$\alpha_s$ from hadron multiplicities via SUSY-like relation between anomalous dimensions

TL;DR

This paper discovers a simple, supersymmetry-like relation between anomalous dimensions in QCD that enables an exact solution for hadron multiplicity evolution, leading to a precise determination of the strong coupling constant.

Contribution

It introduces a novel supersymmetry-inspired relation between anomalous dimensions in QCD, allowing for exact solutions and improved understanding of hadron multiplicities.

Findings

Derived an exact solution for fragmentation function evolution equations.

Measured mba_s(5) from experimental data with improved precision.

Extended knowledge of the ratio of minus components in fragmentation functions.

Abstract

We recover in QCD an amazingly simple relationship between the anomalous dimensions, resummed through next-to-next-to-leading-logarithmic order, in the Dokshitzer-Gribov-Lipatov-Altarelli-Parisi evolution equations for the first Mellin moments $D_{q,g}(\mu^2)$ of the quark and gluon fragmentation functions, which correspond to the average hadron multiplicities in jets initiated by quarks and gluons, respectively. This relationship, which is independent of the number of quark flavors, dramatically improves previous treatments by allowing for an exact solution of the evolution equations. So far, such relationships have only been known from supersymmetric QCD, where $C_F/C_A=1$. This also allows us to extend our knowledge of the ratio $D_g^-(\mu^2)/D_q^-(\mu^2)$ of the minus components by one order in $\sqrt{\alpha_s}$. Exploiting available next-to-next-to-next-to-leading-order information on the ratio $D_g^+(\mu^2)/D_q^+(\mu^2)$ of the dominant plus components, we fit the world data of $D_{q,g}(\mu^2)$ for charged hadrons measured in $e^+e^-$ annihilation to obtain $\alpha_s^{(5)}(M_Z)=0.1205\genfrac{}{}{0pt}{}{+0.016}{-0.0020}$.