Diffraction driven steep rise of spin structure function gLT=g1+g2 at small x and DIS sum rules

We derive a unitarity relationship between the spin structure function g_LT(x,Q²)=g₁(x,Q²)+g₂(x,Q²), 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,Q²)~g²(x,Q¯²)~(1/x)^2(1+δ_g), where δ_g is an exponent of small-x rise of the unpolarized gluon density in the proton g(x,Q¯²) at a moderate hard scale Q¯² for light flavour contribution and large hard scale Q¯²~m_f² for heavy flavour contribution. It invalidates the Burkhardt-Cottingham sum rule. The found small-x rise of diffraction driven g_LT(x,Q²) is steeper than given by the Wandzura-Wilczek relation under conventional assumptions on small-x behaviour of g₁(x,Q²).