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Journal of High Energy Physics

, 2015:33 | Cite as

\( {K}^{+}\to {\pi}^{+}\nu \overline{\nu} \) and \( {K}_L\to {\pi}^0\nu \overline{\nu} \) in the Standard Model: status and perspectives

  • Andrzej J. Buras
  • Dario ButtazzoEmail author
  • Jennifer Girrbach-Noe
  • Robert Knegjens
Open Access
Regular Article - Theoretical Physic

Abstract

In view of the recent start of the NA62 experiment at CERN that is expected to measure the \( {K}^{+}\to {\pi}^{+}\nu \overline{\nu} \) branching ratio with a precision of 10%, we summarise the present status of this promising decay within the Standard Model (SM). We do likewise for the closely related \( {K}_L\to {\pi}^0\nu \overline{\nu} \), which will be measured by the KOTO experiment around 2020. As the perturbative QCD and electroweak corrections in both decays are under full control, the dominant uncertainties within the SM presently originate from the CKM parameters |V cb |, |V ub | and γ. We show this dependence with the help of analytic expressions as well as accurate interpolating formulae. Unfortunately a clarification of the discrepancies between inclusive and exclusive determinations of |V cb | and |V ub | from tree-level decays will likely require results from the Belle II experiment available at the end of this decade. Thus we investigate whether higher precision on both branching ratios is achievable by determining |V cb |, |V ub | and γ by means of other observables that are already precisely measured. In this context ε K and ΔM s,d , together with the expected progress in QCD lattice calculations will play a prominent role. We find \( \mathrm{\mathcal{B}}\left({K}^{+}\to {\pi}^{+}\nu \overline{\nu}\right)=\left(9.11 \pm 0.72\right) \times 1{0}^{-11} \) and \( \mathrm{\mathcal{B}}\left({K}_L\to {\pi}^0\nu \overline{\nu}\right)\Big) = \left(3.00 \pm 0.30\right) \times 1{0}^{-11} \), which is more precise than using averages of the present tree-level values of |V cb |, |V ub | and γ. Furthermore, we point out the correlation between \( \mathrm{\mathcal{B}}\left({K}^{+}\to {\pi}^{+}\nu \overline{\nu}\right),\ \overline{\mathrm{\mathcal{B}}}\left({B}_{\mathrm{s}}\to {\mu}^{+}{\mu}^{-}\right) \) and γ within the SM, that is only very weakly dependent on other CKM parameters. Finally, we update the correlation of \( {K}_L\to {\pi}^0\nu \overline{\nu} \) with the ratio ε /ε in the SM taking the recent progress on ε /ε from lattice QCD and the large N approach into account.

