The Invisible Renormalon

We study the structure of renormalons in the Heavy Quark Effective Theory, by expanding the heavy quark propagator in powers of $1/m_Q$. We demonstrate that the way in which renormalons appear depends on the regularisation scheme used to define the effective theory. In order to investigate the relation between ultraviolet renormalons and power divergences of matrix elements of higher-dimensional operators in the heavy quark expansion, we perform calculations in dimensional regularisation and in three different cut-off regularisation schemes. In the case of the kinetic energy operator, we find that the leading ultraviolet renormalon which corresponds to a quadratic divergence, is absent in all but one (the lattice) regularisation scheme. The nature of this ``invisible renormalon'' remains unclear.

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