Kaon mixing beyond the SM from Nf = 2 tmQCD and model independent constraints from the UTA

  • The ETM collaboration
  • V. Bertone
  • N. Carrasco
  • M. Ciuchini
  • P. Dimopoulos
  • R. Frezzotti
  • V. Giménez
  • V. Lubicz
  • G. Martinelli
  • F. Mescia
  • M. Papinutto
  • G. C. Rossi
  • L. Silvestrini
  • S. Simula
  • C. Tarantino
  • A. Vladikas
Open Access
Article

Abstract

We present the first unquenched, continuum limit, lattice QCD results for the matrix elements of the operators describing neutral kaon oscillations in extensions of the Standard Model. Owing to the accuracy of our calculation on ∆S = 2 weak Hamiltonian matrix elements, we are able to provide a refined Unitarity Triangle analysis improving the bounds coming from model independent constraints on New Physics. In our nonperturbative computation we use a combination of Nf = 2 maximally twisted sea quarks and Osterwalder-Seiler valence quarks in order to achieve both O(a)-improvement and continuum-like renormalization properties for the relevant four-fermion operators. The calculation of the renormalization constants has been performed non-perturbatively in the RI-MOM scheme. Based on simulations at four values of the lattice spacing and a number of quark masses we have extrapolated/interpolated our results to the continuum limit and physical light/strange quark masses.

