A determination of the average up-down, strange and charm quark masses from $N_f=2+1+1$

Abstract

We present a lattice QCD determination of the average up-down, strange and charm quark masses based on simulations performed by the European Twisted Mass Collaboration with $N_f = 2 + 1 + 1$ dynamical fermions. We simulated at three different values of the lattice spacing, the smallest being approximately $0.06fm$, and with pion masses as small as $210 \text{MeV}$. Our results are: $m_{ud}(2\text{GeV})=3.70(17)\text{MeV}$, $m_s(2\text{GeV})=99.2(3.9)\text{MeV}$, $m_c(m_c)=1.350(49)\text{GeV}$, $m_s/m_{ud}=26.64(30)$ and $m_c/m_s=11.65(12)$.