The quark-mass dependence of the potential energy between static colour sources in the QCD vacuum with light and strange quarks

The low-lying energy spectrum of the static-colour-source-anti-source system in a vacuum containing light and strange quarks is computed using lattice QCD for a range of different light quark masses. The resulting levels are described using a simple model Hamiltonian and the parameters in this model are extrapolated to the physical light-quark masses. In this framework, the QCD string tension is found to be $\sqrt{\sigma }=445(3{)}_{\mathrm{s}\mathrm{t}\mathrm{a}\mathrm{t}}(6{)}_{\mathrm{s}\mathrm{y}\mathrm{s}}$ MeV.