Abstract
The decays \( {K}^{+}\to {\pi}^{+}\nu \overline{\nu} \) and \( {K}_L\to\ {\pi}^0\nu \overline{\nu} \), being the theoretically cleanest rare decays of mesons, are very sensitive probes of New Physics (NP). In view of the excellent prospects of reaching the Standard Model (SM) sensitivity for \( {K}^{+}\to {\pi}^{+}\nu \overline{\nu} \) by the NA62 experiment at CERN and for \( {K}_L\to\ {\pi}^0\nu \overline{\nu} \) by the KOTO experiment at J-PARC, we study them in the simplest extensions of the SM in which stringent correlations between these two decays and other flavour observables are present. We first consider simple models with tree-level Z and Z′ contributions in which either Minimal Flavour Violation (MFV) or a U(2)3 symmetry is imposed on the quark flavour-violating couplings. We then compare the resulting correlations with those present in generic models in which the latter couplings are arbitrary, subject to the constraints from ΔF = 2 processes, electroweak and collider data. Of particular interest are the correlations with ε′/ε and K L → μ + μ − which limit the size of NP contributions to \( {K}^{+}\to {\pi}^{+}\nu \overline{\nu} \) and \( {K}_L\to\ {\pi}^0\nu \overline{\nu} \), depending on the Dirac structure of couplings and the relevant operators. But in MFV models also the constraint from B s → μ + μ − turns out to be important. We take into account the recent results from lattice QCD and large N approach that indicate ε′/ε in the SM to be significantly below the data. While in many models the enhancement of ε′/ε implies the suppression of \( {K}_L\to\ {\pi}^0\nu \overline{\nu} \), we present two models in which ε′/ε and \( {K}_L\to\ {\pi}^0\nu \overline{\nu} \) can be simultaneously enhanced relative to SM predictions. A correlation between \( {K}^{+}\to {\pi}^{+}\nu \overline{\nu} \) and B → K(K *)μ + μ −, found by us in the simple models considered here, should be of interest for NA62 and LHCb experimentalists at CERN in the coming years. The one with \( B\to K\left({K}^{\ast}\right)\nu \overline{\nu} \) will be tested at Belle II.
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References
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].
F. Newson et al., Prospects for \( {K}^{+}\to {\pi}^{+}\nu \overline{\nu} \) at CERN in NA62, arXiv:1411.0109 [INSPIRE].
A. Romano, The \( {K}^{+}\to {\pi}^{+}\nu \overline{\nu} \) decay in the NA62 experiment at CERN, arXiv:1411.6546 [INSPIRE].
T.K. Komatsubara, Experiments with K-Meson Decays, Prog. Part. Nucl. Phys. 67 (2012) 995 [arXiv:1203.6437] [INSPIRE].
KOTO collaboration, K. Shiomi, \( {K}_L^0\to {\pi}^0\nu \overline{\nu} \) at KOTO, arXiv:1411.4250 [INSPIRE].
M. Gorbahn and U. Haisch, Effective Hamiltonian for non-leptonic |ΔF | = 1 decays at NNLO in QCD, Nucl. Phys. B 713 (2005) 291 [hep-ph/0411071] [INSPIRE].
A.J. Buras, M. Gorbahn, U. Haisch and U. Nierste, The Rare decay \( {K}^{+}\to p{i}^{+}\nu \overline{\nu} \) at the next-to-next-to-leading order in QCD, Phys. Rev. Lett. 95 (2005) 261805 [hep-ph/0508165] [INSPIRE].
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].
J. Brod and M. Gorbahn, Electroweak Corrections to the Charm Quark Contribution to \( {K}^{+}\to {\pi}^{+}\nu \overline{\nu} \), Phys. Rev. D 78 (2008) 034006 [arXiv:0805.4119] [INSPIRE].
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].
G. Buchalla and A.J. Buras, Two loop large-m t electroweak corrections to K → π neutrino anti-neutrino for arbitrary Higgs boson mass, Phys. Rev. D 57 (1998) 216 [hep-ph/9707243] [INSPIRE].
