SUM-RULE FOR THE TWIST-4 LONGITUDINAL STRUCTURE-FUNCTION

We investigate the twist four longitudinal structure function F-L(tau= 4) of deep inelastic scattering and show that the integral of F-L(tau= 4)/x is related to the expectation value of the fermionic part of the light-front Hamiltonian density at fixed momentum transfer. We show th at the new relation, in addition to providing physical intuition on F- L(tau=4), relates the quadratic divergences of F-L(tau=4) to the quark mass correction in light-front QCD and hence provides a new pathway f or the renormalization of the corresponding twist four operator. The m ixing of quark and gluon operators in QCD naturally leads to a twist f our longitudinal gluon structure function and to a new sum rule integr al dxF(L)/x = 4M(2)/Q(2), which is the first sum rule obtained for a t wist four observable. The validity of the sum rule in a non-perturbati ve context is explicitly verified in two-dimensional QCD. (C) 1998 Els evier Science B.V.