  We present a calculation of the parity-violating longitudinal asymmetry in
proton-proton scattering. The calculation is performed in the framework of
chiral effective field theory which is applied systematically to both the
parity-conserving and parity-violating interactions. The asymmetry is
calculated up to next-to-leading order in the parity-odd nucleon-nucleon
potential. At this order the asymmetry depends on two parity-violating
low-energy constants: the weak pion-nucleon coupling constant $h_\pi$ and one
four-nucleon contact coupling. By comparison with the existing data, we obtain
a rather large range for $h_\pi= (1.1\pm 2)\cdot 10^{-6}$. This range is
consistent with theoretical estimations and experimental limits, but more data
are needed to pin down a better constrained value. We conclude that an
additional measurement of the asymmetry around 125 MeV lab energy would be
beneficial to achieve this goal.
