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The Effect of Small-x Resummations on the Evolution of Polarized Structure FunctionsOct 01 1996The impact of the resummation of leading small-$x$ terms in the anomalous dimensions is briefly summarized for the evolution of non--singlet and singlet polarized structure functions.

The Evolution of Unpolarized Singlet Structure Functions at Small xDec 31 1997Jan 01 1998A systematic study is performed of the impact of the various resummed small-$x$ contributions to the anomalous dimensions and coefficient functions on the evolution of unpolarized structure functions in deep-inelastic scattering. The proton structure ... More

The Evolution of Unpolarized and Polarized Structure Functions at Small $x$Aug 28 1996Aug 29 1996A survey is given of recent developments on the resummed small-$x$ evolution, in a framework based on the renormalization group equation, of non--singlet and singlet structure functions in both unpolarized and polarized deep--inelastic scattering. The ... More

On Small-x Resummations for the Evolution of Unpolarized and Polarized Non--Singlet and Singlet Structure FunctionsJul 15 1996A brief survey is given of recent results on the resummation of leading small-x terms for unpolarized and polarized non--singlet and singlet structure function evolution.

The Polarized Two-Loop Massive Pure Singlet Wilson Coefficient for Deep-Inelastic ScatteringApr 18 2019We calculate the polarized massive two--loop pure singlet Wilson coefficient contributing to the structure functions $g_1(x,Q^2)$ analytically in the whole kinematic region. The Wilson coefficient contains Kummer--elliptic integrals. We derive the representation ... More

Algebraic Relations Between Harmonic Sums and Associated QuantitiesNov 04 2003We derive the algebraic relations of alternating and non-alternating finite harmonic sums up to the sums of depth~6. All relations for the sums up to weight~6 are given in explicit form. These relations depend on the structure of the index sets of the ... More

On the Relations Between Polarized Structure FunctionsDec 31 1999The status of the twist--2 and the twist--3 integral relations between polarized structure functions in deep inelastic scattering for electromagnetic and electroweak interactions is reviewed. One novel integral relation for the twist--3 contributions ... More

Relations Between Polarized Structure FunctionsJul 29 1999The status of the twist-2 and the twist-3 integral relations between polarized structure functions in deep inelastic scattering is discussed. The relations can be tested in the upcoming experiments in the range $Q^2 \gsim M_p^2$.

Three loop QCD corrections to heavy quark form factorsMay 09 2019Higher order calculations in perturbative Quantum Field Theories often produce coupled linear systems of differential equations which factorize to first order. Here we present an algorithm to solve such systems in terms of iterated integrals over an alphabet ... More

On the Expectations for Leptoquarks in the Mass Range of O(200 GeV)Mar 10 1997Mar 31 1997A summary is given on the experimental bounds for the couplings and masses of scalar and vector leptoquarks associated to the first fermion generation. We investigate to which extent an interpretation of the recently reported excess of events in the large ... More

O(α_s^3) contributions to F_L^{Q\bar{Q}}(x,Q^2) for large virtualitiesAug 02 2006The $O(\alpha_s^3)$ contributions to the heavy flavor Wilson coefficients for the structure function $F_L(x,Q^2)$ are calculated in the region $Q^2 \gg m^2$ using the renormalization group method.

Mathematical Structure of Anomalous Dimensions and QCD Wilson Coefficients in Higher OrderJul 04 2004The alternating and non-alternating harmonic sums and other algebraic objects of the same equivalence class are connected by algebraic relations which are induced by the product of these quantities and which depend on their index class rather than on ... More

On the Leptoquark Interpretation of the High $Q^2$ Events at HERAJun 16 1997We investigate to which extent an interpretation of the recently observed excess of events in the high $Q^2$ range at HERA in terms of single leptoquark production is compatible with bounds from other experiments.

