Vector correlator and scale determination in lattice QCD

We implement a proposal made in [arXiv:1107.4388] to determine the lattice spacing by matching the lattice vector correlator at a reference distance scale with the same correlator obtained by a dispersion relation based on the $R$-ratio determined experimentally. We work with the isovector current, requiring a separation of the isovector hadronic final states on the phenomenological side. We also discuss the finite-size effect on the correlator, which must be controlled in order for the method to be applicable.