Numerical computation of the effective-one-body potential q using self-force results

The effective-one-body theory (EOB) describes the conservative dynamics of compact binary systems in terms of an effective Hamiltonian approach. The Hamiltonian for moderately eccentric motion of two nonspinning compact objects in the extreme mass-ratio limit is given in terms of three potentials: a(upsilon), (d) over bar(upsilon), q(upsilon). By generalizing the first law of mechanics for (nonspinning) black hole binaries to eccentric orbits, [A. Le Tiec, Phys. Rev. D 92, 084021 (2015).] recently obtained new expressions for (d) over bar(upsilon) and q(upsilon) in terms of quantities that can be readily computed using the gravitational self-force approach. Using these expressions we present a new computation of the EOB potential q(upsilon) by combining results from two independent numerical self-force codes. We determine q(upsilon) for inverse binary separations in the range 1/1200 <= upsilon less than or similar to 1/6. Our computation thus provides the first-ever strong-field results for q(upsilon). We also obtain (d) over bar(upsilon) in our entire domain to a fractional accuracy of greater than or similar to 10(-8). We find that our results are compatible with the known post-Newtonian expansions for (d) over bar(upsilon) and q(upsilon) in the weak field, and agree with previous (less accurate) numerical results for (d) over bar(upsilon) in the strong field.