Deep inelastic scattering in conformal QCD
Abstract
We consider the Regge limit of a CFT correlation function of two vector and two scalar operators, as appropriate to study smallx deep inelastic scattering in mathcal{N} = 4 SYM or in QCD assuming approximate conformal symmetry. After clarifying the nature of the Regge limit for a CFT correlator, we use its conformal partial wave expansion to obtain an impact parameter representation encoding the exchange of a spin j Reggeon for any value of the coupling constant. The CFT impact parameter space is the threedimensional hyperbolic space H _{3}, which is the impact parameter space for high energy scattering in the dual AdS space. We determine the smallx structure functions associated to the exchange of a Reggeon. We discuss unitarization from the point of view of scattering in AdS and comment on the validity of the eikonal approximation. We then focus on the weak coupling limit of the theory where the amplitude is dominated by the exchange of the BFKL pomeron. Conformal invariance fixes the form of the vector impact factor and its decomposition in transverse spin 0 and spin 2 components. Our formalism reproduces exactly the general results predict by the Regge theory, both for a scalar target and for γ*  γ* scattering. We compute current impact factors for the specific examples of mathcal{N} = 4 SYM and QCD, obtaining very simple results. In the case of the Rcurrent of mathcal{N} = 4 SYM, we show that the transverse spin 2 component vanishes. We conjecture that the impact factors of all chiral primary operators of mathcal{N} = 4 SYM only have components with 0 transverse spin.
 Publication:

Journal of High Energy Physics
 Pub Date:
 March 2010
 DOI:
 10.1007/JHEP03(2010)133
 arXiv:
 arXiv:0911.0043
 Bibcode:
 2010JHEP...03..133C
 Keywords:

 Deep Inelastic Scattering;
 AdSCFT Correspondence;
 High Energy Physics  Theory;
 High Energy Physics  Phenomenology
 EPrint:
 44+16 pages, 7 figures. Some corrections