Repercussions of flavour symmetry breaking on CP violation in D-meson decays

  • Thorsten Feldmann
  • Soumitra Nandi
  • Amarjit Soni


We investigate to what extent the recently measured value for a non-vanishing direct CP asymmetry in D 0 → K + K and D0 → π + π decays can be accommodated in the Standard Model (SM) or extensions with a constrained flavour sector, for instance from a sequential 4th generation of quarks (4 G). From the comparison with D 0 → K π + branching ratios, we establish large U-spin symmetry (ds) breaking effects with large strong phases between different interfering amplitudes. On the basis of conservative estimates on amplitude ratios — which are supported by an analysis of the breaking of a cu symmetry in non-leptonic B0 decays — we find that, in the SM, direct CP asymmetries in the π + π or K + K modes (or in their difference) of the order of several per mille are still plausible. Due to the constraints on the new CP phases in the 4 G model, only moderate effects compared to the SM estimates are possible. We suggest CP studies at LHCb as well as at (Super)B-factories of several distinctive modes, such as D + → \( \overline K \) (∗)0 π +, ϕπ + and D s  → K (∗)0 π +, ϕπ +(K +) etc., which should shed more light on the short- and long-distance issues underlying CP violation in non-leptonic D-meson decays.


Rare Decays CP violation Standard Model Beyond Standard Model 


  1. [1]
    T.E. Browder, T. Gershon, D. Pirjol, A. Soni and J. Zupan, New physics at a super flavor factory, Rev. Mod. Phys. 81 (2009) 1887 [arXiv:0802.3201] [INSPIRE].ADSCrossRefGoogle Scholar
  2. [2]
    M. Artuso, B. Meadows and A.A. Petrov, Charm meson decays, Ann. Rev. Nucl. Part. Sci. 58 (2008) 249 [arXiv:0802.2934] [INSPIRE].ADSCrossRefGoogle Scholar
  3. [3]
    M. Antonelli, D.M. Asner, D.A. Bauer, T.G. Becher, M. Beneke, et al., Flavor physics in the quark sector, Phys. Rept. 494 (2010) 197 [arXiv:0907.5386] [INSPIRE].ADSCrossRefGoogle Scholar
  4. [4]
    M. Artuso, D. Asner, P. Ball, E. Baracchini, G. Bell, et al., B, D and K decays, Eur. Phys. J. C 57 (2008) 309 [arXiv:0801.1833] [INSPIRE].ADSGoogle Scholar
  5. [5]
    K. Agashe, G. Perez and A. Soni, Flavor structure of warped extra dimension models, Phys. Rev. D 71 (2005) 016002 [hep-ph/0408134] [INSPIRE].ADSGoogle Scholar
  6. [6]
    M. Blanke, A.J. Buras, B. Duling, S. Gori and A. Weiler, ∆ F = 2 observables and fine-tuning in a warped extra dimension with custodial protection, JHEP 03 (2009) 001 [arXiv:0809.1073] [INSPIRE].ADSCrossRefGoogle Scholar
  7. [7]
    S. Casagrande, F. Goertz, U. Haisch, M. Neubert and T. Pfoh, Flavor physics in the Randall-Sundrum model: I. Theoretical setup and electroweak precision tests, JHEP 10 (2008) 094 [arXiv:0807.4937] [INSPIRE].ADSCrossRefGoogle Scholar
  8. [8]
    M. Bauer, S. Casagrande, U. Haisch and M. Neubert, Flavor physics in the Randall-Sundrum model: II. Tree-level weak-interaction processes, JHEP 09 (2010) 017 [arXiv:0912.1625] [INSPIRE].ADSCrossRefGoogle Scholar
