We produce the first numerical predictions of the dynamical diquark model of multiquark exotic hadrons. Using Born-Oppenheimer potentials calculated numerically on the lattice, we solve coupled and uncoupled systems of Schrödinger equations to obtain mass eigenvalues for multiplets of states that are, at this stage, degenerate in spin and isospin. Assuming reasonable values for these fine-structure splittings, we obtain a series of bands of exotic states with a common parity eigenvalue that agree well with the experimentally observed charmoniumlike states, and we predict a number of other unobserved states. In particular, the most suitable fit to known pentaquark states predicts states below the charmonium-plus-nucleon threshold. Finally, we examine the strictest form of Born-Oppenheimer decay selection rules for exotics and, finding them to fail badly, we propose a resolution by relaxing the constraint that exotics must occur as heavy-quark spin-symmetry eigenstates.

We incorporate fine-structure corrections into the dynamical diquark model of multiquark exotic hadrons. These improvements include effects due to finite diquark size, spin-spin couplings within the diquarks, and most significantly, isospin-dependent couplings in the form of pionlike exchanges expected to occur between the light quarks within the diquarks. Using a simplified two-parameter interaction Hamiltonian, we obtain fits in which the isoscalar J P C = 1 ++ state-identified as the X(3872)-appears naturally as the lightest exotic (including all states that are predicted by the model but have not yet been observed), while the Zc(3900) and Zc(4020) decay predominantly to J/ψ and ηc, respectively, in accord with experiment. We explore implications of this model for the excited tetraquark multiplets and the pentaquarks.

In infinite volume the gradient flow transformation can be interpreted as a continuous real-space Wilsonian renormalization group (RG) transformation. This approach allows one to determine the continuous RG 𝛽 function, an alternative to the finite-volume step-scaling function. Unlike step-scaling, where the lattice must provide the only scale, the continuous 𝛽 function can be used even in the confining regime where dimensional transmutation generates a physical scale Λ QCD . We investigate a pure gauge SU(3) Yang-Mills theory both in the deconfined and the confined phases and determine the continuous 𝛽 function in both. Our investigation is based on simulations done with the tree-level Symanzik gauge action on lattice volumes up to 32 4 using both Wilson and Zeuthen gradient flow (GF) measurements. Our continuum GF 𝛽 function exhibits considerably slower running than the universal 2-loop perturbative prediction, and at strong couplings it runs even slower than the 1-loop prediction.

No abstract

In infinite volume the gradient flow transformation can be interpreted as a continuous real-space Wilsonian renormalization group (RG) transformation. This approach allows one to determine the continuous RG 𝛽 function, an alternative to the finite-volume step-scaling function. Unlike step-scaling, where the lattice must provide the only scale, the continuous 𝛽 function can be used even in the confining regime where dimensional transmutation generates a physical scale Λ QCD . We investigate a pure gauge SU(3) Yang-Mills theory both in the deconfined and the confined phases and determine the continuous 𝛽 function in both. Our investigation is based on simulations done with the tree-level Symanzik gauge action on lattice volumes up to 32 4 using both Wilson and Zeuthen gradient flow (GF) measurements. Our continuum GF 𝛽 function exhibits considerably slower running than the universal 2-loop perturbative prediction, and at strong couplings it runs even slower than the 1-loop prediction.