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].
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].
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].
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].
M. Blanke, New Physics Signatures in Kaon Decays, PoS(KAON13)010 [arXiv:1305.5671] [INSPIRE].
C. Smith, Rare K decays: Challenges and Perspectives, arXiv:1409.6162 [INSPIRE].
A.J. Buras, D. Buttazzo, J. Girrbach-Noe and R. Knegjens, \( {K}^{+}\to {\pi}^{+}\nu \overline{\nu} \) and \( {K}_L\to\ {\pi}^0\nu \overline{\nu} \) in the Standard Model: status and perspectives, JHEP 11 (2015) 033 [arXiv:1503.02693] [INSPIRE].
A.J. Buras, Minimal flavour violation and beyond: Towards a flavour code for short distance dynamics, Acta Phys. Polon. B 41 (2010) 2487 [arXiv:1012.1447] [INSPIRE].
A.J. Buras and J. Girrbach, BSM models facing the recent LHCb data: A First look, Acta Phys. Polon. B 43 (2012) 1427 [arXiv:1204.5064] [INSPIRE].
A.J. Buras, A. Romanino and L. Silvestrini, \( K\to \pi \nu \overline{\nu} \) : A Model independent analysis and supersymmetry, Nucl. Phys. B 520 (1998) 3 [hep-ph/9712398] [INSPIRE].
G. Colangelo and G. Isidori, Supersymmetric contributions to rare kaon decays: Beyond the single mass insertion approximation, JHEP 09 (1998) 009 [hep-ph/9808487] [INSPIRE].
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].
A.J. Buras, T. Ewerth, S. Jager and J. Rosiek, \( {K}^{+}\to {\pi}^{+}\nu \overline{\nu} \) and \( {K}_L\to\ {\pi}^0\nu \overline{\nu} \) decays in the general MSSM, Nucl. Phys. B 714 (2005) 103 [hep-ph/0408142] [INSPIRE].
A. Crivellin, L. Hofer, U. Nierste and D. Scherer, Phenomenological consequences of radiative flavor violation in the MSSM, Phys. Rev. D 84 (2011) 035030 [arXiv:1105.2818] [INSPIRE].
A.J. Buras, A. Poschenrieder, S. Uhlig and W.A. Bardeen, Rare K and B Decays in the Littlest Higgs Model without T-Parity, JHEP 11 (2006) 062 [hep-ph/0607189] [INSPIRE].
M. Blanke, A.J. Buras, B. Duling, S. Recksiegel and C. Tarantino, FCNC Processes in the Littlest Higgs Model with T-Parity: a 2009 Look, Acta Phys. Polon. B 41 (2010) 657 [arXiv:0906.5454] [INSPIRE].
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].
M. Blanke, A.J. Buras, B. Duling, K. Gemmler and S. Gori, Rare K and B Decays in a Warped Extra Dimension with Custodial Protection, JHEP 03 (2009) 108 [arXiv:0812.3803] [INSPIRE].
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].
D.M. Straub, Anatomy of flavour-changing Z couplings in models with partial compositeness, JHEP 08 (2013) 108 [arXiv:1302.4651] [INSPIRE].
A.J. Buras, F. De Fazio, J. Girrbach and M.V. Carlucci, The Anatomy of Quark Flavour Observables in 331 Models in the Flavour Precision Era, JHEP 02 (2013) 023 [arXiv:1211.1237] [INSPIRE].
A.J. Buras, F. De Fazio and J. Girrbach, 331 models facing new b → sμ + μ − data, JHEP 02 (2014) 112 [arXiv:1311.6729] [INSPIRE].
A.J. Buras, F. De Fazio and J. Girrbach-Noe, Z − Z′ mixing and Z-mediated FCNCs in SU(3) C × SU(3) L × U(1) X models, JHEP 08 (2014) 039 [arXiv:1405.3850] [INSPIRE].
