Abstract
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.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
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].
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].
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].
K. Symanzik, Continuum Limit and Improved Action in Lattice Theories. 1. Principles and ϕ 4 Theory, Nucl. Phys. B 226 (1983) 187 [INSPIRE].
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].
R. Frezzotti and G.C. Rossi, Chirally improving Wilson fermions. 1. O(a) improvement, JHEP 08 (2004) 007 [hep-lat/0306014] [INSPIRE].
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].
K.G. Wilson, Nonlagrangian models of current algebra, Phys. Rev. 179 (1969) 1499 [INSPIRE].
D.B. Renner, X. Feng, K. Jansen and M. Petschlies, Nonperturbative QCD corrections to electroweak observables, PoS(LATTICE 2011)022 [arXiv:1206.3113] [INSPIRE].
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].
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].
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].
A. Shindler, Chiral Ward identities, automatic O(a) improvement and the gradient flow, Nucl. Phys. B 881 (2014) 71 [arXiv:1312.4908] [INSPIRE].
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].
M. Lüscher, Topological effects in QCD and the problem of short distance singularities, Phys. Lett. B 593 (2004) 296 [hep-th/0404034] [INSPIRE].
ALPHA collaboration, R. Frezzotti, S. Sint and P. Weisz, O(a) improved twisted mass lattice QCD, JHEP 07 (2001) 048 [hep-lat/0104014] [INSPIRE].
A. Shindler, Twisted mass lattice QCD, Phys. Rept. 461 (2008) 37 [arXiv:0707.4093] [INSPIRE].
T. Banks and A. Casher, Chiral Symmetry Breaking in Confining Theories, Nucl. Phys. B 169 (1980) 103 [INSPIRE].
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].
M. Lüscher and F. Palombi, Universality of the topological susceptibility in the SU(3) gauge theory, JHEP 09 (2010) 110 [arXiv:1008.0732] [INSPIRE].
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].
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.
Author information
Authors and Affiliations
Corresponding author
Additional information
ArXiv ePrint: 1412.0456
Rights and permissions
Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (https://creativecommons.org/licenses/by/4.0), which permits use, duplication, adaptation, distribution, and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
About this article
Cite this article
Cichy, K., Garcia-Ramos, E. & Jansen, K. Short distance singularities and automatic O(a) improvement: the cases of the chiral condensate and the topological susceptibility. J. High Energ. Phys. 2015, 48 (2015). https://doi.org/10.1007/JHEP04(2015)048
Received:
Revised:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP04(2015)048