Searcharxiv⌕ Search

arXiv subjects

J. Blümlein

Publications and source records attributed to J. Blümlein.

At least 145 records · Page 8Linked to original sources
arXiv2009

Variable-Flavor-Number Scheme in Analysis of Heavy-Quark Electro-Production Data

We check the impact of the factorization scheme employed in the calculation of the heavy-quark deep-inelastic scattering (DIS) electro-production on the PDFs determined in the NNLO QCD analysis of the world inclusive neutral-current DIS data combined with the ones on the neutrino-nucleon DIS di-muon production and the fixed-target Drell-Yan process. The charm-quark DIS contribution is calculated in the general-mass variable-flavor-number (GMVFN) scheme: At asymptotically large values of the momentum transfer $Q$ it is given by the zero-mass 4-flavor scheme and at the value of $Q$ equal to the charm-quark mass it is smoothly matched with the 3-flavor scheme using the Buza-Matiounine-Smith-van Neerven prescription. The PDFs obtained in this variant of the fit are very similar to the ones obtained in the fit with a 3-flavor scheme employed. Our 5-flavor PDFs derived from the 3-flavor ones using the NNLO matching conditions are used to calculate the rates of $W^{\pm}/Z$ and $t\bar{t}$ production at the Tevatron collider and the LHC at NNLO.

hep-ph↗
arXiv2009

Moments of the 3--loop corrections to the heavy flavor contribution to $F_2(x,Q^2)$ for $Q^2\gg m^2$

We calculate moments of the $O(α_s^3)$ 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 elements (OMEs) and the known light flavor Wilson coefficients. The calculation of moments of the massive OMEs involves a first independent recalculation of moments of the fermionic contributions to all 3--loop anomalous dimensions of the unpolarized twist--2 local composite operators stemming from the light--cone expansion \cite{url}.

hep-ph↗
arXiv2009

From Moments to Functions in Quantum Chromodynamics

Single-scale quantities, like the QCD anomalous dimensions and Wilson coefficients, obey difference equations. Therefore their analytic form can be determined from a finite number of moments. We demonstrate this in an explicit calculation by establishing and solving large scale recursions by means of computer algebra for the anomalous dimensions and Wilson coefficients in unpolarized deeply inelastic scattering from their Mellin moments to 3-loop order.

hep-ph↗
arXiv2009

Determining the closed forms of the $O(a_s^3)$ anomalous dimensions and Wilson coefficients from Mellin moments by means of computer algebra

Single scale quantities, as anomalous dimensions and hard scattering cross sections, in renormalizable Quantum Field Theories are found to obey difference equations of finite order in Mellin space. It is often easier to calculate fixed moments for these quantities compared to a direct attempt to derive them in terms of harmonic sums and their generalizations involving the Mellin parameter $N$. Starting from a sufficiently large number of given moments, we establish linear recurrence relations of lowest possible order with polynomial coefficients of usually high degree. Then these recurrence equations are solved in terms of d'Alembertian solutions where the involved nested sums are represented in optimal nested depth. Given this representation, it is then an easy task to express the result in terms of harmonic sums. In this process we compactify the result such that no algebraic relations occur among the sums involved. We demonstrate the method for the QCD unpolarized anomalous dimensions and massless Wilson coefficients to 3--loop order treating the contributions for individual color coefficients. For the most complicated subproblem 5114 moments were needed in order to produce a recurrence of order 35 whose coefficients have degrees up to 938. About four months of CPU time were needed to establish and solve the recurrences for the anomalous dimensions and Wilson coefficients on a 2 GHz machine requiring less than 10 GB of memory. No algorithm is known yet to provide such a high number of moments for 3--loop quantities. Yet the method presented shows that it is possible to establish and solve recurrences of rather large order and and degree, occurring in physics problems, uniquely, fast and reliably with computer algebra.