S. Bertolini, M. Fabbrichesi and J.O. Eeg, Theory of the CP-violating parameter ϵ′/ϵ, Rev. Mod. Phys. 72 (2000) 65 [hep-ph/9802405] [INSPIRE].
A.J. Buras and M. Jamin, ε′/ε at the NLO: 10 years later, JHEP 01 (2004) 048 [hep-ph/0306217] [INSPIRE].
A. Pich, ε′/ε in the standard model: Theoretical update, hep-ph/0410215 [INSPIRE].
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].
S. Bertolini, J.O. Eeg, A. Maiezza and F. Nesti, New physics in ϵ′ from gluomagnetic contributions and limits on Left-Right symmetry, Phys. Rev. D 86 (2012) 095013 [arXiv:1206.0668] [INSPIRE].
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].
A.J. Buras, M. Gorbahn, S. Jäger and M. Jamin, Improved anatomy of ε′/ε in the Standard Model, arXiv:1507.06345 [INSPIRE].
Z. Bai et al., Standard-model prediction for direct CP-violation in K → ππ decay, arXiv:1505.07863 [INSPIRE].
A.J. Buras and J.-M. Gerard, Upper Bounds on ε′/ε Parameters B (1/2)6 and B (3/2)8 from Large-N QCD and other News, arXiv:1507.06326 [INSPIRE].
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].
Y. Grossman and Y. Nir, \( {K}_L\to\ {\pi}^0\nu \overline{\nu} \) beyond the standard model, Phys. Lett. B 398 (1997) 163 [hep-ph/9701313] [INSPIRE].
M. Blanke, Insights from the Interplay of \( K\to \pi \nu \overline{\nu} \) and ϵ K on the New Physics Flavour Structure, Acta Phys. Polon. B 41 (2010) 127 [arXiv:0904.2528] [INSPIRE].
R. Barbieri, D. Buttazzo, F. Sala and D.M. Straub, Flavour physics and flavour symmetries after the first LHC phase, JHEP 05 (2014) 105 [arXiv:1402.6677] [INSPIRE].
A.J. Buras, F. De Fazio and J. Girrbach, The Anatomy of Z’ and Z with Flavour Changing Neutral Currents in the Flavour Precision Era, JHEP 02 (2013) 116 [arXiv:1211.1896] [INSPIRE].
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].
R. Barbieri, G. Isidori, J. Jones-Perez, P. Lodone and D.M. Straub, U(2) and Minimal Flavour Violation in Supersymmetry, Eur. Phys. J. C 71 (2011) 1725 [arXiv:1105.2296] [INSPIRE].
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].
M. Blanke and A.J. Buras, Lower bounds on ΔM s,d from constrained minimal flavour violation, JHEP 05 (2007) 061 [hep-ph/0610037] [INSPIRE].
A.J. Buras and J. Girrbach, On the Correlations between Flavour Observables in Minimal U(2)3 Models, JHEP 01 (2013) 007 [arXiv:1206.3878] [INSPIRE].
A.J. Buras and J. Girrbach, Left-handed Z′ and Z FCNC quark couplings facing new b → sμ + μ − data, JHEP 12 (2013) 009 [arXiv:1309.2466] [INSPIRE].
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].
M. Ciuchini, E. Franco, G. Martinelli and L. Reina, The ΔS = 1 effective Hamiltonian including next-to-leading order QCD and QED corrections, Nucl. Phys. B 415 (1994) 403 [hep-ph/9304257] [INSPIRE].
A.J. Buras, P. Gambino and U.A. Haisch, Electroweak penguin contributions to nonleptonic ΔF = 1 decays at NNLO, Nucl. Phys. B 570 (2000) 117 [hep-ph/9911250] [INSPIRE].
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 K L → μ + μ −, Nucl. Phys. B 546 (1999) 299 [hep-ph/9811471] [INSPIRE].
S. Aoki et al., Review of lattice results concerning low-energy particle physics, Eur. Phys. J. C 74 (2014) 2890 [arXiv:1310.8555] [INSPIRE].
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].
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].
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].
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].
