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Author Kivel, N. ♦ Polyakov, M. V. ♦ Vladimirov, A.
Source arXiv.org
Content type Text
File Format PDF
Date of Submission 2008-09-11
Language English
Subject Domain (in DDC) Computer science, information & general works ♦ Natural sciences & mathematics ♦ Physics
Subject Keyword High Energy Physics - Phenomenology ♦ Nuclear Theory ♦ physics:hep-ph ♦ physics:nucl-th
Abstract We demonstrate that in the region of Bjorken x ~m_\pi^2/(4\pi F_\pi)^2 and/or x ~ t /(4\pi F_\pi)^2 the standard ChPT for the pion GPDs fails and one must perform all order resummation of ChPT. 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 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 behaviour q(x)~1/x^\omega, the leading large impact parameter ($b_\perp\to\infty$) asymptotics of the quark distribution in the transverse plane has the form ($m_\pi=0$) $q(x,b_\perp)\sim 1/x^\omega\ \ln^{\omega}(b_\perp^2)/b_\perp^{2{(1+\omega)}}$. This result is model independent and it is controlled completely by the all order resummed ChPT developed in this paper. This asymptotic interweaves with small-$x$ behaviour 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.
Educational Use Research
Learning Resource Type Article
Page Count 19


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