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(Abridged) Short-period gas giant exoplanets are susceptible to intenseatmospheric escape due to their large scale heights and strong high-energyirradiation. This process is thought to occur ubiquitously, but to date we haveonly detected direct evidence of atmospheric escape in hot Jupiters and warmNeptunes. The paucity of cases for intermediate, Saturn-sized exoplanets atvarying levels of irradiation precludes a detailed understanding of theunderlying physics in atmospheric escape of hot gas giants. Our objectives hereare to assess the high-energy environment of the warm ($T_\mathrm{eq} = 970$ K)Saturn WASP-29 b and search for signatures of atmospheric escape. We usedfar-ultraviolet (FUV) observations from the Hubble Space Telescope to analyzethe flux time series of H I, C II, Si III, Si IV, and N V during the transit ofWASP-29 b. At 3$\sigma$ confidence, we rule out any in-transit absorption of HIlarger than 92% in the Lyman-$\alpha$ blue wing and 19% in the red wing. Wefound an in-transit flux decrease of $39\%^{+12\%}_{-11\%}$ in the ground-stateC II emission line at 133.45 nm. But due to this signal being significantlypresent in only one visit, it is difficult to attribute a planetary or stellarorigin for the ground-state C II signal. We place 3$\sigma$ absorption upperlimits of 40%, 49% and 24% for Si III, Si IV, and for excited-state C II at133.57 nm, respectively. Low activity levels and the faint X-ray luminositysuggest that WASP-29 is an old, inactive star. An energy-limited approximationcombined with the reconstructed EUV spectrum of the host suggests that theplanet is losing its atmosphere at a rate of $4 \times 10^9$ g s$^{-1}$. Thenon-detection at Lyman-$\alpha$ could be partly explained by a low fraction ofescaping neutral hydrogen, or by the state of fast radiative blow-out we inferfrom the reconstructed stellar Lyman-$\alpha$ line.

HST PanCET program: Non-detection of atmospheric escape in the warm Saturn-sized planet WASP-29 b