arXiv subjects
Publications and source records attributed to Helmut Böttcher.
We report on recent results on higher twist contributions to the unpolarized structure functions $F_2^{p,d}(x,Q^2)$ at N$^3$LO in the large $x$ region and constraints on the twist--3 contribution to polarized structure function $g_2(x,Q^2)$.
The results of a recent next-to-leading order QCD analysis of the world data on polarized deep inelastic scattering are reported. New parameterizations are derived for the quark and gluon distributions, accounting for the massive Wilson coefficient for the charm quarks, and the value of $α_s(M_z^2)$ is determined with correlated errors. We obtain $α_s^{\rm NLO}(M_Z^2)= 0.1132 {array}{l} + 0.0056 -0.0095 {array}$. Limits on potential higher twist contributions to the structure function $g_1(x,Q^2)$ are derived. We also compare to the results obtained by other groups.
A QCD analysis of the world data on polarized deep inelastic scattering is presented in next--to--leading order, including the heavy flavor Wilson coefficient in leading order in the fixed flavor number scheme. New parameterizations are derived for the quark and gluon distributions and the value of $α_s(M_z^2)$ is determined. The impact of the variation of both the renormalization and factorization scales on the distributions and the value of $α_s$ is studied. We obtain $α_s^{\rm NLO}(M_Z^2) = 0.1132~~\begin{array}{l} + 0.0056 \\ -0.0095 \end{array}$. The first moments of the polarized twist--2 parton distribution functions are calculated with correlated errors to allow for comparisons with results from lattice QCD simulations. Potential higher twist contributions to the structure function $g_1(x,Q^2)$ are determined and found to be compatible with zero both for proton and deuteron targets.
We report on a recent extraction of the higher twist contributions to the deep inelastic structure functions $F_2^{ep,ed}(x,Q^2)$ in the large $x$ region. It is shown that the size of the extracted higher twist contributions is strongly correlated with the higher order corrections applied to the leading twist part. A gradual lowering of the higher twist contributions going from NLO to N$^4$LO is observed, where in the latter case only the leading large $x$ terms were considered.
The higher twist contributions to the deeply inelastic structure functions $F_2^{p}(x,Q^2)$ and $F_2^{d}(x,Q^2)$ for larger values of the Bjorken variable $x$ are extracted extrapolating the {twist--2} contributions measured in the large $W^2$ region to the region $4 \GeV^2 \leq W^2 \leq 12.5 \GeV^2$ applying target mass corrections. We compare the results for the NLO, NNLO and N$^3$LO analyzes and include also the large $x$ at N$^4$LO to the Wilson coefficients. A gradual lowering of the higher twist contributions going from NLO to N$^4$LO is observed, which stresses the importance of higher order corrections.
A non--singlet QCD analysis of the structure function $F_2(x,q^2)$ in LO, NLO, NNLO and N$^3$LO is performed based on the world data for charged lepton scattering. We determine the valence quark parton densities and present their parameterization and that of the correlated errors in a wide range of $x$ and $Q^2$. In the analysis we determined the QCD--scale $Λ_{\rm QCD, N_f = 4}^{\bar{\rm MS}} = 265 \pm 27 \MeV {\rm (NLO)}, 226 \pm 25 \MeV {\rm (NNLO)}, 234 \pm 26 \MeV {\rm (N^3LO)}$, with a remainder uncertainty of $\pm 2\MeV$ for the yet unknown 4--loop anomalous dimension, corresponding to $α_s(M_Z^2) = 0.1148 \pm 0.0019 {\rm NLO}, 0.1134 {\tiny{\begin{array}{c} +0.0019 -0.0021 \end{array}}} {\rm NNLO}, 0.1141 {\tiny{\begin{array}{c} +0.0020 -0.0022 \end{array}}} {\rm N^3LO}$. A comparison is performed to other determinations of the QCD scale and $α_s(M_Z^2)$ in deeply inelastic scattering. The higher twist contributions of $F_2^p(x,Q^2)$ and $F_2^d(x,Q^2)$ are extracted in the large $x$ region, subtracting the twist--2 contributions obtained in the NLO, NNLO and N$^3$LO analysis.