  9. [9]
    H. Davoudiasl, G. Perez and A. Soni, The little Randall-Sundrum model at the large hadron collider, Phys. Lett. B 665 (2008) 67 [arXiv:0802.0203] [INSPIRE].ADSCrossRefGoogle Scholar
  10. [10]
    A.K. Das and C. Kao, A two Higgs doublet model for the top quark, Phys. Lett. B 372 (1996) 106 [hep-ph/9511329] [INSPIRE].ADSCrossRefGoogle Scholar
  11. [11]
    G.-H. Wu and A. Soni, Novel CP-violating effects in B decays from charged Higgs in a two Higgs doublet model for the top quark, Phys. Rev. D 62 (2000) 056005 [hep-ph/9911419] [INSPIRE].ADSGoogle Scholar
  12. [12]
    S. Bar-Shalom, S. Nandi and A. Soni, Two Higgs doublets with 4th generation fermions - Models for TeV-scale compositeness, Phys. Rev. D 84 (2011) 053009 [arXiv:1105.6095] [INSPIRE].ADSGoogle Scholar
  13. [13]
    M. Ciuchini, E. Franco, D. Guadagnoli, V. Lubicz, M. Pierini, et al., \( D - \overline D \) mixing and new physics: general considerations and constraints on the MSSM, Phys. Lett. B 655 (2007) 162 [hep-ph/0703204] [INSPIRE].ADSCrossRefGoogle Scholar
  14. [14]
    A.J. Buras, B. Duling, T. Feldmann, T. Heidsieck, C. Promberger, et al., The impact of a 4th generation on mixing and CP-violation in the charm system, JHEP 07 (2010) 094 [arXiv:1004.4565] [INSPIRE].ADSCrossRefGoogle Scholar
  15. [15]
    S. Nandi and A. Soni, Constraining the mixing matrix for standard model with four generations: time dependent and semi-leptonic CP asymmetries in \( B_d^0 \) , Bs and D 0 , Phys. Rev. D 83 (2011) 114510 [arXiv:1011.6091] [INSPIRE].ADSGoogle Scholar
  16. [16]
    M. Bobrowski, A. Lenz, J. Riedl and J. Rohrwild, How large can the SM contribution to CP-violation in \( {D^0} - {\overline D^0} \) mixing be?, JHEP 03 (2010) 009 [arXiv:1002.4794] [INSPIRE].ADSCrossRefGoogle Scholar
  17. [17]
    Y. Grossman, A.L. Kagan and Y. Nir, New physics and CP-violation in singly Cabibbo suppressed D decays, Phys. Rev. D 75 (2007) 036008 [hep-ph/0609178] [INSPIRE].ADSGoogle Scholar
  18. [18]
    LHCb collaboration, R. Aaij et al., Evidence for CP-violation in time-integrated D0 → h− h+ decay rates, Phys. Rev. Lett. 108 (2012) 111602 [arXiv:1112.0938] [INSPIRE].ADSCrossRefGoogle Scholar
  19. [19]
    I.I. Bigi, A. Paul and S. Recksiegel, Conclusions from CDF results on CP-violation in D0 → π+ π− K + K − and future tasks, JHEP 06 (2011) 089 [arXiv:1103.5785] [INSPIRE].ADSCrossRefGoogle Scholar
  20. [20]
    I.I. Bigi and A. Paul, On CP asymmetries in two-, three- and four-body D decays, JHEP 03 (2012) 021 [arXiv:1110.2862] [INSPIRE].ADSCrossRefGoogle Scholar
  21. [21]
    G. Isidori, J.F. Kamenik, Z. Ligeti and G. Perez, Implications of the LHCb evidence for charm CP-violation, Phys. Lett. B 711 (2012) 46 [arXiv:1111.4987] [INSPIRE].ADSCrossRefGoogle Scholar
  22. [22]
    J. Brod, A.L. Kagan and J. Zupan, On the size of direct CP-violation in singly Cabibbo-suppressed D decays, arXiv:1111.5000 [INSPIRE].
  23. [23]
