We propose two novel formulations of the hopping parameter expansion for finite density QCD using Wilson fermions, while keeping the gauge action intact. We use the complex Langevin equation to circumvent the sign problem in the theory. We perform si
mulations at very high order of the expansion, such that convergence is directly observable. We compare results to the full QCD results, and see agreement at sufficiently high orders. These results provide support for the use of complex Langevin dynamics to study QCD at nonzero density, both in the full and the expanded theory, and for the convergence of the latter.
We study the temperature dependence of bottomonium for temperatures in the range $0.4 T_c < T < 2.1 T_c$, using nonrelativistic dynamics for the bottom quark and full relativistic lattice QCD simulations for $N_f=2$ light flavors on a highly anisotro
pic lattice. We find that the $Upsilon$ is insensitive to the temperature in this range, while the $chi_b$ propagators show a crossover from the exponential decay characterizing the hadronic phase to a power-law behaviour consistent with nearly-free dynamics at $T simeq 2 T_c$.
