NNLO analysis of unpolarized DIS structure functions
We present the results of a NNLO QCD analysis of the World data on unpolarized DIS Non-Singlet Structure functions.
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arXiv subjects
J. Blümlein
Publications and source records attributed to J. Blümlein.
QCD threshold corrections to Higgs decay and to hadroproduction in $l^+l^-$ annihilation
We 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 distribution obtained using renormalisation group invariance and the mass factorisation theorem that they satisfy and Sudakov resummation of soft gluons.
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$O(α_s^2)$ Timelike Wilson Coefficients for Parton-Fragmentation Functions in Mellin Space
We calculate the Mellin moments of the $O(α_s^2)$ 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 structural relations between harmonic sums one finds that besides the single harmonic sums only three basic sums and their derivatives w.r.t. the summation index contribute. The Mellin moments are analytically continued to complex values of the Mellin variable. This representation significantly reduces the large complexity being present in $x$--space calculations and allow very compact and fast numerical implementations.
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Mellin Moments of the Next-to-next-to Leading Order Coefficient Functions for the Drell-Yan Process and Hadronic Higgs-Boson Production
We 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 and structural relations between harmonic sums one finds that besides the single harmonic sums only five basic sums and their derivatives w.r.t. the summation index contribute. This representation reduces the large complexity being present in x-space calculations and is well suited for fast numerical implementations.
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Scheme-invariant NNLO evolution for unpolarized DIS structure functions
We 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 $α_s(M_Z^2)$ to $\sim 1$% in order to match the accuracy forseen for experimental errors from future high statistics measurements.
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The 16th Moment of the Non--Singlet Structure Functions $F_2(x,Q^2)$ and $F_L(x,Q^2)$ to $O(α_s^3)$
We present the results of an analytic next--to--next--to leading order QCD calculation of the non--singlet anomalous dimension $γ_{\rm NS}^+(N)$ and the coefficient functions $C_{2,L}(N)$ associated to the deeply inelastic structure functions $F_2(x,Q^2)$ and $F_L(x,Q^2)$ for the Mellin moment N=16. Comparisons are made with results in the literature.
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Non-Singlet QCD Analysis of the Structure Function F_2 in 3-Loops
First 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 analytically. The value for $α_s(M_Z)$ is determined to be $0.1135 +/- 0.0023/0.0026$ compatible with results from other QCD analyses. Low moments for $u_v(x)$, $d_v(x)$ and $u_v(x) - d_v(x)$ with correlated errors are calculated which may be compared with results from lattice simulations.
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NNLO coefficient functions of Higgs and Drell--Yan cross sections in Mellin space
We 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. Various algebraic relations among these finite sums reduce the complexity of the results suitable for fast numerical evaluations. It is shown that only five non--trivial functions occur besides Euler's $ψ$--function in the representation of these Wilson coefficients.
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Mathematical Structure of Anomalous Dimensions and QCD Wilson Coefficients in Higher Order
The 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 their value. We show how to find a basis of the associated algebra. The length of the basis $l$ is found to be $\leq 1/d$, where $d$ is the depth of the sums considered and is given by the 2nd {\sc Witt} formula. It can be also determined counting the {\sc Lyndon} words of the respective index set. There are two further classes of relations: structural relations between {\sc Nielsen}--type integrals and relations due to the specific structure of {\sc Feynman} diagrams which lead to a considerable reduction of the set of basic functions. The relations derived can be used to simplify results of higher order calculations in QED and QCD. We also report on results calculating the 16th non--singlet moment of unpolarized structure functions at 3--loop order in the $\bar{\rm MS}$ scheme.
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Algebraic Relations Between Harmonic Sums and Associated Quantities
We 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 harmonic sums only, but not on their value. They are therefore valid for all other mathematical objects which obey the same multiplication relation or can be obtained as a special case thereof, as the harmonic polylogarithms. We verify that the number of independent elements for a given index set can be determined by counting the Lyndon words which are associated to this set. The algebraic relations between the finite harmonic sums can be used to reduce the high complexity of the expressions for the Mellin moments of the Wilson coefficients and splitting functions significantly for massless field theories as QED and QCD up to three loop and higher orders in the coupling constant and are also of importance for processes depending on more scales. The ratio of the number of independent sums thus obtained to the number of all sums for a given index set is found to be $\leq 1/d$ with $d$ the depth of the sum independently of the weight. The corresponding counting relations are given in analytic form for all classes of harmonic sums to arbitrary depth and are tabulated up to depth $d=10$.
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NLL QED Corrections to Deep Inelastic Scattering
The $O(α^2\log(Q^2/m_e^2))$ leptonic QED corrections to unpolarized deeply inelastic electron-nucleon scattering are calculated in the mixed variables.
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Twist-2 Heavy Flavor Contributions to the Structure Function $g_2(x,Q^2)$
The twist--2 heavy flavor contributions to the polarized structure function $g_2(x,Q^2)$ are calculated. We show that this part of $g_2(x,Q^2)$ is related to the heavy flavor contribution to $g_1(x,Q^2)$ by the Wandzura--Wilczek relation to all orders in the strong coupling constant. Numerical results are presented.
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Polarized Parton Densities
In 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 $1σ$ statistical errors were derived and parameterized. The strong coupling constant $α_s(M_Z^2)$ is determined $α_s(M_Z^2) = 0.113 \pm 0.004 {\rm (stat.)} \pm~0.004 {\rm (fac.)} +0.008/-0.005 {\rm (ren.)}$ Comparisons of the low moments of the parton densities with recent lattice results are given. A detailed error-analysis of the gluon density is performed.
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O(α^2 L) Radiative Corrections to Deep Inelastic ep Scattering
The leptonic QED radiative corrections are calculated in the next-to-leading log approximation ${\cal O}[α^2 \ln(Q^2/m_e^2)]$ for unpolarized deeply inelastic $ep$--scattering in the case of mixed variables. The corrections are determined using mass factorization in the OMS--scheme for the double--differential scattering cross sections.
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Universal QED Corrections to Polarized Electron Scattering in Higher Orders
We 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 leading terms propertional to (alpha ln^2(x))^k to all orders.
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Polarized Deep Inelastic Diffractive Scattering near the Light Cone
Polarized 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 via g_1^{D(3)} by a Wandzura--Wilczek relation.
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QCD Analysis of Polarized Scattering Data and New Polarized Parton Distributions
In 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$σ$ error bands. Furthermore the value of $α_s(M_Z^2)$ is determined. Finally a number of low moments of the polarized parton densities are compared with results from lattice simulations.
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QCD Analysis of Polarized Deep Inelastic Data and Parton Distributions
A 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 $x ε[10^{-9},1], Q^2 ε[1,10^6] \GeV^2$. The extrapolation far outside the domain of the current measurements is given both to allow for applications at higher values of $Q^2$ and to be able to calculate integral properties of the present distributions. The values of $Λ_{\rm QCD}$ and $α_s(M_z)$ are determined. Emphasis is put on the derivation of the fully correlated $1σ$ error bands for these distributions, which are also given in terms of parameterizations and are directly applicable to determine experimental errors of other polarized observables. The impact of the variation of both the renormalization and factorization scales on the value of $α_s$ is studied. Finally we perform a factorization--scheme invariant QCD analysis based on the observables $g_1(x,Q^2)$ and $d g_1(x,Q^2)/d \log(Q^2)$ in next-to-leading order, which is compared to the standard analysis. A series of low moments of parton densities, accounting for error correlation, are given to allow for comparison with results from lattice simulations.
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