Back-to-Back Inclusive Dijets in Deep Inelastic Scattering at Small x: Complete NLO Results and Predictions.

We compute the back-to-back dijet cross section in deep inelastic scattering at small x to next-to-leading order (NLO) in the color glass condensate effective field theory. Our result can be factorized into a convolution of the Weizsäcker-Williams gluon transverse-momentum-dependent distribution function (WW gluon TMD) with a universal soft factor and an NLO coefficient function. The soft factor includes both double and single logarithms in the ratio of the relative transverse momentum P_{⊥} of the dijet pair to the dijet momentum imbalance q_{⊥}; its renormalization group (RG) evolution is resummed into the Sudakov factor. Likewise, the WW TMD obeys a nonlinear RG equation in x that is kinematically constrained to satisfy both the lifetime and rapidity ordering of the projectile. Exact analytical expressions are obtained for the NLO coefficient function of transversely and longitudinally polarized photons. Our results allow for the first quantitative separation of the dynamics of Sudakov suppression from that of gluon saturation. They can be extended to other final states and provide a framework for precision tests of novel QCD many-body dynamics at the Electron-Ion Collider.

Mutual information of spin systems from autoregressive neural networks.

We describe a direct method to estimate the bipartite mutual information of a classical spin system based on Monte Carlo sampling enhanced by autoregressive neural networks. It enables us to study arbitrary geometries of subsystems, and it can be generalized to classical field theories. We demonstrate it on the Ising model for four partitionings, including a multiply connected even-odd division. We show that the area law is satisfied for temperatures away from the critical temperature: the constant term is universal, whereas the proportionality coefficient is different for the even-odd partitioning.

Simulating first-order phase transition with hierarchical autoregressive networks.

We apply the hierarchical autoregressive neural network sampling algorithm to the two-dimensional Q-state Potts model and perform simulations around the phase transition at Q=12. We quantify the performance of the approach in the vicinity of the first-order phase transition and compare it with that of the Wolff cluster algorithm. We find a significant improvement as far as the statistical uncertainty is concerned at a similar numerical effort. In order to efficiently train large neural networks we introduce the technique of pretraining. It allows us to train some neural networks using smaller system sizes and then employ them as starting configurations for larger system sizes. This is possible due to the recursive construction of our hierarchical approach. Our results serve as a demonstration of the performance of the hierarchical approach for systems exhibiting bimodal distributions. Additionally, we provide estimates of the free energy and entropy in the vicinity of the phase transition with statistical uncertainties of the order of 10^{-7} for the former and 10^{-3} for the latter based on a statistics of 10^{6} configurations.

Analysis of autocorrelation times in neural Markov chain Monte Carlo simulations.

We provide a deepened study of autocorrelations in neural Markov chain Monte Carlo (NMCMC) simulations, a version of the traditional Metropolis algorithm which employs neural networks to provide independent proposals. We illustrate our ideas using the two-dimensional Ising model. We discuss several estimates of autocorrelation times in the context of NMCMC, some inspired by analytical results derived for the Metropolized independent sampler (MIS). We check their reliability by estimating them on a small system where analytical results can also be obtained. Based on the analytical results for MIS, we propose a loss function and study its impact on the autocorrelation times. Although, this function's performance is a bit inferior to the traditional Kullback-Leibler divergence, it offers two training algorithms which in some situations may be beneficial. By studying a small 4×4 system, we gain access to the dynamics of the training process, which we visualize using several observables. Furthermore, we quantitatively investigate the impact of imposing global discrete symmetries of the system in the neural network training process on the autocorrelation times. Eventually, we propose a scheme which incorporates partial heat-bath updates, which considerably improves the quality of the training. The impact of the above enhancements is discussed for a 16×16 spin system. The summary of our findings may serve as guidance to the implementation of NMCMC simulations for more complicated models.