The Higgs Mechanism …. giving masses to the W and Z0 , and to the fermions in the Standard Model. Reference: “The Standard Model Higgs Boson” by Ivo van Vulpen, Lecture Particle Physics II October 2013. See web site for copy of article.

i are real i |i |2 V() = 0 when i |i |2 =  2 /

The gauge is “fixed” by choosing a “rotation” operation in SU(2) which transforms the vacuum Higgs field as follows:  That is: exp ( - i ½    )  = = The vacuum state undergoes a “spontaneous symmetry breaking” (into the new ) in which the ground state energy is unchanged.

h << 0 = Pauli spin matrices.

Lecture Particle Physics II October 2013. Reference: “The Standard Model Higgs Boson”, by Ivo van Vulpen, Lecture Particle Physics II October 2013.

Take Hermitian conjugate what is left of the scalar field The W+ and W- The Z and the photon

Reference: “The Standard Model Convert to W+ and W- Zero mass for photon Reference: “The Standard Model Higgs Boson”, by Ivo van Vulpen, Lecture Particle Physics II October 2013.

V() = 2 * -  [*]2 = 2 2 -   4 = 0  is unknown in Standard Model

Lecture Particle Physics II October 2013. … don’t know  but can determine  measured! Reference: “The Standard Model Higgs Boson”, by Ivo van Vulpen, Lecture Particle Physics II October 2013.

Lecture Particle Physics II October 2013. a “flavor” singlet An interaction Lagrangian density can be constructed which is invariant under SU(2) x U(1) of Standard Model interaction term! Reference: “The Standard Model Higgs Boson”, by Ivo van Vulpen, Lecture Particle Physics II October 2013.

Lecture Particle Physics II October 2013. Not only does this term describe an interaction between the Higgs field, when spontaneous symmetry breaking occurs (as in the previous case) the term generates masses for the fermions! a flavor singlet But note: only get the electron mass! Reference: “The Standard Model Higgs Boson”, by Ivo van Vulpen, Lecture Particle Physics II October 2013.

Lecture Particle Physics II October 2013. 1. 2. 3. Reference: “The Standard Model Higgs Boson”, by Ivo van Vulpen, Lecture Particle Physics II October 2013.

Recall: one only gets the -1/2 flavor (electron) -- or down quark mass! So we must add another term Reference: “The Standard Model Higgs Boson”, by Ivo van Vulpen, Lecture Particle Physics II October 2013.

Lecture Particle Physics II October 2013. Mass terms for the quarks (leaving out Hermitian Conjugate) down type: up type: .. There are complications to follow! Reference: “The Standard Model Higgs Boson”, by Ivo van Vulpen, Lecture Particle Physics II October 2013.

SUMMARY The vacuum Higgs field undergoes a spontaneous SU(2) symmetry breaking with one component disappearing, two becoming massless bosons and the third becoming the massive Higgs particle. At the same time the interaction Lagrangian density for the W, Z and photon remains unaltered (has SU(2) symmetry) -- but gains mass terms for the W and the Z0 (through the Higgs interaction terms) -- while the photon remains massless. The Higgs mechanism generates masses of the particles in the Standard Model.