Advertisement

Model independent determination of the CKM phase γ using input from \( {D}^0\hbox{-} {\overline{D}}^0 \) mixing

  • Samuel Harnew
  • Jonas Rademacker
Open Access
Regular Article - Experimental Physics

Abstract

We present a new, amplitude model-independent method to measure the CP violation parameter γ in B DK and related decays. Information on charm interference parameters, usually obtained from charm threshold data, is obtained from charm mixing. By splitting the phase space of the D meson decay into several bins, enough information can be gained to measure γ without input from the charm threshold. We demonstrate the feasibility of this approach with a simulation study of B DK with DK + π π + π . We compare the performance of our novel approach to that of a previously proposed binned analysis which uses charm interference parameters obtained from threshold data. While both methods provide useful constraints, the combination of the two by far outperforms either of them applied on their own. Such an analysis would provide a highly competitive measurement of γ. Our simulation studies indicate, subject to assumptions about data yields and the amplitude structure of D 0K + π π + π , a statistical uncertainty on γ of ~ 12° with existing data and ~ 4° for the LHCb-upgrade.

Keywords

CKM angle gamma CP violation Charm physics B physics Hadron-Hadron Scattering 

Notes

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.

References

  1. [1]
    M. Gronau and D. Wyler, On determining a weak phase from CP asymmetries in charged B decays, Phys. Lett. B 265 (1991) 172 [INSPIRE].CrossRefADSGoogle Scholar
  2. [2]
    M. Gronau and D. London, How to determine all the angles of the unitarity triangle from B dDK s and B s0 → , Phys. Lett. B 253 (1991) 483 [INSPIRE].CrossRefADSGoogle Scholar
  3. [3]
    D. Atwood, I. Dunietz and A. Soni, Enhanced CP-violation with \( B\to {\mathrm{KD}}^0\left({\overline{\mathrm{D}}}^0\right) \) modes and extraction of the CKM angle gamma, Phys. Rev. Lett. 78 (1997) 3257 [hep-ph/9612433] [INSPIRE].CrossRefADSGoogle Scholar
  4. [4]
    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].ADSGoogle Scholar
  5. [5]
    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].Google Scholar
  6. [6]
    J. Rademacker and G. Wilkinson, Determining the unitarity triangle gamma with a four-body amplitude analysis of B + → (K + K π + π )D K ± decays, Phys. Lett. B 647 (2007) 400 [hep-ph/0611272] [INSPIRE].CrossRefADSGoogle Scholar
  7. [7]
    D. Atwood and A. Soni, Role of charm factory in extracting CKM phase information via BDK, Phys. Rev. D 68 (2003) 033003 [hep-ph/0304085] [INSPIRE].ADSGoogle Scholar
  8. [8]
    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].ADSGoogle Scholar
  9. [9]
    CLEO collaboration, N. Lowrey et al., Determination of the D 0K π + π 0 and D 0K π + π + π Coherence Factors and Average Strong-Phase Differences Using Quantum-Correlated Measurements, Phys. Rev. D 80 (2009) 031105 [arXiv:0903.4853] [INSPIRE].Google Scholar
  10. [10]
    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].Google Scholar
  11. [11]
    CLEO collaboration, R.A. Briere et al., First model-independent determination of the relative strong phase between D 0 and \( {\overline{D}}^0\to {K}_s^0{\pi}^{+}{\pi}^{-} \) and its impact on the CKM Angle γ/ϕ 3 measurement, Phys. Rev. D 80 (2009) 032002 [arXiv:0903.1681] [INSPIRE].Google Scholar
  12. [12]
    CLEO collaboration, D.M. Asner et al., Determination of the D 0K + π Relative Strong Phase Using Quantum-Correlated Measurements in \( {e}^{+}{e}^{-}\to {D}^0{\overline{D}}^0 \) at CLEO, Phys. Rev. D 78 (2008) 012001 [arXiv:0802.2268] [INSPIRE].Google Scholar
  13. [13]
    CLEO collaboration, J. Insler et al., Studies of the decays D 0 → K S0 K π + and D 0 → K S0 K + π , Phys. Rev. D 85 (2012) 092016 [arXiv:1203.3804] [INSPIRE].Google Scholar
  14. [14]
    J. Libby, S. Malde, A. Powell, G. Wilkinson, D.M. Asner et al., New determination of the D 0K π + π 0 and D 0K π + π + π coherence factors and average strong-phase differences, Phys. Lett. B 731 (2014) 197 [arXiv:1401.1904] [INSPIRE].CrossRefADSGoogle Scholar
  15. [15]
    S. Harnew and J. Rademacker, Charm mixing as input for model-independent determinations of the CKM phase γ, Phys. Lett. B 728 (2014) 296 [arXiv:1309.0134] [INSPIRE].CrossRefADSGoogle Scholar
  16. [16]
    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].ADSGoogle Scholar
  17. [17]
