LHCb collaboration, Update of the LHCb combination of the CKM angle γ, LHCb-CONF-2018-002 (2018).
LHCb collaboration, Measurement of the CKM angle γ from a combination of LHCb results, JHEP 12 (2016) 087 [arXiv:1611.03076] [INSPIRE].
B. Sen, M. Walker and M. Woodroofe, On the unified method with nuisance parameters, Stat. Sinica 19 (2009) 301.
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.
Author information
Authors and Affiliations
Consortia
Corresponding author
Additional information
ArXiv ePrint: 1806.01202
Deceased (Y. Shcheglov)
C. Göbel, and V. Salustino Guimaraes are associated to Universidade Federal do Rio de Janeiro (UFRJ), Rio de Janeiro, Brazil
N. Beliy, J. He, W. Huang, P.-R. Li, X. Lyu, W. Qian, J. Qin, M. Saur, M. Szymanski, D. Vieira, Q. Xu, Y. Zheng, H. Cai, L. Sun, B. Dey, W. Hu, Y. Wang, D. Xiao, Y. Xie, M. Xu, H. Yin, J. Yu and D. Zhang are associated to Center for High Energy Physics, Tsinghua University, Beijing, China
D. A. Milanes, I. A. Monroy and J. A. Rodriguez Lopez are associated to LPNHE, Université Pierre et Marie Curie, Université Paris Diderot, CNRS/IN2P3, Paris, France
O. Grünberg, M. Heß, N. Meinert, H. Viemann and R. Waldi are associated to Physikalisches Institut, Ruprecht-Karls-Universität Heidelberg, Heidelberg, Germany
C. J. G. Onderwater is associated to Nikhef National Institute for Subatomic Physics, Amsterdam, The Netherlands
T. Likhomanenko, A. Malinin, O. Morgunova, A. Nogay, A. Petrov, V. Shevchenko, F. Baryshnikov, S. Didenko, A. Golutvin, N. Polukhina, E. Shmanin, G. Panshin, S. Strokov and A. Vagner are associated to Institute of Theoretical and Experimental Physics (ITEP), Moscow, Russia
L. M. Garcia Martin, L. Henry, F. Martinez Vidal, A. Oyanguren, C. Remon Alepuz, J. Ruiz Vidal and C. Sanchez Mayordomo are associated to ICCUB, Universitat de Barcelona, Barcelona, Spain
C. A. Aidala, C. L. Da Silva and J. M. Durham are associated to Syracuse University, Syracuse, NY, United States
Rights and permissions
Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made.
The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder.
To view a copy of this licence, visit https://creativecommons.org/licenses/by/4.0/.
About this article
Cite this article
The LHCb collaboration., Aaij, R., Adeva, B. et al. Measurement of the CKM angle γ using B± → DK± with D → K 0S π+π−, K 0S K+K− decays. J. High Energ. Phys. 2018, 176 (2018). https://doi.org/10.1007/JHEP08(2018)176
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP08(2018)176