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Sebastian Klein - One of the best experts on this subject based on the ideXlab platform.
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The Polarized Three-Loop Anomalous Dimensions from On-Shell Massive Operator Matrix Elements
arXiv: High Energy Physics - Phenomenology, 2019Co-Authors: Arnd Behring, A. De Freitas, A. Von Manteuffel, Carsten Schneider, Sebastian Klein, J. Blümlein, A. Goedicke, K. SchönwaldAbstract:We calculate all contributions $\propto T_F$ to the polarized three-loop anomalous dimensions in the M-scheme using massive Operator Matrix elements and compare to results in the literature. This includes the complete anomalous dimensions $\gamma_{qq}^{(2),\rm PS}$ and $\gamma_{qg}^{(2)}$. We also obtain the complete two-loop polarized anomalous dimensions in an independent calculation. While for most of the anomalous dimensions the usual direct computation methods in Mellin $N$-space can be applied since all recurrences factorize at first order, this is not the case for $\gamma_{qg}^{(2)}$. Due to the necessity of deeper expansions of the master integrals in the dimensional parameter $\varepsilon = D-4$, we had to use the method of arbitrary high moments to eliminate elliptic contributions in intermediate steps. 4000 moments were generated to determine this anomalous dimension and 2640 moments turned out to be sufficient. As an aside, we also recalculate the contributions $\propto T_F$ to the three-loop QCD $\beta$-function.
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The polarized three-loop anomalous dimensions from on-shell massive Operator Matrix elements
Nuclear Physics B, 2019Co-Authors: Arnd Behring, A. De Freitas, A. Von Manteuffel, Carsten Schneider, Sebastian Klein, J. Blümlein, A. Goedicke, K. SchönwaldAbstract:Abstract We calculate all contributions ∝ T F to the polarized three–loop anomalous dimensions in the M–scheme using massive Operator Matrix elements and compare to results in the literature. This includes the complete anomalous dimensions γ q q ( 2 ) , PS and γ q g ( 2 ) . We also obtain the complete two–loop polarized anomalous dimensions in an independent calculation. While for most of the anomalous dimensions the usual direct computation methods in Mellin N–space can be applied since all recurrences factorize at first order, this is not the case for γ q g ( 2 ) . Due to the necessity of deeper expansions of the master integrals in the dimensional parameter e = D − 4 , we had to use the method of arbitrary high moments to eliminate elliptic contributions in intermediate steps. 4000 moments were generated to determine this anomalous dimension and 2640 moments turned out to be sufficient. As an aside, we also recalculate the contributions ∝ T F to the three–loop QCD β–function.
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The O(αs3nfTF2CA,F) contributions to the gluonic massive Operator Matrix elements
Nuclear Physics B, 2013Co-Authors: Johannes Blümlein, Sebastian Klein, A. Hasselhuhn, Carsten SchneiderAbstract:Abstract The O ( α s 3 n f T F 2 C A , F ) terms to the massive gluonic Operator Matrix elements are calculated for general values of the Mellin variable N using a new summation technique. These twist-2 Matrix elements occur as transition functions in the variable flavor number scheme at NNLO. The calculation uses sum-representations in generalized hypergeometric series turning into harmonic sums. The analytic continuation to complex values of N is provided.
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F C A,F ) Contributions to the Gluonic Massive Operator Matrix Elements
2012Co-Authors: A. Hasselhuhn, Sebastian Klein, Carsten SchneiderAbstract:The O(� 3nfT 2 F CA,F) terms to the massive gluonic Operator Matrix elements are calculated for general values of the Mellin variable N. These twist-2 Matrix elements occur as transition functions in the variable flavor number scheme at NNLO. The calculation uses sum-representations in generalized hypergeometric series turning into harmonic sums. The analytic continuation to complex values of N is provided.
