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DOI•

3-loop contributions to heavy flavor Wilson coefficients of neutral and charged current DIS

Alexander Hasselhuhn
13 Jan 2014-
About: The article was published on 2014-01-13 and is currently open access. It has received 21 citations till now. The article focuses on the topics: Charged current & Loop (topology).
Citations
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Proceedings Article•DOI•
Parton distributions for the LHC

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R. S. Thorne, W. J. Stirling, Alan D. Martin, G. Watt
01 Jan 2007
TL;DR: In this paper, a preliminary set of updated NLO parton distributions and their uncertainties determined from CCFR and NuTeV dimuon cross sections are presented, along with additional jet data from HERA and the Tevatron.
Abstract: We present a preliminary set of updated NLO parton distributions. For the first time we have a quantitative extraction of the strange quark and antiquark distributions and their uncertainties determined from CCFR and NuTeV dimuon cross sections. Additional jet data from HERA and the Tevatron improve our gluon extraction. Lepton asymmetry data and neutrino structure functions improve the flavour separation, particularly constraining the down quark valence distribution.

1,288 citations

Journal Article•DOI•
Approximation theory and methods, by M. J. D. Powell. Pp 339. £25 (hardcover), £8·50 (paperback). 1981. ISBN 0-521-22472-1/29514-9 (Cambridge University Press)

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Alan J. Davies
01 Mar 1984-The Mathematical Gazette
TL;DR: In this article, the authors consider the problem of finding the best approximation operator for a given function, and the uniqueness of best approximations and the existence of best approximation operators.
Abstract: Preface 1. The approximation problem and existence of best approximations 2. The uniqueness of best approximations 3. Approximation operators and some approximating functions 4. Polynomial interpolation 5. Divided differences 6. The uniform convergence of polynomial approximations 7. The theory of minimax approximation 8. The exchange algorithm 9. The convergence of the exchange algorithm 10. Rational approximation by the exchange algorithm 11. Least squares approximation 12. Properties of orthogonal polynomials 13. Approximation of periodic functions 14. The theory of best L1 approximation 15. An example of L1 approximation and the discrete case 16. The order of convergence of polynomial approximations 17. The uniform boundedness theorem 18. Interpolation by piecewise polynomials 19. B-splines 20. Convergence properties of spline approximations 21. Knot positions and the calculation of spline approximations 22. The Peano kernel theorem 23. Natural and perfect splines 24. Optimal interpolation Appendices Index.

841 citations

Book Chapter•DOI•
A Schematic Model of Baryons and Mesons

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Murray Gell-Mann1•
California Institute of Technology1
01 Mar 2015
TL;DR: In this article, the authors assume that the strong interactions of baryons and mesons are correctly described in terms of the broken "eightfold way", and they are tempted to look for some fundamental explanation of the situation.
Abstract: If we assume that the strong interactions of baryons and mesons are correctly described in terms of the broken "eightfold way", we are tempted to look for some fundamental explanation of the situation. A highly promised approach is the purely dynamical "bootstrap" model for all the strongly interacting particles within which one may try to derive isotopic spin and strangeness conservation and broken eightfold symmetry from self-consistency alone. Of course, with only strong interactions, the orientation of the asymmetry in the unitary space cannot be specified; one hopes that in some way the selection of specific components of the F-spin by electromagnetism and the weak interactions determines the choice of isotopic spin and hypercharge directions.

361 citations

The renormalization of the axial anomaly in dimensional regularization

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S. A. Larin
01 Jan 1992
TL;DR: In this article, the prescription for the γ5 matrix within dimensional regularization in multiloop calculations is elaborated and the three-loop anomalous dimension of the singlet axial current is calculated.
Abstract: The prescription for the γ5 matrix within dimensional regularization in multiloop calculations is elaborated. The three-loop anomalous dimension of the singlet axial current is calculated.

257 citations

Journal Article•DOI•
Multiple Hypergeometric Functions and Applications

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W. R. Buckland
01 Jan 1977-Journal of the Operational Research Society

143 citations

References
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Book•
Higher Transcendental Functions

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Bateman Manuscript, Harry Bateman, Arthur Erdélyi
01 Jan 1981

7,882 citations

"3-loop contributions to heavy flavo..." refers background in this paper

  • ...Most of what is known about these functions can be found in [257–264]....

