Abstract
We present results of our computation of the topological susceptibility with N f = 2 and N f = 2 + 1 + 1 flavours of maximally twisted mass fermions, using the method of spectral projectors. We perform a detailed study of the quark mass dependence and discretization effects. We make an attempt to confront our data with chiral perturbation theory and extract the chiral condensate from the quark mass dependence of the topological susceptibility. We compare the value with the results of our direct computation from the slope of the mode number. We emphasize the role of autocorrelations and the necessity of long Monte Carlo runs to obtain results with good precision. We also show our results for the spectral projector computation of the ratio of renormalization constants Z P /Z S .
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
E. Witten, Current algebra theorems for the U(1) Goldstone boson, Nucl. Phys. B 156 (1979) 269 [INSPIRE].
G. Veneziano, U(1) without instantons, Nucl. Phys. B 159 (1979) 213 [INSPIRE].
M. Creutz, Anomalies, gauge field topology and the lattice, Annals Phys. 326 (2011) 911 [arXiv:1007.5502] [INSPIRE].
P. Hasenfratz, V. Laliena and F. Niedermayer, The index theorem in QCD with a finite cutoff, Phys. Lett. B 427 (1998) 125 [hep-lat/9801021] [INSPIRE].
L. Giusti, G. Rossi, M. Testa and G. Veneziano, The U(A)(1) problem on the lattice with Ginsparg-Wilson fermions, Nucl. Phys. B 628 (2002) 234 [hep-lat/0108009] [INSPIRE].
L. Giusti, G. Rossi and M. Testa, Topological susceptibility in full QCD with Ginsparg-Wilson fermions, Phys. Lett. B 587 (2004) 157 [hep-lat/0402027] [INSPIRE].
M. Lüscher, Topological effects in QCD and the problem of short distance singularities, Phys. Lett. B 593 (2004) 296 [hep-th/0404034] [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].
M. Lüscher and F. Palombi, Universality of the topological susceptibility in the SU(3) gauge theory, JHEP 09 (2010) 110 [arXiv:1008.0732] [INSPIRE].
S. Schaefer and F. Virotta, Autocorrelations in hybrid Monte Carlo simulations, PoS (LATTICE 2010) 042 [arXiv:1011.5151] [INSPIRE].
ETM collaboration, P. Boucaud et al., Dynamical twisted mass fermions with light quarks, Phys. Lett. B 650 (2007) 304 [hep-lat/0701012] [INSPIRE].
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].
ETM collaboration, R. Baron et al., Light meson physics from maximally twisted mass lattice QCD, JHEP 08 (2010) 097 [arXiv:0911.5061] [INSPIRE].
R. Baron et al., Light hadrons from lattice QCD with light (u, d), strange and charm dynamical quarks, JHEP 06 (2010) 111 [arXiv:1004.5284] [INSPIRE].
European Twisted Mass collaboration, R. Baron et al., Computing K and D meson masses with N f = 2 + 1 + 1 twisted mass lattice QCD, Comput. Phys. Commun. 182 (2011) 299 [arXiv:1005.2042] [INSPIRE].
ETM collaboration, R. Baron et al., Light hadrons from N f = 2 + 1 + 1 dynamical twisted mass fermions, PoS (LATTICE 2010) 123 [arXiv:1101.0518] [INSPIRE].
P. Weisz, Continuum limit improved lattice action for pure Yang-Mills theory. 1, Nucl. Phys. B 212 (1983) 1 [INSPIRE].
Y. Iwasaki, Renormalization group analysis of lattice theories and improved lattice action: two-dimensional nonlinear O(N) σ-model, Nucl. Phys. B 258 (1985) 141 [INSPIRE].
Y. Iwasaki, K. Kanaya, T. Kaneko and T. Yoshie, Scaling in SU(3) pure gauge theory with a renormalization group improved action, Phys. Rev. D 56 (1997) 151 [hep-lat/9610023] [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].
R. Frezzotti and G. Rossi, Chirally improving Wilson fermions. 1. O(a) improvement, JHEP 08 (2004) 007 [hep-lat/0306014] [INSPIRE].
