SUSY-like relation of the splitting functions in evolution of gluon and quark jet multiplicities

Anatoly Kotikov

doi:10.1051/epjconf/201819104006

Abstract

We show the new relationship [1] between the anomalous dimensions, resummed through next-to-next-to-leading-logarithmic order, in the Dokshitzer-Gribov-Lipatov-Altarelli-Parisi (DGLAP) evolution equations for the first Mellin moments Dq,g(μ2) of the quark and gluon fragmentation functions, which correspond to the average hadron multiplicities in jets initiated by quarks and gluons, respectively. So far, such relationships have only been known from supersymmetric (SUSY) QCD. Exploiting available next-to-nextto- next-to-leading-order (NNNLO) information on the ratio D+g (μ2)=D+q (μ2) of the dominant plus components, the fit of the world data of Dq,g(μ2) for charged hadrons measured in e+e- annihilation leads to α(5)s (MZ) = 0:1205 +0:0016 -0:0020.

Highlights

Dokshitzer-Gribov-Lipatov-Altarelli-Parisi (DGLAP) evolution equations for the first Mellin moments Dq,g(μ2) of the quark and gluon fragmentation functions, which correspond to the average hadron multiplicities in jets initiated by quarks and gluons, respectively
Once Da(x, μ20) are assumed to be known, their μ2 dependences are governed by the timelike DGLAP evolution equations [4, 5], whose splitting functions Pba(x) are known at next-to-next-to-leading order [6]
The first Mellin moment Da(μ2) ≡ Da(1, μ2) is of particular interest in its own right because it corresponds to the average hadron multiplicity nh a of jets initiated by parton a

Summary

Introduction

Dokshitzer-Gribov-Lipatov-Altarelli-Parisi (DGLAP) evolution equations for the first Mellin moments Dq,g(μ2) of the quark and gluon fragmentation functions, which correspond to the average hadron multiplicities in jets initiated by quarks and gluons, respectively. Once Da(x, μ20) are assumed to be known, their μ2 dependences are governed by the timelike DGLAP evolution equations [4, 5], whose splitting functions Pba(x) are known at next-to-next-to-leading order [6].

Results

Conclusion