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 gLT(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 gLT(x,Q2)∼g2(x,Q2)∼(1/x)2(1+δg), where δg is an exponent of small-x rise of the unpolarized gluon density in the proton g(x,Q2) at a moderate hard scale Q2 for light flavour contribution and large hard scale Q2∼mf2 for heavy flavour contribution. It invalidates the Burkhardt-Cottingham sum rule. The found small-x rise of diffraction driven gLT(x,Q2) is steeper than given by the Wandzura-Wilczek relation under conventional assumptions on small-x behaviour of g1(x,Q2).