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Massive 3-loop Ladder Diagrams for Quarkonic Local Operator Matrix Elements
Nuclear Physics B, 2012Co-Authors: Jakob Ablinger, Johannes Blümlein, Carsten Schneider, Sebastian Klein, A. Hasselhuhn, F. WißbrockAbstract:Abstract 3-loop diagrams of the ladder-type, which emerge for local quarkonic twist-2 Operator Matrix elements, are computed directly for general values of the Mellin variable N using Appell-function representations and applying modern summation technologies provided by the package Sigma and the method of hyperlogarithms. In some of the diagrams generalized harmonic sums with ξ ∈ { 1 , 1 / 2 , 2 } emerge beyond the usual nested harmonic sums. As the asymptotic representation of the corresponding integrals shows, the generalized sums conspire giving well behaved expressions for large values of N . These diagrams contribute to the 3-loop heavy flavor Wilson coefficients of the structure functions in deep-inelastic scattering in the region Q 2 ≫ m 2 .
Carsten Schneider - One of the best experts on this subject based on the ideXlab platform.
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The three-loop single mass polarized pure singlet Operator Matrix element
Nuclear Physics B, 2020Co-Authors: Jakob Ablinger, Arnd Behring, Johannes Blümlein, A. De Freitas, A. Von Manteuffel, Carsten Schneider, K. SchönwaldAbstract:Abstract We calculate the massive polarized three-loop pure singlet Operator Matrix element A Q q ( 3 ) , PS in the single mass case in the Larin scheme. This Operator Matrix element contributes to the massive polarized three-loop Wilson coefficient H Q q ( 3 ) , PS in deep-inelastic scattering and constitutes a three-loop transition Matrix element in the variable flavor number scheme. We provide analytic results in Mellin N and in x space and study the behaviour of this Operator Matrix element in the region of small and large values of the Bjorken variable x.
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The two-mass contribution to the three-loop polarized gluonic Operator Matrix element Agg,Q(3)
Nuclear Physics B, 2020Co-Authors: Jakob Ablinger, Johannes Blümlein, A. De Freitas, Carsten Schneider, M. Saragnese, A. Goedicke, K. SchönwaldAbstract:Abstract We compute the two-mass contributions to the polarized massive Operator Matrix element A g g , Q ( 3 ) at third order in the strong coupling constant α s in Quantum Chromodynamics analytically. These corrections are important ingredients for the matching relations in the variable flavor number scheme and for the calculation of Wilson coefficients in deep–inelastic scattering in the asymptotic regime Q 2 ≫ m c 2 , m b 2 . The analytic result is expressed in terms of nested harmonic, generalized harmonic, cyclotomic and binomial sums in N-space and by iterated integrals involving square-root valued arguments in z space, as functions of the mass ratio. Numerical results are presented. New two–scale iterative integrals are calculated.
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The three-loop polarized pure singlet Operator Matrix element with two different masses
Nuclear Physics B, 2020Co-Authors: Jakob Ablinger, Johannes Blümlein, A. De Freitas, Carsten Schneider, M. Saragnese, K. SchönwaldAbstract:Abstract We present the two-mass QCD contributions to the polarized pure singlet Operator Matrix element at three loop order in x-space. These terms are relevant for calculating the polarized structure function g 1 ( x , Q 2 ) at O ( α s 3 ) as well as for the matching relations in the variable flavor number scheme and the polarized heavy quark distribution functions at the same order. The result for the Operator Matrix element is given in terms of generalized iterated integrals. These integrals depend on the mass ratio through the main argument, and the alphabet includes square–root valued letters.
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The Polarized Three-Loop Anomalous Dimensions from On-Shell Massive Operator Matrix Elements
arXiv: High Energy Physics - Phenomenology, 2019Co-Authors: Arnd Behring, A. De Freitas, A. Von Manteuffel, Carsten Schneider, Sebastian Klein, J. Blümlein, A. Goedicke, K. SchönwaldAbstract:We calculate all contributions $\propto T_F$ to the polarized three-loop anomalous dimensions in the M-scheme using massive Operator Matrix elements and compare to results in the literature. This includes the complete anomalous dimensions $\gamma_{qq}^{(2),\rm PS}$ and $\gamma_{qg}^{(2)}$. We also obtain the complete two-loop polarized anomalous dimensions in an independent calculation. While for most of the anomalous dimensions the usual direct computation methods in Mellin $N$-space can be applied since all recurrences factorize at first order, this is not the case for $\gamma_{qg}^{(2)}$. Due to the necessity of deeper expansions of the master integrals in the dimensional parameter $\varepsilon = D-4$, we had to use the method of arbitrary high moments to eliminate elliptic contributions in intermediate steps. 4000 moments were generated to determine this anomalous dimension and 2640 moments turned out to be sufficient. As an aside, we also recalculate the contributions $\propto T_F$ to the three-loop QCD $\beta$-function.