Keywords

Rare Decays Kaon Physics Standard Model 

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]
    G. Buchalla and A.J. Buras, QCD corrections to rare K and B decays for arbitrary top quark mass, Nucl. Phys. B 400 (1993) 225 [INSPIRE].CrossRefADSGoogle Scholar
  2. [2]
    M. Misiak and J. Urban, QCD corrections to FCNC decays mediated by Z penguins and W boxes, Phys. Lett. B 451 (1999) 161 [hep-ph/9901278] [INSPIRE].CrossRefADSGoogle Scholar
  3. [3]
    G. Buchalla and A.J. Buras, The rare decays \( K\to \pi \nu \overline{\nu},\ B\ \to\ X\nu \overline{\nu} \) and B → ℓ+ℓ−: An Update, Nucl. Phys. B 548 (1999) 309 [hep-ph/9901288] [INSPIRE].CrossRefADSGoogle Scholar
  4. [4]
    A.J. Buras, M. Gorbahn, U. Haisch and U. Nierste, The Rare decay \( {K}^{+}\to {\pi}^{+}\nu \overline{\nu} \) at the next-to-next-to-leading order in QCD, Phys. Rev. Lett. 95 (2005) 261805 [hep-ph/0508165] [INSPIRE].CrossRefADSGoogle Scholar
  5. [5]
    A.J. Buras, M. Gorbahn, U. Haisch and U. Nierste, Charm quark contribution to \( {K}^{+}\to {\pi}^{+}\nu \overline{\nu} \) at next-to-next-to-leading order,JHEP 11 (2006) 002 [Erratum ibid. 1211 (2012) 167] [hep-ph/0603079] [INSPIRE].
  6. [6]
    M. Gorbahn and U. Haisch, Effective Hamiltonian for non-leptonicF| = 1 decays at NNLO in QCD, Nucl. Phys. B 713 (2005) 291 [hep-ph/0411071] [INSPIRE].CrossRefADSGoogle Scholar
  7. [7]
    J. Brod and M. Gorbahn, Electroweak Corrections to the Charm Quark Contribution to \( {\mathrm{K}}^{+}\to {\pi}^{+}\nu \overline{\nu} \), Phys. Rev. D 78 (2008) 034006 [arXiv:0805.4119] [INSPIRE].ADSGoogle Scholar
  8. [8]
    J. Brod, M. Gorbahn and E. Stamou, Two-Loop Electroweak Corrections for the \( K\to \pi \nu \overline{\nu} \) Decays, Phys. Rev. D 83 (2011) 034030 [arXiv:1009.0947] [INSPIRE].ADSGoogle Scholar
  9. [9]
    G. Buchalla and A.J. Buras, Two loop large m t electroweak corrections to \( K\to \pi \nu \overline{\nu} \) for arbitrary Higgs boson mass, Phys. Rev. D 57 (1998) 216 [hep-ph/9707243] [INSPIRE].ADSGoogle Scholar
  10. [10]
    G. Isidori, F. Mescia and C. Smith, Light-quark loops in \( K\to \pi \nu \overline{\nu} \), Nucl. Phys. B 718 (2005) 319 [hep-ph/0503107] [INSPIRE].CrossRefADSGoogle Scholar
  11. [11]
    F. Mescia and C. Smith, Improved estimates of rare K decay matrix-elements from K ℓ3 decays, Phys. Rev. D 76 (2007) 034017 [arXiv:0705.2025] [INSPIRE].ADSGoogle Scholar
  12. [12]
    A.J. Buras, F. Schwab and S. Uhlig, Waiting for precise measurements of \( {K}^{+}\to {\pi}^{+}\nu \overline{\nu} \) and \( {K}_L\to {\pi}^0\nu \overline{\nu} \), Rev. Mod. Phys. 80 (2008) 965 [hep-ph/0405132] [INSPIRE].CrossRefADSGoogle Scholar
  13. [13]
    G. Isidori, Flavor Physics with light quarks and leptons, eConf C 060409 (2006) 035 [hep-ph/0606047] [INSPIRE].Google Scholar
  14. [14]
    C. Smith, Theory review on rare K decays: Standard model and beyond, hep-ph/0608343 [INSPIRE].
  15. [15]
    T.K. Komatsubara, Experiments with K-Meson Decays, Prog. Part. Nucl. Phys. 67 (2012) 995 [arXiv:1203.6437] [INSPIRE].CrossRefADSGoogle Scholar
  16. [16]
