The heavy fermion contributions to the massive three loop form factors
We compute the non-singlet nh terms to the massive three loop vector-, axialvector-, scalar- and pseudoscalar form factors in a direct analytic calculation using the method of large moments. This method has the advantage, that the master integrals have to be dealt with only in their moment represent...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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Elsevier
2019-12-01
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| Series: | Nuclear Physics B |
| Online Access: | http://www.sciencedirect.com/science/article/pii/S0550321319302378 |
| _version_ | 1831760215387668480 |
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| author | J. Blümlein P. Marquard N. Rana C. Schneider |
| author_facet | J. Blümlein P. Marquard N. Rana C. Schneider |
| author_sort | J. Blümlein |
| collection | DOAJ |
| description | We compute the non-singlet nh terms to the massive three loop vector-, axialvector-, scalar- and pseudoscalar form factors in a direct analytic calculation using the method of large moments. This method has the advantage, that the master integrals have to be dealt with only in their moment representation, allowing to also consider quantities which obey differential equations, which are not first order factorizable (elliptic and higher), already at this level. To obtain all the associated recursions, up to 8000 moments had to be calculated. A new technique has been applied to solve the associated differential equation systems. Here the decoupling is performed such, that only minimal depth ε–expansions had to be performed for non–first-order factorizing systems, minimizing the calculation of initial values. The pole terms in the dimensional parameter ε can be completely predicted using renormalization group methods, as confirmed by the present results. A series of contributions at O(ε0) have first order factorizable representations. For a smaller number of color–zeta projections this is not the case. All first order factorizing terms can be represented by harmonic polylogarithms. We also obtain analytic results for the non–first-order factorizing terms by Taylor series in a variable x, for which we have calculated at least 2000 expansion coefficients, in an approximation. Based on this representation the form factors can be given in the Euclidean region and in the region q2≈0. Numerical results are presented. |
| first_indexed | 2024-12-22T03:48:12Z |
| format | Article |
| id | doaj.art-d1cec4d704ed447fb6e9d29f185bd0de |
| institution | Directory Open Access Journal |
| issn | 0550-3213 |
| language | English |
| last_indexed | 2024-12-22T03:48:12Z |
| publishDate | 2019-12-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Nuclear Physics B |
| spelling | doaj.art-d1cec4d704ed447fb6e9d29f185bd0de2022-12-21T18:40:05ZengElsevierNuclear Physics B0550-32132019-12-01949The heavy fermion contributions to the massive three loop form factorsJ. Blümlein0P. Marquard1N. Rana2C. Schneider3Deutsches Elektronen–Synchrotron, DESY, Platanenallee 6, D-15738 Zeuthen, GermanyDeutsches Elektronen–Synchrotron, DESY, Platanenallee 6, D-15738 Zeuthen, Germany; Corresponding author.Deutsches Elektronen–Synchrotron, DESY, Platanenallee 6, D-15738 Zeuthen, Germany; INFN, Sezione di Milano, Via Celoria 16, I-20133 Milano, ItalyResearch Institute for Symbolic Computation (RISC), Johannes Kepler University, Altenbergerstraße 69, A–4040, Linz, AustriaWe compute the non-singlet nh terms to the massive three loop vector-, axialvector-, scalar- and pseudoscalar form factors in a direct analytic calculation using the method of large moments. This method has the advantage, that the master integrals have to be dealt with only in their moment representation, allowing to also consider quantities which obey differential equations, which are not first order factorizable (elliptic and higher), already at this level. To obtain all the associated recursions, up to 8000 moments had to be calculated. A new technique has been applied to solve the associated differential equation systems. Here the decoupling is performed such, that only minimal depth ε–expansions had to be performed for non–first-order factorizing systems, minimizing the calculation of initial values. The pole terms in the dimensional parameter ε can be completely predicted using renormalization group methods, as confirmed by the present results. A series of contributions at O(ε0) have first order factorizable representations. For a smaller number of color–zeta projections this is not the case. All first order factorizing terms can be represented by harmonic polylogarithms. We also obtain analytic results for the non–first-order factorizing terms by Taylor series in a variable x, for which we have calculated at least 2000 expansion coefficients, in an approximation. Based on this representation the form factors can be given in the Euclidean region and in the region q2≈0. Numerical results are presented.http://www.sciencedirect.com/science/article/pii/S0550321319302378 |
| spellingShingle | J. Blümlein P. Marquard N. Rana C. Schneider The heavy fermion contributions to the massive three loop form factors Nuclear Physics B |
| title | The heavy fermion contributions to the massive three loop form factors |
| title_full | The heavy fermion contributions to the massive three loop form factors |
| title_fullStr | The heavy fermion contributions to the massive three loop form factors |
| title_full_unstemmed | The heavy fermion contributions to the massive three loop form factors |
| title_short | The heavy fermion contributions to the massive three loop form factors |
| title_sort | heavy fermion contributions to the massive three loop form factors |
| url | http://www.sciencedirect.com/science/article/pii/S0550321319302378 |
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