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Register a new userAnalytic derivation of the leading-order gluon distribution function G(x,Q^2) = xg(x,Q^2) from the proton structure function F_2^p(x,Q^2)
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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.
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Light-front Hamiltonian dynamics is used to relate low-energy constituent quark models to deep inelastic unpolarized structure functions of the nucleon. The approach incorporates the correct Pauli principle prescription consistently and it allows a transparent investigation of the effects due to the spin-dependent SU(6)-breaking terms in the quark model Hamiltonian. Both Goldstone-boson-exchange interaction and hyperfine-potential models are discussed in a unified scheme and a detailed comparison, between the two(apparently) different potential prescriptions, is presented.
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.
Measurements of the proton and deuteron $F_2$ structure functions are presented. The data, taken at Jefferson Lab Hall C, span the four-momentum transfer range $0.06 < Q^2 < 2.8$ GeV$^2$, and Bjorken $x$ values from 0.009 to 0.45, thus extending the knowledge of $F_2$ to low values of $Q^2$ at low $x$. Next-to-next-to-leading order calculations using recent parton distribution functions start to deviate from the data for $Q^2<2$ GeV$^2$ at the low and high $x$-values. Down to the lowest value of $Q^2$, the structure function is in good agreement with a parameterization of $F_2$ based on data that have been taken at much higher values of $Q^2$ or much lower values of $x$, and which is constrained by data at the photon point. The ratio of the deuteron and proton structure functions at low $x$ remains well described by a logarithmic dependence on $Q^2$ at low $Q^2$.
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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}.
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