    A.J. Buras and J. Girrbach, Towards the Identification of New Physics through Quark Flavour Violating Processes, Rept. Prog. Phys. 77 (2014) 086201 [arXiv:1306.3775] [INSPIRE].CrossRefADSGoogle Scholar
  17. [17]
    M. Blanke, New Physics Signatures in Kaon Decays, PoS KAON13 (2013) 010 [arXiv:1305.5671] [INSPIRE].
  18. [18]
    C. Smith, Rare K decays: Challenges and Perspectives, arXiv:1409.6162 [INSPIRE].
  19. [19]
    A.J. Buras, D. Buttazzo, J. Girrbach-Noe and R. Knegjens, Can we reach the Zeptouniverse with rare K and B s,d decays?, JHEP 11 (2014) 121 [arXiv:1408.0728] [INSPIRE].CrossRefADSGoogle Scholar
  20. [20]
    F. Newson et al., Prospects for \( {K}^{+}\to\ {\pi}^{+}\nu \overline{\nu} \) at CERN in NA62, arXiv:1411.0109 [INSPIRE].
  21. [21]
    A. Romano, The \( {K}^{+}\to\ {\pi}^{+}\nu \overline{\nu} \) decay in the NA62 experiment at CERN, arXiv:1411.6546 [INSPIRE].
  22. [22]
    KOTO collaboration, K. Shiomi, \( {K}_L^0\to\ {\pi}^0\nu \overline{\nu} \) at KOTO, arXiv:1411.4250 [INSPIRE].
  23. [23]
    A.J. Buras, F. De Fazio and J. Girrbach, ΔI = 1/2 rule, ε′/ε and \( K\ \to\ \pi \nu \overline{\nu} \) in Z′(Z) and G models with FCNC quark couplings, Eur. Phys. J. C 74 (2014) 2950 [arXiv:1404.3824] [INSPIRE].CrossRefADSGoogle Scholar
  24. [24]
    C. Bobeth, U. Haisch, A. Lenz, B. Pecjak and G. Tetlalmatzi-Xolocotzi, On new physics in ΔΓd, JHEP 06 (2014) 040 [arXiv:1404.2531] [INSPIRE].CrossRefADSGoogle Scholar
  25. [25]
    C. Bobeth, M. Gorbahn and S. Vickers, Weak annihilation and new physics in charmless BMM decays,Eur. Phys. J. C 75 (2015) 340 [arXiv:1409.3252] [INSPIRE].CrossRefADSGoogle Scholar
  26. [26]
    J. Brod, A. Lenz, G. Tetlalmatzi-Xolocotzi and M. Wiebusch, New physics effects in tree-level decays and the precision in the determination of the quark mixing angle γ, Phys. Rev. D 92 (2015) 033002 [arXiv:1412.1446] [INSPIRE].ADSGoogle Scholar
  27. [27]
    UTfit collaboration, M. Bona et al., The Unitarity Triangle Fit in the Standard Model and Hadronic Parameters from Lattice QCD: A Reappraisal after the Measurements of Δm(s) and BR(Bτ ν τ), JHEP 10 (2006) 081 [hep-ph/0606167] [INSPIRE].
  28. [28]
    J. Charles et al., Current status of the Standard Model CKM fit and constraints on ΔF = 2 New Physics, Phys. Rev. D 91 (2015) 073007 [arXiv:1501.05013] [INSPIRE].ADSGoogle Scholar
  29. [29]
    S.H. Kettell, L.G. Landsberg and H.H. Nguyen, Alternative technique for standard model estimation of the rare kaon decay branchings BR( \( K\to \pi v\overline{\nu} \) ) (SM), Phys. Atom. Nucl. 67 (2004) 1398 [hep-ph/0212321] [INSPIRE].CrossRefADSGoogle Scholar
  30. [30]
    A.J. Buras and J. Girrbach, Stringent tests of constrained Minimal Flavor Violation through ΔF =2 transitions, Eur. Phys. J. C 73 (2013) 2560 [arXiv:1304.6835] [INSPIRE].CrossRefADSGoogle Scholar
  31. [31]
    Fermilab Lattice, MILC collaboration, C.M. Bouchard et al., Neutral B-Meson Mixing Parameters in and beyond the SM with 2+1 Flavor Lattice QCD, PoS LATTICE2014 (2014) 378 [arXiv:1412.5097] [INSPIRE].
  32. [32]
    Fermilab Lattice, MILC collaborations, D. Du et al., Bπℓν semileptonic form factors from unquenched lattice QCD and determination of |V ub|, PoS LATTICE2014 (2014) 385 [arXiv:1411.6038] [INSPIRE].
