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J. Blümlein

Publications and source records attributed to J. Blümlein.

At least 181 records · Page 10Linked to original sources
arXiv2002

Polarized Deep Inelastic Diffractive ep Scattering: Operator Approach

Polarized 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 Bjorken region applying the generalized optical theorem. The diffractive structure functions $g_1^{D(3)}$ and $g_2^{D(3)}$ are calculated in the twist-2 approximation and are expressed by diffractive parton distributions, which are derived from pseudo-scalar two-variable operator expectation values. In this approximation the structure functions $g_2^{D(3)}$ is obtained from $g_1^{D(3)}$ by a Wandzura-Wilczek relation similar as for deep inelastic scattering. The evolution equations are given. We also comment on the higher twist contributions in the light-cone expansion.

hep-ph↗
arXiv2001

On the Scaling Violations of Diffractive Structure Functions: Operator Approach

A 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. Evolution equations of the diffractive hadronic matrix elements are derived at the level of the twist-2 contributions and are compared to those of inclusive deep-inelastic forward scattering (DIS). The diffractive parton densities are obtained as projections of two-variable parton distributions. We also comment on the higher twist contributions in the light-cone expansion.

hep-ph↗
arXiv2001

QCD Analysis of Polarized Deep Inelastic Scattering Data

A 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 $α_s(M_Z)$ is determined. Emphasis is put on the derivation of fully correlated error bands for these distributions which 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 a factorization-scheme invariant QCD analysis based on the observables $g_1(x,Q^2)$ and $d g_1(x,Q^2)/d \log(Q^2)$ is performed in next-to-leading order, which is compared to the standard analysis.

hep-ph↗
arXiv2001

Twist-4 Gluon Recombination Corrections for Deep Inelastic Structure Functions

We 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 $\partial F_2(x,Q^2)/\partial \log Q^2$. It is shown that these contributions diminish the strongly rising twist--2 terms towards small values of $x$.

hep-ph↗
arXiv2001

The Drell-Levy-Yan Relation: ep vs $e^+e^-$ Scattering to $O(α_s^2)$

We 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 ($q^2>0$) regions, with respect to physical evolution kernels for the two processes to $O(α_s^2)$. We also comment on a relation proposed by Gribov and Lipatov.

hep-ph↗
arXiv2000

Target Mass Corrections to the Spin-dependent Structure Functions

The 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 functions is considered.

hep-ph↗
arXiv2000

Harmonic Sums and Mellin Transforms up to two-loop Order

A 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 QCD up to two--loop order, as the unpolarized and polarized splitting functions, coefficient functions, and hard scattering cross sections for space and time-like momentum transfer. The finite harmonic sums are calculated explicitly in the linear representation. Algebraic relations connecting these sums are derived to obtain representations based on a reduced set of basic functions. The Mellin transforms of all the corresponding Nielsen functions are calculated.

hep-ph↗
arXiv2000

On the Drell-Levy-Yan Relation to $O(α_s^2)$

We 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 (q^2>0) regions respectively. Here q denotes the momentum of the virtual photon exchanged in the deep inelastic scattering process or the annihilation process. An extension of the DLY-relation, which originally was only derived in the scaling parton model, to all orders in QCD leads to a connection between the two evolution kernels determining the q^2-dependence of the DIS structure functions and the fragmentation functions respectively. In relation to this we derive the transformation relations between the space-and time-like splitting functions up to next-to-leading order (NLO) and the coefficient functions up to NNLO both for unpolarized and polarized scattering. It is shown that the evolution kernels describing the combined singlet evolution for the structure functions F_2(x,Q^2), F_L(x,Q^2) where Q^2=|q^2| or $F_2(x,Q^2), \partial F_2(x,Q^2)/\partial \ln(Q^2)$ and the corresponding fragmentation functions satisfy the DLY relation up to next-to-leading order. We also comment on a relation proposed by Gribov and Lipatov.

hep-ph↗
arXiv1999

On the Relations Between Polarized Structure Functions

The 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 can be tested in the upcoming high statistics measurements of the structure function $g_2(x,Q^2)$ in the range $Q^2 \gsim M_p^2$.

hep-ph↗
arXiv1999

The Virtual Compton Amplitude in the Generalized Bjorken Region: Twist--2 Contributions

A 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 anomalous dimensions are derived both in the non-local and the local light cone expansion and their properties are discussed in detail. Evolution equations for these operators are derived using different representations. General two- and single-variable evolution equations are presented for the expectation values of these operators for non-forward scattering. The Compton amplitude is calculated in terms of these distribution amplitudes. In the limit of forward scattering a new derivation of the integral relations between the twist-2 contributions to the structure functions is given. Special limiting cases which are derived from the general relations are discussed, as the forward case, near-forward scattering, and vacuum-meson transition. Solutions of the two-variable evolution equations for non-forward scattering are presented.

hep-ph↗
arXiv1999

Relations Between Polarized Structure Functions

The 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 $Q^2 \gsim M_p^2$.

hep-ph↗
arXiv1999

Relations among Higher Order QCD corrections

We 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 construct factorisation scheme invariants and show that they are DLY-invariant.

hep-ph↗
arXiv1999

Representation of the virtual Compton amplitude for polarized scattering in the generalized Bjorken region

The 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 the expectation value of the corresponding scalar operator of twist 2. This allows important simplifications. In the limit of forward scattering the integral relations between the twist-2 contributions of the structure functions are implied directly.

hep-ph↗
arXiv1998

Target Mass Corrections for Polarized Structure Functions and New Sum Rules

The 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 derived both in Mellin-$n$ and $x$-space. The impact of the target mass corrections on the general relations between the twist--2 and twist--3 parts of the structure functions is studied and three new relations between the twist--3 contributions are derived.

hep-ph↗
arXiv1998

Relations among QCD corrections beyond leading order

The status of various relations among higher order QCD corrections is discussed. In particular, Drell-Levy-Yan relation and Supersymmetric relation are studied at the two-loop level. We have also investigated the validity of such relations for physical observables.

hep-ph↗
arXiv1998

Less Singular Terms and Small x Evolution in a Soluble Model

We calculate the effect of the less singular terms at small x on the evolution of the coefficient function in ϕ^3 theory in six dimensions, which result from a complete solution of the ladder equation. Scale-invariant next-to-leading order contributions are also studied. We show that the small x approximation does not deliver the dominant contributions.

hep-ph↗
arXiv1998

The Unpolarized Gluon Anomalous Dimension at Small x

We discuss the quantitative consequences of the resummation of the small-x contributions to the anomalous dimensions beyond next-to-leading order in alpha_s and up to next order in ln(1/x) (NLx) in a framework based on the renormalization group equations. We find large and negative effects leading to negative values for the {\sf total} splitting function P_{gg}(x,alpha_s) already for x \lsim 0.01 at Q^2 \simeq 20 GeV^2. Terms less singular than those under consideration turn out to be quantitatively as important and need to be included. We derive the effects of the conformal part of the NLx contributions to the anomalous dimensions and discuss the exponent omega describing the s^omega behavior of inclusive cross sections.

hep-ph↗