Question

One of the important ways in which the Higgs boson was detected at the Large Hadron Collider was by observing a type of decay in which the Higgs—which decays too quickly to be observed directly—is immediately transformed into two photons emitted back to back. Two photons, with momenta $3.31\times {10}^{-17}kgm/s$, were detected. What is the mass of the Higgs boson? Give your answer as a multiple of the proton mass.

Short answer

The mass of the Higgs boson is$m_H=132m_p$

Step-by-step solution

Given Information 

We have given two photons, with momenta$3.31\times {10}^{-17}kgm/s$

We need to find the mass of the Higgs boson.

Simplify 

Consider:

$$\begin{gathered} \text{Thesppedoflight,}c=3\times {10}^{8}m/s \\ \text{Themassofproton,}{m}_p=1.67\times {10}^{-27}kg \\ \text{Momentumofphoton,}p=\left(3.31\times {10}^{-17}kg\times m/s\right) \end{gathered}$$

Using formula:

$E^2-{\left(pc\right)}^2={E^2}_0...\left(1\right)$

Calculating $E$from equation (1)

$$\begin{gathered} {E^2}_0=E^2-{\left(pc\right)}^2\left(Whereis{E}_0=0.\right) \\ \Rightarrow E=2pc \\ E=2\left(3.31\times {10}^{-17}kg\times m/s\right)\times \left(3.0\times {10}^{8}m/s\right) \\ E=1.99\times {10}^{-8}J \end{gathered}$$

Now, finding the Higgs boson :

localid="1652250350638" $$\begin{gathered} E=m_H{c}^2 \\ {m}_H=\frac{E}{c^2} \\ {m}_H=\frac{1.99\times {10}^{-8}J}{{\left(3.00\times {10}^{8}m/s\right)}^2} \\ {m}_H=2.21\times {10}^{-25}kg \end{gathered}$$ (Substitute value in the equation )

Mass of the Higgs boson is given as :

localid="1652250363146" $$\begin{gathered} m_H=\frac{mH}{m_p} \\ {m}_H=\frac{2.21\times {10}^{-25}kg}{1.67\times {10}^{-27}kg} \\ {m}_H=132m_p \end{gathered}$$