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Register a new userTwist-2 Heavy Flavor Contributions to the Structure Function $g_2(x,Q^2)$
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The twist--2 heavy flavor contributions to the polarized structure function $g_2(x,Q^2)$ are calculated. We show that this part of $g_2(x,Q^2)$ is related to the heavy flavor contribution to $g_1(x,Q^2)$ by the Wandzura--Wilczek relation to all orders in the strong coupling constant. Numerical results are presented.
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The logarithmic contributions to the massive twist-2 operator matrix elements for deep-inelastic scattering are calculated to $O(alpha_s^3)$for general values of the Mellin variable $N$.
We calculate moments of the $O(alpha_s^3)$ heavy flavor contributions to the Wilson coefficients of the structure function $F_2(x,Q^2)$ in the region $Q^2gg m^2$. The massive Wilson coefficients are obtained as convolutions of massive operator matrix elements (OMEs) and the known light flavor Wilson coefficients. The calculation of moments of the massive OMEs involves a first independent recalculation of moments of the fermionic contributions to all 3--loop anomalous dimensions of the unpolarized twist--2 local composite operators stemming from the light--cone expansion cite{url}.
We consider the effect of higher twist operators of the Wilson operator product expansion in the structure function $F_{2}(x,Q^{2})$ at small-$x$, taking into account QCD effective charges whose infrared behavior is constrained by a dynamical mass scale. The higher twist corrections are obtained from the renormalon formalism. Our analysis is performed within the conventional framework of next-to-leading order, with the factorization and renormalization scales chosen to be $Q^{2}$. The infrared properties of QCD are treated in the context of the generalized double-asymptotic-scaling approximation. We show that the corrections to $F_{2}$ associated with twist-four and twist-six are both necessary and sufficient for a good description of the deep infrared experimental data.
We derive a second-order linear differential equation for the leading order gluon distribution function G(x,Q^2) = xg(x,Q^2) which determines G(x,Q^2) directly from the proton structure function F_2^p(x,Q^2). This equation is derived from the leading order DGLAP evolution equation for F_2^p(x,Q^2), and does not require knowledge of either the individual quark distributions or the gluon evolution equation. Given an analytic expression that successfully reproduces the known experimental data for F_2^p(x,Q^2) in a domain x_min<=x<=x_max, Q_min^2<=Q^2<=Q_max^2 of the Bjorken variable x and the virtuality Q^2 in deep inelastic scattering, G(x,Q^2) is uniquely determined in the same domain. We give the general solution and illustrate the method using the recently proposed Froissart bound type parametrization of F_2^p(x,Q^2) of E. L. Berger, M. M. Block and C-I. Tan, PRL 98, 242001, (2007). Existing leading-order gluon distributions based on power-law description of individual parton distributions agree roughly with the new distributions for x>~10^-3 as they should, but are much larger for x<~10^-3.
We present new experimental results of the $^3$He spin structure function $g_2$ in the resonance region at $Q^2$ values between 1.2 and 3.0 (GeV/c)$^2$. Spin dependent moments of the neutron were then extracted. Our main result, the resonance contribution to the neutron $d_2$ matrix element, was found to be small at $<Q^2>$=2.4 (GeV/c)$^2$ and in agreement with the Lattice QCD calculation. The Burkhardt-Cottingham sum rule for $^3$He and the neutron was tested with the measured data and using the Wandzura-Wilczek relation for the low $x$ unmeasured region. A small deviation was observed at $Q^2$ values between 0.5 and 1.2 (GeV/c)$^2$ for the neutron.
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