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The polarized three-loop anomalous dimensions from on-shell massive Operator Matrix elements
Nuclear Physics B, 2019Co-Authors: Arnd Behring, A. De Freitas, A. Von Manteuffel, Carsten Schneider, Sebastian Klein, J. Blümlein, A. Goedicke, K. SchönwaldAbstract:Abstract We calculate all contributions ∝ T F to the polarized three–loop anomalous dimensions in the M–scheme using massive Operator Matrix elements and compare to results in the literature. This includes the complete anomalous dimensions γ q q ( 2 ) , PS and γ q g ( 2 ) . We also obtain the complete two–loop polarized anomalous dimensions in an independent calculation. While for most of the anomalous dimensions the usual direct computation methods in Mellin N–space can be applied since all recurrences factorize at first order, this is not the case for γ q g ( 2 ) . Due to the necessity of deeper expansions of the master integrals in the dimensional parameter e = D − 4 , we had to use the method of arbitrary high moments to eliminate elliptic contributions in intermediate steps. 4000 moments were generated to determine this anomalous dimension and 2640 moments turned out to be sufficient. As an aside, we also recalculate the contributions ∝ T F to the three–loop QCD β–function.
Johannes Blümlein - One of the best experts on this subject based on the ideXlab platform.
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The three-loop single mass polarized pure singlet Operator Matrix element
Nuclear Physics B, 2020Co-Authors: Jakob Ablinger, Arnd Behring, Johannes Blümlein, A. De Freitas, A. Von Manteuffel, Carsten Schneider, K. SchönwaldAbstract:Abstract We calculate the massive polarized three-loop pure singlet Operator Matrix element A Q q ( 3 ) , PS in the single mass case in the Larin scheme. This Operator Matrix element contributes to the massive polarized three-loop Wilson coefficient H Q q ( 3 ) , PS in deep-inelastic scattering and constitutes a three-loop transition Matrix element in the variable flavor number scheme. We provide analytic results in Mellin N and in x space and study the behaviour of this Operator Matrix element in the region of small and large values of the Bjorken variable x.
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The three-loop polarized pure singlet Operator Matrix element with two different masses
Nuclear Physics B, 2020Co-Authors: Jakob Ablinger, Johannes Blümlein, A. De Freitas, Carsten Schneider, M. Saragnese, K. SchönwaldAbstract:Abstract We present the two-mass QCD contributions to the polarized pure singlet Operator Matrix element at three loop order in x-space. These terms are relevant for calculating the polarized structure function g 1 ( x , Q 2 ) at O ( α s 3 ) as well as for the matching relations in the variable flavor number scheme and the polarized heavy quark distribution functions at the same order. The result for the Operator Matrix element is given in terms of generalized iterated integrals. These integrals depend on the mass ratio through the main argument, and the alphabet includes square–root valued letters.
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The two-mass contribution to the three-loop polarized gluonic Operator Matrix element Agg,Q(3)
Nuclear Physics B, 2020Co-Authors: Jakob Ablinger, Johannes Blümlein, A. De Freitas, Carsten Schneider, M. Saragnese, A. Goedicke, K. SchönwaldAbstract:Abstract We compute the two-mass contributions to the polarized massive Operator Matrix element A g g , Q ( 3 ) at third order in the strong coupling constant α s in Quantum Chromodynamics analytically. These corrections are important ingredients for the matching relations in the variable flavor number scheme and for the calculation of Wilson coefficients in deep–inelastic scattering in the asymptotic regime Q 2 ≫ m c 2 , m b 2 . The analytic result is expressed in terms of nested harmonic, generalized harmonic, cyclotomic and binomial sums in N-space and by iterated integrals involving square-root valued arguments in z space, as functions of the mass ratio. Numerical results are presented. New two–scale iterative integrals are calculated.
