Dimensional regularization of local singularities in the fourth post-Newtonian two-point-mass Hamiltonian

The article delivers the only still unknown coefficient in the 4th post-Newtonian energy expression for binary point masses on circular orbits as a function of orbital angular frequency. Apart from a single coefficient, which is known solely numerically, all the coefficients are given as exact numbers. The shown Hamiltonian is presented in the center-of-mass frame and out of its 57 coefficients, 51 are given fully explicitly. Those coefficients are six coefficients more than previously achieved [P. Jaranowski and G. Sch\"afer, Phys. Rev. D 86, 061503(R) (2012)]. The local divergences in the point-mass model are uniquely controlled by the method of dimensional regularization. As an application, the last stable circular orbit is determined as a function of the symmetric-mass-ratio parameter.