On the $k_{\perp}$ dependent gluon density of the protonJun 23 1995The $k_{\perp}$ dependent gluon distribution is calculated accounting for the resummation of small~$x$ effects due to the Lipatov equation. It is represented by a convolution of a gluon density in the collinear limit and a universal function ${\cal G}(x,k^2,\mu)$ ... More

QCD Evolution of Structure Functions at Small xSep 21 1999The status of the resummation of small x contributions to the unpolarized and polarized deep inelastic structure functions is reviewed.

On the $k_{\perp}$ dependent gluon density in hadrons and the photonJun 28 1995The $k_{\perp}$ dependent gluon distribution for protons, pions,and photons is calculated accounting for the resummation of small~$x$ effects due to the Lipatov equation. It is represented by a convolution of a gluon density in the collinear limit and ... More

On the Theoretical Status of Deep Inelastic ScatteringDec 11 1995The theoretical status of perturbative QED and QCD corrections to deep inelastic scattering is reviewed.

The two-mass contribution to the three-loop pure singlet operator matrix elementNov 17 2017We present the two-mass QCD contributions to the pure singlet operator matrix element at three loop order in x-space. These terms are relevant for calculating the structure function $F_2(x,Q^2)$ at $O(\alpha_s^3)$ as well as for the matching relations ... More

QCD Analysis of Polarized Deep Inelastic Scattering DataJul 31 2001A QCD analysis of the world data on inclusive polarized deep inelastic scattering of leptons on nucleons is presented in leading and next-to-leading order. New parameterizations are derived for the quark and gluon distributions and the value of $\alpha_s(M_Z)$ ... More

Integral Relations for Twist 2 abd Twist 3 Contributions to Polarized Structure FunctionsJun 01 1997We discuss the relations between the twist 2 and twist 3 contributions to polarized deep-inelastic scattering structure functions both for neutral and charged current interactions which are predicted by the operator product expansion in lowest order in ... More

On the Twist 2 and Twist 3 Contributions to the Spin-dependent Electroweak Structure FunctionsDec 10 1996Dec 15 1996The twist 2 and twist 3 contributions of the polarized deep-inelastic structure functions are calculated both for neutral and charged current interactions using the operator product expansion in lowest order in QCD. The relations between the different ... More

Universal QED Corrections to Polarized Electron Scattering in Higher OrdersJul 22 2002We derive QED radiators for the universal corrections to polarized electron scattering. To 5th order in the coupling constant the flavor non-singlet and singlet contributions are calculated. We derive the non-singlet and singlet exponentiation of the ... More

The Resummed Gluon Anomalous Dimension and Structure Functions at Small xJul 27 1997Mar 25 1998The impact of the resummed next-to-leading logarithmic small-$x$ contributions to the anomalous dimension $\gamma_{gg}$ is evaluated for the unpolarized parton densities and structure functions of the nucleon. These new terms diminish the gluon distribution ... More

The Asymptotic 3-Loop Heavy Flavor Corrections to the Charged Current Structure Functions $F_L^{W^+-W^-}(x,Q^2)$ and $F_2^{W^+-W^-}(x,Q^2)$Sep 20 2016We calculate the massive Wilson coefficients for the heavy flavor contributions to the non-singlet charged current deep-inelastic scattering structure functions $F_L^{W^+}(x,Q^2)-F_L^{W^-}(x,Q^2)$ and $F_2^{W^+}(x,Q^2)-F_2^{W^-}(x,Q^2)$ in the asymptotic ... More

The $ρ$ parameter at three loops and elliptic integralsJul 13 2018We describe the analytic calculation of the master integrals required to compute the two-mass three-loop corrections to the $\rho$ parameter. In particular, we present the calculation of the master integrals for which the corresponding differential equations ... More

New Exclusion Limits on Dark Gauge Forces from Proton Bremsstrahlung in Beam-Dump DataNov 15 2013We re-analyze published proton beam dump data taken at the U70 accelerator at IHEP Serpukhov with the $\nu$-calorimeter I experiment in 1989 to set mass-coupling limits for dark gauge forces. The corresponding data have been used for axion and light Higgs ... More

NLL QED Corrections to Deep Inelastic ScatteringSep 12 2003The $O(\alpha^2\log(Q^2/m_e^2))$ leptonic QED corrections to unpolarized deeply inelastic electron-nucleon scattering are calculated in the mixed variables.

