# Flavor constraints on scenarios with two or three heavy squark generations

- 86 Downloads
- 10 Citations

## Abstract

We re-assess constraints from flavor-changing neutral currents in the kaon system on supersymmetric scenarios with a light gluino, two heavy generations of squarks and a lighter third generation. We compute for the first time limits in scenarios with three heavy squark families, taking into account QCD corrections at the next-to-leading order. We compare our limits with those in the case of two heavy families. We use the mass insertion approximation and consider contributions from gluino exchange to constrain the mixing between the first and second squark generation. While it is not possible to perform a general analysis, we assess the relevance of each kind of flavor- and CP-violating parameters. We also provide ready to use magic numbers for the computation of the Wilson coefficients at 2 GeV for these scenarios.

## Keywords

Magic Number Gluino Mass Squark Masse Squark Generation Mass Insertion## Notes

### Acknowledgements

We would like to thank Joachim Brod, Christian Hoelbling, Luca Silvestrini, and Javier Virto for very helpful discussions. This work was supported by the German Research Foundation (DFG) via the Junior Research Group “SUSY Phenomenology” within the Collaborative Research Center 676 “Particles, Strings and the Early Universe” and by the INFN. We acknowledge the Aspen Center for Theoretical Physics for a very stimulating environment which prompted the beginning of this work. L. V.-S. thanks the University of Hamburg for its hospitality. Finally, we thank the Galileo Galilei Institute for Theoretical Physics for its hospitality during later stages of the work.

