The Atmospheric Muon Lifetime, with the Lead Absorption Potential for Muons and References to the Standard Model of Particle Physics

Muon is one of twelve fundamental particles and has the longest free-particle lifetime. It decays into three leptons through an exchange of weak vector bosons W$+$/W-. Muons are present in atmospheric secondary cosmic rays and reach the sea level. By detecting the time delay between arrival of muons and appearance of decay electrons in a scintillation detector, we will measure muon's lifetime at rest. From the lifetime we can find the ratio g$_{\mathrm{w}}$~/M$_{\mathrm{W}}$~of the weak coupling constant g$_{\mathrm{w}}$~(a weak analog of the electric charge) to mass of the W-boson M$_{\mathrm{W}}$. Vacuum expectation value v of the Higgs field, which determines masses Standard Model (SM) particles, can be calculated as v$=$2M$_{\mathrm{W}}$c$^{\mathrm{2}}$/g$_{\mathrm{w}}$~$=(\tau $m$_{\mathrm{\mu }}$c$^{\mathrm{2}}$/6$\pi ^{\mathrm{3}}$\^{h})$^{\mathrm{1/4}}$m$_{\mathrm{\mu }}$c$^{\mathrm{2}}$~regarding muon mass m$_{\mathrm{\mu }}$~and muon lifetime $\tau $ only. Using the experimental value for~M$_{\mathrm{W}}$c$^{\mathrm{2}}$~$=$ 80.4 GeV,~we will find weak coupling constant g$_{\mathrm{w}}$.~With the SM relation e$=$g$_{\mathrm{w}}$sin$\theta \surd $hc$\varepsilon_{\mathrm{0}}$~and experimental value of the Z$_{\mathrm{0}}$-photon weak mixing angle~$\theta =$29$^{\mathrm{o}}$~we use our muon lifetime to find the elementary electric charge e value. In this experiment we will also determine the sea level fluxes of low-energy (\textless 160 MeV) and high-energy cosmic muons, then will shield the detector with varying thicknesses of lead plates and from the new values of fluxes find the energy-dependent muon stopping power in lead.