Charmonium-nucleon interactions from the time-dependent HAL QCD method

The charmonium-nucleon effective central interactions have been computed by the time-dependent HAL QCD method. This gives an updated result of a previous study based on the time-independent method, which is now known to be problematic because of the difficulty in achieving the ground-state saturation. We discuss that the result is consistent with the heavy quark symmetry. No bound state is observed from the analysis of the scattering phase shift; however, this shall lead to a future search of the hidden-charm pentaquarks by considering channel-coupling effects.Comment: 8 pages, 8 figure

Lattice QCD Study of the Nucleon-Charmonium Interaction

The $J/\psi$-nucleon interaction is studied by lattice QCD calculations. At the leading order of the derivative expansion, the interaction consists of four terms: the central, the spin-spin, and two types of tensor forces. We determine these spin-dependent forces quantitatively by using the time-dependent HAL QCD method. We find that the spin-spin force is the main cause of the hyperfine splitting between the $J=1/2$ and the $J=3/2$ states, while the two tensor forces have much smaller effects on the S-wave scattering processes.Comment: 5 pages, 4 figure

Non-convex optimization problems for maximum hands-off control

The maximum hands-off control is the optimal solution to the L0 optimal control problem. It has the minimum support length among all feasible control inputs. To avoid computational difficulties arising from its combinatorial nature, the convex approximation method that replaces the L0 norm by the L1 norm in the cost function has been employed on standard. However, this approximation method does not necessarily obtain the maximum hands-off control. In response to this limitation, this paper newly introduces a non-convex approximation method and formulates a class of non-convex optimal control problems that are always equivalent to the maximum hands-off control problem. Based on the results, this paper describes the computation method that quotes algorithms designed for the difference of convex functions optimization. Finally, this paper confirms the effectiveness of the non-convex approximation method with a numerical example.Comment: 8 page