QCD corrections to $F_L(x,Q^2)$Sep 18 1996We perform a numerical study of the QCD corrections to the structure function $F_L(x,Q^2)$ in the HERA energy range. The $K$--factors are of $O(30%)$ and larger in parts of the kinematic range. The relative corrections to $F_L^{c\overline{c}}$ turn out ... More

Mellin Moments of the Next-to-next-to Leading Order Coefficient Functions for the Drell-Yan Process and Hadronic Higgs-Boson ProductionJan 19 2005Mar 21 2005We calculate the Mellin moments of the next-to-next-to leading order coefficient functions for the Drell--Yan and Higgs production cross sections. The results can be expressed in terms of multiple finite harmonic sums of maximal weight w = 4. Using algebraic ... More

QCD Analysis of Polarized Deep Inelastic Data and Parton DistributionsMar 17 2002May 24 2002A QCD analysis of the world data on polarized deep inelastic scattering is presented in leading and next-to-leading order. New parameterizations are derived for the quark and gluon distributions for the kinematic range $x \epsilon [10^{-9},1], Q^2 \epsilon ... More

Polarized Deep Inelastic Diffractive ep Scattering: Operator ApproachFeb 08 2002Feb 11 2002Polarized inclusive deep-inelastic diffractive scattering is dealt with in a quantum field theoretic approach. The process can be described in the general framework of non-forward scattering processes using the light-cone expansion in the generalized ... More

On the Scaling Violations of Diffractive Structure Functions: Operator ApproachJun 04 2001Oct 30 2001A quantum field theoretic treatment of inclusive deep-inelastic diffractive scattering is given. The process can be described in the general framework of non-forward scattering processes using the light-cone expansion in the generalized Bjorken region. ... More

Scheme-invariant NNLO evolution for unpolarized DIS structure functionsNov 08 2004We discuss the combination of NNLO standard QCD evolution and scheme-invariant analysis for unpolarized DIS structure functions data as a method to reduce the theoretical errors on the determination of $\alpha_s(M_Z^2)$ to $\sim 1$% in order to match ... More

Target Mass Corrections for Polarized Structure Functions and New Sum RulesDec 22 1998The target mass corrections are calculated for all structure functions of neutral and charged current deep inelastic scattering in lowest order in the coupling constant. Representations of the correction to the twist--2 and twist--3 contributions are ... More

Polarized Parton DensitiesDec 31 2002In this talk we summarize main results of a recent determination of the polarized deeply inelastic parton distributions to NLO from the world data. In the analysis the LO and NLO parton densities and their $1\sigma$ statistical errors were derived and ... More

Target Mass Corrections to the Spin-dependent Structure FunctionsDec 11 1998Aug 31 2000The target mass corrections to the twist-2 contributions of the spin-dependent structure functions are calculated using operator product expansion in lowest order in QCD. The influence of such corrections to the different relations between the structure ... More

On the twist-2 contributions to polarized structure functionsJul 09 1996The twist--2 contributions to the polarized structure functions in deep inelastic lepton--hadron scattering are calculated including the exchange of weak bosons and using both the operator product expansion and the covariant parton model. A new relation ... More

O(α^2 L) Radiative Corrections to Deep Inelastic ep ScatteringNov 13 2002The leptonic QED radiative corrections are calculated in the next-to-leading log approximation ${\cal O}[\alpha^2 \ln(Q^2/m_e^2)]$ for unpolarized deeply inelastic $ep$--scattering in the case of mixed variables. The corrections are determined using mass ... More

The Singlet Contribution to the Structure Function $g_1(x,Q^2)$ at Small $x$Jun 06 1996The resummation of $O(\alpha_s^{l+1} \ln^{2l} x)$ terms in the evolution equation of the singlet part of $g_1(x,Q^2)$ is carried out. The corresponding singlet evolution kernels are calculated explicitely. The leading small-$x$ contribution to the three-loop ... More

