Abstract
In light of a discrepancy of the direct CP violation in K → ππ decays, ε′/εK , we investigate gluino contributions to the electroweak penguin, where flavor violations are induced by squark trilinear couplings. Top-Yukawa contributions to ΔS = 2 observables are taken into account, and vacuum stability conditions are evaluated in detail. It is found that this scenario can explain the discrepancy of ε′/εK for the squark mass smaller than 5.6 TeV. We also show that the gluino contributions can amplify \( \mathrm{\mathcal{B}}\left(K\to \pi \nu \overline{\nu}\right) \), ℬ(KS → μ+μ−)eff and ΔACP(b → sγ). Such large effects could be measured in future experiments.
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RBC and UKQCD collaborations, Z. Bai et al., Standard Model prediction for direct CP-violation in K → ππ decay, Phys. Rev. Lett. 115 (2015) 212001 [arXiv:1505.07863] [INSPIRE].
T. Blum et al., The K → (ππ)I=2 decay amplitude from lattice QCD, Phys. Rev. Lett. 108 (2012) 141601 [arXiv:1111.1699] [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].
E. Pallante and A. Pich, Final state interactions in kaon decays, Nucl. Phys. B 592 (2001) 294 [hep-ph/0007208] [INSPIRE].
E. Pallante, A. Pich and I. Scimemi, The Standard Model prediction for ε ′ /ε, Nucl. Phys. B 617 (2001) 441 [hep-ph/0105011] [INSPIRE].
T. Hambye, S. Peris and E. de Rafael, ΔI = 1/2 and ε ′ /ε in large N c QCD, JHEP 05 (2003) 027 [hep-ph/0305104] [INSPIRE].
H.G. Mullor, Updated Standard Model prediction for the kaon direct CP-violating ratio ε ′ /ε, talk at IX CPAN days, Santander Spain, 23-25 October 2017.
A.J. Buras, M. Gorbahn, S. Jäger and M. Jamin, Improved anatomy of ε ′ /ε in the Standard Model, JHEP 11 (2015) 202 [arXiv:1507.06345] [INSPIRE].
T. Kitahara, U. Nierste and P. Tremper, Singularity-free next-to-leading order ΔS = 1 renormalization group evolution and ε ′ K /ε K in the Standard Model and beyond, JHEP 12 (2016) 078 [arXiv:1607.06727] [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. Abouzaid et al., Precise measurements of direct CP-violation, CPT symmetry and other parameters in the neutral kaon system, Phys. Rev. D 83 (2011) 092001 [arXiv:1011.0127] [INSPIRE].
Particle Data Group collaboration, C. Patrignani et al., Review of particle physics, Chin.Phys. C 40 (2016) 100001 [INSPIRE].
A.J. Buras and J.-M. Gérard, Upper bounds on ε ′ /ε parameters B (1/2)6 and B (3/2)8 from large N QCD and other news, JHEP 12 (2015) 008 [arXiv:1507.06326] [INSPIRE].
A.J. Buras and J.-M. Gerard, Final state interactions in K → ππ decays: ΔI = 1/2 rule vs. ε ′ /ε, Eur. Phys. J. C 77 (2017) 10 [arXiv:1603.05686] [INSPIRE].
M. Tanimoto and K. Yamamoto, Probing SUSY with 10 TeV stop mass in rare decays and CP-violation of kaon, PTEP 2016 (2016) 123B02 [arXiv:1603.07960] [INSPIRE].
M. Endo, T. Kitahara, S. Mishima and K. Yamamoto, Revisiting kaon physics in general Z scenario, Phys. Lett. B 771 (2017) 37 [arXiv:1612.08839] [INSPIRE].
C. Bobeth, A.J. Buras, A. Celis and M. Jung, Yukawa enhancement of Z-mediated new physics in ΔS = 2 and ΔB = 2 processes, JHEP 07 (2017) 124 [arXiv:1703.04753] [INSPIRE].
CMS collaboration, Search for supersymmetry in multijet events with missing transverse momentum in proton-proton collisions at 13 TeV, Phys. Rev. D 96 (2017) 032003 [arXiv:1704.07781] [INSPIRE].
ATLAS collaboration, Search for squarks and gluinos in final states with jets and missing transverse momentum using 36 fb −1 of \( \sqrt{s}=13 \) TeV pp collision data with the ATLAS detector, arXiv:1712.02332 [INSPIRE].
