Second order QCD contributions to thrust and spherocity

In e⁺e^? annihilation there are regions of high spherocity S and low thrust $\text{T(S >}\text{16}\text{3π}{}^2\text{and}\text{T <}\text{2}\text{3}$ in which these distributions are given in QCD perturbation theory by the subprocesses e⁺e^? → qq?GG and e⁺e^? → qq?qq? neglecting only cubic and higher order terms in α_S. We give the corresponding QCD predictions which suggest that the calculable corrections to these variables may be slowly convergent.     

QCD analysis of twist-4 contributions to the g i structure functions

We analyze the twist-4 contributions to Bjorken and Ellis-Jaffe sum rules for spin-dependent structure function g ₁(x, Q ²). We investigate the anomalous dimensions of the twist-4 operators which determine the logarithmic correction to the 1/Q ² behavior of the twist-4 contribution by evaluating off-shell Green’s functions in both flavor non-singlet and singlet case. It is shown that the operators which are proportional to the equation of motion play an important role to extract the anomalous dimensions of physical operators. The calculations to solve the operator mixing of higher-twist operators are given in detail     

Higher order QCD corrections to an exclusive two-photon process

We calculate the next-to-leading order QCD corrections in the $\text{MS}$ scheme to the coefficient functions in an operator product expansion of the amplitude T(q², p²) for the process $\text{γ}{}^1\text{(q) + γ}{}^1\text{(p) →}\text{helicity-zero}$, flavour non-singlet meson in which ?q² is large and ?p² ? 0. For an asymptotic wave function the complete O(α_s) correction for a pseudoscalar meson is about 16% for p² = 0 and α_s = 0.3; most of this correction can be removed by using a modified evolution equation for the wave function, leaving a correction of about 7%. For large p² the complete O(α_s) correction for a pseudoscalar meson is about 10%. We discuss how our results can be combined with similar calculations for the pion form factor F_π(Q²) to give a prediction: F_π(Q²) = Aα_s(Q²)T_π²(q², 0)(1 + Bα_s) that is independent of the as yet unknown two-loop anomalous dimension matrix.     

Higher order QCD corrections to the energy-energy correlation function

We calculate theO(α _s ² correction to the energy-energy correlation cross section using a Sterman-Weinberg type resolution criterion to account for higher-order/nonperturbative effects. We find that the energy-energy correlation function as well as the asymmetry is sensitive to the choice of resolution parameters.     

Gluonic corrections to quark vacuum condensate contributions to two-point functions in QCD

We present the α _s corrections to quark vacuum condensate contributions to various types of current correlation functions. Their relevance to the first Weinberg sum rule is discussed. A new derivation of the relation between theA ₁-mass and the ?-mass is presented. The higher order corrections to the socalled non-perturbative quark mass are also discussed.     

Pion structure functions from lattice QCD

We compute 〈x〉 and 〈x²〉 of the valence quarks in a pion, on the lattice using Wilson fermions in the quenced approximat We find 〈x〉 = 0.49±0.08 and 〈x²〉 = 0.02 at a scale μ ≅ 7 GeV, in a good agreement with experimental data.     

QCD analysis of non-singlet electromagnetic structure functions

A direct analysis of all data on the nonsinglet combination of electromagnetic structure functionsF ₂ ^p ?F ₂ ⁿ is shown to yield a value of the QCD scale-breaking parameter \(\Lambda _{\overline {{\rm M}S} } = 0.36 \pm 0.16\) Gev, in good agreement with that obtained from non-singlet neutrino data. The ratiod _v /u _v , extracted using the results of a previous neutrino analysis, shows an excess of up-quarks to down-quarks of about a factor of five at largex.     

Higher order corrections and the scale parameter in QCD

I estimate the influence of the higher order corrections on the determination of the scale parameter Λ². I find a sizeable effect (a reduction of Λ² by a factor 3 to 4). This factor can be relevant in the comparison of Λ² with the characteristic confinement parameters.     

QCD analysis of non-singlet neutrino structure functions

We present a systematic analysis of all available neutrinoxF ₃ data, using an analytic parametrisation which incorporates second order QCD predictions forQ ² evolution. We find $$\Lambda _{\overline {MS} } = 0.30 \pm 0.13{\rm{ }}GeV$$ where the error is statistical, and both Fermi andW-boson propagator corrections have been made to the data. Neglect of the former has negligible effects, but neglect of the latter would increase Λ by ～0.1 GeV. We find that higher-twist effects are small and negative, and estimate their effect on the determination of Λ. We are unable to fit the data with higher-twist terms alone.     

Diquark contributions to the nucleon deep inelastic structure functions

The contributions of diquarks to the nucleon structure functions are discussed in the framework of the parton model and in the most general case of both vector and scalar diquarks inside unpolarized and polarized nucleons. The vector diquark anomalous magnetic moment and the scalar-vector and vector-scalar diquark transitions are also taken into account. The properties of the diquarks and of their form factors, required in order for the resulting scaling violations to be compatible with the observed ones, are discussed.     

Higher order contributions in finite temperature renormalization group

We apply to the O(N) λφ⁴ model the finite temperature renormalization group method, in which the temperature-dependent effective coupling constant and mass are introduced. It is pointed out that the improvement by use of the two-loop renormalization-group coefficients is important at high temperature and drastically changes the lowest order result. We also show that the two-loop renormalization-group coefficients are exact in the large-N limit.     

Processes involving fragmentation functions beyond the leading order in QCD

We point out that the electron propagator, calculated from a truncated Johnson-Baker-Willey equation, suffers from the following defects: lack of renormalizability gauge dependence of the electron electromagnetic mass, as well as unacceptable analytic structure.     

Higher order QCD corrections to the photoproduction of a direct photon at HERA

The contribution of resolved photons to the photoproduction cross section of direct photons is reexamined. Higher order,O(α ² α _s), QCD corrections to this contribution are calculated and turn out to be important at HERA energies. The observation of direct photons in the medium-p _⊥ range (p _⊥～5 GeV/c) should provide the opportunity to measure the gluon content of the photon.     

Higher twist and higher order contributions to the pion electromagnetic form factor

The andO ( _S ² ) corrections to the leading term of the perturbative QCD calculation of the pion electromagnetic form factor are examined numerically. Both sets of terms provide significant corrections for values ofQ ² between 1 and 15 GeV²/c².Parts of this work were done while one of us (JP) was a visitor at the national INT, the University of Maryland and TRIUMF. He is grateful to those institutions for their hospitality. We have benefitted from discussions with A. Mueller and G. Sterman. This work is supported in part by the U.S. Department of Energy.