D0-brane tension in string field theory

We compute the D0-brane tension in string field theory by representing it as a tachyon lump of the D1-brane compactified on a circle of radius $R$. To this aim, we calculate the lump solution in level truncation up to level L=8. The normalized D0-brane tension is independent on $R$. The compactification radius is therefore chosen in order to cancel the subleading correction $1\mathrm{/}{L}^2$. We show that an optimal radius $R^{\ast }$ indeed exists and that at $R^{\ast }$ the theoretical prediction for the tension is reproduced at the level of ${10}^{-5}$. As a byproduct of our calculation we also discuss the determination of the marginal tachyon field at $R\to 1$.