Harmonic Sums and Mellin Transforms up to two-loop OrderOct 05 1998Aug 31 2000A systematic study is performed on the finite harmonic sums up to level four. These sums form the general basis for the Mellin transforms of all individual functions $f_i(x)$ of the momentum fraction $x$ emerging in the quantities of massless QED and ... More

NNLO coefficient functions of Higgs and Drell--Yan cross sections in Mellin spaceJul 05 2004We calculate the Mellin moments of next-to-next-to-leading order coefficient functions of the Drell-Yan and Higgs production cross sections. The results can be expressed in term of finite harmonic sums which are maximally threefold up to weight four. ... More

QCD Analysis of Polarized Scattering Data and New Polarized Parton DistributionsJun 27 2002In this talk results from a new QCD analysis in leading (LO) and next--to--leading (NLO) order are presented. New parametrizations of the polarized quark and gluon densities are derived together with parametrizations of their fully correlated 1$\sigma$ ... More

On the twist-2 contributions to polarized structure functions and new sum rulesMar 25 1996Mar 26 1996The twist-2 contributions to the polarized structure functions in deep inelastic lepton--hadron scattering are calculated including the exchange of weak bosons and using both the operator product expansion and the covariant parton model. A new relation ... More

Polarized Deep Inelastic Diffractive Scattering near the Light ConeJul 20 2002Polarized inclusive deep-inelastic scattering is formulated in the light cone expansion. The QCD evolution of the leading twist distribution functions is derived. It is shown that the twist--2 contribution to the structure functions g_2^{D(3)} is obtained ... More

On the Mellin Transform of the Coefficient Functions of $F_L(x,Q^2)$Aug 18 1997Aug 20 1997The Mellin-transforms of the next-to-leading order Wilson coefficients of the longitudinal structure function are evaluated.

Small-x Resummation for the Structure Functions $F_2^p$, $F_L^p$ and $F_2^γ$Jun 16 1997The numerical effects of the known all-order leading and next-to-leading logarithmic small-$x$ contributions to the anomalous dimensions and coefficient functions of the unpolarized singlet evolution are discussed for the structure functions $F_2^{ ep}(x,Q^2)$, ... More

On the Resummation of $α\ln^2 x$ Terms for Non-Singlet Structure Functions in QED and QCDApr 01 1996The resummation of $O(\alpha^{l+1} \ln^{2l} x)$ terms in the evolution kernels of non--singlet combinations of structure functions is investigated for both QED abd QCD. Numerical results are presented for unpolarized and polarized structure functions. ... More

QCD threshold corrections to Higgs decay and to hadroproduction in $l^+l^-$ annihilationApr 30 2006We present threshold enhanced QCD corrections to the bottom quark energy distribution in Higgs boson decay and to hadroproduction in $l^+l^-$ annihilation beyond leading order in the strong coupling constant. This is achieved using the resummed decay ... More

$O(α_s^2)$ Timelike Wilson Coefficients for Parton-Fragmentation Functions in Mellin SpaceApr 03 2006We calculate the Mellin moments of the $O(\alpha_s^2)$ coefficient functions for the unpolarized and polarized fragmentation functions. They can be expressed in terms of multiple finite harmonic sums of maximal weight {\sf w = 4}. Using algebraic and ... More

Recent Results on the 3-Loop Heavy Flavor Wilson Coefficients in Deep-Inelastic ScatteringJul 29 2013We report on recent progress in the calculation of the 3-loop massive Wilson coefficients in deep-inelastic scattering at general values of $N$ for neutral and charged current reactions in the asymptotic region $Q^2 \gg m^2$.

The 16th Moment of the Non--Singlet Structure Functions $F_2(x,Q^2)$ and $F_L(x,Q^2)$ to $O(α_s^3)$Nov 08 2004We present the results of an analytic next--to--next--to leading order QCD calculation of the non--singlet anomalous dimension $\gamma_{\rm NS}^+(N)$ and the coefficient functions $C_{2,L}(N)$ associated to the deeply inelastic structure functions $F_2(x,Q^2)$ ... More

3-Loop Corrections to the Heavy Flavor Wilson Coefficients in Deep-Inelastic ScatteringFeb 01 2016A survey is given on the status of 3-loop heavy flavor corrections to deep-inelastic structure functions at large enough virtualities $Q^2$.