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The massive 3-loop Operator Matrix elements with two masses and the generalized variable flavor number scheme
Proceedings of 13th International Symposium on Radiative Corrections (Applications of Quantum Field Theory to Phenomenology) — PoS(RADCOR2017), 2018Co-Authors: Abilio De Freitas, Jakob Ablinger, Johannes Blümlein, Carsten Schneider, K. Schönwald, F. Wißbrock, A. Goedicke, A. De FreitasAbstract:We report on our latest results in the calculation of the two–mass contributions to 3–loop Operator Matrix elements (OMEs). These OMEs are needed to compute the corresponding contributions to the deep-inealstic scattering structure functions and to generalize the variable flavor number scheme by including both charm and bottom quarks. We present the results for the non-singlet and Agq,Q OMEs, and compare the size of their contribution relative to the single mass case. Results for the gluonic OME Agg,Q are given in the physical case, going beyond those presented in a previous publication where scalar diagrams were computed. We also discuss our recently published two–mass contribution to the pure singlet OME, and present an alternative method of calculating the corresponding diagrams.
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The two-mass contribution to the three-loop pure singlet Operator Matrix element
Nuclear Physics B, 2018Co-Authors: Jakob Ablinger, Johannes Blümlein, A. De Freitas, Carsten Schneider, K. SchönwaldAbstract:Abstract We 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 ( α s 3 ) as well as for the matching relations in the variable flavor number scheme and the heavy quark distribution functions at the same order. The result for the Operator Matrix element is given in terms of generalized iterated integrals that include square root letters in the alphabet, depending also on the mass ratio through the main argument. Numerical results are presented.
I. Bierenbaum - One of the best experts on this subject based on the ideXlab platform.
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The logarithmic contributions to the O(\alpha _s^3) asymptotic massive Wilson coefficients and Operator Matrix elements in deeply inelastic scattering
The European physical journal. C Particles and fields, 2014Co-Authors: Arnd Behring, Johannes Blümlein, A. De Freitas, I. Bierenbaum, S. Klein, F. WißbrockAbstract: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 in Mellin \(N\)-space.
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the logarithmic contributions to the o alpha_s 3 asymptotic massive wilson coefficients and Operator Matrix elements in deeply inelastic scattering
arXiv: High Energy Physics - Phenomenology, 2014Co-Authors: Arnd Behring, A. De Freitas, I. Bierenbaum, S. Klein, J. Blümlein, F WisbrockAbstract: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.
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Heavy flavor Operator Matrix elements at $O(a_s^3)$
arXiv: High Energy Physics - Phenomenology, 2008Co-Authors: I. Bierenbaum, Johannes Blümlein, S. KleinAbstract: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.
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two loop massive Operator Matrix elements for unpolarized heavy flavor production to o ǫ
Nuclear Physics, 2008Co-Authors: I. Bierenbaum, Sebastian Klein, J. Blümlein, Carsten SchneiderAbstract:We calculate the O(� 2 ) massive 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 ≫ m 2 , up to the O(") contributions. These terms contribute through the renormalization of the O(� 3 ) heavy flavor Wilson coefficients of the structure function F2(x,Q 2 ). The calculation has been performed using light–cone expansion techniques without using the integration-by-parts method. We represent the individual Feynman diagrams by generalized hypergeometric structures, the "–expansion of which leads to infinite sums depending on the Mellin variable N. These sums are finally expressed in terms of nested harmonic sums using the general summation techniques implemented in the Sigma package.
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Two-Loop Massive Operator Matrix Elements for Unpolarized Heavy Flavor Production to O(epsilon)
Nuclear Physics, 2008Co-Authors: I. Bierenbaum, Johannes Blümlein, Sebastian Klein, Carsten SchneiderAbstract:We calculate the O(� 2 ) massive 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 ≫ m 2 , up to the O(") contributions. These terms contribute through the renormalization of the O(� 3 ) heavy flavor Wilson coefficients of the structure function F2(x,Q 2 ). The calculation has been performed using light–cone expansion techniques without using the integration-by-parts method. We represent the individual Feynman diagrams by generalized hypergeometric structures, the "–expansion of which leads to infinite sums depending on the Mellin variable N. These sums are finally expressed in terms of nested harmonic sums using the general summation techniques implemented in the Sigma package.
Jakob Ablinger - One of the best experts on this subject based on the ideXlab platform.