    Y. Hochberg and Y. Nir, Relating direct CP-violation in D decays and the forward-backward asymmetry in \( t\overline t \) production, arXiv:1112.5268 [INSPIRE].
  24. [24]
    A. Rozanov and M. Vysotsky, (∆A CP )LHCb and the fourth generation, arXiv:1111.6949 [INSPIRE].
  25. [25]
    D. Pirtskhalava and P. Uttayarat, CP violation and flavor SU(3) breaking in D-meson decays, Phys. Lett. B 712 (2012) 81 [arXiv:1112.5451] [INSPIRE].ADSCrossRefGoogle Scholar
  26. [26]
    H.-Y. Cheng and C.-W. Chiang, Direct CP-violation in two-body hadronic charmed meson decays, Phys. Rev. D 85 (2012) 034036 [Erratum ibid. D 85 (2012) 079903] [arXiv:1201.0785] [INSPIRE].ADSGoogle Scholar
  27. [27]
    B. Bhattacharya, M. Gronau and J.L. Rosner, CP asymmetries in singly-Cabibbo-suppressed D decays to two pseudoscalar mesons, Phys. Rev. D 85 (2012) 054014 [arXiv:1201.2351] [INSPIRE].ADSGoogle Scholar
  28. [28]
    G.F. Giudice, G. Isidori and P. Paradisi, Direct CP-violation in charm and flavor mixing beyond the SM, JHEP 04 (2012) 060 [arXiv:1201.6204] [INSPIRE].ADSCrossRefGoogle Scholar
  29. [29]
    W. Altmannshofer, R. Primulando, C.-T. Yu and F. Yu, New physics models of direct CP-violation in charm decays, JHEP 04 (2012) 049 [arXiv:1202.2866] [INSPIRE].ADSCrossRefGoogle Scholar
  30. [30]
    G. Hiller, M. Jung and S. Schacht, in preparation.Google Scholar
  31. [31]
    CDF collaboration, T. Aaltonen et al., Measurement of CP-violating asymmetries in D0 → π+ π− and D0 → K − K + decays at CDF, Phys. Rev. D 85 (2012) 012009 [arXiv:1111.5023] [INSPIRE].ADSGoogle Scholar
  32. [32]
    Heavy Flavor Averaging Group collaboration, D. Asner et al., Averages of b-hadron, c-hadron and τ -lepton properties, arXiv:1010.1589 [INSPIRE].
  33. [33]
    R. Fleischer, New strategies to extract β and γ from Bd → π+ π− and Bs → k+ k− , Phys. Lett. B 459 (1999) 306 [hep-ph/9903456] [INSPIRE].ADSCrossRefGoogle Scholar
  34. [34]
    R. Fleischer, Extracting γ from B s/d → J/ψKS and \( {B_{{d/s}}} \to D_{{d/s}}^{ + }D_{{d/s}}^{ - } \) , Eur. Phys. J. C 10 (1999) 299 [hep-ph/9903455] [INSPIRE].ADSGoogle Scholar
  35. [35]
    M. Gronau, U spin symmetry in charmless B decays, Phys. Lett. B 492 (2000) 297 [hep-ph/0008292] [INSPIRE].ADSCrossRefGoogle Scholar
  36. [36]
    M. Gronau and J.L. Rosner, U spin symmetry in doubly Cabibbo suppressed charmed meson decays, Phys. Lett. B 500 (2001) 247 [hep-ph/0010237] [INSPIRE].ADSCrossRefGoogle Scholar
  37. [37]
    A. Soni and D.A. Suprun, Determination of γ from charmless B+ → M0 M + decays using U-spin, Phys. Lett. B 635 (2006) 330 [hep-ph/0511012] [INSPIRE].ADSCrossRefGoogle Scholar
  38. [38]
    A. Soni and D.A. Suprun, Determination of γ from charmless B → M1 M2 decays using U-spin, Phys. Rev. D 75 (2007) 054006 [hep-ph/0609089] [INSPIRE].ADSGoogle Scholar
  39. [39]
    M. Jung and T. Mannel, General analysis of U-spin breaking in B decays, Phys. Rev. D 80 (2009) 116002 [arXiv:0907.0117] [INSPIRE].ADSGoogle Scholar
  40. [40]
