Sum rule for the twist four longitudinal structure function

Details Sum rule for the twist four longitudinal structure function Sum rule for the twist four longitudinal structure function

1997-11-12

arxiv.org/abs/hep-ph/9711298v1

Phys.Lett. B417 (1998) 361-368

Physics

High Energy Physics

High Energy Physics - Phenomenology

To appear in Physics Letters B

Scientific paper

10.1016/S0370-2693(97)01410-X

We investigate the twist four longitudinal structure function $F_{L}^{\tau=4}$ of deep inelastic scattering and show that the integral of ${F_{L}^{\tau=4} \over x}$ is related to the expectation value of the fermionic part of the light-front Hamiltonian density at fixed momentum transfer. We show that 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 for the renormalization of the corresponding twist four operator. The mixing of quark and gluon operators in QCD naturally leads to a twist four longitudinal gluon structure function and to a new sum rule $ \int dx {F_L \over x}= 4 {M^2 \over Q^2}$, which is the first sum rule obtained for a twist four observable. The validity of the sum rule in a non-perturbative context is explicitly verified in two-dimensional QCD.

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