  33. [33]
    A.J. Buras, Weak Hamiltonian, CP-violation and rare decays, hep-ph/9806471 [INSPIRE].
  34. [34]
    D. Buttazzo, G. Degrassi, P.P. Giardino, G.F. Giudice, F. Sala, A. Salvio et al., Investigating the near-criticality of the Higgs boson, JHEP 12 (2013) 089 [arXiv:1307.3536] [INSPIRE].CrossRefADSGoogle Scholar
  35. [35]
    G. Isidori, G. Martinelli and P. Turchetti, Rare kaon decays on the lattice, Phys. Lett. B 633 (2006) 75 [hep-lat/0506026] [INSPIRE].CrossRefADSGoogle Scholar
  36. [36]
    G. Buchalla and A.J. Buras, The rare decays \( {K}^{+}\to\ {\pi}^{+}\nu \overline{\nu} \) and K L → μ + μ beyond leading logarithms, Nucl. Phys. B 412 (1994) 106 [hep-ph/9308272] [INSPIRE].CrossRefADSGoogle Scholar
  37. [37]
    K.G. Chetyrkin, J.H. Kuhn, A. Maier, P. Maierhofer, P. Marquard et al., Charm and Bottom Quark Masses: An Update, Phys. Rev. D 80 (2009) 074010 [arXiv:0907.2110] [INSPIRE].ADSGoogle Scholar
  38. [38]
    Particle Data Group collaboration, J. Beringer et al., Review of Particle Physics (RPP), Phys. Rev. D 86 (2012) 010001 [INSPIRE].
  39. [39]
    G. Buchalla and A.J. Buras, \( K\to \pi \nu \overline{\nu} \) and high precision determinations of the CKM matrix, Phys. Rev. D 54 (1996) 6782 [hep-ph/9607447] [INSPIRE].ADSGoogle Scholar
  40. [40]
    G. Buchalla, A.J. Buras and M.E. Lautenbacher, Weak decays beyond leading logarithms, Rev. Mod. Phys. 68 (1996) 1125 [hep-ph/9512380] [INSPIRE].CrossRefADSGoogle Scholar
  41. [41]
    E949 collaboration, A.V. Artamonov et al., New measurement of the \( {K}^{+}\to\ {\pi}^{+}\nu \overline{\nu} \) branching ratio, Phys. Rev. Lett. 101 (2008) 191802 [arXiv:0808.2459] [INSPIRE].
  42. [42]
    E391a collaboration, J.K. Ahn et al., Experimental study of the decay \( {K}_L^0\to\ {\pi}^0\nu \overline{\nu} \), Phys. Rev. D 81 (2010) 072004 [arXiv:0911.4789] [INSPIRE].
  43. [43]
    ORKA collaboration, E.T. Worcester, ORKA, The Golden Kaon Experiment: Precision measurement of \( {K}^{+}\to {\pi}^{+}\nu \overline{\nu} \) and other rare processes, PoS KAON13 (2013) 035 [arXiv:1305.7245] [INSPIRE].
  44. [44]
    S. Aoki et al., Review of lattice results concerning low-energy particle physics, Eur. Phys. J. C 74 (2014) 2890 [arXiv:1310.8555] [INSPIRE].CrossRefADSGoogle Scholar
  45. [45]
    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].
  46. [46]
    A.J. Buras, J.-M. Gérard and W.A. Bardeen, Large-N Approach to Kaon Decays and Mixing 28 Years Later: ΔI = 1/2 Rule, \( {\widehat{B}}_K \) and ΔM K , Eur. Phys. J. C 74 (2014) 2871 [arXiv:1401.1385] [INSPIRE].CrossRefADSGoogle Scholar
  47. [47]
    K. Trabelsi, on behalf of the CKMfitter Group collaboration, World average and experimental overview of γ/φ 3, presented at CKM 2014, http://ckmfitter.in2p3.fr.
  48. [48]
    J. Brod and M. Gorbahn, Next-to-Next-to-Leading-Order Charm-Quark Contribution to the CP-violation Parameter ε K and ΔM K , Phys. Rev. Lett. 108 (2012) 121801 [arXiv:1108.2036] [INSPIRE].CrossRefADSGoogle Scholar
  49. [49]
