The Cluster's Electroweak Symmetry Breaking
A page about electroweak symmetry breaking — how the Higgs mechanism gives mass to W, Z, and fermions.
Electroweak symmetry breaking
Electroweak symmetry breaking (EWSB) is the process by which the SU(2)_L x U(1)_Y electroweak symmetry is spontaneously broken to U(1)_EM (electromagnetism). The Higgs field is a complex SU(2) doublet: phi = (phi^+, phi^0)^T. The Higgs potential is V(phi) = mu^2 |phi|^2 + lambda |phi|^4, with mu^2 < 0. The minimum is at |phi| = v / sqrt(2), where v = (-mu^2 / lambda)^{1/2} ~ 246 GeV. After breaking, three of the four degrees of freedom become the longitudinal modes of W+, W-, and Z0. The remaining degree of freedom is the Higgs boson. In the cluster, EWSB is the process by which the edit SU(2)_L x U(1)_Y symmetry is spontaneously broken to edit U(1)_EM. The edit Higgs field acquires a vacuum expectation value v ~ 246 GeV.
The W and Z masses
After EWSB, the W and Z boson masses are: m_W = (1/2) g v = 80.379 GeV m_Z = (1/2) sqrt(g^2 + g'^2) v = 91.1876 GeV where g is the SU(2) coupling and g' is the U(1) coupling. The Weinberg angle is sin^2 theta_W = 1 - m_W^2 / m_Z^2 ~ 0.23. In the cluster, the edit W and edit Z masses are: m_edit_W = (1/2) edit_g v, m_edit_Z = (1/2) sqrt(edit_g^2 + edit_g'^2) v.
The fermion masses
Fermion masses arise from Yukawa couplings to the Higgs field: L_Y = -y_f phi_bar_L phi_R + h.c. After EWSB, m_f = y_f v / sqrt(2). The Yukawa couplings range from y_e ~ 3 x 10^{-6} (electron) to y_t ~ 1 (top quark). In the cluster, edit fermion masses arise from edit Yukawa couplings: m_edit_f = y_edit_f v / sqrt(2).
The Higgs mass
The Higgs boson mass is m_H = sqrt(2 lambda) v. The measured value is m_H = 125.25 GeV, which implies lambda ~ 0.13. In the cluster, the edit Higgs mass is m_edit_H = sqrt(2 edit_lambda) v.
This breaking
This page is about EWSB. The SU(2)_L x U(1)_Y symmetry is broken to U(1)_EM. The Higgs vev is v = 246 GeV. m_W = 80.379 GeV. m_Z = 91.1876 GeV. m_H = 125.25 GeV. sin^2 theta_W = 0.23. The symmetry breaking is real.