Analytical solution to DGLAP integro-differential equation via complex maps in domains of contour integrals

[1912.02303] Analytical solution to DGLAP integro-differential equation via complex maps in domains of contour integrals Skip to main content Search Submit Donate Log in Search arXiv Press Enter to search · Advanced search High Energy Physics - Theory arXiv:1912.02303 (hep-th) [Submitted on 4 Dec 2019 ( v1 ), last revised 23 Jun 2020 (this version, v2)] Title: Analytical solution to DGLAP integro-differential equation via complex maps in domains of contour integrals Authors: Gustavo Alvarez , Igor Kondrashuk View a PDF of the paper titled Analytical solution to DGLAP integro-differential equation via complex maps in domains of contour integrals, by Gustavo Alvarez and Igor Kondrashuk View PDF HTML (experimental) Abstract: A simple model for QCD dynamics in which the DGLAP integro-differential equation may be solved analytically has been considered in our previous papers arXiv:1611.08787 [hep-ph] and arXiv:1906.07924 [hep-ph]. When such a model contains only one term in the splitting function of the dominant parton distribution, then Bessel function appears to be the solution to this simplified DGLAP equation. To our knowledge, this model with only one term in the splitting function for the first time has been proposed by Blumlein in hep-ph/9506403 . In arXiv:1906.07924 [hep-ph] we have shown that a dual integro-differential equation obtained from the DGLAP equation by a complex map in the plane of the Mellin moment in this model may be considered as the BFKL equation. Then, in arXiv:1906.07924 we have applied a complex diffeomorphism to obtain a standard integral from Gradshteyn and Ryzhik tables starting from the contour integral for parton distribution functions that is usually taken by calculus of residues. This standard integral from these tables appears to be the Laplace transformation of Jacobian for this complex diffeomorphism. Here we write up all the formulae behind this trick in detail and find out certain important points for further development of this strategy. We verify that the inverse Laplace transformation of the Laplace image of the Bessel function may be represented in a form of Barnes contour integral. Comments: 14 pages Subjects: High Energy Physics - Theory (hep-th) ; High Energy Physics - Phenomenology (hep-ph); Mathematical Physics (math-ph) Cite as: arXiv:1912.02303 [hep-th] (or arXiv:1912.02303v2 [hep-th] for this version) https://doi.org/10.48550/arXiv.1912.02303 Focus to learn more arXiv-issued DOI via DataCite Related DOI : https://doi.org/10.1088/2399-6528/ab9dd8 Focus to learn more DOI(s) linking to related resources Submission history From: Igor Kondrashuk [ view email ] [v1] Wed, 4 Dec 2019 23:24:18 UTC (13 KB) [v2] Tue, 23 Jun 2020 15:42:21 UTC (15 KB) Full-text links: Access Paper: View a PDF of the paper titled Analytical solution to DGLAP integro-differential equation via complex maps in domains of contour integrals, by Gustavo Alvarez and Igor Kondrashuk View PDF HTML (experimental) TeX Source view license Current browse context: hep-th < prev | next > new | recent | 2019-12 Change to browse by: hep-ph math math-ph math.MP References & Citations INSPIRE HEP NASA ADS Google Scholar Semantic Scholar export BibTeX citation Loading... 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