  Hydrogen deuteride (HD) rotational line emission can provide reliable
protoplanetary disk gas mass measurements, but it is difficult to observe and
detections have been limited to three T-Tauri disks. No new data have been
available since the \emph{Herschel} Space Observatory mission ended in 2013. We
set out to obtain new disk gas mass constraints by analysing upper limits on HD
1-0 emission in \emph{Herschel}/PACS archival data from the DIGIT key
programme. With a focus on the Herbig Ae/Be disks, whose stars are more
luminous than T Tauris, we determine upper limits for HD in data previosly
analysed for its line detections. Their significance is studied with a grid of
models run with the DALI physical-chemical code, customised to include
deuterium chemistry. Nearly all the disks are constrained to $M_{\rm
gas}\leq0.1\,$M$_{\odot}$, ruling out global gravitational instability. A
strong constraint is obtained for the HD 163296 disk mass, $M_{\rm gas} \leq
0.067\,$M$_{\odot}$, implying $\Delta_{\rm g/d}\leq100$. This HD-based mass
limit is towards the low end of CO-based mass estimates for the disk,
highlighting the large uncertainty in using only CO and suggesting that
gas-phase CO depletion in HD 163296 is at most a factor of a few. The $M_{\rm
gas}$ limits for HD 163296 and HD 100546, both bright disks with massive
candidate protoplanetary systems, suggest disk-to-planet mass conversion
efficiencies of $M_{\rm p}/(M_{\rm gas} + M_{\rm p})\approx10$ to $40\,$% for
present-day values. Near-future observations with SOFIA/HIRMES will be able to
detect HD in the brightest Herbig~Ae/Be disks within $150\,$pc with
$\approx10\,$h integration time.