## References

- 1.K. Kadota, G. Kane, J. Kersten, L. Velasco-Sevilla, Flavour issues for string-motivated heavy scalar spectra with a low gluino mass: the
*G*_{2}-MSSM case. Eur. Phys. J. C**72**, 2004 (2012). arXiv:1107.3105 [hep-ph] ADSCrossRefGoogle Scholar - 2.J.A. Bagger, K.T. Matchev, R.-J. Zhang, QCD corrections to flavor-changing neutral currents in the supersymmetric Standard Model. Phys. Lett. B
**412**, 77–85 (1997). arXiv:hep-ph/9707225 ADSCrossRefGoogle Scholar - 3.R. Contino, I. Scimemi, The supersymmetric flavor problem for heavy first-two generation scalars at next-to-leading order. Eur. Phys. J. C
**10**, 347–356 (1999). arXiv:hep-ph/9809437 ADSCrossRefGoogle Scholar - 4.R. Barbieri, E. Bertuzzo, M. Farina, P. Lodone, D. Zhuridov, Minimal flavour violation with hierarchical squark masses. J. High Energy Phys.
**1012**, 070 (2010). Erratum ibid.,**1102**, 044 (2011). arXiv:1011.0730 [hep-ph] ADSCrossRefGoogle Scholar - 5.E. Bertuzzo, M. Farina, P. Lodone, On the QCD corrections to Δ
*F*=2 FCNC in the supersymmetric SM with hierarchical squark masses. Phys. Lett. B**699**, 98–101 (2011). arXiv:1011.3240 [hep-ph] ADSCrossRefGoogle Scholar - 6.F. Mescia, J. Virto, Natural SUSY and kaon mixing in view of recent results from lattice QCD. Phys. Rev. D
**86**, 095004 (2012). arXiv:1208.0534 [hep-ph] ADSCrossRefGoogle Scholar - 7.M. Ciuchini, E. Franco, D. Guadagnoli, V. Lubicz, V. Porretti, L. Silvestrini, Next-to-leading order strong interaction corrections to the Δ
*F*=2 effective Hamiltonian in the MSSM. J. High Energy Phys.**0609**, 013 (2006). arXiv:hep-ph/0606197 ADSCrossRefGoogle Scholar - 8.J. Virto, Exact NLO strong interaction corrections to the Δ
*F*=2 effective Hamiltonian in the MSSM. J. High Energy Phys.**0911**, 055 (2009). arXiv:0907.5376 [hep-ph] ADSCrossRefGoogle Scholar - 9.M. Ciuchini, E. Franco, V. Lubicz, G. Martinelli, I. Scimemi, L. Silvestrini, Next-to-leading order QCD corrections to Δ
*F*=2 effective Hamiltonians. Nucl. Phys. B**523**, 501–525 (1998). arXiv:hep-ph/9711402 ADSCrossRefGoogle Scholar - 10.M. Ciuchini et al., Δ
*M*_{K}and*ϵ*_{K}in SUSY at the next-to-leading order. J. High Energy Phys.**10**, 008 (1998). Erratum added online, Mar/29/2000. arXiv:hep-ph/9808328 ADSCrossRefGoogle Scholar - 11.A.J. Buras, S. Jäger, J. Urban, Master formulae for Δ
*F*=2 NLO-QCD factors in the Standard Model and beyond. Nucl. Phys. B**605**, 600–624 (2001). arXiv:hep-ph/0102316 ADSCrossRefGoogle Scholar - 12.D.M. Pierce, J.A. Bagger, K.T. Matchev, R.-j. Zhang, Precision corrections in the minimal supersymmetric Standard Model. Nucl. Phys. B
**491**, 3–67 (1997). arXiv:hep-ph/9606211 ADSCrossRefGoogle Scholar - 13.J.F. Donoghue, E. Golowich, B.R. Holstein,
*Dynamics of the Standard Model*. Camb. Monogr. Part. Phys. Nucl. Phys. Cosmol., vol. 2 (1992), pp. 1–540 zbMATHCrossRefGoogle Scholar - 14.J. Brod, M. Gorbahn, Next-to-next-to-leading-order charm-quark contribution to the
*CP*violation parameter*ϵ*_{K}and Δ*M*_{K}. Phys. Rev. Lett.**108**, 121801 (2012). arXiv:1108.2036 [hep-ph] ADSCrossRefGoogle Scholar - 15.V. Bertone et al. (ETM Collaboration), Kaon mixing beyond the SM from
*N*_{f}=2 tmQCD and model independent constraints from the UTA. arXiv:1207.1287 [hep-lat] - 16.R. Babich, N. Garron, C. Hoelbling, J. Howard, L. Lellouch, C. Rebbi,
*K*^{0}–\(\bar{K}^{0}\) mixing beyond the Standard Model and CP-violating electroweak penguins in quenched QCD with exact chiral symmetry. Phys. Rev. D**74**, 073009 (2006). arXiv:hep-lat/0605016 ADSCrossRefGoogle Scholar - 17.A.J. Buras, D. Guadagnoli, Correlations among new
*CP*violating effects in Δ*F*=2 observables. Phys. Rev. D**78**, 033005 (2008). arXiv:0805.3887 [hep-ph] ADSCrossRefGoogle Scholar - 18.T. Blum, P. Boyle, N. Christ, N. Garron, E. Goode et al.,
*K*→(*ππ*)_{I=2}decay amplitude from lattice QCD. Phys. Rev. Lett.**108**, 141601 (2012). arXiv:1111.1699 [hep-lat] ADSCrossRefGoogle Scholar - 19.A.G. Cohen, D. Kaplan, A. Nelson, The More Minimal Supersymmetric Standard Model. Phys. Lett. B
**388**, 588–598 (1996). arXiv:hep-ph/9607394 ADSCrossRefGoogle Scholar - 20.B.S. Acharya, K. Bobkov, G.L. Kane, J. Shao, P. Kumar,
*G*_{2}-MSSM: an*M*theory motivated model of particle physics. Phys. Rev. D**78**, 065038 (2008). arXiv:0801.0478 [hep-ph] ADSCrossRefGoogle Scholar - 21.L. Velasco-Sevilla, Gluinos lighter than squarks and detection at the LHC, in
*Proceedings of the XLVIIth Rencontres de Moriond (EW 2012)*, (2012). arXiv:1205.5787 [hep-ph] Google Scholar - 22.G.F. Giudice, M. Nardecchia, A. Romanino, Hierarchical soft terms and flavor physics. Nucl. Phys. B
**813**, 156–173 (2009). arXiv:0812.3610 [hep-ph] ADSzbMATHCrossRefGoogle Scholar - 23.S. Dürr et al., Precision computation of the kaon bag parameter. Phys. Lett. B
**705**, 477–481 (2011). arXiv:1106.3230 [hep-lat] ADSCrossRefGoogle Scholar - 24.E. Gamiz et al. (HPQCD Collaboration, UKQCD Collaboration), Unquenched determination of the kaon parameter
*B*_{K}from improved staggered fermions. Phys. Rev. D**73**, 114502 (2006). arXiv:hep-lat/0603023 ADSCrossRefGoogle Scholar - 25.J. Laiho, R.S. Van de Water, Pseudoscalar decay constants, light-quark masses, and
*B*_{K}from mixed-action lattice QCD. PoS**LATTICE2011**, 293 (2011). arXiv:1112.4861 [hep-lat] Google Scholar - 26.C. Kelly, Continuum results for light hadronic quantities using domain wall fermions with the Iwasaki and DSDR gauge actions. Contribution to The XXIX International Symposium on Lattice Field Theory, 10–16 July 2011. arXiv:1201.0706 [hep-lat]
- 27.T. Bae et al. (SWME Collaboration), Kaon
*B*parameter from improved staggered fermions in*N*_{f}=2+1 QCD. Phys. Rev. Lett.**109**, 041601 (2012). arXiv:1111.5698 [hep-lat] ADSCrossRefGoogle Scholar - 28.C. Hoelbling, Precision flavor physics from the lattice. arXiv:1206.7075 [hep-ph]
- 29.J. Laiho, E. Lunghi, R. Van de Water, Flavor physics in the LHC era: the role of the lattice. PoS
**LATTICE2011**, 018 (2011). arXiv:1204.0791 [hep-ph] Google Scholar - 30.P. Boyle, N. Garron, R. Hudspith (RBC Collaboration, UKQCD Collaboration), Neutral kaon mixing beyond the standard model with
*n*_{f}=2+1 chiral fermions. Phys. Rev. D**86**, 054028 (2012). arXiv:1206.5737 [hep-lat] ADSCrossRefGoogle Scholar - 31.J. Beringer et al. (Particle Data Group), Review of particle physics. Phys. Rev. D
**86**, 010001 (2012). http://pdg.lbl.gov/ ADSCrossRefGoogle Scholar - 32.K. Chetyrkin, J.H. Kühn, M. Steinhauser, RunDec: a Mathematica package for running and decoupling of the strong coupling and quark masses. Comput. Phys. Commun.
**133**, 43–65 (2000). arXiv:hep-ph/0004189 ADSzbMATHCrossRefGoogle Scholar - 33.C. Tamarit, Decoupling heavy sparticles in hierarchical SUSY scenarios: two-loop renormalization group equations. arXiv:1204.2292 [hep-ph]
- 34.C. Tamarit, Decoupling heavy sparticles in effective SUSY scenarios: unification, Higgs masses and tachyon bounds. J. High Energy Phys.
**1206**, 080 (2012). arXiv:1204.2645 [hep-ph] ADSCrossRefGoogle Scholar