Keywords

Lattice QCD Beyond Standard Model 

References

  1. [1]
    F. Gabbiani, E. Gabrielli, A. Masiero and L. Silvestrini, A complete analysis of FCNC and CP constraints in general SUSY extensions of the standard model, Nucl. Phys. B 477 (1996) 321 [hep-ph/9604387] [INSPIRE].ADSCrossRefGoogle Scholar
  2. [2]
    G. Beall, M. Bander and A. Soni, Constraint on the Mass Scale of a Left-Right Symmetric Electroweak Theory from the K(L) K(S) Mass Difference, Phys. Rev. Lett. 48 (1982) 848 [INSPIRE].ADSCrossRefGoogle Scholar
  3. [3]
    F. Gabbiani and A. Masiero, FCNC in generalized supersymmetric theories, Nucl. Phys. B 322 (1989) 235 [INSPIRE].ADSCrossRefGoogle Scholar
  4. [4]
    E. Gabrielli, A. Masiero and L. Silvestrini, Flavor changing neutral currents and CP-violating processes in generalized supersymmetric theories, Phys. Lett. B 374 (1996) 80 [hep-ph/9509379] [INSPIRE].ADSCrossRefGoogle Scholar
  5. [5]
    RBC and UKQCD collaborations, P. Boyle, N. Garron and R. Hudspith, Neutral kaon mixing beyond the standard model with n f = 2 + 1 chiral fermions, Phys. Rev. D 86 (2012) 054028 [arXiv:1206.5737] [INSPIRE].ADSGoogle Scholar
  6. [6]
    A. Donini, V. Giménez, L. Giusti and G. Martinelli, Renormalization group invariant matrix elements of ΔS = 2 and ΔI = 3/2 four fermion operators without quark masses, Phys. Lett. B 470 (1999) 233 [hep-lat/9910017] [INSPIRE].ADSCrossRefGoogle Scholar
  7. [7]
    R. Babich et al., \( {K^0}-{{\overline{K}}^0} \) mixing beyond the standard model and CP-violating electroweak penguins in quenched QCD with exact chiral symmetry, Phys. Rev. D 74 (2006) 073009 [hep-lat/0605016] [INSPIRE].ADSGoogle Scholar
  8. [8]
    ETM collaboration, M. Constantinou et al., B K -parameter from N f = 2 twisted mass lattice QCD, Phys. Rev. D 83 (2011) 014505 [arXiv:1009.5606] [INSPIRE].ADSGoogle Scholar
  9. [9]
    UTfit collaboration, M. Bona et al., Model-independent constraints on ΔF = 2 operators and the scale of new physics, JHEP 03 (2008) 049 [arXiv:0707.0636] [INSPIRE].ADSCrossRefGoogle Scholar
  10. [10]
    Alpha collaboration, R. Frezzotti, P.A. Grassi, S. Sint and P. Weisz, Lattice QCD with a chirally twisted mass term, JHEP 08 (2001) 058 [hep-lat/0101001] [INSPIRE].Google Scholar
  11. [11]
    R. Frezzotti and G. Rossi, Chirally improving Wilson fermions. I. O(a) improvement, JHEP 08 (2004) 007 [hep-lat/0306014] [INSPIRE].ADSCrossRefGoogle Scholar
  12. [12]
    R. Frezzotti and G. Rossi, Chirally improving Wilson fermions. II. Four-quark operators, JHEP 10 (2004) 070 [hep-lat/0407002] [INSPIRE].ADSCrossRefGoogle Scholar
  13. [13]
    J.A. Bagger, K.T. Matchev and R.-J. Zhang, QCD corrections to flavor changing neutral currents in the supersymmetric standard model, Phys. Lett. B 412 (1997) 77 [hep-ph/9707225] [INSPIRE].ADSCrossRefGoogle Scholar
  14. [14]
    C. Allton et al., B parameters for ΔS = 2 supersymmetric operators, Phys. Lett. B 453 (1999) 30 [hep-lat/9806016] [INSPIRE].ADSCrossRefGoogle Scholar
  15. [15]
    A.J. Buras, M. Misiak and J. Urban, Two loop QCD anomalous dimensions of flavor changing four quark operators within and beyond the standard model, Nucl. Phys. B 586 (2000) 397 [hep-ph/0005183] [INSPIRE].ADSCrossRefGoogle Scholar
  16. [16]
    G. Martinelli, C. Pittori, C.T. Sachrajda, M. Testa and A. Vladikas, A general method for nonperturbative renormalization of lattice operators, Nucl. Phys. B 445 (1995) 81 [hep-lat/9411010] [INSPIRE].ADSCrossRefGoogle Scholar
  17. [17]
    E. Franco and V. Lubicz, Quark mass renormalization in the MS-bar and RI schemes up to the NNLO order, Nucl. Phys. B 531 (1998) 641 [hep-ph/9803491] [INSPIRE].ADSCrossRefGoogle Scholar
  18. [18]
    ETM collaboration, M. Constantinou et al., Non-perturbative renormalization of quark bilinear operators with N f = 2 (tmQCD) Wilson fermions and the tree-level improved gauge action, JHEP 08 (2010) 068 [arXiv:1004.1115] [INSPIRE].ADSCrossRefGoogle Scholar
  19. [19]
  20. [20]
    M. Misiak, S. Pokorski and J. Rosiek, Supersymmetry and FCNC effects, Adv. Ser. Direct. High Energy Phys. 15 (1998) 795 [hep-ph/9703442] [INSPIRE]. To appear in Advanced Series on Directions in High-Energy Physics. Review Volume: Heavy Flavors II, A.J. Buras and M. Lindner eds., World Scientific, Singapore.
  21. [21]
    M. Ciuchini, G. Degrassi, P. Gambino and G. Giudice, Next-to-leading QCD corrections to BX sγ in supersymmetry, Nucl. Phys. B 534 (1998) 3 [hep-ph/9806308] [INSPIRE].ADSGoogle Scholar
  22. [22]
    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].ADSCrossRefGoogle Scholar
  23. [23]
    M. Blanke, A.J. Buras, D. Guadagnoli and C. Tarantino, Minimal Flavour Violation Waiting for Precise Measurements of ΔM s , S Ψϕ , \( A_{\mathrm{SL}}^s \) , |V ub|, γ and \( B_{s,d}^0\to {\mu^{+}}{\mu^{-}} \), JHEP 10 (2006) 003 [hep-ph/0604057] [INSPIRE].ADSGoogle Scholar
  24. [24]
    A. 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].ADSCrossRefGoogle Scholar
  25. [25]
    G. D’Ambrosio, G. Giudice, G. Isidori and A. Strumia, Minimal flavor violation: An Effective field theory approach, Nucl. Phys. B 645 (2002) 155 [hep-ph/0207036] [INSPIRE].ADSCrossRefGoogle Scholar
  26. [26]
    C. Csáki, A. Falkowski and A. Weiler, The flavor of the composite pseudo-goldstone Higgs, JHEP 09 (2008) 008 [arXiv:0804.1954] [INSPIRE].ADSCrossRefGoogle Scholar
  27. [27]
    C. Aubin, J. Laiho and R.S. Van de Water, The neutral kaon mixing parameter B K from unquenched mixed-action lattice QCD, Phys. Rev. D 81 (2010) 014507 [arXiv:0905.3947] [INSPIRE].ADSGoogle Scholar
