Applications of the leading-order Dokshitzer-Gribov-Lipatov-Altarelli-Parisi evolution equations to the combined HERA data on deep inelastic scattering

Abstract

We recently derived explicit solutions of the leading-order Dokshitzer-Gribov-Lipatov-AltarelliParisi (DGLAP) equations for the Q 2 evolution of the singlet structure function Fs(x, Q 2 ) and the gluon distribution G(x, Q 2 ) using very efficient Laplace transform techniques. We apply our results here to a study of the HERA data on deep inelastic ep scattering as recently combined by the H1 and ZEUS groups. We use initial distributions F γp 2 (x, Q 2 0 ) and G(x, Q 2 0 ) determined for x < 0.1 by a global fit to the HERA data, and extended to x = 1 using the shapes of those distributions determined in the CTEQ6L and MSTW2008LO analyses from fits to other data. Our final results are insensitive at small x to the details of the extension. We obtain the singlet quark distribution Fs(x, Q 2 0 ) from F γp 2 (x, Q 2 0 ) using small non-singlet quark distributions taken from either the CTEQ6L or the MSTW2008LO analyses, evolve Fs and G to arbitrary Q 2 , and then convert the results to individual quark distributions. Finally, we show directly from a study of systematic trends in a comparison of the evolved F γp 2 (x, Q 2 ) with the HERA data, that the assumption of leading-order DGLAP evolution is inconsistent with those data.

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“…(5) and [7,8]. Those models provide good fits to the HERA data at small x and Q 2 above 1-2 GeV 2 , so we would like our extended model to be compatible with them at large Q 2 .…”

“…It has been argued in a series of papers [5][6][7][8][9] that the DIS structure function F γp 2 is basically hadronic in nature, reflecting the strong hadronic interactions initiated by the γ * , and should show the saturated Froissart bounded behavior [10][11][12][13] observed for other hadronic scattering processes [14][15][16] and real γp scattering [17,18]. The arguments are summarized in Ref.…”

“…In [7,8] we presented an accurate fit to the HERA data for Q 2 ≥ 0.85 GeV 2 , x 0.1, using the data as combined by the ZEUS and H1 groups [19] and the Froissart-bounded model proposed by Berger, Block, and Tan [6],…”

“…(5) and [6][7][8] replaced by 2mν. Absorbing powers of ln(Q 2 + µ 2 ) from the coefficient functions, we then write the argument of the energy-dependent logarithms as 2mν/(Q 2 + µ 2 ).…”

“…We take the coefficient function A(Q 2 ), B(Q 2 ), C(Q 2 ) to have the logarithmic form at large Q 2 assumed in [6][7][8] since this behavior describes the large-Q 2 HERA data well, but have modified the arguments to eliminate the divergences that appeared in [6] for Q 2 → 0, taking…”