  The fragmentation functions D_{a -> H}(x,mu^2) of a heavy hadron H, with mass
m_H, satisfy the phase-space constraint D_{a - > H}(x,mu^2)=0 for x <
m_H^2/mu^2, which is violated by the naive mu^2 evolution equations. Using
appropriately generalized mu^2 evolution equations, we reconsider the inclusive
hadroproduction of prompt J/psi mesons with high transverse momenta in the
framework of the factorization formalism of nonrelativistic quantum
chromodynamics, and determine the resulting shifts in the values of the leading
colour-octet matrix elements, which are fitted to data from the Fermilab
Tevatron.
