Absence of pi^2 terms in physical anomalous dimensions in DIS: verification and resulting predictions

Abstract

We study the higher-order corrections to structure functions in inclusive deep-inelastic scattering (DIS) in massless perturbative QCD, in the context of the conjectured absence of even-n values of the Riemann zeta-function zeta_n, i.e., of powers of pi^2, in Euclidean physical quantities. We provide substantial additional support for this conjecture by demonstrating that it holds, as far as it can be tested by the results of diagram computations, for the physical anomalous dimensions of structure functions at the fourth and fifth order in the strong coupling constant alpha_s. The conjecture is then employed to predict hitherto unknown zeta_4 and zeta_6 contributions to the anomalous dimensions for parton distributions and to the coefficient functions for the longitudinal structure function F_L.

11 pages, LaTeX

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Cited by in corpus (13)

• Five-loop contributions to low-N non-singlet anomalous dimensions in QCD
• Low moments of the four-loop splitting functions in QCD
• Four-loop splitting functions in QCD -- The quark-quark case
• Four-loop splitting functions in QCD -- The gluon-to-quark case
• Resummation of small-x double logarithms in QCD: inclusive deep-inelastic scattering
• The $N_f{C}_F^3$ contribution to the non-singlet splitting function at four-loop order
• Complete $N_f^2$ contributions to four-loop pure-singlet splitting functions
• The $\overline{\mathrm{MS}}$-scheme ${\alpha }_s^5$ QCD contributions to the Adler function and Bjorken polarized sum rule in the Crewther-type two-fold $\{\beta \}$-expanded representation
• Higher-order behaviour of two-point current correlators
• Four-loop large-n_f contributions to the non-singlet structure functions F_2 and F_L
• R*-operation and five-loop calculations
• Riemann $\zeta (4)$ function contributions to $O\left({{\alpha }_s}^5\right)$ terms of Adler D-function and Bjorken polarized sum rule in $SU\left(N_c\right)$ QCD: results and consequences
• Four-loop anomalous dimension of flavor non-singlet quark operator of twist two and Lorentz spin N for general gauge group: transcendental part