    Belle collaboration, I. Adachi, First measurement of ϕ 3 with a binned model-independent Dalitz plot analysis of B +−DK +− , D → K s0 π + π decay, arXiv:1106.4046 [INSPIRE].
  18. [18]
    LHCb collaboration, A model-independent Dalitz plot analysis of B ±DK ± with D → K S0 h + h (h = π, K) decays and constraints on the CKM angle γ, Phys. Lett. B 718 (2012) 43 [arXiv:1209.5869] [INSPIRE].ADSGoogle Scholar
  19. [19]
    Heavy Flavor Averaging Group collaboration, Y. Amhis et al., Averages of B-Hadron, C-Hadron and tau-lepton properties as of early 2012, arXiv:1207.1158 [INSPIRE].
  20. [20]
    LHCb collaboration, Measurement of \( {D}^0--{\overline{D}}^0 \) Mixing Parameters and Search for CP Violation Using D 0K + π Decays, Phys. Rev. Lett. 111 (2013) 251801 [arXiv:1309.6534] [INSPIRE].CrossRefGoogle Scholar
  21. [21]
    CDF collaboration, T. Aaltonen et al., Evidence for \( {D}^0-{\overline{D}}^0 \) mixing using the CDF II Detector, Phys. Rev. Lett. 100 (2008) 121802 [arXiv:0712.1567] [INSPIRE].CrossRefADSGoogle Scholar
  22. [22]
    Belle collaboration, M. Staric et al., Evidence for \( {D}^0\hbox{-} {\overline{D}}^0 \) Mixing, Phys. Rev. Lett. 98 (2007) 211803 [hep-ex/0703036] [INSPIRE].CrossRefGoogle Scholar
  23. [23]
    BaBar collaboration, B. Aubert et al., Evidence for \( {D}^0-{\overline{D}}^0 \) Mixing, Phys. Rev. Lett. 98 (2007) 211802 [hep-ex/0703020] [INSPIRE].CrossRefADSGoogle Scholar
  24. [24]
    BaBar collaboration, B. Aubert et al., Measurement of \( {D}^0-{\overline{D}}^0 \) mixing from a time-dependent amplitude analysis of D 0K + π π 0 decays, Phys. Rev. Lett. 103 (2009) 211801 [arXiv:0807.4544] [INSPIRE].CrossRefADSGoogle Scholar
  25. [25]
    BaBar collaboration, B. Aubert et al., Measurement of \( {D}^0\hbox{-} {\overline{D}}^0 \) Mixing using the Ratio of Lifetimes for the Decays D 0K π + and K + K , Phys. Rev. D 80 (2009) 071103 [arXiv:0908.0761] [INSPIRE].ADSGoogle Scholar
  26. [26]
    LHCb collaboration, Observation of \( {D}^0-{\overline{D}}^0 \) oscillations, Phys. Rev. Lett. 110 (2013) 101802 [arXiv:1211.1230] [INSPIRE].CrossRefGoogle Scholar
  27. [27]
    LHCb collaboration, Measurement of the CKM angle γ from a combination of B ±Dh ± analyses, Phys. Lett. B 726 (2013) 151 [arXiv:1305.2050] [INSPIRE].Google Scholar
  28. [28]
    LHCb Collaboration, Improved constraints on γ from B ±DK ± decays including first results on 2012 data, LHCb-CONF-2013-006.
  29. [29]
    M. Rama, Effect of \( D-\overline{D} \) mixing in the extraction of gamma with B D°K and B D 0 π decays, Phys. Rev. D 89 (2014) 014021 [arXiv:1307.4384] [INSPIRE].ADSMathSciNetGoogle Scholar
  30. [30]
    MARK-III collaboration, D. Coffman et al., Resonant substructure in Kπππ decays of D mesons, Phys. Rev. D 45 (1992) 2196 [INSPIRE].Google Scholar
  31. [31]
    LHCb collaboration, Model-independent search for CP violation in D 0K K + π π + and D 0π π + π + π decays, Phys. Lett. B 726 (2013) 623 [arXiv:1308.3189] [INSPIRE].Google Scholar
  32. [32]
    A. Bondar and A. Poluektov, On model-independent measurement of the angle ϕ 3 using Dalitz plot analysis, hep-ph/0703267 [INSPIRE].
  33. [33]
    LHCb collaboration, Observation of the suppressed AdS modes B ± → [π± K π + π ]D K ± and B ± → [π ± K π + π ]D π ±, Phys. Lett. B 723 (2013) 44 [arXiv:1303.4646] [INSPIRE].Google Scholar
  34. [34]
    CERN. Geneva. The LHC experiments Committee ; LHCC, Framework TDR for the LHCb Upgrade : Technical Design Report, CERN-LHCC-2012-007.
  35. [35]
    Heavy Flavor Averaging Group collaboration, Y. Amhis et al., Averages of B-Hadron, C-Hadron and tau-lepton properties as of early 2012, arXiv:1207.1158 [INSPIRE].
  36. [36]
    Particle Data group, J. A. Olive et al., Review of Particle Physics, Chin. Phys. C 38 (2014) 090001.Google Scholar
  37. [37]
    D.M. Kunze, D.S. Gabriel and D.A. Garcia, Distributed parametric optimization with the Geneva library, in Data Driven e-Science, S. Lin and E. Yen eds., pg. 303, Springer, 2011.Google Scholar
  38. [38]
    F. James, MINUIT Function Minimization and Error Analysis: Reference Manual Version 94.1, CERN-D-506, 1994.Google Scholar
  39. [39]
    LHCb collaboration, Measurement of the CKM angle γ using B ±DK ± with D → K S0 π + π , K S0 K + K decays, JHEP 1410 (2014) 97 [arXiv:1408.2748] [INSPIRE].Google Scholar

Copyright information

© The Author(s) 2015

Authors and Affiliations

  1. 1.H H Wills Physics LaboratoryUniversity of BristolBristolU.K.

Personalised recommendations