M. Endo, S. Mishima, D. Ueda and K. Yamamoto, Chargino contributions in light of recent ε ′ /ε, Phys. Lett. B 762 (2016) 493 [arXiv:1608.01444] [INSPIRE].
T. Kitahara, U. Nierste and P. Tremper, Supersymmetric explanation of CP-violation in K →ππ decays, Phys. Rev. Lett. 117 (2016) 091802 [arXiv:1604.07400] [INSPIRE].
A. Crivellin, G. D’Ambrosio, T. Kitahara and U. Nierste, \( K\to \pi \nu \overline{\nu} \) in the MSSM in light of the ε ′ K /ε K anomaly, Phys. Rev. D 96 (2017) 015023 [arXiv:1703.05786] [INSPIRE].
V. Chobanova et al., Probing SUSY effects in K 0 S → μ + μ −, arXiv:1711.11030 [INSPIRE].
G. D’Ambrosio and T. Kitahara, Direct CP violation in K → μ + μ −, Phys. Rev. Lett. 119 (2017) 201802 [arXiv:1707.06999] [INSPIRE].
B. Grzadkowski, M. Iskrzynski, M. Misiak and J. Rosiek, Dimension-six terms in the Standard Model Lagrangian, JHEP 10 (2010) 085 [arXiv:1008.4884] [INSPIRE].
E.E. Jenkins, A.V. Manohar and M. Trott, Renormalization group evolution of the Standard Model dimension six operators I: formalism and λ dependence, JHEP 10 (2013) 087 [arXiv:1308.2627] [INSPIRE].
E.E. Jenkins, A.V. Manohar and M. Trott, Renormalization group evolution of the Standard Model dimension six operators II: Yukawa dependence, JHEP 01 (2014) 035 [arXiv:1310.4838] [INSPIRE].
R. Alonso, E.E. Jenkins, A.V. Manohar and M. Trott, Renormalization group evolution of the Standard Model dimension six operators III: gauge coupling dependence and phenomenology, JHEP 04 (2014) 159 [arXiv:1312.2014] [INSPIRE].
J. Aebischer, A. Crivellin, M. Fael and C. Greub, Matching of gauge invariant dimension-six operators for b → s and b → c transitions, JHEP 05 (2016) 037 [arXiv:1512.02830] [INSPIRE].
P.Z. Skands et al., SUSY Les Houches accord: interfacing SUSY spectrum calculators, decay packages and event generators, JHEP 07 (2004) 036 [hep-ph/0311123] [INSPIRE].
B.C. Allanach et al., SUSY Les Houches accord 2, Comput. Phys. Commun. 180 (2009) 8 [arXiv:0801.0045] [INSPIRE].
S. Bertolini, F. Borzumati, A. Masiero and G. Ridolfi, Effects of supergravity induced electroweak breaking on rare B decays and mixings, Nucl. Phys. B 353 (1991) 591 [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, New physics patterns in ε ′ /ε and ε K with implications for rare kaon decays and ΔM K, JHEP 04 (2016) 071 [arXiv:1601.00005] [INSPIRE].
A. Masiero and H. Murayama, Can ε ′ /ε be supersymmetric?, Phys. Rev. Lett. 83 (1999) 907 [hep-ph/9903363] [INSPIRE].
K.S. Babu, B. Dutta and R.N. Mohapatra, Seesaw constrained MSSM, solution to the SUSY CP problem and a supersymmetric explanation of ε ′ /ε, Phys. Rev. D 61 (2000) 091701 [hep-ph/9905464] [INSPIRE].
S. Khalil and T. Kobayashi, Supersymmetric CP-violation ε ′ /ε due to asymmetric A-matrix, Phys. Lett. B 460 (1999) 341 [hep-ph/9906374] [INSPIRE].
S. Baek, J.H. Jang, P. Ko and J.-H. Park, Fully supersymmetric CP-violations in the kaon system, Phys. Rev. D 62 (2000) 117701 [hep-ph/9907572] [INSPIRE].
R. Barbieri, R. Contino and A. Strumia, ε ′ from supersymmetry with nonuniversal A terms?, Nucl. Phys. B 578 (2000) 153 [hep-ph/9908255] [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].
