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

Abstract

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 ${\alpha }_s^2$ multiplying $⟨\overline{\psi }\psi ⟩/M^3$ 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 OPE to determine a value for the condensate, fitting the 4th, 6th, 8th and 10th time-moments simultaneously. Our result, $⟨\overline{s}s{⟩}^{\overline{\text{MS}}}(2\text{GeV})=-(296(11)\mathrm{MeV}{)}^3$, agrees well with HPQCD's earlier, more direct, lattice QCD determination~\cite{McNeile:2012xh}. 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.

arXiv comment14 pages, 4 figures

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