    J. Brod and M. Gorbahn, ε K at Next-to-Next-to-Leading Order: The Charm-Top-Quark Contribution, Phys. Rev. D 82 (2010) 094026 [arXiv:1007.0684] [INSPIRE].ADSGoogle Scholar
  50. [50]
    A.J. Buras, M. Jamin and P.H. Weisz, Leading and Next-to-leading QCD Corrections to ε Parameter and \( {B}^0-{\overline{B}}^0 \) Mixing in the Presence of a Heavy Top Quark, Nucl. Phys. B 347 (1990) 491 [INSPIRE].CrossRefADSGoogle Scholar
  51. [51]
    J. Urban, F. Krauss, U. Jentschura and G. Soff, Next-to-leading order QCD corrections for the \( {B}^0-{\overline{B}}^0 \) mixing with an extended Higgs sector, Nucl. Phys. B 523 (1998) 40 [hep-ph/9710245] [INSPIRE].CrossRefADSGoogle Scholar
  52. [52]
    ATLAS, CDF, CMS, D0 collaborations, First combination of Tevatron and LHC measurements of the top-quark mass, arXiv:1403.4427 [INSPIRE].
  53. [53]
    G. Ricciardi, Status of |V cb| and |V ub| CKM matrix elements, arXiv:1412.4288 [INSPIRE].
  54. [54]
    G. Ricciardi, Determination of the CKM matrix elements |V xb|, Mod. Phys. Lett. A 28 (2013) 1330016 [arXiv:1305.2844] [INSPIRE].MathSciNetCrossRefADSGoogle Scholar
  55. [55]
    P. Gambino, Inclusive semileptonic B decays and |V cb|. In memoriam Kolya Uraltsev, Int. J. Mod. Phys. A 30 (2015) 1543002 [arXiv:1501.00314] [INSPIRE].CrossRefADSGoogle Scholar
  56. [56]
    Fermilab Lattice, MILC collaborations, J.A. Bailey et al., Update of |V cb| from the \( \overline{B}\to\ {D}^{\ast}\ell \nu \) form factor at zero recoil with three-flavor lattice QCD, Phys. Rev. D 89 (2014) 114504 [arXiv:1403.0635] [INSPIRE].
  57. [57]
    A. Alberti, P. Gambino, K.J. Healey and S. Nandi, Precision Determination of the Cabibbo-Kobayashi-Maskawa Element V cb, Phys. Rev. Lett. 114 (2015) 061802 [arXiv:1411.6560] [INSPIRE].CrossRefADSGoogle Scholar
  58. [58]
    S. Descotes-Genon, J. Matias and J. Virto, An analysis of B d,s mixing angles in presence of New Physics and an update of \( {B}_s\to {K}^{0\ast }{{\overline{K}}^0}^{\ast } \), Phys. Rev. D 85 (2012) 034010 [arXiv:1111.4882] [INSPIRE].ADSGoogle Scholar
  59. [59]
    K. De Bruyn, R. Fleischer, R. Knegjens, P. Koppenburg, M. Merk and N. Tuning, Branching Ratio Measurements of B s Decays, Phys. Rev. D 86 (2012) 014027 [arXiv:1204.1735] [INSPIRE].ADSGoogle Scholar
  60. [60]
    K. De Bruyn, R. Fleischer, R. Knegjens, P. Koppenburg, M. Merk et al., Probing New Physics via the B s0 → μ + μ Effective Lifetime, Phys. Rev. Lett. 109 (2012) 041801 [arXiv:1204.1737] [INSPIRE].CrossRefADSGoogle Scholar
  61. [61]
    G. D’Ambrosio, G.F. Giudice, G. Isidori and A. Strumia, Minimal flavor violation: An Effective field theory approach, Nucl. Phys. B 645 (2002) 155 [hep-ph/0207036] [INSPIRE].CrossRefADSGoogle Scholar
  62. [62]
    A.J. Buras, P. Gambino, M. Gorbahn, S. Jager and L. Silvestrini, Universal unitarity triangle and physics beyond the standard model, Phys. Lett. B 500 (2001) 161 [hep-ph/0007085] [INSPIRE].CrossRefADSGoogle Scholar
  63. [63]
    G. Buchalla and A.J. Buras, sin 2β from \( K\to \pi \nu \overline{\nu} \), Phys. Lett. B 333 (1994) 221 [hep-ph/9405259] [INSPIRE].CrossRefADSGoogle Scholar
  64. [64]