$O(α_s^2)$ and $O(α_s^3)$ Heavy Flavor Contributions to Transversity at $Q^2 \gg m^2$Sep 08 2009In deep-inelastic processes the heavy flavor Wilson coefficients factorize for $Q^2 \gg m^2$ into the light flavor Wilson coefficients of the corresponding process and the massive operator matrix elements (OMEs). We calculate the $O(\alpha_s^2)$ and $O(\alpha_s^3)$ ... More

Representation of the virtual Compton amplitude for polarized scattering in the generalized Bjorken regionMay 10 1999The Compton amplitude is calculated in terms of expectation values of light-ray quark operators. As a technical tool we apply the nonlocal light-cone expansion. Thereby we express the expectation value of the vector light-ray operator with the help of ... More

NNLO analysis of unpolarized DIS structure functionsJun 29 2006We present the results of a NNLO QCD analysis of the World data on unpolarized DIS Non-Singlet Structure functions.

Target Mass Corrections in Diffractive ScatteringJun 17 2007We describe the twist-2 contributions to inclusive unpolarized and polarized deep-inelastic diffractive scattering in an operator approach. The representation refers to the observed large rapidity gap but does not require reference to a pomeron picture. ... More

On the Resummation of the $α\ln^2 z Terms for QED Corrections to Deep-Inelastic $ep$ Scattering and $e^+e^-$ AnnihilationNov 02 1996The resummation of the $\alpha \ln^2(z)$ non-singlet contributions is performed for initial state QED corrections. As examples, the effect of the resummation on neutral-current deep-inelastic scattering and the $e^+ e^- \rightarrow \mu^+ \mu^-$ scattering ... More

Moments of the 3--loop corrections to the heavy flavor contribution to $F_2(x,Q^2)$ for $Q^2\gg m^2$Jul 15 2009We calculate moments of the $O(\alpha_s^3)$ heavy flavor contributions to the Wilson coefficients of the structure function $F_2(x,Q^2)$ in the region $Q^2\gg m^2$. The massive Wilson coefficients are obtained as convolutions of massive operator matrix ... More

Generalized Harmonic, Cyclotomic, and Binomial Sums, their Polylogarithms and Special NumbersOct 21 2013A survey is given on mathematical structures which emerge in multi-loop Feynman diagrams. These are multiply nested sums, and, associated to them by an inverse Mellin transform, specific iterated integrals. Both classes lead to sets of special numbers. ... More

The Small-x Evolution of Unpolarized and Polarized Structure FunctionsOct 21 1996A brief overview is presented of recent developments concerning resummed small-x evolution, based upon the renormalization group equation. The non-singlet and singlet structure functions are discussed for both polarized and unpolarized deep-inelastic ... More

Evaluation of Multi-Sums for Large Scale ProblemsFeb 20 2012A big class of Feynman integrals, in particular, the coefficients of their Laurent series expansion w.r.t.\ the dimension parameter $\ep$ can be transformed to multi-sums over hypergeometric terms and harmonic sums. In this article, we present a general ... More

Heavy Flavour Production in Deep--Inelastic Scattering - Two--Loop Massive Operator Matrix Elements and BeyondOct 17 2007Oct 18 2007We calculate the O($\eps$)--term of the two--loop massive operator matrix elements for twist 2--operators, which contribute to the heavy flavour Wilson coefficients in unpolarized deep--inelastic scattering in the asymptotic limit $Q^2 \gg m^2.$ Our calculation ... More

Two-Loop Massive Operator Matrix Elements for Polarized and Unpolarized Deep-Inelastic ScatteringJun 19 2007The $O(\alpha_s^2)$ massive operator matrix elements for unpolarized and polarized heavy flavor production at asymptotic values $Q^2 >> m^2$ are calculated in Mellin space without applying the integration-by-parts method. We confirm previous results given ... More

