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The effective-one-body theory (EOB) describes the conservative dynamics ofcompact binary systems in terms of an effective Hamiltonian approach. TheHamiltonian for moderately eccentric motion of two non-spinning compact objectsin the extreme mass-ratio limit is given in terms of three potentials: $a(v),\bar{d}(v), q(v)$. By generalizing the first law of mechanics for(non-spinning) black hole binaries to eccentric orbits, [\prd{\bf92}, 084021(2015)] recently obtained new expressions for $\bar{d}(v)$ and $q(v)$ in termsof quantities that can be readily computed using the gravitational self-forceapproach. Using these expressions we present a new computation of the EOBpotential $q(v)$ by combining results from two independent numerical self-forcecodes. We determine $q(v)$ for inverse binary separations in the range $1/1200\le v \lesssim 1/6$. Our computation thus provides the first-ever strong-fieldresults for $q(v)$. We also obtain $\bar{d}(v)$ in our entire domain to afractional accuracy of $\gtrsim 10^{-8}$. We find to our results are compatiblewith the known post-Newtonian expansions for $\bar{d}(v)$ and $q(v)$ in theweak field, and agree with previous (less accurate) numerical results for$\bar{d}(v)$ in the strong field.

Numerical computation of the EOB potential q using self-force results