The hadronic vacuum polarization and automatic O(a) improvement for twisted mass fermions

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 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 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 O(a) improvement is retained if the theory is tuned to maximal twist.

arXiv comment25 pages, 1 ancillary file; version published in JHEP

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Cited by in corpus (9)

• First Physics Results at the Physical Pion Mass from $N_f=2$ Wilson Twisted Mass Fermions at Maximal Twist
• The light-quark contribution to the leading HVP term of the muon $g-2$ from twisted-mass fermions
• Strange and charm HVP contributions to the muon ($g-2)$ including QED corrections with twisted-mass fermions
• Unitarity Bounds for Semileptonic Decays in Lattice QCD
• Constraints for the semileptonic $B\to D^{(\ast )}$ form factors from lattice QCD simulations of two-point correlation functions
• Leading hadronic contributions to the running of the electroweak coupling constants from lattice QCD
• Leading-order hadronic contributions to the electron and tau anomalous magnetic moments
• Short distance singularities and automatic O($a$) improvement: the cases of the chiral condensate and the topological susceptibility
• Leading-order hadronic contributions to the lepton anomalous magnetic moments from the lattice