Illuminating the 1/x moment of parton distribution functions

The Weisberger relation, an exact statement of the parton model, elegantly relates a high-energy physics observable, the 1/x moment of parton distribution functions, to a nonperturbative low-energy observable: the dependence of the nucleon mass on the value of the quark mass or its corresponding quark condensate. We show that contemporary fits to nucleon structure functions fail to determine this 1/x moment; however, deeply virtual Compton scattering can be described in terms of a novel F1/x(t) form factor which illuminates this physics. An analysis of exclusive photon-induced processes in terms of the parton-nucleon scattering amplitude with Regge behavior reveals a failure of the high Q factorization of exclusive processes at low t in terms of the Generalized Parton-Distribution Functions which has been widely believed to hold in the past. We emphasize the need for more data for the DVCS process at large t in future or upgraded facilities. 1 The Weisberger relation The importance of the 1/x moment of parton distribution functions (pdf’s) was stressed in a 1972 paper byW.Weisberger [1]. There he derived a relation between the 1/x moment and the derivative of the squared proton mass with Talk and poster presented at MeNu07, part of a work in preparation. October 2007 arXiv:0710.0981[nucl.th] SLAC-PUB-12857 Invited talk presented at 11th International Conference On Meson-Nucleon Physics And The Structure Of The Nucleon (MENU 2007), 9/10/2007-9/14/2007, Juelich, Germany Brodsky, Llanes-Estrada and Szczepaniak Illuminating ∫ dx x respect to the squared parton mass defined at the same renormalization scale μ. In modern notation and normalization [2], Weisberger’s result reads δM N δmi (μ) = ∫ 1