Chapter 32 - Elementary Particles - Search and Learn - Page 946: 3

\begin{array}{|c|c|c|c|c|c|} \hline \rm{Decay}& \rm Spin & {\rm Mass/Energy(MeV/ }c^2)&{\rm Charge} (e)&\rm Baryon \;number&\rm Lepton \;number\\ \hline \rm t\rightarrow W^++b& \frac{1}{2}=1- \frac{1}{2}& 137500\gt\overbrace{80385+4180}^{84565}& \frac{2}{3}=1-\frac{1}{3}&\frac{1}{3}=0+\frac{1}{3}&0=0+0\\ \hline \rm W^+\rightarrow u+\overline{d}&1= \frac{1}{2}+ \frac{1}{2}& 80385\gt\overbrace{2.3+4.8}^{7.1}& 1=\frac{2}{3}+\frac{1}{3}&0=\frac{1}{3}-\frac{1}{3}&0=0+0\\ \hline \rm \overline{t}\rightarrow W^-+\overline{b}& \frac{1}{2}=1- \frac{1}{2}& 137500\gt\overbrace{80385+4180}^{84565}& -\frac{2}{3}=-1+\frac{1}{3}&-\frac{1}{3}=0-\frac{1}{3}&0=0+0\\ \hline \rm W^-\rightarrow \mu^-+\overline{\nu_\mu}&1= \frac{1}{2}+ \frac{1}{2}& 80385\gt\overbrace{105.7+0.00014}^{105.7}& -1=-1+0 &0=0+0 &0=1-1\\ \hline \end{array}

In the table below, if the sum of spin is equal, so the spin is conserved. And the same for charge, Beryon number, and Lepton number. But for Mass-energy, the mass of the daughters must be less than the mass of the initial particle, as you see in the table below. \begin{array}{|c|c|c|c|c|c|} \hline \rm{Decay}& \rm Spin & {\rm Mass/Energy(MeV/ }c^2)&{\rm Charge} (e)&\rm Baryon \;number&\rm Lepton \;number\\ \hline \rm t\rightarrow W^++b& \frac{1}{2}=1- \frac{1}{2}& 137500\gt\overbrace{80385+4180}^{84565}& \frac{2}{3}=1-\frac{1}{3}&\frac{1}{3}=0+\frac{1}{3}&0=0+0\\ \hline \rm W^+\rightarrow u+\overline{d}&1= \frac{1}{2}+ \frac{1}{2}& 80385\gt\overbrace{2.3+4.8}^{7.1}& 1=\frac{2}{3}+\frac{1}{3}&0=\frac{1}{3}-\frac{1}{3}&0=0+0\\ \hline \rm \overline{t}\rightarrow W^-+\overline{b}& \frac{1}{2}=1- \frac{1}{2}& 137500\gt\overbrace{80385+4180}^{84565}& -\frac{2}{3}=-1+\frac{1}{3}&-\frac{1}{3}=0-\frac{1}{3}&0=0+0\\ \hline \rm W^-\rightarrow \mu^-+\overline{\nu_\mu}&1= \frac{1}{2}+ \frac{1}{2}& 80385\gt\overbrace{105.7+0.00014}^{105.7}& -1=-1+0 &0=0+0 &0=1-1\\ \hline \end{array} It is obvious now that all decays of the given figure are conserved in spin, mass-energy, charge, Baryon number, and Lepton number.