Jet substructure observables have significantly extended the search program for physics beyond the Standard Model at the Large Hadron Collider. The state-of-the-art tools have been motivated by theoretical calculations, but there has never been a direct comparison between data and calculations of jet substructure observables that are accurate beyond leading-logarithm approximation. Such observables are significant not only for probing the collinear regime of QCD that is largely unexplored at a hadron collider, but also for improving the understanding of jet substructure properties that are used in many studies at the Large Hadron Collider. This Letter documents a measurement of the first jet substructure quantity at a hadron collider to be calculated at next-to-next-to-leading-logarithm accuracy. The normalized, differential cross-section is measured as a function of log$_{10}\rho^2$, where $\rho$ is the ratio of the soft-drop mass to the ungroomed jet transverse momentum. This quantity is measured in dijet events from 32.9 fb$^{-1}$ of $\sqrt{s} = 13$ TeV proton-proton collisions recorded by the ATLAS detector. The data are unfolded to correct for detector effects and compared to precise QCD calculations and leading-logarithm particle-level Monte Carlo simulations.
Jet substructure quantities are measured using jets groomed with the soft-drop grooming procedure in dijet events from 32.9 fb$^{-1}$ of $pp$ collisions collected with the ATLAS detector at $\sqrt{s} = 13$ TeV. These observables are sensitive to a wide range of QCD phenomena. Some observables, such as the jet mass and opening angle between the two subjets which pass the soft-drop condition, can be described by a high-order (resummed) series in the strong coupling constant $\alpha_S$. Other observables, such as the momentum sharing between the two subjets, are nearly independent of $\alpha_S$. These observables can be constructed using all interacting particles or using only charged particles reconstructed in the inner tracking detectors. Track-based versions of these observables are not collinear safe, but are measured more precisely, and universal non-perturbative functions can absorb the collinear singularities. The unfolded data are directly compared with QCD calculations and hadron-level Monte Carlo simulations. The measurements are performed in different pseudorapidity regions, which are then used to extract quark and gluon jet shapes using the predicted quark and gluon fractions in each region. All of the parton shower and analytical calculations provide an excellent description of the data in most regions of phase space.
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