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The three-loop single mass polarized pure singlet Operator Matrix element
Nuclear Physics B, 2020Co-Authors: Jakob Ablinger, Arnd Behring, Johannes Blümlein, A. De Freitas, A. Von Manteuffel, Carsten Schneider, K. SchönwaldAbstract:Abstract We calculate the massive polarized three-loop pure singlet Operator Matrix element A Q q ( 3 ) , PS in the single mass case in the Larin scheme. This Operator Matrix element contributes to the massive polarized three-loop Wilson coefficient H Q q ( 3 ) , PS in deep-inelastic scattering and constitutes a three-loop transition Matrix element in the variable flavor number scheme. We provide analytic results in Mellin N and in x space and study the behaviour of this Operator Matrix element in the region of small and large values of the Bjorken variable x.
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The three-loop polarized pure singlet Operator Matrix element with two different masses
Nuclear Physics B, 2020Co-Authors: Jakob Ablinger, Johannes Blümlein, A. De Freitas, Carsten Schneider, M. Saragnese, K. SchönwaldAbstract:Abstract We present the two-mass QCD contributions to the polarized pure singlet Operator Matrix element at three loop order in x-space. These terms are relevant for calculating the polarized structure function g 1 ( x , Q 2 ) at O ( α s 3 ) as well as for the matching relations in the variable flavor number scheme and the polarized heavy quark distribution functions at the same order. The result for the Operator Matrix element is given in terms of generalized iterated integrals. These integrals depend on the mass ratio through the main argument, and the alphabet includes square–root valued letters.
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The two-mass contribution to the three-loop polarized gluonic Operator Matrix element Agg,Q(3)
Nuclear Physics B, 2020Co-Authors: Jakob Ablinger, Johannes Blümlein, A. De Freitas, Carsten Schneider, M. Saragnese, A. Goedicke, K. SchönwaldAbstract:Abstract We compute the two-mass contributions to the polarized massive Operator Matrix element A g g , Q ( 3 ) at third order in the strong coupling constant α s in Quantum Chromodynamics analytically. These corrections are important ingredients for the matching relations in the variable flavor number scheme and for the calculation of Wilson coefficients in deep–inelastic scattering in the asymptotic regime Q 2 ≫ m c 2 , m b 2 . The analytic result is expressed in terms of nested harmonic, generalized harmonic, cyclotomic and binomial sums in N-space and by iterated integrals involving square-root valued arguments in z space, as functions of the mass ratio. Numerical results are presented. New two–scale iterative integrals are calculated.
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the two mass contribution to the three loop gluonic Operator Matrix element agg q 3
Nuclear Physics, 2018Co-Authors: Jakob Ablinger, A. De Freitas, Carsten Schneider, J. Blümlein, A. Goedicke, K. SchönwaldAbstract:Abstract We calculate the two-mass QCD contributions to the massive Operator Matrix element A g g , Q at O ( α s 3 ) in analytic form in Mellin N- and z-space, maintaining the complete dependence on the heavy quark mass ratio. These terms are important ingredients for the matching relations of the variable flavor number scheme in the presence of two heavy quark flavors, such as charm and bottom. In Mellin N-space the result is given in the form of nested harmonic, generalized harmonic, cyclotomic and binomial sums, with arguments depending on the mass ratio. The Mellin inversion of these quantities to z-space gives rise to generalized iterated integrals with square root valued letters in the alphabet, depending on the mass ratio as well. Numerical results are presented.
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the two mass contribution to the three loop gluonic Operator Matrix element a_ gg q 3
Nuclear Physics, 2018Co-Authors: Jakob Ablinger, A. De Freitas, Carsten Schneider, J. Blümlein, A. Goedicke, K. SchönwaldAbstract:Abstract We calculate the two-mass QCD contributions to the massive Operator Matrix element A g g , Q at O ( α s 3 ) in analytic form in Mellin N- and z-space, maintaining the complete dependence on the heavy quark mass ratio. These terms are important ingredients for the matching relations of the variable flavor number scheme in the presence of two heavy quark flavors, such as charm and bottom. In Mellin N-space the result is given in the form of nested harmonic, generalized harmonic, cyclotomic and binomial sums, with arguments depending on the mass ratio. The Mellin inversion of these quantities to z-space gives rise to generalized iterated integrals with square root valued letters in the alphabet, depending on the mass ratio as well. Numerical results are presented.
