INCONSISTENCY OF THE EFFECTIVE THEORY FOR ENERGETIC LIGHT QUARKS

For the analysis of exclusive nonleptonic decays of heavy quarks, such as B --> pi + D, B --> rho + D, an effective theory based on QCD has recently been formulated and applied; the main result is that it implies factorization of the decay amplitude. This theory describes sources with very high momentum moving with the velocity of light, whose motion is not affected by finite momentum transfers. In general, it can be applied to any process involving light quarks with large energy and soft interactions. Despite its clear physical meaning, this effective theory is shown to be unstable. This phenomenon arises because the positivity of the energy is not preserved in the expansion leading to the effective hamiltonian. The energy spectrum is unbounded from below and transitions of the "effective quark" into states of arbitrarily negative energies are kinematically possible and have nonzero amplitudes. These processes have no counterpart in the real world and spoil the effective theory of physical meaning.