hep-ph↗
arXiv2009

The Gluonic Operator Matrix Elements at O(α_s^2) for DIS Heavy Flavor Production

We calculate the $O(α_s^2)$ 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 dimensional parameter $\varepsilon$, ($D= 4 + \varepsilon$). These quantities are required for the description of parton distribution functions in the variable flavor number scheme (VFNS). The $O(α_s^2 \varepsilon)$ terms contribute at the level of the $O(α_s^3)$ corrections through renormalization. We also comment on additional terms, which have to be considered in the fixed (FFNV) and variable flavor number scheme, adopting the $\overline{\rm MS}$ scheme for the running coupling constant.

hep-ph↗
arXiv2008

Heavy flavor operator matrix elements at $O(a_s^3)$

The 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 results for fixed moments at ${\sf NNLO}$. This involves a recalculation of fixed moments of the corresponding ${\sf NNLO}$ anomalous dimensions, which we thereby confirm.

hep-ph↗
arXiv2008

Target mass and finite $t$ corrections to diffractive deeply inelastic scattering

The 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. We consider the off-cone twist--2 light-cone operators to derive the target mass and finite $t$ corrections to diffractive deep--inelastic scattering and deep--inelastic scattering. The corrections turn out to be at most proportional to $x |t|/Q^2, x M^2/Q^2, x = x_{\rm BJ} {\rm or} x_\PP$, which suggests an expansion in these parameters. Their contribution varies in size considering diffractive scattering or meson--exchange processes. Relations between different kinematic amplitudes which are determined by one and the same diffractive GPD or its moments are derived. In the limit $t, M^2 \to 0$ one obtains the results of \cite{Blumlein:2001xf} and \cite{Blumlein:2002fw}.

hep-ph↗
arXiv2008

First $O(α_s^3)$ heavy flavor contributions to deeply inelastic scattering

In 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 this way, one can calculate all but the power corrections in $(m^2/Q^2)^k, k > 0$. The heavy flavor operator matrix elements are known to ${\sf NLO}$. We present the last 2--loop result missing in the unpolarized case for the renormalization at 3--loops and first 3--loop results for terms proportional to the color factor $T_F^2$ in Mellin--space. In this calculation, the corresponding parts of the ${\sf NNLO}$ anomalous dimensions \cite{LARIN,MVVandim} are obtained as well.

hep-ph↗
arXiv2008

Higher order corrections to heavy flavour production in deep inelastic scattering

In 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 NLO calculation for these operator matrix elements by calculating the O($ε$) terms of the two--loop expressions and having first investigations into the three--loop diagrams needed to O($α_s^3$).

hep-ph↗
arXiv2007

Heavy Flavour Production in Deep--Inelastic Scattering - Two--Loop Massive Operator Matrix Elements and Beyond

We 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 was performed in Mellin space using Mellin--Barnes integrals and generalized hypergeometric functions. The O($\eps$)--term contributes in the renormalization at 3--loop order.

hep-ph↗
arXiv2007

Difference Equations in Massive Higher Order Calculations

The calculation of massive 2--loop operator matrix elements, required for the higher order Wilson coefficients for heavy flavor production in deeply inelastic scattering, leads to new types of multiple infinite sums over harmonic sums and related functions, which depend on the Mellin parameter $N$. We report on the solution of these sums through higher order difference equations using the summation package {\tt Sigma}.

math-ph↗
arXiv2007

Target Mass Corrections in Diffractive Scattering

We 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. We discuss both the case of vanishing target mass $M$ and momentum transfer $t$ as well as the effects at finite $t$ and $M$, which lead to modifications at large $β$ and low values of $Q^2$.

hep-ph↗
arXiv2007

Calculation of Massive 2-Loop Operator Matrix Elements with Outer Gluon Lines

Massive on-shell operator matrix elements and self-energy diagrams with outer gluon lines are calculated analytically at $O(α_s^2)$, using Mellin-Barnes integrals and representations through generalized hypergeometric functions. This method allows for a direct evaluation without decomposing the integrals using the integration-by-parts method.

hep-ph↗