    A.J. Buras and R. Fleischer, Bounds on the unitarity triangle, sin 2β and \( K\to \pi \nu \overline{\nu} \) decays in models with minimal flavor violation, Phys. Rev. D 64 (2001) 115010 [hep-ph/0104238] [INSPIRE].ADSGoogle Scholar
  65. [65]
    S. Faller, M. Jung, R. Fleischer and T. Mannel, The Golden Modes B 0 → J/ψK S,L in the Era of Precision Flavour Physics, Phys. Rev. D 79 (2009) 014030 [arXiv:0809.0842] [INSPIRE].ADSGoogle Scholar
  66. [66]
    A.J. Buras, Relations between ΔM s,d and B s,dμ + μ in models with minimal flavor violation, Phys. Lett. B 566 (2003) 115 [hep-ph/0303060] [INSPIRE].CrossRefADSGoogle Scholar
  67. [67]
    R. Barbieri, D. Buttazzo, F. Sala and D.M. Straub, Flavour physics from an approximate U(2)3 symmetry, JHEP 07 (2012) 181 [arXiv:1203.4218] [INSPIRE].CrossRefADSGoogle Scholar
  68. [68]
    A.J. Buras and D. Guadagnoli, Correlations among new CP-violating effects in ΔF = 2 observables, Phys. Rev. D 78 (2008) 033005 [arXiv:0805.3887] [INSPIRE].ADSGoogle Scholar
  69. [69]
    A.J. Buras, D. Guadagnoli and G. Isidori, On ε K Beyond Lowest Order in the Operator Product Expansion, Phys. Lett. B 688 (2010) 309 [arXiv:1002.3612] [INSPIRE].CrossRefADSGoogle Scholar
  70. [70]
    A. Caldwell, D. Kollar and K. Kroninger, BAT: The Bayesian Analysis Toolkit, Comput. Phys. Commun. 180 (2009) 2197 [arXiv:0808.2552] [INSPIRE].zbMATHCrossRefADSGoogle Scholar
  71. [71]
    C. Bobeth, M. Gorbahn, T. Hermann, M. Misiak, E. Stamou and M. Steinhauser, B s,d → ℓ + in the Standard Model with Reduced Theoretical Uncertainty, Phys. Rev. Lett. 112 (2014) 101801 [arXiv:1311.0903] [INSPIRE].CrossRefADSGoogle Scholar
  72. [72]
    LHCb, CMS collaborations, V. Khachatryan et al., Observation of the rare B s0 → μ + μ decay from the combined analysis of CMS and LHCb data, Nature 522 (2015) 68 [arXiv:1411.4413] [INSPIRE].
  73. [73]
    G. D’Ambrosio and G. Isidori, \( {K}^{+}\to\ {\pi}^{+}\nu \overline{\nu} \) : A Rising star on the stage of flavor physics, Phys. Lett. B 530 (2002) 108 [hep-ph/0112135] [INSPIRE].CrossRefADSGoogle Scholar
  74. [74]
    NA48 collaboration, J.R. Batley et al., A Precision measurement of direct CP-violation in the decay of neutral kaons into two pions, Phys. Lett. B 544 (2002) 97 [hep-ex/0208009] [INSPIRE].
  75. [75]
    KTeV collaboration, A. Alavi-Harati et al., Measurements of direct CP-violation, CPT symmetry and other parameters in the neutral kaon system, Phys. Rev. D 67 (2003) 012005 [Erratum ibid. D 70 (2004) 079904] [hep-ex/0208007] [INSPIRE].
  76. [76]
    KTeV collaboration, E.T. Worcester, The Final Measurement of ε′/ε from KTeV, arXiv:0909.2555 [INSPIRE].
  77. [77]
    A.J. Buras and J.M. Gérard, 1/N Expansion for Kaons, Nucl. Phys. B 264 (1986) 371 [INSPIRE].CrossRefADSGoogle Scholar
  78. [78]
    W.A. Bardeen, A.J. Buras and J.M. Gérard, The ΔI = 1/2 Rule in the Large-N Limit, Phys. Lett. B 180 (1986) 133 [INSPIRE].CrossRefADSGoogle Scholar
  79. [79]
    A.J. Buras and J.M. Gérard, Isospin Breaking Contributions to ε′/ε, Phys. Lett. B 192 (1987) 156 [INSPIRE].CrossRefADSGoogle Scholar
  80. [80]