KTeV collaboration, E.T. Worcester, The Final Measurement of ε′/ε from KTeV, arXiv:0909.2555 [INSPIRE].
S. Descotes-Genon, L. Hofer, J. Matias and J. Virto, On the impact of power corrections in the prediction of B → K * μ + μ − observables, JHEP 12 (2014) 125 [arXiv:1407.8526] [INSPIRE].
W. Altmannshofer and D.M. Straub, New physics in b → s transitions after LHC run 1, Eur. Phys. J. C 75 (2015) 382 [arXiv:1411.3161] [INSPIRE].
G. Hiller and M. Schmaltz, R K and future b → sℓℓ physics beyond the standard model opportunities, Phys. Rev. D 90 (2014) 054014 [arXiv:1408.1627] [INSPIRE].
W. Altmannshofer and D.M. Straub, Implications of b → s measurements, arXiv:1503.06199 [INSPIRE].
A.J. Buras, J. Girrbach-Noe, C. Niehoff and D.M. Straub, \( B\to {K}^{\left(*\right)}\nu \overline{\nu} \) decays in the Standard Model and beyond, JHEP 02 (2015) 184 [arXiv:1409.4557] [INSPIRE].
M. Gorbahn and U. Haisch, Charm Quark Contribution to K L → μ + μ − at Next-to-Next-to-Leading, Phys. Rev. Lett. 97 (2006) 122002 [hep-ph/0605203] [INSPIRE].
G. Isidori and R. Unterdorfer, On the short distance constraints from K L,S → μ + μ −, JHEP 01 (2004) 009 [hep-ph/0311084] [INSPIRE].
C. Bobeth et al., Upper bounds on rare K and B decays from minimal flavor violation, Nucl. Phys. B 726 (2005) 252 [hep-ph/0505110] [INSPIRE].
U. Haisch and A. Weiler, Determining the Sign of the Z Penguin Amplitude, Phys. Rev. D 76 (2007) 074027 [arXiv:0706.2054] [INSPIRE].
R. Barbieri, P. Campli, G. Isidori, F. Sala and D.M. Straub, B-decay CP-asymmetries in SUSY with a U(2)3 flavour symmetry, Eur. Phys. J. C 71 (2011) 1812 [arXiv:1108.5125] [INSPIRE].
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].
CKMfitter Group collaboration, K. Trabelsi, World average and experimental overview of γ/φ 3, presented at CKM 2014, Vienna Austria (2014), http://ckmfitter.in2p3.fr.
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].
Particle Data Group collaboration, J. Beringer et al., Review of Particle Physics (RPP), Phys. Rev. D 86 (2012) 010001 [INSPIRE].
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].
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].
A.J. Buras, M. Jamin and P.H. Weisz, Leading and Next-to-leading QCD Corrections to ε Parameter and \( {B}^0\hbox{--} {\overline{B}}^0 \) Mixing in the Presence of a Heavy Top Quark, Nucl. Phys. B 347 (1990) 491 [INSPIRE].
K.G. Chetyrkin et al., Charm and Bottom Quark Masses: An Update, Phys. Rev. D 80 (2009) 074010 [arXiv:0907.2110] [INSPIRE].
J. Urban, F. Krauss, U. Jentschura and G. Soff, Next-to-leading order QCD corrections for the \( {B}^0\hbox{--} {\overline{B}}^0 \) mixing with an extended Higgs sector, Nucl. Phys. B 523 (1998) 40 [hep-ph/9710245] [INSPIRE].
ATLAS, CDF, CMS and D0 collaborations, First combination of Tevatron and LHC measurements of the top-quark mass, arXiv:1403.4427 [INSPIRE].
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Buras, A.J., Buttazzo, D. & Knegjens, R. \( K\to \pi \nu \overline{\nu} \) and ε′/ε in simplified new physics models. J. High Energ. Phys. 2015, 166 (2015). https://doi.org/10.1007/JHEP11(2015)166
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DOI: https://doi.org/10.1007/JHEP11(2015)166