ORCID

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 $\langle\overline{\psi}\psi\rangle/M^3$ and terms in $\alpha_s$ multiplying $\langle \alpha_s G^2 \rangle/M^4$, 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, $\langle \overline{s}s \rangle^{\overline{\text{MS}}}(2 \text{GeV}) = -(296(11) \,\mathrm{MeV})^3$, 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.

DOI

10.1103/PhysRevD.100.034506

Publication Date

2019-08-08

Publication Title

Physical Review D

ISSN

2470-0010

Embargo Period

2019-08-24

Organisational Unit

School of Engineering, Computing and Mathematics

Keywords

hep-lat, hep-ph

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