S. Baek, J.H. Jang, P. Ko and J.-H. Park, Gluino squark contributions to CP-violations in the kaon system, Nucl. Phys. B 609 (2001) 442 [hep-ph/0105028] [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].
J.S. Hagelin, S. Kelley and T. Tanaka, Supersymmetric flavor changing neutral currents: exact amplitudes and phenomenological analysis, Nucl. Phys. B 415 (1994) 293 [INSPIRE].
A.J. Buras, S. Jager and J. Urban, Master formulae for ΔF = 2 NLO QCD factors in the Standard Model and beyond, Nucl. Phys. B 605 (2001) 600 [hep-ph/0102316] [INSPIRE].
RBC/UKQCD collaboration, N. Garron, R.J. Hudspith and A.T. Lytle, Neutral kaon mixing beyond the Standard Model with n f = 2 + 1 chiral fermions part 1: bare matrix elements and physical results, JHEP 11 (2016) 001 [arXiv:1609.03334] [INSPIRE].
SWME collaboration, Y.-C. Jang, W. Lee, S. Lee and J. Leem, Update on ε K with lattice QCD inputs, EPJ Web Conf. 175 (2018) 14015 [arXiv:1710.06614] [INSPIRE].
SWME collaboration, J.A. Bailey, Y.-C. Jang, W. Lee and S. Park, Standard Model evaluation of ε K using lattice QCD inputs for \( {\widehat{B}}_K \) and V cb, Phys. Rev. D 92 (2015) 034510 [arXiv:1503.05388] [INSPIRE].
A. Bevan et al., Standard Model updates and new physics analysis with the unitarity triangle fit, Nucl. Phys. Proc. Suppl. 241-242 (2013) 89 [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. Bigi, P. Gambino and S. Schacht, A fresh look at the determination of |V cb| from B→D ∗ ℓν, Phys. Lett. B 769 (2017) 441 [arXiv:1703.06124] [INSPIRE].
B. Grinstein and A. Kobach, Model-independent extraction of |V cb| from \( \overline{B}\to D\ast \ell \overline{\nu} \), Phys. Lett. B 771 (2017) 359 [arXiv:1703.08170] [INSPIRE].
F.U. Bernlochner, Z. Ligeti, M. Papucci and D.J. Robinson, Tensions and correlations in |V cb| determinations, Phys. Rev. D 96 (2017) 091503 [arXiv:1708.07134] [INSPIRE].
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].
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].
NA62 collaboration, E. Cortina Gil et al., The beam and detector of the NA62 experiment at CERN, 2017 JINST 12 P05025 [arXiv:1703.08501] [INSPIRE].
H. Nanjo, KOTO and KOTO step2 to search for the rare kaon decay, \( {K}_L\to {\pi}^0\nu \overline{\nu} \), talk at International workshop on physics at the extended hadron experimental facility of J-PARC, KEK, Tokai Japan, 5-6 March 2016.
G. Ruggiero, Recent results from kaon physics, talk at EPS Conference on High Energy Physics, Venice Italy, 5-12 July 2017.
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].
C. Bobeth, M. Gorbahn and E. Stamou, Electroweak corrections to B s,d → ℓ + ℓ −, Phys. Rev. D 89 (2014) 034023 [arXiv:1311.1348] [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].
G. Ecker and A. Pich, The longitudinal muon polarization in K L → μ + μ −, Nucl. Phys. B 366 (1991) 189 [INSPIRE].
F. Mescia, C. Smith and S. Trine, K L → π 0 e + e − and K L → π 0 μ + μ − : a binary star on the stage of flavor physics, JHEP 08 (2006) 088 [hep-ph/0606081] [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].
LHCb collaboration, Improved limit on the branching fraction of the rare decay K 0 S → μ + μ −, Eur. Phys. J. C 77 (2017) 678 [arXiv:1706.00758] [INSPIRE].
D.M. Santos, Physics of LHCb upgrade(s), talk at FPCP 2017 — Flavor Physics & CP Violation, Prague Czech Republic, 5-9 June 2017.
R. Malm, M. Neubert and C. Schmell, Impact of warped extra dimensions on the dipole coefficients in b → sγ transitions, JHEP 04 (2016) 042 [arXiv:1509.02539] [INSPIRE].
