  We show that the logarithmic derivative of the gauge coupling on the hadronic
mass and the cosmological constant term of a gauge theory are related to the
gluon condensate of the hadron and the vacuum respectively. These relations are
akin to Feynman-Hellmann relations whose derivation for the case at hand are
complicated by the construction of the gauge theory Hamiltonian. We bypass this
problem by using a renormalisation group equation for composite operators and
the trace anomaly. The relations serve as possible definitions of the gluon
condensates themselves which are plagued in direct approaches by power
divergences. In turn these results might help to determine the contribution of
the QCD phase transition to the cosmological constant and test speculative
ideas.
