Luminosities of muon-proton and muon-nucleus collisions at a recently proposed muon-ion collider (MuIC) at Brookhaven National Laboratory (BNL) in the USA have been estimated using A Luminosity Optimizer for High Energy Physics (AloHEP) software keeping in mind beam-beam tune-shift values. It is shown that L$_{\mu p}$ = 3.6x10$^{31}$ cm$^{-2}$s$^{-1}$ and L$_{\mu{\rm -Au}}$ = 2.84x10$^{27}$ cm$^{-2}$s$^{-1}$ values can be achieved at MuIC. The physics search potential of the collider is superior to HERA. However, LHeC will provide 2 orders of higher luminosities at approximately same center-of-mass (CoM) energies.

Construction of future Muon Collider (or dedicated mu-ring) tangential to the energy frontier pp colliders will give opportunity to realize mu-p collisions at multi-TeV center of mass energies at a luminosity of order of $10^{33}$ cm$^{-2}$s$^{-1}$ ($10^{34}$ cm$^{-2}$s$^{-1}$). Obviously, such colliders will essentially enlarge the physics search potential of corresponding muon and hadron colliders for both the SM (especially for clarifying QCD basics) and BSM phenomena. This paper is devoted to review of main parameters of mu-p colliders proposed until now.

There are strong phenomenological arguments favoring the existence of vector-like leptons and quarks in nature. In spite of extensive studies conducted in search of vector-like quarks, there are only a limited number of experimental studies on vector-like leptons. Moreover, these searches do not include all possible decay modes of vector-like leptons. Therefore, the analyses done so far are incomplete. In this letter, we highlight decay channels that are not covered by different experimental analyses, with a focus on L3, ATLAS, and CMS results. We argue that experimental analyses should be redone considering these shortcomings.

Fossil fuels, which meet most of humanity's energy needs, cause climate change due to their high carbon emissions. There are two types of energy sources that can replace fossil fuels: renewable and nuclear. Nuclear energy sources are more advantageous in terms of efficiency and sustainability. The use of Thorium as nuclear fuel in fusion reactors will contribute to the reduction of radioactive waste, due to the much lower production of transuranics. Fusion reactors, which are considered promising, are still in the R&D phase. In this respect, hybrid fusion-fission reactors seem more promising and the recently proposed combination of muon-catalyzed DD fusion with a cascade thorium reactor is worthy of appreciation. In this study, we show that using the DD collider instead of muonic fusion has significant advantages.