Projected sensitivity to the ADD large extra dimensions model inthe monojet plus missing transverse momentum final state atHL-LHC, HE-LHC, and FCC-hh

We present a unified projection of the sensitivity to the Arkani-Hamed–Dimopoulos–Dvali (ADD) model of large extra spatial dimensions in the monojet plus missing transverse momentum final state at three future hadron colliders — the HL-LHC (√s = 14 TeV, 3 ab⁻¹), the HE-LHC (27 TeV, 15 ab⁻¹) and the FCC-hh (100 TeV, 30 ab⁻¹) — for n = 2, 3, 4, 6 extra dimensions, using the same selection, significance estimator and calibration throughout. Signal samples are generated with PYTHIA 8 and combined with the post-fit Standard-Model background yields released by the ATLAS and CMS collaborations on HEPData. Two elements distinguish the analysis. First, the energy scaling of the background to higher √s — including the 13 → 14 TeV step — is measured as a function of E_T^miss from dedicated Z(νν̄)+jets and W(ℓν)+jets samples rather than assumed constant, which reduces the projected FCC-hh reach by some 40% relative to a constant-factor treatment. Second, the framework is anchored to the published ATLAS Run-2 expected 95% CL limits through a transparent n-dependent calibration, determined directly for all five values of n and clustering at 1.096 ± 1.5%; its selection response is independently validated against the published ATLAS cutflow at a matched benchmark. The projected 95% CL exclusion reach in M_D for n = 2 is 12.7, 16.2 and 24.3 TeV at the three colliders, with 5σ discovery reach of 9.8, 12.7 and 18.5 TeV, extending the current ATLAS Run-2 bound of M_D > 11.2 TeV by factors of 1.1–2.2. The calibration scheme is general and provides a template for analogous future-collider studies; the projections should be read within the stated Run-2-anchored detector and uncertainty assumptions. Content from this work may be used under the terms of the Creative Commons Attribution 3.0 licence. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI. Article funded by SCOAP3 and published under licence by Chinese Physical Society and the Institute of High Energy Physics of the Chinese Academy of Science and the Institute of Modern Physics of the Chinese Academy of Sciences and IOP Publishing Ltd.