The Standard Model

The Standard Model is the quantum field theory describing three of the four fundamental forces and all known elementary particles. It is based on the gauge group SU(3)×SU(2)×U(1) and has been extraordinarily successful in predicting experimental results.

Key Concepts

Gauge group: SU(3)_C × SU(2)_L × U(1)_Y
Quarks: 6 flavors, 3 colors, charge ±1/3 or ±2/3
Leptons: 3 charged leptons + 3 neutrinos
Gauge bosons: gluons (8), W±, Z⁰, photon
Higgs mechanism: spontaneous symmetry breaking gives W, Z mass

Key Equations

Covariant derivative

D_\mu = \partial_\mu - igA^a_\mu T^a

Higgs potential

V(\phi) = -\mu^2|\phi|^2 + \lambda|\phi|^4

W boson mass

M_W = \frac{1}{2}gv,\quad v\approx 246\text{ GeV}

Weinberg angle

\sin^2\theta_W \approx 0.231

Worked Example

Example Problem

Problem

The W boson mass is M_W = gv/2 with v=246 GeV and g²=4π×α/sin²θ_W. Find M_W using sin²θ_W=0.231, α=1/128.

Solution

g² = 4π×(1/128)/0.231 = 0.4267. g=0.6533. M_W = 0.6533×246/2 = 80.3 GeV.

Practice

Exercises

7 problems

1 of 7

The Higgs vev is v=246 GeV. The top quark Yukawa coupling is y_t≈1. Find the top quark mass m_t = y_t v/√2 in GeV.

Your answer

GeV

2 of 7

The Z boson mass is M_Z = M_W/cosθ_W. With M_W=80.4 GeV and sin²θ_W=0.231, find M_Z in GeV.

Your answer

GeV

3 of 7

The proton has quark content uud. Given charge of u=+2/3 and d=-1/3 (in units of e), find the proton charge in units of e.

Unlock Exercise 3