Exposing the QCD Splitting Function with CMS Open Data

The splitting function is a universal property of quantum chromodynamics (QCD) which describes how energy is shared between partons. Despite its ubiquitous appearance in many QCD calculations, the splitting function cannot be measured directly, since it always appears multiplied by a collinear singularity factor. Recently, however, a new jet substructure observable was introduced which asymptotes to the splitting function for sufficiently high jet energies. This provides a way to expose the splitting function through jet substructure measurements at the Large Hadron Collider. In this Letter, we use public data released by the CMS experiment to study the two-prong substructure of jets and test the $1\to 2$ splitting function of QCD. To our knowledge, this is the first ever physics analysis based on the CMS Open Data.

Figure 1

Jet $p_T$ spectrum from the CMS Open Data compared to three parton shower generators. Indicated is the $p_T>150\mathrm{GeV}$ cut used in later analyses.

Figure 2

Schematic of the soft drop algorithm, which removes angular-ordered branches whose momentum fraction $z$ is below $z_{\mathrm{cut}}{\theta }^{\beta }$. The final groomed kinematics are indicated by the $g$ subscript.

Figure 3

Track jet mass spectra before and after the soft drop procedure with $\beta =0$ (i.e., mMDT with $\mu =1$), comparing the CMS Open Data to Pythia.

Figure 4

Double-differential distribution of track $z_g$ versus ${\theta }_g$ in the CMS Open Data, i.e., the dimensionless probability density $p(z_g,{\theta }_g)$ whose integral is 1.

Figure 5

Distribution of $z_g$ from mMDT and soft drop. The theory distribution is from an all-particle prediction yet agrees very well with the track-based distributions.