modeled as a bag or an elementary string.

Challenges
----------

### Precision Values of the\
Quark Masses

In contrast to the beautiful and inspiring situation regarding $\alpha_s$, our present determinations of $m_u$ and $m_d$ are an embarrassment. They are uncertain at the factor-of-two level, at least. Despite their crucial importance for the structure of the world[^2], they are by far the worst measured fundamental parameters of physics. It is a major challenge for lattice gauge theory to improve this situation.

Again, a comparison may be in order. Quite properly, tremendous effort has been put into measuring neutrino masses. Yet the precise values of neutrino masses are no more fundamental than light quark masses, and they are much less important for the structure of the world. In any case, it is unlikely we will reach a profound understanding of one without the other, since in unified theories quarks and leptons come as a package.

Besides this general sort of motivation, there are several more specific reasons to be especially interested in the values of $m_u$ and $m_d$. We would like to be absolutely sure that $m_u \neq 0$, since this empowers the P- and T-violating $\theta$ parameter, which provides the prime 