Chapter 36: Q. 42 (page 1060)

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 $3.31 \times 10^{- 17} k g m / s$ , were detected. What is the mass of the Higgs boson? Give your answer as a multiple of the proton mass.

Short Answer

Expert verified

The mass of the Higgs boson is $m_{H} = 132 m_{p}$

Step by step solution

Given Information

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

We need to find the mass of the Higgs boson.

Simplify

Consider:

$Thesppedoflight, c = 3 \times 10^{8} m / s Themassofproton, m_{p} = 1.67 \times 10^{- 27} k g Momentumofphoton, p = (3.31 \times 10^{- 17} k g \times m / s)$

Using formula:

$E^{2} - {(p c)}^{2} = {E^{2}}_{0} . . . (1)$

Calculating $E$ from equation (1)

${E^{2}}_{0} = E^{2} - {(p c)}^{2} (W h e r e i s E_{0} = 0 .) \Rightarrow E = 2 p c E = 2 (3.31 \times 10^{- 17} k g \times m / s) \times (3.0 \times 10^{8} m / s) E = 1.99 \times 10^{- 8} J$

Now, finding the Higgs boson :

localid="1652250350638" $E = m_{H} c^{2} m_{H} = \frac{E}{c^{2}} m_{H} = \frac{1.99 \times 10^{- 8} J}{{(3.00 \times 10^{8} m / s)}^{2}} m_{H} = 2.21 \times 10^{- 25} k g$ (Substitute value in the equation )

Mass of the Higgs boson is given as :

localid="1652250363146" $m_{H} = \frac{m H}{m_{p}} m_{H} = \frac{2.21 \times 10^{- 25} k g}{1.67 \times 10^{- 27} k g} m_{H} = 132 m_{p}$

Unlock Step-by-Step Solutions & Ace Your Exams!

Full Textbook Solutions
Get detailed explanations and key concepts
Unlimited Al creation
Al flashcards, explanations, exams and more...
Ads-free access
To over 500 millions flashcards
Money-back guarantee
We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

Recommended explanations on Physics Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Short Answer

Step by step solution

Given Information

Simplify

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Particle Model of Matter

Magnetism and Electromagnetic Induction

Electric Charge Field and Potential

Famous Physicists

Electricity and Magnetism

Astrophysics

Study anywhere. Anytime. Across all devices.