T. Hurth, E. Lunghi and W. Porod, Untagged \( \overline{B}\to {X_s}_{+d\gamma } \) CP asymmetry as a probe for new physics, Nucl. Phys. B 704 (2005) 56 [hep-ph/0312260] [INSPIRE].
J.A. Evans and D. Shih, FormFlavor manual, arXiv:1606.00003 [INSPIRE].
M. Misiak et al., Updated NNLO QCD predictions for the weak radiative B-meson decays, Phys. Rev. Lett. 114 (2015) 221801 [arXiv:1503.01789] [INSPIRE].
BaBar collaboration, P. del Amo Sanchez et al., Study of B → Xγ decays and determination of |V td /V ts|, Phys. Rev. D 82 (2010) 051101 [arXiv:1005.4087] [INSPIRE].
A. Crivellin and L. Mercolli, B → X d γ and constraints on new physics, Phys. Rev. D 84 (2011) 114005 [arXiv:1106.5499] [INSPIRE].
M. Benzke, S.J. Lee, M. Neubert and G. Paz, Long-distance dominance of the CP asymmetry in B → X s,d + γ decays, Phys. Rev. Lett. 106 (2011) 141801 [arXiv:1012.3167] [INSPIRE].
A.L. Kagan and M. Neubert, Direct CP-violation in B → X s γ decays as a signature of new physics, Phys. Rev. D 58 (1998) 094012 [hep-ph/9803368] [INSPIRE].
BaBar collaboration, J.P. Lees et al., Measurements of direct CP asymmetries in B → X s γ decays using sum of exclusive decays, Phys. Rev. D 90 (2014) 092001 [arXiv:1406.0534] [INSPIRE].
Belle collaboration, T. Horiguchi et al., Evidence for isospin violation and measurement of CP asymmetries in B → K ∗(892)γ, Phys. Rev. Lett. 119 (2017) 191802 [arXiv:1707.00394] [INSPIRE].
A. Ishikawa, private communication.
Belle II collaboration, S. Sandilya, Prospects for rare decays at Belle II, PoS(CKM2016)080 [arXiv:1706.01027] [INSPIRE].
J.-H. Park, Metastability bounds on flavour-violating trilinear soft terms in the MSSM, Phys. Rev. D 83 (2011) 055015 [arXiv:1011.4939] [INSPIRE].
S.R. Coleman, The fate of the false vacuum. 1. Semiclassical theory, Phys. Rev. D 15 (1977) 2929 [Erratum ibid. D 16 (1977) 1248] [INSPIRE].
C.L. Wainwright, CosmoTransitions: computing cosmological phase transition temperatures and bubble profiles with multiple fields, Comput. Phys. Commun. 183 (2012) 2006 [arXiv:1109.4189] [INSPIRE].
C.G. Callan Jr. and S.R. Coleman, The fate of the false vacuum. 2. First quantum corrections, Phys. Rev. D 16 (1977) 1762 [INSPIRE].
M. Endo, T. Moroi, M.M. Nojiri and Y. Shoji, Renormalization-scale uncertainty in the decay rate of false vacuum, JHEP 01 (2016) 031 [arXiv:1511.04860] [INSPIRE].
J. Hisano and S. Sugiyama, Charge-breaking constraints on left-right mixing of stau’s, Phys. Lett. B 696 (2011) 92 [Erratum ibid. B 719 (2013) 472] [arXiv:1011.0260] [INSPIRE].
T. Kitahara, Vacuum stability constraints on the enhancement of the h → γγ rate in the MSSM, JHEP 11 (2012) 021 [arXiv:1208.4792] [INSPIRE].
T. Kitahara and T. Yoshinaga, Stau with large mass difference and enhancement of the Higgs to diphoton decay rate in the MSSM, JHEP 05 (2013) 035 [arXiv:1303.0461] [INSPIRE].
M. Carena, S. Gori, I. Low, N.R. Shah and C.E.M. Wagner, Vacuum stability and Higgs diphoton decays in the MSSM, JHEP 02 (2013) 114 [arXiv:1211.6136] [INSPIRE].
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Endo, M., Goto, T., Kitahara, T. et al. Gluino-mediated electroweak penguin with flavor-violating trilinear couplings. J. High Energ. Phys. 2018, 19 (2018). https://doi.org/10.1007/JHEP04(2018)019
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DOI: https://doi.org/10.1007/JHEP04(2018)019