Twist-2 Light-Ray Operators: Anomalous Dimensions and Evolution EquationsNov 20 1997Nov 25 1997The non-singlet and singlet anomalous dimensions of the twist--2 light-ray operators for unpolarized and polarized deep inelastic scattering are calculated in $O(\alpha_s)$. We apply these results for the derivation of evolution equations for partition ... More

Five-Loop Static Contribution to the Gravitational Interaction Potential of Two Point MassesFeb 28 2019We compute the static contribution to the gravitational interaction potential of two point masses in the velocity-independent five-loop (and 5th post-Newtonian) approximation to the harmonic coordinates effective action in a direct calculation. The computation ... More

Parton distributions and Tevatron jet dataMay 26 2011We study the impact of Tevatron jet data on a global fit of parton distribution functions and on the determination of the value of the strong coupling constant. The consequences are illustrated for cross sections of Higgs boson production at Tevatron ... More

Target mass and finite $t$ corrections to diffractive deeply inelastic scatteringDec 10 2008The quantum field theoretic treatment of inclusive deep--inelastic diffractive scattering given in a previous paper \cite{BGR2006} is discussed in detail using an equivalent formulation with the aim to derive a representation suitable for data analysis. ... More

Evolution Kernels for Light-Ray Operators: Twist 2 and Twist 3 ContributionsMay 29 1997The general evolution kernels of the twist 2 light-ray operators for unpolarized and polarized deep inelastic scattering are calculated in ${\cal O}(\alpha_s)$. From these evolution kernels a series of special evolution equations can be derived, among ... More

Leptoquark Pair Production in Hadronic InteractionsOct 18 1996The scalar and vector leptoquark pair production cross sections in hadronic collisions are calculated. In a model independent analysis we consider the most general C and P conserving couplings of gluons to both scalar and vector leptoquarks described ... More

First $O(α_s^3)$ heavy flavor contributions to deeply inelastic scatteringJun 27 2008In the asymptotic limit $Q^2 \gg m^2$, the heavy flavor Wilson coefficients for deep--inelastic scattering factorize into the massless Wilson coefficients and the universal heavy flavor operator matrix elements resulting from light--cone expansion. In ... More

Non-Singlet QCD Analysis of the Structure Function F_2 in 3-LoopsJul 07 2004Jul 09 2004First results of a non--singlet QCD analysis of the structure function $F_2(x,Q^2)$ in 3--loop order based on the non--singlet world data are presented. Correlated errors are determined and their propagation through the evolution equations is performed ... More

The Virtual Compton Amplitude in the Generalized Bjorken Region: Twist--2 ContributionsMar 29 1999Sep 23 1999A systematic derivation is presented of the twist-2 anomalous dimensions of the general quark and gluon light-ray operators in the generalized Bjorken region in leading order both for unpolarized and polarized scattering. Various representations of the ... More

Vector Leptoquark Pair Production in $e^+e^-$ AnnihilationOct 28 1996The cross section for vector leptoquark pair production in $e^+e^-$ annihilation is calculated for the case of finite anomalous gauge boson couplings $\kappa_{\gamma, Z}$ and $\lambda_{\gamma, Z}$. The minimal cross section is found to behave $\propto ... More

ABM news and benchmarksAug 23 2013We report on progress in the determination of the unpolarised nucleon PDFs within the ABM global fit framework. The data used in the ABM analysis are updated including the charm-production and the high-Q2 neutral-current samples obtained at the HERA collider, ... More

Less Singular Terms and Small x Evolution in a Soluble ModelNov 30 1998We calculate the effect of the less singular terms at small x on the evolution of the coefficient function in \phi^3 theory in six dimensions, which result from a complete solution of the ladder equation. Scale-invariant next-to-leading order contributions ... More