    T. Hambye, G.O. Kohler, E.A. Paschos, P.H. Soldan and W.A. Bardeen, 1/N corrections to the hadronic matrix elements of Q 6 and Q 8 in K → ππ decays, Phys. Rev. D 58 (1998) 014017 [hep-ph/9802300] [INSPIRE].ADSGoogle Scholar
  81. [81]
    Z. Bai et al., Standard-model prediction for direct CP-violation in K → ππ decay, arXiv:1505.07863 [INSPIRE].
  82. [82]
    T. Blum et al., K → ππ ΔI = 3/2 decay amplitude in the continuum limit, Phys. Rev. D 91 (2015) 074502 [arXiv:1502.00263] [INSPIRE].ADSGoogle Scholar
  83. [83]
    A.J. Buras, M. Gorbahn, S. äger and M. Jamin, Improved anatomy of ε′/ε in the Standard Model, arXiv:1507.06345 [INSPIRE].
  84. [84]
    A.J. Buras and J.-M. Gérard, Upper Bounds on ε′/ε Parameters B 6(61/2) and B 8(83/2) from Large-N QCD and other News, arXiv:1507.06326 [INSPIRE].
  85. [85]
    A.J. Buras and L. Silvestrini, Upper bounds on \( K\to \pi \nu \overline{\nu} \) and K L → π 0 e + e− from ε′/ε and KL → μ+μ−, Nucl. Phys. B 546 (1999) 299 [hep-ph/9811471] [INSPIRE].CrossRefADSGoogle Scholar
  86. [86]
    A.J. Buras, G. Colangelo, G. Isidori, A. Romanino and L. Silvestrini, Connections between ε′/ε and rare kaon decays in supersymmetry, Nucl. Phys. B 566 (2000) 3 [hep-ph/9908371] [INSPIRE].ADSGoogle Scholar
  87. [87]
    M. Blanke, A.J. Buras, S. Recksiegel, C. Tarantino and S. Uhlig, Correlations between ε′/ε and rare K decays in the littlest Higgs model with T-parity, JHEP 06 (2007) 082 [arXiv:0704.3329] [INSPIRE].CrossRefADSGoogle Scholar
  88. [88]
    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].CrossRefADSGoogle Scholar
  89. [89]
    A.J. Buras, D. Buttazzo and R. Knegjens, \( K\ \to\ \pi \nu \overline{\nu} \) and ε′/ε in Simplified New Physics Models, arXiv:1507.08672 [INSPIRE].
  90. [90]
    M. Blanke, A.J. Buras and S. Recksiegel, Quark flavour observables in the Littlest Higgs model with T-parity after LHC Run 1, arXiv:1507.06316 [INSPIRE].
  91. [91]
    A.J. Buras, M. Jamin and M.E. Lautenbacher, The Anatomy of ε′/ε beyond leading logarithms with improved hadronic matrix elements, Nucl. Phys. B 408 (1993) 209 [hep-ph/9303284] [INSPIRE].CrossRefADSGoogle Scholar
  92. [92]
    A.J. Buras, J. Girrbach-Noe, C. Niehoff and D.M. Straub, \( B\ \to\ {K}^{\left(\ast \right)}\nu \overline{\nu} \) decays in the Standard Model and beyond, JHEP 02 (2015) 184 [arXiv:1409.4557] [INSPIRE].MathSciNetCrossRefADSGoogle Scholar
  93. [93]
    V. Cirigliano, G. Ecker, H. Neufeld, A. Pich and J. Portoles, Kaon Decays in the Standard Model, Rev. Mod. Phys. 84 (2012) 399 [arXiv:1107.6001] [INSPIRE].CrossRefADSGoogle Scholar
  94. [94]
    T. Blum et al., Lattice determination of the K → (ππ) I=2 Decay Amplitude A 2, Phys. Rev. D 86 (2012) 074513 [arXiv:1206.5142] [INSPIRE].ADSGoogle Scholar

Copyright information

© The Author(s) 2015

Authors and Affiliations

  • Andrzej J. Buras
    • 1
    • 2
  • Dario Buttazzo
    • 1
    • 2
    Email author
  • Jennifer Girrbach-Noe
    • 1
    • 2
  • Robert Knegjens
    • 1
    • 2
  1. 1.TUM Institute for Advanced StudyGarchingGermany
  2. 2.Physik DepartmentTechnische Universität MünchenGarchingGermany

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