  28. [28]
    Y. Aoki et al., Continuum Limit of B K from 2 + 1 Flavor Domain Wall QCD, Phys. Rev. D 84 (2011) 014503 [arXiv:1012.4178] [INSPIRE].ADSGoogle Scholar
  29. [29]
    J. Laiho and R.S. Van de Water, Pseudoscalar decay constants, light-quark masses and B K from mixed-action lattice QCD, PoS(LATTICE 2011) 293 [arXiv:1112.4861] [INSPIRE].
  30. [30]
    S. Dürr et al., Precision computation of the kaon bag parameter, Phys. Lett. B 705 (2011) 477 [arXiv:1106.3230] [INSPIRE].ADSCrossRefGoogle Scholar
  31. [31]
    T. Bae et al., Kaon B-parameter from improved staggered fermions in N f = 2 + 1 QCD, Phys. Rev. Lett. 109 (2012) 041601 [arXiv:1111.5698] [INSPIRE].ADSCrossRefGoogle Scholar
  32. [32]
    G. Colangelo et al., Review of lattice results concerning low energy particle physics, Eur. Phys. J. C 71 (2011) 1695 [arXiv:1011.4408] [INSPIRE].ADSCrossRefGoogle Scholar
  33. [33]
    P. Dimopoulos, \( {K^0}-{{\overline{K}}^0} \) on the Lattice, arXiv:1101.3069 [INSPIRE].
  34. [34]
    J. Laiho, Light quark physics from lattice QCD, arXiv:1106.0457 [INSPIRE].
  35. [35]
    RBC and QKQCD collaborations, J. Wennekers, Neutral Kaon Mixing Beyond the Standard Model from 2+1 Flavour Domain Wall QCD, PoS(LATTICE 2008) 269 [arXiv:0810.1841] [INSPIRE].
  36. [36]
    CP-PACS collaboration, Y. Nakamura et al., Kaon B-parameters for Generic ΔS = 2 Four-Quark Operators in Quenched Domain Wall QCD, PoS(LAT2006) 089 [hep-lat/0610075] [INSPIRE].
  37. [37]
    M. Bochicchio, L. Maiani, G. Martinelli, G.C. Rossi and M. Testa, Chiral Symmetry on the Lattice with Wilson Fermions, Nucl. Phys. B 262 (1985) 331 [INSPIRE].ADSCrossRefGoogle Scholar
  38. [38]
    K. Osterwalder and E. Seiler, Gauge Field Theories on the Lattice, Annals Phys. 110 (1978) 440 [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  39. [39]
    P. Dimopoulos, H. Simma and A. Vladikas, Quenched B K -parameter from Osterwalder-Seiler tmQCD quarks and mass-splitting discretization effects, JHEP 07 (2009) 007 [arXiv:0902.1074] [INSPIRE].Google Scholar
  40. [40]
    N. Carrasco et al., \( {K^0}-{{\overline{K}}^0} \) mixing in the Standard Model from N f = 2 + 1 + 1 Twisted Mass Lattice QCD, PoS(LATTICE 2011) 276 [arXiv:1111.1262] [INSPIRE].
  41. [41]
    F. Farchioni et al., Pseudoscalar decay constants from N f = 2 + 1 + 1 twisted mass lattice QCD, PoS(LATTICE 2010) 128 [arXiv:1012.0200] [INSPIRE].
  42. [42]
    ETM collaboration, S. Dinter et al., Sigma terms and strangeness content of the nucleon with N f = 2 + 1 + 1 twisted mass fermions, JHEP 08 (2012) 037 [arXiv:1202.1480] [INSPIRE].ADSCrossRefGoogle Scholar
  43. [43]
    R. Frezzotti, G. Martinelli, M. Papinutto and G. Rossi, Reducing cutoff effects in maximally twisted lattice QCD close to the chiral limit, JHEP 04 (2006) 038 [hep-lat/0503034] [INSPIRE].ADSCrossRefGoogle Scholar
  44. [44]
    S.R. Sharpe and J.M. Wu, Twisted mass chiral perturbation theory at next-to-leading order, Phys. Rev. D 71 (2005) 074501 [hep-lat/0411021] [INSPIRE].ADSGoogle Scholar
  45. [45]
    S. Aoki and O. Bär, Twisted-mass QCD, O(a) improvement and Wilson chiral perturbation theory, Phys. Rev. D 70 (2004) 116011 [hep-lat/0409006] [INSPIRE].ADSGoogle Scholar
  46. [46]
    ETM collaboration, P. Boucaud et al., Dynamical twisted mass fermions with light quarks, Phys. Lett. B 650 (2007) 304 [hep-lat/0701012] [INSPIRE].ADSCrossRefGoogle Scholar
  47. [47]
    ETM collaboration, P. Boucaud et al., Dynamical Twisted Mass Fermions with Light Quarks: Simulation and Analysis Details, Comput. Phys. Commun. 179 (2008) 695 [arXiv:0803.0224] [INSPIRE].ADSCrossRefGoogle Scholar
  48. [48]
    P. Weisz, Continuum Limit Improved Lattice Action for Pure Yang-Mills Theory. 1., Nucl. Phys. B 212 (1983) 1 [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  49. [49]
    ETM collaboration, B. Blossier et al., Average up/down, strange and charm quark masses with N f = 2 twisted mass lattice QCD, Phys. Rev. D 82 (2010) 114513 [arXiv:1010.3659] [INSPIRE].ADSGoogle Scholar
  50. [50]
    D. Becirevic and G. Villadoro, Remarks on the hadronic matrix elements relevant to the SUSY \( {K^0}-{{\overline{K}}^0} \) mixing amplitude, Phys. Rev. D 70 (2004) 094036 [hep-lat/0408029] [INSPIRE].ADSGoogle Scholar
  51. [51]
    A. Donini, V. Giménez, G. Martinelli, M. Talevi and A. Vladikas, Nonperturbative renormalization of lattice four fermion operators without power subtractions, Eur. Phys. J. C 10 (1999) 121 [hep-lat/9902030] [INSPIRE].ADSGoogle Scholar
  52. [52]
    M. Ciuchini et al., Next-to-leading order QCD corrections to ΔF = 2 effective Hamiltonians, Nucl. Phys. B 523 (1998) 501 [hep-ph/9711402] [INSPIRE].ADSCrossRefGoogle Scholar
  53. [53]
    S. Weinberg, The quantum theory of fields, I, Cambridge University Press, Cambridge U.K. (1996).Google Scholar
  54. [54]
    M. Constantinou, V. Lubicz, H. Panagopoulos and F. Stylianou, O(a 2) corrections to the one-loop propagator and bilinears of clover fermions with Symanzik improved gluons, JHEP 10 (2009) 064 [arXiv:0907.0381] [INSPIRE].ADSCrossRefGoogle Scholar
  55. [55]
    M. Constantinou et al., Perturbative renormalization factors and O(a 2) corrections for lattice 4-fermion operators with improved fermion/gluon actions, Phys. Rev. D 83 (2011) 074503 [arXiv:1011.6059] [INSPIRE].ADSGoogle Scholar
  56. [56]
    K. Chetyrkin and A. Retey, Renormalization and running of quark mass and field in the regularization invariant and MS-bar schemes at three loops and four loops, Nucl. Phys. B 583 (2000) 3 [hep-ph/9910332] [INSPIRE].ADSCrossRefGoogle Scholar