    M. Jung and T. Mannel, Model-independent analysis of U-spin breaking in non-leptonic B-decays, PoS EFT 09 (2009) 003.Google Scholar
  41. [41]
    J. Laiho, E. Lunghi and R. Van de Water, (2010).Google Scholar
  42. [42]
    H. Na, C.T. Davies, E. Follana, J. Koponen, G.P. Lepage, et al., D → π, lν semileptonic decays, |Vcd | and 2nd row unitarity from lattice QCD, Phys. Rev. D 84 (2011) 114505 [arXiv:1109.1501] [INSPIRE].ADSGoogle Scholar
  43. [43]
    M. Golden and B. Grinstein, Enhanced CP-violations in hadronic charm decays, Phys. Lett. B 222 (1989) 501 [INSPIRE].ADSCrossRefGoogle Scholar
  44. [44]
    D. Atwood and A. Soni, The possibility of large direct CP-violation in B → K π - Like modes due to long distance rescattering effects and implications for the angle γ, Phys. Rev. D 58 (1998) 036005 [hep-ph/9712287] [INSPIRE].ADSGoogle Scholar
  45. [45]
    R. Fleischer, Rescattering and electroweak penguin effects in strategies to constrain and determine the CKM angle γ from B → πK decays, Eur. Phys. J. C 6 (1999) 451 [hep-ph/9802433] [INSPIRE].ADSGoogle Scholar
  46. [46]
    N. Deshpande, X.-G. He, W.-S. Hou and S. Pakvasa, Electroweak penguins, final state interaction phases and CP-violation in B → K π decays, Phys. Rev. Lett. 82 (1999) 2240 [hep-ph/9809329] [INSPIRE].ADSCrossRefGoogle Scholar
  47. [47]
    J.L. Rosner, On large final state phases in heavy meson decays, Phys. Rev. D 60 (1999) 074029 [hep-ph/9903543] [INSPIRE].ADSGoogle Scholar
  48. [48]
    A.J. Buras and R. Fleischer, Constraints on the CKM angle γ and strong phases from B → πK decays, Eur. Phys. J. C 16 (2000) 97 [hep-ph/0003323] [INSPIRE].ADSCrossRefGoogle Scholar
  49. [49]
    A.J. Buras, R. Fleischer, S. Recksiegel and F. Schwab, Anatomy of prominent B and K decays and signatures of CP-violating new physics in the electroweak penguin sector, Nucl. Phys. B 697 (2004) 133 [hep-ph/0402112] [INSPIRE].ADSCrossRefGoogle Scholar
  50. [50]
    T. Feldmann and T. Hurth, Non-factorizable contributions to B → ππ decays, JHEP 11 (2004) 037 [hep-ph/0408188] [INSPIRE].ADSCrossRefGoogle Scholar
  51. [51]
    H.-Y. Cheng, C.-K. Chua and A. Soni, Final state interactions in hadronic B decays, Phys. Rev. D 71 (2005) 014030 [hep-ph/0409317] [INSPIRE].ADSGoogle Scholar
  52. [52]
    M. Gronau and J.L. Rosner, Rate and CP-asymmetry sum rules in B → K π, Phys. Rev. D 74 (2006) 057503 [hep-ph/0608040] [INSPIRE].ADSGoogle Scholar
  53. [53]
    T. Feldmann, M. Jung and T. Mannel, Is there a non-standard-model contribution in non-leptonic b → s decays?, JHEP 08 (2008) 066 [arXiv:0803.3729] [INSPIRE].ADSCrossRefGoogle Scholar
  54. [54]
    H.-Y. Cheng and C.-K. Chua, Revisiting charmless hadronic B u,d decays in QCD factorization, Phys. Rev. D 80 (2009) 114008 [arXiv:0909.5229] [INSPIRE].ADSGoogle Scholar
  55. [55]
    D. Atwood, I. Dunietz and A. Soni, Enhanced CP-violation with B → K D0 (anti-D0) modes and extraction of the CKM angle γ, Phys. Rev. Lett. 78 (1997) 3257 [hep-ph/9612433] [INSPIRE].ADSCrossRefGoogle Scholar
