Dijet azimuthal decorrelation in $e^+e^-$ annihilation

We examine non-global and clustering logarithms in the distribution of the azimuthal decorrelation between two jets in $e^+e^-\to$ dijet events, where the jets are defined with $E$-scheme recombination in the generalized $k_t$ algorithm. We calculate at one loop and to all orders the leading global single logarithms in the distribution of the said observable. We also compute at fixed order up to four loops at finite $N_c$ the non-global and clustering logarithms, and numerically resum them to all orders in the large-$N_c$ approximation. We compare our results at $\mathcal{O}(\alpha_s)$ and $\mathcal{O}(\alpha_s^2)$ with those of the EVENT2 fixed-order Monte Carlo program and find agreement of the leading singular behavior of the azimuthal decorrelation distribution. We find that the impact of non-global logarithms on the resummed distribution in the anti-$k_t$ algorithm is substantial, while it is significantly smaller in the $k_t$ algorithm. Furthermore, the combined clustering and non-global logarithms in the $k_t$ algorithm have an even smaller effect on the distribution. Finally, we use the program Gnole to calculate the resummed distribution at NLL accuracy, thus achieving state-of-the-art accuracy for the resummation of this quantity.