Large-N summation of chiral logs for generalized parton distributions

We demonstrate that in the region of Bjorken x(Bj) similar to m(pi)(2)/(4 pi F-pi)(2) and/ or x(Bj) similar to vertical bar t vertical bar /(4 pi F-pi)(2) the standard chi PT for the pion generalized parton distributions (GPDs) fails and one must perform all order resummation of chi PT. We perform such resummation in the large-N limit of the O(N + 1) extension of the chiral theory. Explicit resummation allows us to reveal novel phenomena-the form of the leading chiral correction to pion parton distribution functions (PDFs) and GPDs depends on the small x asymptotic of the pion PDFs. In particular, if the pion PDF in the chiral limit has the Regge-like small x behavior q(x) similar to 1/x(omega), the leading large impact parameter (b(perpendicular to)-> infinity) asymptotics of the quark distribution in the transverse plane has the form (m(pi) = 0) q(x; b(perpendicular to)) similar to 1/x(omega) 1n(omega) (b(perpendicular to)(2)) / b(perpendicular to)(2)((1+omega)). This result is model independent and it is controlled completely by the all order resummed chi PT developed in this paper. This asymptotic interweaves with small-x behavior of usual PDFs, hence it depends on the scale, at which the corresponding PDF is defined. This is a new and interesting result in which the chiral expansion meets the QCD evolution.