  The debris disk surrounding $\beta$~Pictoris has been observed with ALMA to
contain a belt of CO gas with a distinct peak at $\sim$85 au. This CO clump is
thought to be the result of a region of enhanced density of solids that collide
and release CO through vaporisation. The parent bodies are thought to be
comparable to solar system comets, in which CO is trapped inside a water ice
matrix. Since H$_2$O should be released along with CO, we aim to put an upper
limit on the H$_2$O gas mass in the disk of $\beta$ Pictoris. We use archival
data from the Heterodyne Instrument for the Far-Infrared (HIFI) aboard the
Herschel Space Observatory to study the ortho-H$_2$O 1$_{10}$-1$_{01}$ emission
line. The line is undetected. Using a python implementation of the radiative
transfer code RADEX, we convert upper limits on the line flux to H$_2$O gas
masses. The resulting lower limits on the CO/H$_2$O mass ratio are compared to
the composition of solar system comets. Depending on the assumed gas spatial
distribution, we find a 95% upper limit on the ortho-H$_2$O line flux of $7.5
\times 10^{-20}$ W m$^{-2}$ or $1.2 \times 10^{-19}$ W m$^{-2}$. These
translate into an upper limit on the H$_2$O mass of $7.4 \times 10^{16}$-$1.1
\times 10^{18}$ kg depending on both the electron density and gas kinetic
temperature. The range of derived gas-phase CO/H$_2$O ratios is marginally
consistent with low-ratio solar system comets.
