Transverse spin effects and holography

Abstract

Abstract. The holographic sum rules for GPDs and the appearance of holographic variables in the TMD models are discussed. The relation between GPDs and TMDs in the spirit of Veneziano duality is suggested. The derivation of Burkardt sum rule for Sivers function clarifying its relation to Ji's sum rules for GPDs is presented. The possibility of its generalization for the case pf separate quark flavours implying the nodes of Sivers functions is discussed.

Relating transverse structure of various parton distributions

“…Here, we demonstrate a novel relation between the TMDs and the GPDs which relates the t( square of momentum transferred) dependence of GPDs with the p 2 ⊥ dependence of TMDs. This may reflect the sort of Veneziano-like s ↔ t duality (see [16], section 4). The p 2 ⊥ dependence in TMDs coming form AdS/QCD wavefunction explains why the TMDs in lattice calculations show approximate x and p 2 ⊥ factorization.…”

Novel effects in twist-three SSA

“…Note also that this may be understood as appearance of gluonic poles due to the physical components [8] of gluonic fields. Another support of this picture is provided by the fact, that imaginary phase in 10 allows to derive [9] Burkardt sum rules from conservation laws.…”

Evolution of sum rules and positivity constraints

“…The contribution of gluonic pole to energy momentum should be nullified [3] due to the absence of the relevant structure p µ ε νSpn in the matrix element < p|T µν |p >. As a result…”

“…The resuting angular momentum conservation, in turn, is combined with momentum conservation when the Ji's sum rules and equivalence principle is considered, being related to Burkardt sum rules [9]. Note that such way of preservation of Burkardt sum rule allows one to generalize it [3] to be valid for each flavour separately, which should lead to nodes [10] and may be related to the extension of equivalence principle [11].…”

“…We also recall how Burkardt sum rule [4] may be related [3] to energy-momentum conservation by a sort of analytic continuation to complex domain of partonic momentum fractions. Its validity after account of QCD evolution [5] is due to the boundary condition and is similar to the stability of twist-3 contribution to Burkhardt-Cottingham sum rule [6].…”