Calculation of Massive 2-Loop Operator Matrix Elements with Outer Gluon LinesFeb 26 2007Massive on-shell operator matrix elements and self-energy diagrams with outer gluon lines are calculated analytically at $O(\alpha_s^2)$, using Mellin-Barnes integrals and representations through generalized hypergeometric functions. This method allows ... More

Logarithmic $O(α_s^3)$ contributions to the DIS Heavy Flavor Wilson Coefficients at $Q^2 \gg m^2$Aug 04 2010Aug 16 2010The logarithmic contributions to the massive twist-2 operator matrix elements for deep-inelastic scattering are calculated to $O(\alpha_s^3)$for general values of the Mellin variable $N$.

The Gluonic Operator Matrix Elements at O(α_s^2) for DIS Heavy Flavor ProductionJan 06 2009We calculate the $O(\alpha_s^2)$ gluonic operator matrix elements for the twist--2 operators, which contribute to the heavy flavor Wilson coefficients in unpolarized deeply inelastic scattering in the region $Q^2 \gg m^2$, up to the linear terms in the ... More

The asymptotic behavior of the heavy quark form factors at higher orderOct 21 2018In the asymptotic limit $Q^2 \gg m^2$, the heavy quark form factors exhibit Sudakov behavior. We study the corresponding renormalization group equations of the heavy quark form factors which do not only govern the structure of infrared divergences, but ... More

2- and 3-Loop Heavy Flavor Corrections to TransversitySep 08 2009We calculate the two- and three-loop massive operator matrix elements (OMEs) contributing to the heavy flavor Wilson coefficients of transversity. We obtain the complete result for the two-loop OMEs and compute the first thirteen Mellin moments at three-loop ... More

On the Evolution Kernels of Twist 2 Light-Ray Operators for Unpolarized and Polarized Deep Inelastic ScatteringMay 08 1997May 28 1997The non-singlet and singlet evolution kernels of the twist--2 light-ray operators for unpolarized and polarized deep inelastic scattering are calculated in $O(\alpha_s)$ for the general case of virtualities $q^2, q'^2 \neq 0$. Special cases as the kernels ... More

Leptoquark Pair Production at HERAAug 29 1996The scalar and vector leptoquark pair production cross sections for deep inelastic $ep$ scattering are calculated. Estimates are presented for the search potential at HERA.

Parton Distributions and $α_s$ for the LHCMar 05 2013Mar 16 2013We report on recent determinations of NNLO parton distributions and of $\alpha_s(M_Z)$ based on the world deep-inelastic data, supplemented by collider data. Some applications are discussed for semi-inclusive processes at the LHC.

Heavy-quark production in deep-inelastic scatteringJul 27 2013We report recent experimental and theoretical progress concerning the heavy-quark electro-production in the context of the ABM11 parton distribution function (PDF) fit. In the updated ABM11 analysis, including the recent combined HERA charm data, the ... More

Determination of $α_s$ and $m_c$ in deep-inelastic scatteringJul 04 2013We describe the determination of the strong coupling constant $\alpha_s(M_Z^2)$ and of the charm-quark mass $m_c(m_c)$ in the $\bar{\rm MS}$-scheme, based on the QCD analysis of the unpolarized World deep-inelastic scattering data. At NNLO the values ... More

Evaluating Two-Loop massive Operator Matrix Elements with Mellin-Barnes IntegralsJul 27 2006We calculate massive 5-propagator 2-loop integrals for operator matrix elements in the light-cone expansion, using Mellin-Barnes techniques and representations through generalized hypergeometric functions.

