  Discriminating quark and gluon jets is a long-standing topic in collider
phenomenology. In this paper, we address this question using the Lund jet plane
substructure technique introduced in recent years. We present two complementary
approaches: one where the quark/gluon likelihood ratio is computed
analytically, to single-logarithmic accuracy, in perturbative QCD, and one
where the Lund declusterings are used to train a neural network. For both
approaches, we either consider only the primary Lund plane or the full
clustering tree. The analytic and machine-learning discriminants are shown to
be equivalent on a toy event sample resumming exactly leading collinear single
logarithms, where the analytic calculation corresponds to the exact likelihood
ratio. On a full Monte Carlo event sample, both approaches show a good
discriminating power, with the machine-learning models usually being superior.
We carry on a study in the asymptotic limit of large logarithm, allowing us to
gain confidence that this superior performance comes from effects that are
subleading in our analytic approach. We then compare our approach to other
quark-gluon discriminants in the literature. Finally, we study the resilience
of our quark-gluon discriminants against the details of the event sample and
observe that the analytic and machine-learning approaches show similar
behaviour.
