Diffraction driven steep rise of spin structure function $g_{LT}=g_1+g_2$ at small x and DIS sum rules

Abstract

We derive a unitarity relationship between the spin structure function $g_{LT}(x,Q^2)=g_1(x,Q^2)+g_2(x,Q^2)$, the LT interference diffractive structure function and the spin-flip coupling of the pomeron to nucleons. Our diffractive mechanism gives rise to a dramatic small-$x$ rise $g_{LT}(x,Q^2)\sim g^2(x,{\bar{Q}}^2)\sim (1/x{)}^{2(1+{\delta }_g)}$, where ${\delta }_g$ is an exponent of small-$x$ rise of the unpolarized gluon density in the proton $g(x,{\bar{Q}}^2)$ at a moderate hard scale ${\bar{Q}}^2$ for light flavour contribution and large hard scale ${\bar{Q}}^2\sim m_f^2$ for heavy flavour contribution. It invalidates the Burkhardt-Cottingham sum rule. The found small-$x$ rise of diffraction driven $g_{LT}(x,Q^2)$ is steeper than given by the Wandzura-Wilczek relation under conventional assumptions on small-$x$ behaviour of $g_1(x,Q^2)$.

Comments: 13 pages, 3 figures, the overlay of fig.2 and fig.3 in the combined PS files has been coorrected