Light quark masses with overlap fermions in quenched QCD

We present the results of a computation of the sum of the strange and average up-down quark masses with overlap fermions in the quenched approximation. Since the overlap regularization preserves chiral symmetry at finite cutoff and volume, no additive quark mass renormalization is required and the results are $\mathcal{O}\mathrm{}\left(a\right)\mathrm{}$ improved. Our simulations are performed at $\beta =6.0\mathrm{}$ and volume ${V=16\mathrm{}}^3\times 32,$ which correspond to a lattice cutoff of $\sim 2\hspace{0.5em}\mathrm{GeV}$ and to an extension of $\sim 1.4\hspace{0.5em}\mathrm{fm}.$ The logarithmically divergent renormalization constant has been computed nonperturbatively in the RI/MOM scheme. By using the K-meson mass as experimental input, we obtain ${(m}_s+\mathrm{m̂}{)}^{\mathrm{RI}}\left(2\mathrm{}\hspace{0.5em}\mathrm{GeV}\right)=120\mathrm{}\left(7\right)\mathrm{}\left(21\right)\mathrm{}\hspace{0.5em}\mathrm{MeV},$ which corresponds to $m_s^{\overline{\mathrm{MS}}}\left(2\mathrm{}\hspace{0.5em}\mathrm{GeV}\right)=102\mathrm{}\left(6\right)\mathrm{}\left(18\right)\mathrm{}\hspace{0.5em}\mathrm{MeV}$ if continuum perturbation theory and $\chi \mathrm{PT}$ are used. By using the Gell-Mann–Oakes–Renner relation we also obtain $〈\overline{\psi }\psi {〉}^{\overline{\mathrm{MS}}}(2\mathrm{}\hspace{0.5em}\mathrm{GeV}{)/N}_f$ $=-0.0190\left(11\right)\mathrm{}\left(33\right)\mathrm{}$ ${\mathrm{GeV}}^3=-\left[267\right(5\left)\mathrm{}\right(15)\mathrm{}\hspace{0.5em}\mathrm{MeV}{]}^3,$ where the errors are statistical and systematic respectively.