  The spin-dependent operators for heavy quarkonium hybrids have been recently
obtained in a nonrelativistic effective field theory approach up to
next-to-leading order in the heavy-quark mass expansion. In the effective field
theory for hybrids several operators not found in standard quarkonia appear,
including an operator suppressed by only one power of the heavy-quark mass. We
compute the matching coefficients for these operators in the short
heavy-quark-antiquark distance regime, $r\ll 1/\Lambda_{\rm QCD}$, by matching
weakly-coupled potential NRQCD to the effective field theory for hybrids. In
this regime the perturbative and nonperturbative contributions to the matching
coefficients factorize, and the latter can be expressed in terms of purely
gluonic correlators whose form we explicitly calculate with the aid of the
transformation properties of the gluon fields under discrete symmetries. We
detail our previous comparison with direct lattice computations of the
charmonium hybrid spectrum, from which the unknown nonperturbative
contributions can be obtained, and extend it to data sets with different
light-quark masses.