Copyright information

© SISSA 2013

Authors and Affiliations

  • The ETM collaboration
  • V. Bertone
    • 1
  • N. Carrasco
    • 2
  • M. Ciuchini
    • 3
  • P. Dimopoulos
    • 4
  • R. Frezzotti
    • 4
    • 5
  • V. Giménez
    • 2
  • V. Lubicz
    • 6
    • 3
  • G. Martinelli
    • 7
    • 8
  • F. Mescia
    • 9
  • M. Papinutto
    • 10
    • 11
  • G. C. Rossi
    • 4
    • 5
  • L. Silvestrini
    • 8
  • S. Simula
    • 3
  • C. Tarantino
    • 6
    • 3
  • A. Vladikas
    • 5
  1. 1.Physikalisches InstitutAlbert-Ludwigs-Universität FreiburgFreiburg i. BGermany
  2. 2.Departament de Física Teòrica and IFICUniversitat de València-CSICValènciaSpain
  3. 3.INFN, Sezione di Roma Tre, c/o Dipartimento di FisicaUniversità Roma TreRomeItaly
  4. 4.Dipartimento di FisicaUniversità di Roma “Tor Vergata”RomeItaly
  5. 5.INFN, Sezione di “Tor Vergata”, c/o Dipartimento di FisicaUniversità di Roma “Tor Vergata”RomeItaly
  6. 6.Dipartimento di FisicaUniversità Roma TreRomeItaly
  7. 7.Scuola Internazionale Superiore di Studi Avanzati (SISSA)TriesteItaly
  8. 8.NFN, Sezione di RomaRomeItaly
  9. 9.Departament d’Estructura i Constituents de la Matèria, and Institut de Ciències del CosmosUniversitat de BarcelonaBarcelonaSpain
  10. 10.Laboratoire de Physique Subatomique et de Cosmologie, UJF/CNRS-IN2P3/INPGGrenobleFrance
  11. 11.Departamento de Física Teórica and Instituto de Física Teórica UAM/CSICUniversidad Autónoma de MadridMadridSpain

Personalised recommendations