  56. [56]
    D. Atwood, I. Dunietz and A. Soni, Improved methods for observing CP-violation in B + − → K D and measuring the CKM phase γ, Phys. Rev. D 63 (2001) 036005 [hep-ph/0008090] [INSPIRE].ADSGoogle Scholar
  57. [57]
    Y. Grossman, theory introduction talk presented at CERN workshop on CP violation of charm hadrons, 12 January 2012 [].
  58. [58]
    M.J. Savage, SU(3) violations in the nonleptonic decay of charmed hadrons, Phys. Lett. B 257 (1991) 414 [INSPIRE].ADSCrossRefGoogle Scholar
  59. [59]
    A.J. Buras, B. Duling, T. Feldmann, T. Heidsieck, C. Promberger and S. Recksiegel, Patterns of flavour violation in the presence of a fourth generation of quarks and leptons, Journal of High Energy Physics 9 (2010) 106 [arXiv:1002.2126].ADSCrossRefGoogle Scholar
  60. [60]
    A. Soni, A.K. Alok, A. Giri, R. Mohanta and S. Nandi, The fourth family: a natural explanation for the observed pattern of anomalies in B − CP asymmetries, Phys. Lett. B 683 (2010) 302 [arXiv:0807.1971] [INSPIRE].ADSCrossRefGoogle Scholar
  61. [61]
    M. Bobrowski, A. Lenz, J. Riedl and J. Rohrwild, How much space is left for a new family of fermions?, Phys. Rev. D 79 (2009) 113006 [arXiv:0902.4883] [INSPIRE].ADSGoogle Scholar
  62. [62]
    A. Soni, A.K. Alok, A. Giri, R. Mohanta and S. Nandi, SM with four generations: selected implications for rare B and K decays, Phys. Rev. D 82 (2010) 033009 [arXiv:1002.0595] [INSPIRE].ADSGoogle Scholar
  63. [63]
    Particle Data Group collaboration, K. Nakamura et al., Review of particle physics, J. Phys. G 37 (2010) 075021 [INSPIRE].ADSCrossRefGoogle Scholar
  64. [64]
    I.I. Bigi and H. Yamamoto, Interference between Cabibbo allowed and doubly forbidden transitions in D → K S K L+ pi’s decays, Phys. Lett. B 349 (1995) 363 [hep-ph/9502238] [INSPIRE].ADSCrossRefGoogle Scholar
  65. [65]
    H.J. Lipkin and Z.-z. Xing, Flavor symmetry, k0 - anti-K 0 mixing and new physics effects on CP-violation in D+− and D+ −s decays, Phys. Lett. B 450 (1999) 405 [hep-ph/9901329] [INSPIRE].ADSCrossRefGoogle Scholar
  66. [66]
    CKMfitter Group collaboration, J. Charles et al., 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].ADSCrossRefGoogle Scholar
  67. [67]
    T. Feldmann, C. Promberger and S. Recksiegel, Characterising new physics models by effective dimensionality of parameter space, Eur. Phys. J. C 72 (2012) 1867 [arXiv:1009.5283] [INSPIRE].ADSCrossRefGoogle Scholar
  68. [68]
    J. Brod, Y. Grossman, A.L. Kagan and J. Zupan, A consistent picture for large penguins in D → π + π− , k + k− , arXiv:1203.6659 [INSPIRE].

Copyright information

© SISSA, Trieste, Italy 2012

Authors and Affiliations

  • Thorsten Feldmann
    • 1
  • Soumitra Nandi
    • 1
  • Amarjit Soni
    • 2
  1. 1.Theoretische Elementarteilchenphysik, Naturwissenschaftlich Technische FakultatUniversit¨at SiegenSiegenGermany
  2. 2.Physics DepartmentTheory Group, Brookhaven National LaboratoryUptonU.S.A

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