  In the heavy quark limit, properties of heavy mesons and doubly heavy baryons
are related by heavy quark-diquark symmetry. This problem is reanalyzed in the
framework of Non-Relativistic QCD (NRQCD). We introduce a novel method for
deriving Potential NRQCD (pNRQCD) Lagrangians for composite fields from vNRQCD,
which contains quarks and antiquarks as explicit degrees of freedom and
maintains manifest power counting in the velocity via a label formalism. A
Hubbard-Stratonovich transformation is used to eliminate four quark
interactions in vNRQCD and then quarks and antiquarks are integrated out to get
effective Lagrangians for composite fields. This method is used to rederive
Lagrangians for the Q\bar Q and QQ sectors of pNRQCD and give a correct
derivation of the O(1/m_Q) prediction for the hyperfine splitting of doubly
heavy baryons.
