Particle Physics

Particle physics studies the fundamental constituents of matter and their interactions. The Standard Model classifies all known particles and three of the four fundamental forces. Particle accelerators are essential tools for producing and studying these particles.

Key Concepts

Quarks (6 flavors): up, down, charm, strange, top, bottom
Leptons: electron, muon, tau, and three neutrinos
Conservation laws: charge, lepton number, baryon number, energy, momentum
Antiparticles: same mass, opposite quantum numbers
Threshold energy for particle creation: E_th = Σm_final c²

Key Equations

Threshold energy (fixed target)

E_{th} = \frac{[\sum m_f c^2]^2 - [\sum m_i c^2]^2}{2 m_{target} c^2} + \sum m_i c^2

Center-of-mass energy

s = (\sum E_i)^2/c^4 - |\sum\mathbf{p}_i|^2/c^2

Breit-Wigner resonance

\sigma(E) = \frac{\sigma_{max}}{1 + 4(E-E_0)^2/\Gamma^2}

Synchrotron radius

r = \frac{p}{qB} = \frac{\gamma m v}{qB}

Worked Example

Example Problem

Problem

Find the threshold lab energy to create a proton-antiproton pair in p+p→p+p+p+p̄. (m_p=938.3 MeV/c²)

Solution

E_th = (4m_p)²c⁴/(2m_p c²) - m_p c² × ... using E_th=(Σm_f²-(2m_p)²)/(2m_p) + 2m_p. Σm_f=4m_p. E_th = [(4m_p)²-(2m_p)²]/(2m_p) + 2m_p... Standard result: E_th = 7m_p c² = 6.57 GeV.

Practice

Exercises

7 problems

1 of 7

Find the rest energy of the pion (m_π=139.6 MeV/c²) in MeV.

Your answer

MeV

2 of 7

A proton is accelerated to kinetic energy K=938.3 MeV (= m_p c²). Find γ.

Your answer

3 of 7

At the LHC, two protons collide at √s = 13 TeV. Find √s in units of m_p c² = 938.3 MeV.

Unlock Exercise 3