Heavy flavor operator matrix elements at $O(a_s^3)$Dec 12 2008The heavy quark effects in deep--inelastic scattering in the asymptotic regime $Q^2 \gg m^2$ can be described by heavy flavor operator matrix elements. Complete analytic expressions for these objects are currently known to ${\sf NLO}$. We present first ... More

Higher order corrections to heavy flavour production in deep inelastic scatteringJun 03 2008In the asymptotic limit $Q^2 \gg m^2$, the non-power corrections to the heavy flavour Wilson coefficients in deep--inelastic scattering are given in terms of massless Wilson coeffcients and massive operator matrix elements. We start extending the existing ... More

Higher Order Heavy Quark Corrections to Deep-Inelastic ScatteringNov 20 2014The 3-loop heavy flavor corrections to deep-inelastic scattering are essential for consistent next-to-next-to-leading order QCD analyses. We report on the present status of the calculation of these corrections at large virtualities $Q^2$. We also describe ... More

Iterated Binomial Sums and their Associated Iterated IntegralsJul 03 2014We consider finite iterated generalized harmonic sums weighted by the binomial $\binom{2k}{k}$ in numerators and denominators. A large class of these functions emerges in the calculation of massive Feynman diagrams with local operator insertions starting ... More

3-Loop Heavy Flavor Corrections to DIS with two Massive Fermion LinesJun 29 2011We report on recent results obtained for the massive operator matrix elements which contribute to the massive Wilson coefficients in deep-inelastic scattering for $Q^2 \gg m_i^2$ in case of sub-processes with two fermion lines and different mass assignment. ... More

Heavy Quark Form Factors at Three Loops in the Planar LimitApr 19 2018We compute the color-planar and complete light quark non-singlet contributions to the heavy quark form factors in the case of the axialvector, scalar and pseudoscalar currents at three loops in perturbative QCD. We evaluate the master integrals applying ... More

Automated Solution of First Order Factorizable Systems of Differential Equations in One VariableOct 29 2018We present an algorithm which allows to solve analytically linear systems of differential equations which factorize to first order. The solution is given in terms of iterated integrals over an alphabet where its structure is implied by the coefficient ... More

The Multiple Zeta Value Data MineJul 15 2009Nov 14 2009We provide a data mine of proven results for multiple zeta values (MZVs) of the form $\zeta(s_1,s_2,...,s_k)=\sum_{n_1>n_2>...>n_k>0}^\infty \{1/(n_1^{s_1} >... n_k^{s_k})\}$ with weight $w=\sum_{i=1}^k s_i$ and depth $k$ and for Euler sums of the form ... More

Modern Summation Methods and the Computation of 2- and 3-loop Feynman DiagramsJun 24 2010By symbolic summation methods based on difference fields we present a general strategy that transforms definite multi-sums, e.g., in terms of hypergeometric terms and harmonic sums, to indefinite nested sums and products. We succeeded in this task with ... More

Summary of Working Group I: Hadron StructureJul 22 1997A summary is given on the main aspects which were discussed by the working group. They include new results on the deep inelastic scattering structure functions $F_2, xF_3, F_L$ and $F_2^{c\bar{c}}$ and their parametrizations, the measurement of the gluon ... More

Twist-4 Gluon Recombination Corrections for Deep Inelastic Structure FunctionsFeb 02 2001Feb 04 2001We calculate twist--4 coefficient functions for the deep inelastic structure function $F_2(x,Q^2)$ associated to 4--gluon operator matrix elements for general values of the Bjorken variable $x$ and study the numerical effect on the slope $\partial F_2(x,Q^2)/\partial ... More

The Drell-Levy-Yan Relation: ep vs $e^+e^-$ Scattering to $O(α_s^2)$Jan 22 2001We study the validity of a relation by Drell, Levy and Yan (DLY) connecting the deep inelastic structure (DIS) functions and the single-particle fragmentation functions in $e^+e^-$ annihilation which are defined in the spacelike ($q^2<0$) and timelike ... More

Relations among Higher Order QCD correctionsMay 27 1999We study the scheme transformation of next to leading order QCD corrections to various processes. An interesting relation by Drell, Levy and Yan (DLY) among space like and time like processes is studied carefully in the next to leading order level. We ... More

On the Gluon Regge Trajectory in $O(α_s^2)$Jun 12 1998We recalculate the gluon Regge trajectory in next-to-leading order to clarify a discrepancy between two results in the literature on the constant part. We confirm the result obtained by Fadin et al.~\cite{FFK}. The effects on the anomalous dimension and ... More