A semi-analytical x-space solution for parton evolution — Application to non-singlet and singlet DGLAP equation

A bstract We present a novel semi-analytical method for parton evolution. It is based on constructing a family of analytic functions spanning x -space which is closed under the considered evolution equation. Using these functions as a basis, the original integro-differential evolution equation trans...

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Published inThe journal of high energy physics Vol. 2024; no. 7; pp. 72 - 29
Main Authors Haug, Juliane, Schüle, Oliver, Wunder, Fabian
Format Journal Article
LanguageEnglish
Published Berlin/Heidelberg Springer Berlin Heidelberg 09.07.2024
Springer Nature B.V
SpringerOpen
Subjects
Algorithms
Analytic functions
Classical and Quantum Gravitation
Differential equations
Elementary Particles
Evolutionary computation
Factorization
Mathematical analysis
Methods
Ordinary differential equations
Parton Distributions
Partons
Physics
Physics and Astronomy
Quantum Field Theories
Quantum Field Theory
Quantum Physics
Regular Article - Theoretical Physics
Relativity Theory
Renormalization Group
String Theory
Subsystems
Factorization
Renormalization Group
Parton Distributions
Online AccessGet full text
ISSN1029-8479
1126-6708
1127-2236
1029-8479
DOI10.1007/JHEP07(2024)072

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Abstract A bstract We present a novel semi-analytical method for parton evolution. It is based on constructing a family of analytic functions spanning x -space which is closed under the considered evolution equation. Using these functions as a basis, the original integro-differential evolution equation transforms into a system of coupled ordinary differential equations, which can be solved numerically by restriction to a suitably chosen finite subsystem. The evolved distributions are obtained as analytic functions in x with numerically obtained coefficients, providing insight into the analytic behavior of the evolved parton distributions. As a proof-of-principle, we apply our method to the leading order non-singlet and singlet DGLAP equation. Comparing our results to traditional Mellin-space methods, we find good agreement. The method is implemented in the code POMPOM in Mathematica as well as in Python.
AbstractList We present a novel semi-analytical method for parton evolution. It is based on constructing a family of analytic functions spanning x-space which is closed under the considered evolution equation. Using these functions as a basis, the original integro-differential evolution equation transforms into a system of coupled ordinary differential equations, which can be solved numerically by restriction to a suitably chosen finite subsystem. The evolved distributions are obtained as analytic functions in x with numerically obtained coefficients, providing insight into the analytic behavior of the evolved parton distributions. As a proof-of-principle, we apply our method to the leading order non-singlet and singlet DGLAP equation. Comparing our results to traditional Mellin-space methods, we find good agreement. The method is implemented in the code POMPOM in Mathematica as well as in Python.
Abstract We present a novel semi-analytical method for parton evolution. It is based on constructing a family of analytic functions spanning x-space which is closed under the considered evolution equation. Using these functions as a basis, the original integro-differential evolution equation transforms into a system of coupled ordinary differential equations, which can be solved numerically by restriction to a suitably chosen finite subsystem. The evolved distributions are obtained as analytic functions in x with numerically obtained coefficients, providing insight into the analytic behavior of the evolved parton distributions. As a proof-of-principle, we apply our method to the leading order non-singlet and singlet DGLAP equation. Comparing our results to traditional Mellin-space methods, we find good agreement. The method is implemented in the code POMPOM in Mathematica as well as in Python.
A bstract We present a novel semi-analytical method for parton evolution. It is based on constructing a family of analytic functions spanning x -space which is closed under the considered evolution equation. Using these functions as a basis, the original integro-differential evolution equation transforms into a system of coupled ordinary differential equations, which can be solved numerically by restriction to a suitably chosen finite subsystem. The evolved distributions are obtained as analytic functions in x with numerically obtained coefficients, providing insight into the analytic behavior of the evolved parton distributions. As a proof-of-principle, we apply our method to the leading order non-singlet and singlet DGLAP equation. Comparing our results to traditional Mellin-space methods, we find good agreement. The method is implemented in the code POMPOM in Mathematica as well as in Python.
ArticleNumber 72
Author Wunder, Fabian
Haug, Juliane
Schüle, Oliver
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Snippet A bstract We present a novel semi-analytical method for parton evolution. It is based on constructing a family of analytic functions spanning x -space which is...
We present a novel semi-analytical method for parton evolution. It is based on constructing a family of analytic functions spanning x -space which is closed...
We present a novel semi-analytical method for parton evolution. It is based on constructing a family of analytic functions spanning x-space which is closed...
Abstract We present a novel semi-analytical method for parton evolution. It is based on constructing a family of analytic functions spanning x-space which is...
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SubjectTerms Algorithms
Analytic functions
Classical and Quantum Gravitation
Differential equations
Elementary Particles
Evolutionary computation
Factorization
Mathematical analysis
Methods
Ordinary differential equations
Parton Distributions
Partons
Physics
Physics and Astronomy
Quantum Field Theories
Quantum Field Theory
Quantum Physics
Regular Article - Theoretical Physics
Relativity Theory
Renormalization Group
String Theory
Subsystems
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Title A semi-analytical x-space solution for parton evolution — Application to non-singlet and singlet DGLAP equation
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