MIT Center for Theoretical Physics – a Leinweber Institute

It is a long-standing problem to prove that the number of distinct topological types of Calabi-Yau threefolds is finite. A related proposition, Reid’s fantasy, conjectures that all Calabi-Yau threefolds are connected in a single moduli space through extremal transitions. Finiteness of topological types has been proven for the class of elliptic and genus one fibered Calabi-Yau threefolds, which recently have been shown to constitute the vast majority of known Calabi-Yau threefolds; the moduli space of elliptic CY3’s is connected. In this letter, we demonstrate that all non-fibered Calabi-Yau threefolds in two of the largest known classes (toric hypersurfaces and complete intersections in products of projective spaces) are connected to fibered Calabi-Yau threefolds through a simple class of geometric transitions involving the shrinking of a single divisor from a fibered geometry. This suggests that non-fibered Calabi-Yau threefolds are rare special cases that are reached by simplifying fibered Calabi-Yau threefolds, and points to a natural path towards proving finiteness and Reid’s fantasy for Calabi-Yau threefolds.

The couplings between hadrons encode the dynamics of quantum chromodynamics. While many couplings can be calculated from decay widths, in some cases the decays are kinematically forbidden and hence are not directly accessible. We use a Regge framework to determine these couplings from high-energy polarized scattering processes. We apply this to the $πΔ$ photoproduction that was recently studied at GlueX and provide the first determination of the complete set of $NΔ$ couplings to $ρ$, $b_1$, and $a_2$.

Differential cross sections are the currency of scientific exchange in particle and nuclear physics. Recently, machine learning methods have enabled unbinned and high-dimensional cross section measurements through new approaches to unfolding. A key challenge with unfolding is that it is a bi-level optimization problem where constraints are available at the detector level while the target is at the particle level, linked by a stochastic detector response. Further complications arise when the particle-level and detector-level distributions have non-overlapping or only partially overlapping support, which can destabilize training and degrade unfolding performance. In this paper, we introduce a new unbinned unfolding technique called the Reweighting Adversarial Network (RAN), which can be viewed as a generalization of the Moment Unfolding protocol to accommodate full phase-space unfolding. RANs address the bi-level optimization problem through a particle-level reweighting function steered by a Wasserstein critic at the detector level. RANs do not require overlapping support at the detector level, nor multiple iterations of training. We evaluate the performance of RANs with Gaussian data and jet substructure studies, including cases specifically designed to stress test the method under vanishing support overlap. We demonstrate that RANs outperform state-of-the-art methods in accuracy and have a lower computational overhead.

We study the stochastic dynamics of heavy quarks propagating through the strongly coupled plasma of $\mathcal{N}=4$ supersymmetric Yang-Mills (SYM) theory at nonzero temperature in terms of the corresponding Kolmogorov equation, which correctly describes their kinetic equilibration and the non-Gaussian fluctuations in their momenta without having to restrict their velocity to the non-relativistic regime. Leveraging the heavy quark limit, we show that the evolution of the momentum space distribution function can be reformulated as a Hamilton-Jacobi problem, and therefore can be solved in terms of first-order ordinary differential equations. We solve these evolution equations in an infinite thermal plasma with a constant temperature for initial conditions specified by spherically symmetric heavy quark momentum distributions with a phenomenologically motivated shape that is steeply falling at large momentum. To highlight the distinctive features of the kinetic equilibration process, we compare their solutions with Fokker-Planck dynamics with the same drag coefficient and fluctuations chosen by hand to guarantee equilibration. We find qualitatively similar dynamics at small momentum, and very different dynamics at large momentum, where, much like in jet quenching phenomena, the steepness of the momentum distribution gives a larger relevance to unlikely events in which a heavy quark loses little momentum in a given time step. Such events are much less unlikely in the Kolmogorov evolution than in Fokker-Planck evolution with the same mean energy loss, meaning that equilibration at large momentum is significantly delayed. Our results provide a systematic description of heavy quarks propagating through strongly coupled plasma from the ultra-relativistic to the non-relativistic regime and point the way towards implementation in phenomenological studies.