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Journal Article•DOI•
Asymptotic Freedom in Parton Language

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Guido Altarelli1, Giorgio Parisi2•
École Normale Supérieure1, Institut des Hautes Études Scientifiques2
08 Aug 1977-Nuclear Physics
TL;DR: In this article, the main body of predictions of the theory for deep-inleastic scattering on either unpolarized or polarized targets is re-obtained by a method which only makes use of the simplest tree diagrams and is entirely phrased in parton language with no reference to the conventional operator formalism.

4,692 citations

"3-loop contributions to heavy flavo..." refers background or methods in this paper

  • ...The reasoning follows the idea of calculating leading logarithms in the Altarelli-Parisi picture of scaling violations [34], and will be presented later in this Section....

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  • ...4, where also an asymptotic calculation following the ideas of [34] is presented....

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  • ...In order to gain further confidence in the emergence of a minus sign in the asymptotic representation (522), as well as to understand how this observation relates to the pure singlet Wilson coefficients at 2-loop order, the calculation of leading logarithmic contributions is performed using the method also applied by Altarelli and Parisi [34], cf. also [334]....

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  • ...160 [34] G. Altarelli and G. Parisi....

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  • ...Like in the case of purely massless ladder rungs [34], see also [334, 337], the integral becomes nested in both the momentum and the Sudakov variables α1, α2,...

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Journal Article•DOI•
Higher Transcendental Functions

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Thomas M. Macrobert
01 Feb 1955-Nature
TL;DR: Higher Transcendental Functions Based on notes left by the late Prof. Harry Bateman, and compiled by the Staff of the Bateman Project as discussed by the authors, are presented in Table 1.
Abstract: Higher Transcendental Functions Based, in part, on notes left by the late Prof. Harry Bateman, and compiled by the Staff of the Bateman Project. Vol. 1. Pp. xxvi + 302. 52s. Vol. 2. Pp. xvii + 396. 60s. (London: McGraw-Hill Publishing Company, Ltd., 1953.)

4,428 citations

Journal Article•DOI•
Unitary Symmetry and Leptonic Decays

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Nicola Cabibbo1•
CERN1
15 Jun 1963-Physical Review Letters
TL;DR: In this article, an analysis of leptonic decays based on unitary symmetry for strong interactions and the V-A theory for weak interactions is presented, and an explanation for the observed predominance of the LAMBDA yields + e/sup -/ + nu decay over the lamBDA /sup −/ yields n + e /sup + n decay.
Abstract: An analysis of leptonic decays based on unitary symmetry for strong interactions (eightfold way) and the V-A theory for weak interactions is presented. An explanation for the observed predominance of the LAMBDA yields + e/sup -/ + nu decay over the LAMBDA /sup -/ yields n + e/sup -/ + nu decay is obtained. Branching ratios predicted for electron modes with DELTA S, 1 are presented; the ratios for the above decays agree well with experimental results. (D.C.W.)

3,957 citations

"3-loop contributions to heavy flavo..." refers background or methods in this paper

  • ...with Vij denoting the CKM matrix elements [175, 176], and s and d the strange and down quark parton distributions....

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  • ...where eu = ec = 2/3, ed = es = −1/3, and Vij are the CKM matrix elements [175, 176]....

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Journal Article•DOI•
Regularization and Renormalization of Gauge Fields

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Gerard 't Hooft1, M.J.G. Veltman1•
Utrecht University1
01 Jul 1972-Nuclear Physics
TL;DR: In this article, a new regularization and renormalization procedure for gauge theories is presented, which is particularly well suited for the treatment of gauge theories and is transparent when anomalies such as the Bell-Jackiw-Adler anomaly may occur.

3,722 citations

"3-loop contributions to heavy flavo..." refers background in this paper

  • ...(113) Also the Dirac algebra is continued to D spacetime dimensions, which causes a problem with γ5 and the Levi-Civita symbol εμνρσ, since both are inherently four dimensional objects [89]....

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