Abstract
The vacuum polarization tensor and the corresponding vacuum polarization function are the basis for calculations of numerous observables in lattice QCD. Examples are the hadronic contributions to lepton anomalous magnetic moments, the running of the electroweak and strong couplings and quark masses. Quantities which are derived from the vacuum polarization tensor often involve a summation of current correlators over all distances in position space leading thus to the appearance of short-distance terms. The mechanism of \( \mathcal{O}(a) \) improvement in the presence of such short-distance terms is not directly covered by the usual arguments of on-shell improvement of the action and the operators for a given quantity. If such short-distance contributions appear, the property of \( \mathcal{O}(a) \) improvement needs to be reconsidered. We discuss the effects of these short-distance terms on the vacuum polarization function for twisted mass lattice QCD and find that even in the presence of such terms automatic \( \mathcal{O}(a) \) improvement is retained if the theory is tuned to maximal twist.
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References
T. Blum, Lattice calculation of the lowest order hadronic contribution to the muon anomalous magnetic moment, Phys. Rev. Lett. 91 (2003) 052001 [hep-lat/0212018] [INSPIRE].
QCDSF collaboration, M. Gockeler et al., Vacuum polarization and hadronic contribution to muon g − 2 from lattice QCD, Nucl. Phys. B 688 (2004) 135 [hep-lat/0312032] [INSPIRE].
C. Aubin and T. Blum, Calculating the hadronic vacuum polarization and leading hadronic contribution to the muon anomalous magnetic moment with improved staggered quarks, Phys. Rev. D 75 (2007) 114502 [hep-lat/0608011] [INSPIRE].
X. Feng, K. Jansen, M. Petschlies and D.B. Renner, Two-flavor QCD correction to lepton magnetic moments at leading-order in the electromagnetic coupling, Phys. Rev. Lett. 107 (2011) 081802 [arXiv:1103.4818] [INSPIRE].
P. Boyle, L. Del Debbio, E. Kerrane and J. Zanotti, Lattice determination of the hadronic contribution to the muon g − 2 using dynamical domain wall fermions, Phys. Rev. D 85 (2012) 074504 [arXiv:1107.1497] [INSPIRE].
M. Della Morte, B. Jager, A. Juttner and H. Wittig, Towards a precise lattice determination of the leading hadronic contribution to (g − 2) μ , JHEP 03 (2012) 055 [arXiv:1112.2894] [INSPIRE].
D. Bernecker and H.B. Meyer, Vector correlators in lattice QCD: methods and applications, Eur. Phys. J. A 47 (2011) 148 [arXiv:1107.4388] [INSPIRE].
C. Aubin, T. Blum, M. Golterman and S. Peris, Model-independent parametrization of the hadronic vacuum polarization and g − 2 for the muon on the lattice, Phys. Rev. D 86 (2012) 054509 [arXiv:1205.3695] [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].
X. Feng et al., Computing the hadronic vacuum polarization function by analytic continuation, Phys. Rev. D 88 (2013) 034505 [arXiv:1305.5878] [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].
T. Blum et al., The muon (g − 2) theory value: present and future, arXiv:1311.2198 [INSPIRE].
R. Frezzotti and G.C. Rossi, Chirally improving Wilson fermions. 1. O(a) improvement, JHEP 08 (2004) 007 [hep-lat/0306014] [INSPIRE].
A. Shindler, Twisted mass lattice QCD, Phys. Rept. 461 (2008) 37 [arXiv:0707.4093] [INSPIRE].
K. Symanzik, Continuum limit and improved action in lattice theories. 1. principles and ϕ 4 theory, Nucl. Phys. B 226 (1983) 187 [INSPIRE].
K. Symanzik, Continuum limit and improved action in lattice theories. 2. O(N ) nonlinear σ-model in perturbation theory, Nucl. Phys. B 226 (1983) 205 [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].
K. Cichy, E. Garcia-Ramos and K. Jansen, Short distance singularities and automatic O(a) improvement: the cases of the chiral condensate and the topological susceptibility, arXiv:1412.0456 [INSPIRE].
R. Baron, P. Boucaud, J. Carbonell, A. Deuzeman, V. Drach 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].
K. Osterwalder and E. Seiler, Gauge field theories on the lattice, Annals Phys. 110 (1978) 440 [INSPIRE].
R. Frezzotti and G.C. Rossi, Chirally improving Wilson fermions. II. Four-quark operators, JHEP 10 (2004) 070 [hep-lat/0407002] [INSPIRE].
M. Petschlies et al., private communication.
R. Frezzotti, G. Martinelli, M. Papinutto and G.C. Rossi, Reducing cutoff effects in maximally twisted lattice QCD close to the chiral limit, JHEP 04 (2006) 038 [hep-lat/0503034] [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].
P. Weisz, Renormalization and lattice artifacts, arXiv:1004.3462 [INSPIRE].
B. Sheikholeslami and R. Wohlert, Improved continuum limit lattice action for QCD with Wilson fermions, Nucl. Phys. B 259 (1985) 572 [INSPIRE].
M. Constantinou et al., The chromomagnetic operator on the lattice, PoS(LATTICE 2013)316 [arXiv:1311.5057] [INSPIRE].
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].
M. Luscher and P. Weisz, On-shell improved lattice gauge theories, Commun. Math. Phys. 97 (1985) 59 [Erratum ibid. 98 (1985) 433] [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.C. Rossi, Twisted mass lattice QCD with mass nondegenerate quarks, Nucl. Phys. Proc. Suppl. 128 (2004) 193 [hep-lat/0311008] [INSPIRE].
ETM collaboration, R. Baron et al., Light meson physics from maximally twisted mass lattice QCD, JHEP 08 (2010) 097 [arXiv:0911.5061] [INSPIRE].
ETM collaboration, P. Dimopoulos, R. Frezzotti, G. Herdoiza, C. Urbach and U. Wenger, Scaling and low energy constants in lattice QCD with N f = 2 maximally twisted Wilson quarks, PoS(LATTICE 2007)102 [arXiv:0710.2498] [INSPIRE].
ETM collaboration, C. Alexandrou et al., Light baryon masses with dynamical twisted mass fermions, Phys. Rev. D 78 (2008) 014509 [arXiv:0803.3190] [INSPIRE].
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Burger, F., Hotzel, G., Jansen, K. et al. The hadronic vacuum polarization and automatic \( \mathcal{O}(a) \) improvement for twisted mass fermions. J. High Energ. Phys. 2015, 73 (2015). https://doi.org/10.1007/JHEP03(2015)073
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DOI: https://doi.org/10.1007/JHEP03(2015)073