R. Frezzotti and G. Rossi, Chirally improving Wilson fermions. II. Four-quark operators, JHEP 10 (2004) 070 [hep-lat/0407002] [INSPIRE].
A. Shindler, Twisted mass lattice QCD, Phys. Rept. 461 (2008) 37 [arXiv:0707.4093] [INSPIRE].
R. Frezzotti and G. Rossi, Twisted mass lattice QCD with mass nondegenerate quarks, Nucl. Phys. Proc. Suppl. 128 (2004) 193 [hep-lat/0311008] [INSPIRE].
T. Chiarappa et al., Numerical simulation of QCD with u, d, s and c quarks in the twisted-mass Wilson formulation, Eur. Phys. J. C 50 (2007) 373 [hep-lat/0606011] [INSPIRE].
F. Farchioni et al., Exploring the phase structure of lattice QCD with twisted mass quarks, Nucl. Phys. Proc. Suppl. 140 (2005) 240 [hep-lat/0409098] [INSPIRE].
F. Farchioni et al., The phase structure of lattice QCD with Wilson quarks and renormalization group improved gluons, Eur. Phys. J. C 42 (2005) 73 [hep-lat/0410031] [INSPIRE].
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].
XLF collaboration, K. Jansen, M. Papinutto, A. Shindler, C. Urbach and I. Wetzorke, Quenched scaling of Wilson twisted mass fermions, JHEP 09 (2005) 071 [hep-lat/0507010] [INSPIRE].
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].
ETM collaboration, K. Jansen, F. Karbstein, A. Nagy and M. Wagner, \( {\varLambda_{{\overline{M}S}}} \) from the static potential for QCD with N f = 2 dynamical quark flavors, JHEP 01 (2012) 025 [arXiv:1110.6859] [INSPIRE].
ETM collaboration, K. Ottnad et al., η and η ′ mesons from N f = 2 + 1 + 1 twisted mass lattice QCD, JHEP 11 (2012) 048 [arXiv:1206.6719] [INSPIRE].
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].
C. Alexandrou, M. Constantinou, T. Korzec, H. Panagopoulos and F. Stylianou, Renormalization constants of local operators for Wilson type improved fermions, Phys. Rev. D 86 (2012) 014505 [arXiv:1201.5025] [INSPIRE].
K. Cichy, K. Jansen and P. Korcyl, Non-perturbative renormalization in coordinate space for N f = 2 maximally twisted mass fermions with tree-level Symanzik improved gauge action, Nucl. Phys. B 865 (2012) 268 [arXiv:1207.0628] [INSPIRE].
D. Palao, ETMC preliminary result for N f = 4 renormalization constants, private communication.
ETM collaboration, B. Blossier et al., Renormalisation constants of quark bilinears in lattice QCD with four dynamical Wilson quarks, PoS (LATTICE 2011) 233 [arXiv:1112.1540] [INSPIRE].
ETM collaboration, P. Dimopoulos et al., Renormalization constants for Wilson fermion lattice QCD with four dynamical flavours, PoS (LATTICE 2010) 235 [arXiv:1101.1877] [INSPIRE].
G. Colangelo, S. Dürr and C. Haefeli, Finite volume effects for meson masses and decay constants, Nucl. Phys. B 721 (2005) 136 [hep-lat/0503014] [INSPIRE].
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].
ALPHA collaboration, U. Wolff, Monte Carlo errors with less errors, Comput. Phys. Commun. 156 (2004) 143 [Erratum ibid. 176 (2007) 383] [hep-lat/0306017] [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].
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, Short distance singularities and automatic O(a) improvement, in preparation.
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
Consortia
Corresponding author
Additional information
ArXiv ePrint: 1312.5161
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
The ETM collaboration., Cichy, K., Garcia-Ramos, E. et al. Topological susceptibility from the twisted mass Dirac operator spectrum. J. High Energ. Phys. 2014, 119 (2014). https://doi.org/10.1007/JHEP02(2014)119
Received:
Revised:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP02(2014)119