Supersymmetry unification, naturalness, and discovery prospects at HL-LHC and HE-LHC

An overview of recent developments in supersymmetry, supergravity and unification and prospects for supersymmetry discovery at the current and future high energy colliders and elsewhere are discussed. Currently several empirical data point to supersymmetry as an underlying symmetry of particle physics. These include the unification of gauge couplings within supersymmetry, prediction within supergravity unification that the Higgs boson mass lie below 130 GeV supported by the observation of the Higgs boson mass at ~125 GeV, and vacuum stability up to the Planck scale for the observed value of the Higgs boson mass while the standard model does not do that. Additionally, of course, supersymmetry solves the big hierarchy problem arising from the quadratic divergence to the Higgs boson mass square in the Standard Model, and provides a frame work that allows for extrapolation of physics from the electroweak scale to the grand unification scale consistent with experiment. Currently there is no alternative paradigm that does that. However, the large loop corrections needed to lift the mass of the Higgs boson from its tree value to the experimentally observed values imply that the scale of weak scale supersymmetry lies in the TeV region making the observation of sparticles more challenging. The lightest of the sparticles could still lie with in reach of the High Luminosity (HL)-LHC and High Energy (HE)-LHC operating at an optimal luminosity of 2.5 × 10$^{35}$ cm$^{−2}$ s$^{−1}$ at a center of mass energy of 27 TeV. Variety of other experiments related to search for dark matter, improved experiments on the measurement of g$_{μ}$ − 2 and EDMs of elementary particles could lend further support for new physics beyond the standard model and specifically supersymmetry. Supergravity theories may also contain hidden sectors which may interact with the visible sector gravitationally and also via extra-weak or ultra-weak interactions. In this case a variety of new signals might arise in indirect detection and at LHC in the form of long lived charged sparticles which can either decay inside the detector or outside. We note that the discovery of sparticles will establish supersymmetry as a fundamental symmetry of nature, and its confirmation will also lend support for strings.