We highlight the progress, current status, and open challenges of QCD-driven physics, in theory and in experiment. We discuss how the strong interaction is intimately connected to a broad sweep of physical problems, in settings ranging from astrophysics and cosmology to strongly coupled, complex systems in particle and condensed-matter physics, as well as to searches for physics beyond the Standard Model. We also discuss how success in describing the strong interaction impacts other fields, and, in turn, how such subjects can impact studies of the strong interaction. In the course of the work we offer a perspective on the many research streams which flow into and out of QCD, as well as a vision for future developments.

We calculate the heavy quarkonium energy levels and decay widths in a quark-gluon plasma, whose temperature T and screening mass m _D satisfy the hierarchy mα _s ≫ T ≫ mα _s ² ≫m _D (m being the heavy-quark mass), at order mα _s ⁵ . We first sequentially integrate out the scales m, mα _s and T, and, next, we carry out the calculations in the resulting effective theory using techniques of integration by regions. A collinear region is identified, which contributes at this order. We also discuss the implications of our results concerning heavy quarkonium suppression in heavy ion collisions.

We calculate the up-, down-, strange-, charm-, and bottom-quark masses using the MILC highly improved staggered-quark ensembles with four flavors of dynamical quarks. We use ensembles at six lattice spacings ranging from $a\approx 0.15$ to 0.03 fm and with both physical and unphysical values of the two light and the strange sea-quark masses. We use a new method based on heavy-quark effective theory (HQET) to extract quark masses from heavy-light pseudoscalar meson masses. Combining our analysis with our separate determination of ratios of light-quark masses we present masses of the up, down, strange, charm, and bottom quarks. Our results for the $\overline{\mathrm{MS}}$-renormalized masses are $m_u(2\mathrm{GeV})=2.130(41)\mathrm{MeV}$, $m_d(2\mathrm{GeV})=4.675(56)\mathrm{MeV}$, $m_s(2\mathrm{GeV})=92.47(69)\mathrm{MeV}$, $m_c(3\mathrm{GeV})=983.7(5.6)\mathrm{MeV}$, and $m_c(m_c)=1273(10)\mathrm{MeV}$, with four active flavors; and $m_b(m_b)=4195(14)\mathrm{MeV}$ with five active flavors. We also obtain ratios of quark masses $m_c/m_s=11.783(25)$, $m_b/m_s=53.94(12)$, and $m_b/m_c=4.578(8)$. The result for $m_c$ matches the precision of the most precise calculation to date, and the other masses and all quoted ratios are the most precise to date. Moreover, these results are the first with a perturbative accuracy of ${\alpha }_s^4$. As byproducts of our method, we obtain the matrix elements of HQET operators with dimension 4 and 5: ${\overline{\mathrm{\Lambda }}}_{\mathrm{MRS}}=555(31)\mathrm{MeV}$ in the minimal renormalon-subtracted (MRS) scheme, ${\mu }_{\pi }^2=0.05(22){\mathrm{GeV}}^2$, and ${\mu }_G^2(m_b)=0.38(2){\mathrm{GeV}}^2$. The MRS scheme [ Phys. Rev. D 97, 034503 (2018)] is the key new aspect of our method.

We construct a nonrelativistic effective field theory description of heavy quarkonium hybrids from QCD. We identify the symmetries of the system made of a heavy quark, a heavy antiquark, and glue in the static limit. Corrections to this limit can be obtained order by order in an expansion in the inverse of the mass $m$ of the heavy quark. At order $1/m$ in the expansion, we obtain, at the level of potential nonrelativistic QCD, a system of coupled Schrödinger equations that describes hybrid spin-symmetry multiplets, including the mixing of different static energies into the hybrid states, an effect known as $\mathrm{\Lambda }$ doubling in molecular physics. In the short distance, the static potentials depend on two nonperturbative parameters, the gluelump mass and the quadratic slope, which can be determined from lattice calculations. We adopt a renormalon subtraction scheme for the calculation of the perturbative part of the potential. We numerically solve the coupled Schrödinger equations and obtain the masses for the lowest lying spin-symmetry multiplets for $c\overline{c}$, $b\overline{c}$, and $b\overline{b}$ hybrids. The $\mathrm{\Lambda }$-doubling effect breaks the degeneracy between opposite-parity spin-symmetry multiplets and lowers the mass of the multiplets that get mixed contributions of different static energies. We compare our findings to the experimental data, direct lattice computations, and sum rule calculations, and discuss the relation to the Born-Oppenheimer approximation.