A muon collider would enable the big jump ahead in energy reach that is needed for a fruitful exploration of fundamental interactions. The challenges of producing muon collisions at high luminosity and 10 TeV centre of mass energy are being investigated by the recently-formed International Muon Collider Collaboration. This Review summarises the status and the recent advances on muon colliders design, physics and detector studies. The aim is to provide a global perspective of the field and to outline directions for future work.

We investigate possible interactions between neutrinos and massive scalar bosons via $g_{\varphi }\overline{\nu }\nu \varphi$ (or massive vector bosons via $g_V\overline{\nu }{\gamma }^{\mu }\nu V_{\mu }$) and explore the allowed parameter space of the coupling constant $g_{\varphi }$ (or $g_V$) and the scalar (or vector) boson mass $m_{\varphi }$ (or $m_V$) by requiring that these secret neutrino interactions (SNIs) should not spoil the success of big bang nucleosynthesis (BBN). Incorporating the SNIs into the evolution of the early Universe in the BBN era, we numerically solve the Boltzmann equations and compare the predictions for the abundances of light elements with observations. It turns out that the constraint on $g_{\varphi }$ and $m_{\varphi }$ in the scalar-boson case is rather weak, due to a small number of degrees of freedom (d.o.f.). However, in the vector-boson case, the most stringent bound on the coupling $g_V\lesssim 6\times {10}^{-10}$ at 95% confidence level is obtained for $m_V\simeq 1\mathrm{MeV}$, while the bound becomes much weaker $g_V\lesssim 8\times {10}^{-6}$ for smaller masses $m_V\lesssim {10}^{-4}\mathrm{MeV}$. Moreover, we discuss in some detail how the SNIs affect the cosmological evolution and the abundances of the lightest elements.

The precise values of the running quark and lepton masses $m_f(\mu )$, which are defined in the modified minimal subtraction scheme with $\mu$ being the renormalization scale and the subscript $f$ referring to all the charged fermions in the Standard Model (SM), are very useful for the model building of fermion masses and flavor mixing and for the precision calculations in the SM or its new-physics extensions. In this paper, we calculate the running fermion masses by taking account of the up-to-date experimental results collected by Particle Data Group and the latest theoretical higher-order calculations of relevant renormalization-group equations and matching conditions in the literature. The emphasis is placed on the quantitative estimation of current uncertainties on the running fermion masses, and the linear error propagation method is adopted to quantify the uncertainties, which has been justified by the Monte Carlo simulations. We identify two main sources of uncertainties, i.e., one from the experimental inputs and the other from the truncations at finite-order loops. The correlations among the uncertainties of running parameters can be remarkable in some cases. The final results of running fermion masses at several representative energy scales are tabulated for further applications.

The axion-like particles (ALPs) are very good candidates of the cosmological dark matter, which can exist in many extensions of the standard model (SM). The mass of the ALPs can be as small as [equation]...

The ANITA experiment has observed two unusual upgoing air shower events, which are consistent with the $\tau$-lepton decay origin. However, these events are in contradiction with the standard neutrino-matter interaction models as well as the EeV diffuse neutrino flux limits set by IceCube and the cosmic ray facilities like AUGER. In this paper, we have reinvestigated the possibility of using the sterile neutrino hypothesis to explain the ANITA anomalous events. The diffuse flux of the sterile neutrinos is less constrained by the IceCube and AUGER experiments due to the small active-sterile mixing angle suppression. The quantum decoherence effect should be included for describing the neutrino flux propagating in the Earth matter, because the interactions between neutrinos and the Earth matter are very strong at the EeV energy scale. After several experimental approximations, we show that the ANITA anomaly itself is able to be explained by the sterile neutrino origin, but we also predict that the IceCube observatory should have more events than ANITA. It makes the sterile neutrino origin very unlikely to account for both of them simultaneously. A more solid conclusion can be drawn by the dedicated ANITA signal simulation.