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We recently derived an explicit expression for the gluon distribution function G(x, Q^2) = xg(x, Q^2) in terms of the proton structure function F_2^{\gamma p} (x, Q^2) in leading-order (LO) QCD by solving the the LO DGLAP equation for the Q^2 evolution of F_2^{\gamma p} (x, Q^2) analytically, using a differential-equation method. We re-derive and extend the results here using a Laplace-transform technique, and show that the singlet quark structure function F_S(x,Q^2) can be determined directly in terms of G from the DGLAP gluon evolution equation. To illustrate the method and check the consistency of existing LO quark and gluon distributions, we used the published values of the LO quark distributions from the CTEQ5L and MRST2001LO analyses to form F_2^{\gamma p} (x, Q^2), and then solved analytically for G(x,Q^2). We find that the analytic and fitted gluon distributions from MRST2001LO agree well with each other for all x and Q^2, while those from CTEQ5L differ significantly from each other for large x values, x>~0.03 - 0.05 at all Q^2. We conclude that the published CTEQ5L distributions are incompatible in this region. Using a non-singlet evolution equation, we obtain a sensitive

Author

Block, Martin M.; Durand, Loyal; McKay, Douglas W.

Published

2008

Language

EN