Sum rules for heavy flavour transitions

Sum rules for differential distributions in inclusive semileptonic decays of heavy flavours are derived in terms of moments of structure functions. The approach based on the operator product expansion allows to construct the systematic expansion in the inverse heavy quark masses. Nonperturbative 1/mQ corrections to the known sum rules and new sum rules are obtained. A transparent physical interpretation of sum rules is presented relating the field-theoretical derivation and the quantum-mechanical approach developed by Lipkin. One of interesting applications is the estimate of deviation from unity for the form factor of exclusive B → D* lν transition at zero recoil. (author)