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I. Bierenbaum

Publications and source records attributed to I. Bierenbaum.

16 recordsLinked to original sources
arXiv2022

$O(α_s^2$) Polarized Heavy Flavor Corrections}to Deep-Inelastic Scattering at $Q^2 \gg m^2$

We calculate the quarkonic $O(α_s^2)$ massive operator matrix elements $ΔA_{Qg}(N), ΔA_{Qq}^{\rm PS}(N)$ and $ΔA_{qq,Q}^{\rm NS}(N)$ for the twist--2 operators and the associated heavy flavor Wilson coefficients in polarized deeply inelastic scattering in the region $Q^2 \gg m^2$ to $O(\varepsilon)$ in the case of the inclusive heavy flavor contributions. The evaluation is performed in Mellin space, without applying the integration-by-parts method. The result is given in terms of harmonic sums. This leads to a significant compactification of the operator matrix elements and massive Wilson coefficients in the region $Q^2 \gg m^2$ derived previously in \cite{BUZA2}, which we partly confirm, and also partly correct. The results allow to determine the heavy flavor Wilson coefficients for $g_1(x,Q^2)$ to $O(α_s^2)$ for all but the power suppressed terms $\propto (m^2/Q^2)^k, k \geq 1$. The results in momentum fraction $z$-space are also presented. We also discuss the small $x$ effects in the polarized case. Numerical results are presented. We also compute the gluonic matching coefficients in the two--mass variable flavor number scheme to $O(\varepsilon)$.

hep-ph↗
arXiv2014

The Logarithmic Contributions to the O(α_s^3) Asymptotic Massive Wilson Coefficients and Operator Matrix Elements in Deeply Inelastic Scattering

We calculate the logarithmic contributions to the massive Wilson coefficients for deep-inelastic scattering in the asymptotic region $Q^2 \gg m^2$ to 3-loop order in the fixed-flavor number scheme and present the corresponding expressions for the massive operator matrix elements needed in the variable flavor number scheme. Explicit expressions are given both in Mellin-$N$ space and $z$-space.

hep-ph↗
arXiv2010

Heavy Flavor DIS Wilson coefficients in the asymptotic regime

We report on results for the heavy flavor contributions to $F_2(x,Q^2)$ in the limit $Q^2\gg m^2$ at {\sf NNLO}. By calculating the massive $3$--loop operator matrix elements, we account for all but the power suppressed terms in $m^2/Q^2$. Recently, the calculation of fixed Mellin moments of all $3$--loop massive operator matrix elements has been finished. We present new all--$N$ results for the $O(n_f)$--terms, thereby confirming the corresponding parts of the $3$--loop anomalous dimensions. Additionally, we report on first genuine $3$--loop results of the ladder--type diagrams for general values of the Mellin variable $N$.

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

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

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

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↗