Impact of Higher Order and Soft Gluon Corrections on the Extraction of Higher Twist Effects in DIS

The impact of recently calculated next-to-next-to-leading order QCD corrections and soft gluon resummations on the extraction of higher twist contributions to the deep-inelastic structure function F_2 is studied using the BCDMS and SLAC data. It is demonstrated to which extent the need for higher twist terms is diminishing due to these higher order effects in the kinematical region, 0.35 \le x \le 0.85 and Q^2>1.2 GeV^2, investigated. In addition, theoretical uncertainties in the extraction of higher twist contributions are discussed, and comparisons to results obtained previously are made.Comment: 16 pages, 3 figure

The Longitudinal Structure Function at the Third Order

We compute the complete third-order contributions to the coefficient functions for the longitudinal structure function F_L, thus completing the next-to-next-to-leading order (NNLO) description of unpolarized electromagnetic deep-inelastic scattering in massless perturbative QCD. Our exact results agree with determinations of low even-integer Mellin moments and of the leading small-x terms in the flavour-singlet sector. In this letter we present compact and accurate parametrizations of the results and illustrate the numerical impact of the NNLO corrections.Comment: 11 pages, LaTeX, 4 eps-figures. DESY preprint number correcte

Bottom quark electroproduction in variable flavor number schemes

Two variable flavor number schemes are used to describe bottom quark production in deep inelastic electron-proton scattering. In these schemes the coefficient functions are derived from mass factorization of the heavy quark coefficient functions presented in a fixed flavor number scheme. Also one has to construct a parton density set with five light flavors (u,d,s,c,b) out of a set which only contains four light flavors (u,d,s,c). In order $\alpha_s^2$ the two sets are discontinuous at $\mu=m_b$ which follows from mass factorization of the heavy quark coefficient functions when it is carried out in the ${\bar {\rm MS}}$-scheme. Both variable flavor number schemes give almost identical predictions for the bottom structure functions $F_{2,b}$ and $F_{L,b}$. Also they both agree well with the corresponding results based on fixed order four-flavor perturbation theory over a wide range in $x$ and $Q^2$.Comment: Latex with seventeen PostScript figure

Reduction of multi-leg loop integrals

I give an efficient algorithm for the reduction of multi-leg one-loop integrals of rank one. The method combines the basic ideas of the spinor algebra approach with the dual vector approach and is applicable to box integrals or higher point integrals, if at least one external leg is massless. This method does not introduce Gram determinants in the denominator. It completes an algorithm recently given by R. Pittau.Comment: 10 pages, 4 figures, uses axodraw.sty, final version, minor change

Approximating the coefficients in semilinear stochastic partial differential equations

We investigate, in the setting of UMD Banach spaces E, the continuous dependence on the data A, F, G and X_0 of mild solutions of semilinear stochastic evolution equations with multiplicative noise of the form dX(t) = [AX(t) + F(t,X(t))]dt + G(t,X(t))dW_H(t), X(0)=X_0, where W_H is a cylindrical Brownian motion on a Hilbert space H. We prove continuous dependence of the compensated solutions X(t)-e^{tA}X_0 in the norms L^p(\Omega;C^\lambda([0,T];E)) assuming that the approximating operators A_n are uniformly sectorial and converge to A in the strong resolvent sense, and that the approximating nonlinearities F_n and G_n are uniformly Lipschitz continuous in suitable norms and converge to F and G pointwise. Our results are applied to a class of semilinear parabolic SPDEs with finite-dimensional multiplicative noise.Comment: Referee's comments have been incorporate

On the Equivalence of Solutions for a Class of Stochastic Evolution Equations in a Banach Space

Acknowledgments: The author wishes to thank Professor Anna Chojnowska-Michalik and the referee for many helpful suggestions and comments.We study a class of stochastic evolution equations in a Banach space E driven by cylindrical Wiener process. Three different analytical concepts of solutions: generalised strong, weak and mild are defined and the conditions under which they are equivalent are given. We apply this result to prove existence, uniqueness and continuity of weak solutions to stochastic delay evolution equations. We also consider two examples of these equations in non-reflexive Banach spaces: a stochastic transport equation with delay and a stochastic delay McKendrick equation

Theoretical Uncertainties in the QCD Evolution of Structure Functions and their Impact on αs(MZ2)\alpha_s(M_Z^2)

The differences are discussed between various next-to-leading order prescriptions for the QCD evolution of parton densities and structure functions. Their quantitative impact is understood to an accuracy of 0.02\%. The uncertainties due to the freedom to choose the renormalization and factorization scales are studied. The quantitative consequences of the different uncertainties on the extraction of the strong coupling constant $\alpha_s$ from scaling violations in deep--inelastic scattering are estimated for the kinematic regime accessible at HERA.Comment: 10 pages Latex, including 3 eps-figures, and a style file. To appear in: Proc. of the International Workshop: QCD and QED in Higher Orders, Rheinsberg, April, 1996, Nucl. Phys. {\bf B} (Proc. Suppl); The lay-out of the paper has been changed, one figure sent separately before has been bound i

Parton Distributions

I discuss our current understanding of parton distributions. I begin with the underlying theoretical framework, and the way in which different data sets constrain different partons, highlighting recent developments. The methods of examining the uncertainties on the distributions and those physical quantities dependent on them is analysed. Finally I look at the evidence that additional theoretical corrections beyond NLO perturbative QCD may be necessary, what type of corrections are indicated and the impact these may have on the uncertainties.Comment: Invited talk at "XXI International Symposium on Lepton and Photon Interactions at High Energies," (Fermilab, Chicago, August 2003). 12 pages, 21 figure

Next-to-next-to-leading order QCD corrections to the photon's parton structure

The next-to-next-to-leading order (NNLO) corrections in massless perturbative QCD are derived for the parton distributions of the photon and the deep inelastic structure functions F_1^gamma and F_2^gamma. We present the full photonic coefficient functions at order alpha alpha_s and calculate the first six even-integer moments of the corresponding O(alpha alpha_s^2) photon-quark and photon-gluon splitting functions together with the moments of the alpha alpha_s^2 coefficient functions which enter only beyond NNLO. These results are employed to construct parametrizations of the splitting functions which prove to be sufficiently accurate at least for momentum fractions x >= 0.05. We also present explicit expressions for the transformation from the MS_bar to the DIS_gamma factorization scheme and write down the solution of the evolution equations. The numerical impact of the NNLO corrections is discussed in both schemes.Comment: 39 pages, LaTeX, 9 eps-figures. A few minor typos and a misprint in Eq. (5.9) correcte