Fragmentation Functions in Next-To-Leading Order QCD

TL;DR

This work constructs fragmentation functions at next-to-leading order from inclusive $e^+e^-$ data, leveraging the longitudinal cross section to tightly constrain the gluon FF and completing the NLO longitudinal coefficient set. By implementing a rigorous factorization framework with $\overline{MS}$ renormalization and VFNS treatment for heavy quarks, it delivers FF sets for charged hadrons, pions, kaons, neutral kaons, and $D^{*\pm}$ mesons, calibrated to ALEPH and other data. The resulting FFs are tested across processes (ep, $p\bar p$, $\gamma\gamma$) to verify universality, and are used to study scaling violation to extract $\Lambda_{\rm QCD}$ and to probe the gluon and charm content of the photon. The improved understanding of fragmentation, especially the gluon sector at small $x$, enhances predictive power for current and future colliders and informs photon structure analyses.\

Abstract

We present new sets of fragmentation functions in next-to-leading order QCD that are determined from e+e- annihilation data of inclusive particle production. In addition to the O(alpha_s) unpolarized cross section the longitudinal cross section is also used to extract the gluon fragmentation function from e+e- annihilation data. As the O(alpha_s) vanishes for longitudinal polarized photons (or Z bosons), the O(alpha_s^2) corrections are required to reduce the scale ambiguities. Recently, P.J. Rijken and W.L. van Neerven presented the longitudinal coefficient functions to next-to-leading order. We confirm part of their results in this thesis and complete the calculation by the results for the color class C_F*T_R that must be included for a consistent comparison with LEP1 data. The complete set of coefficient functions is then used together with novel data from ALEPH to determine the fragmentation functions for charged hadrons. This set, and also sets for charged pions, kaons, and D^* mesons as well as neutral kaons published previously, can then be employed to test QCD in e+e- annihilation, photoproduction, gamma-gamma collisions, p-p_bar scattering and DIS. Finally, we suggest how the improved knowledge on the fragmentation in particular of the gluon could be used to determine the gluon and charm content of the photon.

Figures (40)

• Figure 1: General structure of factorization of a high--energy cross section.
• Figure 2: The IPP process in $e^+e^-$ annihilation.
• Figure 3: Relative importance of the longitudinal cross section. The solid (dotted) curves show the NLO (LO) results for $d\sigma_L/d\sigma_{T+L}$, evaluated at $m_Z$ with our new set of $h^{\pm}$ FF's.
• Figure 4: Dependence of the electroweak charges on the virtuality $Q^2$ of the vector boson. The solid (dotted) lines show the ratios of $Q_{\rm up}(Q^2)$ ($Q_{\rm up}^F(Q^2)$) over $Q_{\rm down}(Q^2)$, respectively. At the $Z$ pole, the relative weight of $Q_{\rm up}^F(Q^2)$ becomes maximal, whereas $Q_{\rm up}(Q^2)$ has its minimum there.
• Figure 5: Scale dependence of the longitudinal cross section in $e^+e^-$ annihilation to LO. While the LO result with $M_f=m_Z$ (solid) falls short of the ALEPH data ale3 by a significant amount, a very low scale of $M_f=20$ GeV (dotted) leads to satisfactory agreement. The plot is taken from binpk, where the calculation with the leading order coefficient functions was misleadingly labeled NLO.