Short distance singularities and automatic O(a) improvement: the cases of the chiral condensate and the topological susceptibility

  • Krzysztof Cichy
  • Elena Garcia-Ramos
  • Karl Jansen
Open Access
Regular Article - Theoretical Physics


Short-distance singularities in lattice correlators can modify their Symanzik expansion by leading to additional O(a) lattice artifacts. At the example of the chiral condensate and the topological susceptibility, we show how to account for these lattice artifacts for Wilson twisted mass fermions and show that the property of automatic O(a) improvement is preserved at maximal twist.


Lattice QCD Lattice Gauge Field Theories Lattice Quantum Field Theory 


Open Access

This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.


  1. [1]
    K. Cichy, E. Garcia-Ramos and K. Jansen, Chiral condensate from the twisted mass Dirac operator spectrum, JHEP 10 (2013) 175 [arXiv:1303.1954] [INSPIRE].ADSCrossRefGoogle Scholar
  2. [2]
    ETM collaboration, K. Cichy, E. Garcia-Ramos and K. Jansen, Topological susceptibility from the twisted mass Dirac operator spectrum, JHEP 02 (2014) 119 [arXiv:1312.5161] [INSPIRE].ADSGoogle Scholar
  3. [3]
    L. Giusti and M. Lüscher, Chiral symmetry breaking and the Banks-Casher relation in lattice QCD with Wilson quarks, JHEP 03 (2009) 013 [arXiv:0812.3638] [INSPIRE].ADSCrossRefGoogle Scholar
  4. [4]
    K. Symanzik, Continuum Limit and Improved Action in Lattice Theories. 1. Principles and ϕ 4 Theory, Nucl. Phys. B 226 (1983) 187 [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  5. [5]
    M. Lüscher, S. Sint, R. Sommer and P. Weisz, Chiral symmetry and O(a) improvement in lattice QCD, Nucl. Phys. B 478 (1996) 365 [hep-lat/9605038] [INSPIRE].ADSCrossRefGoogle Scholar
  6. [6]
    R. Frezzotti and G.C. Rossi, Chirally improving Wilson fermions. 1. O(a) improvement, JHEP 08 (2004) 007 [hep-lat/0306014] [INSPIRE].ADSCrossRefGoogle Scholar
  7. [7]
    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].ADSCrossRefGoogle Scholar
  8. [8]
    K.G. Wilson, Nonlagrangian models of current algebra, Phys. Rev. 179 (1969) 1499 [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  9. [9]
    D.B. Renner, X. Feng, K. Jansen and M. Petschlies, Nonperturbative QCD corrections to electroweak observables, PoS(LATTICE 2011)022 [arXiv:1206.3113] [INSPIRE].
  10. [10]
    ETM collaboration, F. Burger et al., Four-Flavour Leading-Order Hadronic Contribution To The Muon Anomalous Magnetic Moment, JHEP 02 (2014) 099 [arXiv:1308.4327] [INSPIRE].Google Scholar
  11. [11]
    K. Cichy, E. Garcia-Ramos, K. Jansen and A. Shindler, Computation of the chiral condensate using N f = 2 and N f = 2 + 1 + 1 dynamical flavors of twisted mass fermions, PoS(LATTICE 2013) 128 [arXiv:1312.3534] [INSPIRE].
  12. [12]
    K. Cichy, E. Garcia-Ramos, K. Jansen and A. Shindler, Topological susceptibility from twisted mass fermions using spectral projectors, PoS(LATTICE 2013)129 [arXiv:1312.3535] [INSPIRE].
  13. [13]
    A. Shindler, Chiral Ward identities, automatic O(a) improvement and the gradient flow, Nucl. Phys. B 881 (2014) 71 [arXiv:1312.4908] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  14. [14]
    R. Frezzotti and G.C. Rossi, Twisted mass lattice QCD with mass nondegenerate quarks, Nucl. Phys. Proc. Suppl. 128 (2004) 193 [hep-lat/0311008] [INSPIRE].ADSCrossRefGoogle Scholar
  15. [15]
    M. Lüscher, Topological effects in QCD and the problem of short distance singularities, Phys. Lett. B 593 (2004) 296 [hep-th/0404034] [INSPIRE].ADSCrossRefGoogle Scholar
  16. [16]
    ALPHA collaboration, R. Frezzotti, S. Sint and P. Weisz, O(a) improved twisted mass lattice QCD, JHEP 07 (2001) 048 [hep-lat/0104014] [INSPIRE].Google Scholar
  17. [17]
    A. Shindler, Twisted mass lattice QCD, Phys. Rept. 461 (2008) 37 [arXiv:0707.4093] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  18. [18]
    T. Banks and A. Casher, Chiral Symmetry Breaking in Confining Theories, Nucl. Phys. B 169 (1980) 103 [INSPIRE].ADSCrossRefGoogle Scholar
  19. [19]
    G.P. Engel, L. Giusti, S. Lottini and R. Sommer, Chiral symmetry breaking in QCD Lite, Phys. Rev. Lett. 114 (2015) 112001 [arXiv:1406.4987] [INSPIRE].ADSCrossRefGoogle Scholar
  20. [20]
    M. Lüscher and F. Palombi, Universality of the topological susceptibility in the SU(3) gauge theory, JHEP 09 (2010) 110 [arXiv:1008.0732] [INSPIRE].ADSCrossRefMATHGoogle Scholar
  21. [21]
    F. Burger, G. Hotzel, K. Jansen and M. Petschlies, The hadronic vacuum polarization and automatic \( \mathcal{O}(a) \) improvement for twisted mass fermions, JHEP 03 (2015) 073 [arXiv:1412.0546] [INSPIRE].ADSCrossRefGoogle Scholar

Copyright information

© The Author(s) 2015

Authors and Affiliations

  • Krzysztof Cichy
    • 1
    • 2
  • Elena Garcia-Ramos
    • 1
    • 3
  • Karl Jansen
    • 1
  1. 1.NIC, DESYZeuthenGermany
  2. 2.Adam Mickiewicz University, Faculty of PhysicsPoznanPoland
  3. 3.Humboldt Universität zu BerlinBerlinGermany

Personalised recommendations