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Fragmentation Functions of neutral mesons $π^0$ and $k ^0$ with Laplace transform approach

F. Taghavi-Shahri, S. Atashbar Tehrani, M. Zareei

TL;DR

This work develops an analytic approach to DGLAP fragmentation-function evolution using Laplace transforms to obtain neutral-m meson FFs for $π^0$ and $K^0$ at NLO. It decouples the non-singlet and singlet–gluon sectors, solves them in Laplace space, and then reconstructs the FFs via inverse transforms, leveraging HKNS initial distributions at $Q_0=4.5$ GeV and charge-conjugation symmetry to relate neutral FFs to charged ones. The total fragmentation functions are computed with Wilson coefficients and validated against experimental data (TASSO, ALEPH, TOPAZ, OPAL) and global fits (HKNS, AKK, DSS), showing good agreement. This framework provides a controlled, analytically tractable path to include neutral meson data in global fragmentation-function fits, enhancing precision and consistency in QCD analyses.

Abstract

With an analytical solutions of DGLAP evolution equations based on the Laplace transform method , we find the fragmentation functions (FFs) of neutral mesons, $π^0$ and $k ^0$ at NLO approximation. We also calculated the total fragmentation functions of these mesons and compared them with experimental data and those from global fits. The results show a good agreements between our solutions and other models and also are compatible with experimental data.

Fragmentation Functions of neutral mesons $π^0$ and $k ^0$ with Laplace transform approach

TL;DR

This work develops an analytic approach to DGLAP fragmentation-function evolution using Laplace transforms to obtain neutral-m meson FFs for and at NLO. It decouples the non-singlet and singlet–gluon sectors, solves them in Laplace space, and then reconstructs the FFs via inverse transforms, leveraging HKNS initial distributions at GeV and charge-conjugation symmetry to relate neutral FFs to charged ones. The total fragmentation functions are computed with Wilson coefficients and validated against experimental data (TASSO, ALEPH, TOPAZ, OPAL) and global fits (HKNS, AKK, DSS), showing good agreement. This framework provides a controlled, analytically tractable path to include neutral meson data in global fragmentation-function fits, enhancing precision and consistency in QCD analyses.

Abstract

With an analytical solutions of DGLAP evolution equations based on the Laplace transform method , we find the fragmentation functions (FFs) of neutral mesons, and at NLO approximation. We also calculated the total fragmentation functions of these mesons and compared them with experimental data and those from global fits. The results show a good agreements between our solutions and other models and also are compatible with experimental data.

Paper Structure

This paper contains 7 sections, 32 equations, 4 figures.

Table of Contents

  1. Introduction
  2. Fragmentation Functions via decoupling of the DGLAP evolution equations by Laplace transform method
  3. Non- singlet case:
  4. The singlet and gluon case:
  5. Natural pions and kaons fragmentation functions and the role of charge conjugation symmetry
  6. Total Fragmentation Functions
  7. Conclusions and Remarks

Figures (4)

  • Figure 1: Fragmentation functions of natural pion and comparison with AKK, DSS and HKNS global fits.
  • Figure 2: Fragmentation functions of natural kaon and comparison with AKK, DSS and HKNS global fits.
  • Figure 3: Total fragmentation functions of natural pion and comparison with experimental data from TASSO and ALEPH Collaborationstassoaleph at $Q=44 GeV$ and $Q^2=M_z^2$. We also compared our results with HKNS global fit.
  • Figure 4: Total fragmentation functions of natural kaon and proton and comparison with experimental data from TOPAZ and OPAL Collaborations topazopal at $Q=44 GeV$ and $Q^2=M_z^2$. We also compared our results with HKNS global fit.