Expression of Interest for a Phase-II LHCb Upgrade: Opportunities in flavour physics, and beyond, in the HL-LHC era

A Phase-II Upgrade is proposed for the LHCb experiment in order to take full advantage of the flavour-physics opportunities at the HL-LHC, and other topics that can be studied with a forward spectrometer. This Upgrade, which will be installed in Long Shutdown 4 of the LHC (2030), will build on the strengths of the current experiment and the Phase-I Upgrade, but will consist of re-designed sub-systems that can operate at a luminosity of $2 \\times 10^{34}\\,{\\rm cm}^{-2} s^{-1}$, ten times that of the Phase-I Upgrade detector. New and improved detector components will increase the intrinsic performance of the experiment in certain key areas. In particular the installation of a tungsten sampling electromagnetic calorimeter will widen LHCb's capabilities for decays involving $\\pi^0$ and $\\eta$ mesons, electrons, and photons from loop-level penguin processes. The physics motivation is presented, and the prospects for operating the LHCb Interaction Point at high luminosity are assessed. The challenges for the detector are described and possible solutions are discussed. Finally, the key R\\&D areas are summarised, together with a set of initial modifications suitable for implementation during Long Shutdown 3 (2024--2026).