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The European Physical Journal C
ISSN: 1434-6044 (printed version)
ISSN: 1434-6052 (electronic version)
Abstract Volume 1 Issue 1/2 (1998) pp 271-283
theoretical physics:
Infrared contribution to the double-logarithmic small-$x$ asymptotics of structure functions
S.I. Manayenkov, M.G. Ryskin (a)
Petersburg Nuclear Physics Institute, Russian Academy of Science, Gatchina, St.Petersburg district, 188350, Russia
Received: 10 March 1997
Abstract. The role playing by the "soft" ($k_T <1$ GeV/c) region in the small-$x$ behaviour of $g_{1}(x,Q^2)$ and the non-singlet structure function $f_{1,NS}(x,Q^2)$ has been studied with the help of the effective QCD Lagrangian which takes into account the lightest degrees of freedom - the constituent quarks and the $\pi$-mesons (Goldstone bosons). It has been shown that the quark-quark interaction due to the pion exchange has a negative coupling $g$ for the isovector component ($I=1$ in the $t$-channel) of $f_1(x,Q^2)$ and isosinglet component of $g_1(x,Q^2)$. Here the pion induced interaction changes mainly the normalization of the quark distribution (it decreases $f_{1,NS}^{I=1}(x,Q^2)$ two times at $x <3 \cdot 10^{-3}$) and changes slightly the effective exponents $\lambda$ ($f_{1,NS}$, $g_1 \sim x^{-\lambda}$ at $x \rightarrow 0$). On the other hand due to a positive value of coupling $g$ the value of $\lambda$ increases by 15% for the isovector part of $g_1(x,Q^2)$ and up to $\lambda \approx 0.5$ (instead of $\lambda \approx 0.2$ without the pion contribution) for the isoscalar non-singlet structure function $f_{1,NS}^{I=0}(x,Q^2)$.
(a) The work is supported by the Grant INTAS-93-283-ext
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Online publication: December 11, 1997
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