Journal of High Energy Physics

, 2010:27 | Cite as

Renormalization of minimally doubled fermions

  • Stefano Capitani
  • Michael Creutz
  • Johannes Weber
  • Hartmut Wittig
Article

Abstract

We investigate the renormalization properties of minimally doubled fermions, at one loop in perturbation theory. Our study is based on the two particular realizations of Boriçi-Creutz and Karsten-Wilczek. A common feature of both formulations is the breaking of hyper-cubic symmetry, which requires that the lattice actions are supplemented by suitable counterterms. We show that three counterterms are required in each case and determine their coefficients to one loop in perturbation theory. For both actions we compute the vacuum polarization of the gluon. It is shown that no power divergences appear and that all contributions which arise from the breaking of Lorentz symmetry are cancelled by the counterterms. We also derive the conserved vector and axial-vector currents for Karsten-Wilczek fermions. Like in the case of the previously studied Boriçi-Creutz action, one obtains simple expressions, involving only nearest-neighbour sites. We suggest methods how to fix the coefficients of the counterterms non-perturbatively and discuss the implications of our findings for practical simulations.

Keywords

Lattice QCD Lattice Gauge Field Theories Global Symmetries 

References

  1. [1]
    L.H. Karsten, Lattice Fermions in Euclidean Space-Time, Phys. Lett. B 104 (1981) 315 [SPIRES].ADSMATHGoogle Scholar
  2. [2]
    F. Wilczek, Lattice Fermions, Phys. Rev. Lett. 59 (1987) 2397 [SPIRES].MathSciNetADSCrossRefGoogle Scholar
  3. [3]
    M. Creutz, Four-dimensional graphene and chiral fermions, JHEP 04 (2008) 017 [arXiv:0712.1201] [SPIRES].ADSCrossRefGoogle Scholar
  4. [4]
    A. Boriçi, Creutz fermions on an orthogonal lattice, Phys. Rev. D 78 (2008) 074504 [arXiv:0712.4401] [SPIRES].ADSGoogle Scholar
  5. [5]
    K. Cichy, J. Gonzalez Lopez, K. Jansen, A. Kujawa and A. Shindler, Twisted Mass, Overlap and Creutz Fermions: Cut-off Effects at Tree-level of Perturbation Theory, Nucl. Phys. B 800 (2008) 94 [arXiv:0802.3637] [SPIRES].ADSCrossRefGoogle Scholar
  6. [6]
    P.F. Bedaque, M.I. Buchoff, B.C. Tiburzi and A. Walker-Loud, Broken Symmetries from Minimally Doubled Fermions, Phys. Lett. B 662 (2008) 449 [arXiv:0801.3361] [SPIRES].MathSciNetADSGoogle Scholar
  7. [7]
    P.F. Bedaque, M.I. Buchoff, B.C. Tiburzi and A. Walker-Loud, Search for Fermion Actions on Hyperdiamond Lattices, Phys. Rev. D 78 (2008) 017502 [arXiv:0804.1145] [SPIRES].ADSGoogle Scholar
  8. [8]
    M.I. Buchoff, Search for Chiral Fermion Actions on Non-Orthogonal Lattices, PoS(LATTICE2008)068 [arXiv:0809.3943] [SPIRES].
  9. [9]
    M. Creutz, Local chiral fermions, PoS(LATTICE2008)080 [arXiv:0808.0014] [SPIRES].
  10. [10]
    A. Boriçi, Minimally Doubled Fermion Revival, PoS(LATTICE 2008)231 [arXiv:0812.0092] [SPIRES].
  11. [11]
    S. Capitani, J. Weber and H. Wittig, Minimally doubled fermions at one loop, Phys. Lett. B 681 (2009) 105 [arXiv:0907.2825] [SPIRES].MathSciNetADSGoogle Scholar
  12. [12]
    S. Capitani, J. Weber and H. Wittig, Minimally doubled fermions at one-loop level, arXiv:0910.2597 [SPIRES].
  13. [13]
    T. Kimura and T. Misumi, Characters of Lattice Fermions Based on the Hyperdiamond Lattice, arXiv:0907.1371 [SPIRES].
  14. [14]
    T. Kimura and T. Misumi, Lattice Fermions Based on Higher-Dimensional Hyperdiamond Lattices, Prog. Theor. Phys. 123 (2010) 63 [arXiv:0907.3774] [SPIRES].ADSMATHCrossRefGoogle Scholar
  15. [15]
    H.B. Nielsen and M. Ninomiya, Absence of Neutrinos on a Lattice. 1. Proof by Homotopy Theory, Nucl. Phys. B 185 (1981) 20 [SPIRES].MathSciNetADSCrossRefGoogle Scholar
  16. [16]
    H.B. Nielsen and M. Ninomiya, Absence of Neutrinos on a Lattice. 2. Intuitive Topological Proof, Nucl. Phys. B 193 (1981) 173 [SPIRES].MathSciNetADSCrossRefGoogle Scholar
  17. [17]
    H.B. Nielsen and M. Ninomiya, No Go Theorem for Regularizing Chiral Fermions, Phys. Lett. B 105 (1981) 219 [SPIRES].ADSGoogle Scholar
  18. [18]
    B. Sheikholeslami and R. Wohlert, Improved Continuum Limit Lattice Action for QCD with Wilson Fermions, Nucl. Phys. B 259 (1985) 572 [SPIRES].ADSCrossRefGoogle Scholar
  19. [19]
    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 [SPIRES].ADSCrossRefGoogle Scholar
  20. [20]
    A. González-Arroyo and C.P. Korthals-Altes, Asymptotic Freedom Scales For Any Lattice Action, Nucl. Phys. B 205 (1982) 46 [SPIRES].ADSCrossRefGoogle Scholar
  21. [21]
    R.K. Ellis and G. Martinelli, Two Loop Corrections To The Lambda Parameters Of One Plaquette Actions, Nucl. Phys. B 235 (1984) 93 [SPIRES].ADSCrossRefGoogle Scholar
  22. [22]
    S. Capitani, Lattice perturbation theory, Phys. Rept. 382 (2003) 113 [hep-lat/0211036] [SPIRES].MathSciNetADSMATHCrossRefGoogle Scholar
  23. [23]
    J.A.M. Vermaseren, New features of FORM, math-ph/0010025 [SPIRES].
  24. [24]
    J.A.M. Vermaseren, The FORM project, Nucl. Phys. Proc. Suppl. 183 (2008) 19 [arXiv:0806.4080] [SPIRES].ADSCrossRefGoogle Scholar

Copyright information

© SISSA, Trieste, Italy 2010

Authors and Affiliations

  • Stefano Capitani
    • 1
  • Michael Creutz
    • 1
    • 2
  • Johannes Weber
    • 1
    • 3
  • Hartmut Wittig
    • 1
  1. 1.Institut für Kernphysik, Becher Weg 45University of MainzMainzGermany
  2. 2.Physics DepartmentBrookhaven National LaboratoryUptonU.S.A.
  3. 3.Graduate School of Pure and Applied PhysicsTsukuba UniversityTsukubaJapan

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