Fragmentation functions of the pion, kaon, and proton in the NLO approximation: Laplace transform approach

TL;DR

The paper develops an analytic NLO solution for the DGLAP evolution of pion, kaon, and proton fragmentation functions using a Laplace-transform framework. By converting the equations to $\nu$ and $\tau$ spaces and performing two successive Laplace transforms, the authors decouple and solve the non-singlet, singlet, and gluon sectors with HKNS initial inputs, then invert back to $(z,Q^2)$ space. They introduce a mass-based scheme for symmetry breaking in sea-quark FFs and compute the total fragmentation functions at $Q^2=M_Z^2$, finding good agreement with SLD data and global fits (HKNS, AKK, DSS). The approach provides a robust analytic handle on FF evolution and points toward refining initial FFs via global fitting using this method.

Abstract

Using repeated Laplace transform, We find an analytical solution for DGLAP evolution equations for extracting the pion, kaon and proton Fragmentation Functions (FFs) at NLO approximation. We also study the symmetry breaking of the sea quarks Fragmentation Functions, $D_{\bar q}^h (z,Q^2)$ and simply separated them according to their mass ratio. Finally, we calculate the total Fragmentation Functions of these hadrons and compare them with experimental data and those from global fits. Our results show a good agreement with the FFs obtained from global parameterizations as well as with the experimental data.

Figures (4)

• Figure 1: Pion fragmentation functions at $Q^2=M_z^2$ and Comparison with AKK, DSS and HKNS global fits.
• Figure 2: Kaon fragmentation functions at $Q^2=M_z^2$and Comparison with AKK, DSS and HKNS global fits.
• Figure 3: Proton fragmentation functions at $Q^2=M_z^2$and Comparison with AKK, DSS and HKNS global fits.
• Figure 4: Total fragmentation functions of pion, kaon and proton and comparison with experimental data from SLD sld at $Q^2=M_z^2$. We also compared our results with HKNS global fit.