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Low mass stars might offer today the best opportunities to detect andcharacterise planetary systems, especially those harbouring close-in low masstemperate planets. Among those stars, TRAPPIST-1 is exceptional since it hasseven Earth-sized planets, of which three could sustain liquid water on theirsurfaces. Here we present new and deep ALMA observations of TRAPPIST-1 to lookfor an exo-Kuiper belt which can provide clues about the formation andarchitecture of this system. Our observations at 0.88 mm did not detect dustemission, but can place an upper limit of 23$\mu$Jy if the belt is smaller than4 au, and 0.15 mJy if resolved and 100 au in radius. These limits correspond tolow dust masses of $\sim10^{-5}-10^{-2}$ $M_\oplus$, which are expected after 8Gyr of collisional evolution unless the system was born with a $>20$ $M_\oplus$belt of 100 km-sized planetesimals beyond 40 au or suffered a dynamicalinstability. This $20$ $M_\oplus$ mass upper limit is comparable to thecombined mass in TRAPPIST-1 planets, thus it is possible that most of theavailable solid mass in this system was used to form the known planets. Asimilar analysis of the ALMA data on Proxima Cen leads us to conclude that abelt born with a mass $\gtrsim1$ $M_\oplus$ in 100 km-sized planetesimals couldexplain its putative outer belt at 30 au. We recommend that futurecharacterisations of debris discs around low mass stars should focus on nearbyand young systems if possible.

Searching for a cometary belt around Trappist-1 with ALMA