Context. 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 Herschel Space Observatory mission ended in 2013. Aims. We set out to obtain new disk gas mass constraints by analysing upper limits on HD 1 -0 emission in Herschel /PACS archival data from the DIGIT key programme. Methods. 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. Results. Nearly all the disks are constrained to Mgas ≤ 0.1 M , ruling out global gravitational instability. A strong constraint is obtained for the HD 163296 disk mass, Mgas ≤ 0.067 M , implying ∆ g/d ≤ 100. 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 Mgas limits for HD 163296 and HD 100546, both bright disks with massive candidate protoplanetary systems, suggest disk-to-planet mass conversion efficiencies of Mp/(Mgas + Mp) ≈ 10 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 ≈ 10 h integration time.Article number, page 1 of 13 A&A proofs: manuscript no. gasmass in Sections 2 and 3, respectively. In Section 4, we explore the disk mass constraints, with a focus on HD 163296, and discuss the potential for gravitational instability. In Section 5, we compare the mass of disks, stars, and planetary systems for stars over 1.4 M . We also discuss future observations of HD with SOFIA/HIRMES (Richards et al. 2018) and SPICA/SAFARI (Nakagawa et al. 2014;Audley et al. 2018).