Determination of the quark condensate from heavy-light current-current correlators in full lattice QCD

We derive the operator product expansion whose vacuum expectation value gives the time moments of the pseudoscalar heavy-light current-current correlator up to and including terms in alpha(2)(s) multiplying <(psi) over bar psi >/M-3 and terms in alpha(s) multiplying <alpha(s)G(2)>/M-4, where M is the heavy quark mass. Using lattice QCD results for heavy-strange correlators obtained for a variety of heavy quark masses on gluon field configurations including u, d and s quarks in the sea at three values of the lattice spacing, we are able to show that the contribution of the strange-quark condensate to the time moments is very substantial. We use our lattice QCD time moments and the operator product expansion to determine a value for the condensate, fitting the fourth, sixth, eighth and tenth time moments simultaneously. Our result, <(s) over bars >((MS) over bar)(2 GeV) = -(296(11) MeV)(3), agrees well with HPQCD's earlier, more direct, lattice QCD determination [C. McNeile et al. (HPQCD Collaboration), Phys. Rev. D 87, 034503 (2013)]. As well as confirming that the s quark condensate is close in value to the light quark condensate, this demonstrates clearly the consistency of the operator product expansion for fully nonperturbative calculations of matrix elements of short-distance operators in lattice QCD.