Higgs contributions to Weak Bosons With Weak Isospin and Spin

Here we attempt a diagram to show where the Higgs Bosons fit into the Weinberg-Salam Electroweak Unification Bosons, when the symmetry breaking turns on the particle masses.

Initially, all particle masses start out at zero, so that there is weak isospin symmetry. The basic weak interaction bosons are: the weak isospin T = 1 triplet, W+, Wº, and W¯; and the weak isospin T = 0 singlet, the Bº.   Then the Higgs gets a constant value in the vacuum, giving masses to all particles except the photon.  The neutral Wº and Bº bosons mix by a rotation through the Weinberg angle, resulting in the massive Zº, and the remaining massless photon γ.

Spin enters the mixture, since the bosons are all spin 1.  Massless spin 1 bosons travel at the speed of light and do not have a rest frame to measure the Sz = 0 spin component along a single allowed axis or z-axis.  Thus they can only have two spin states, that of Sz = + 1 or along their direction of motion, or Sz = − 1, opposite their direction of motion.  These are also called right circularly polarized, and left circularly polarized, respectively, as with the massless photons.  When the symmetry breaking gives the bosons a mass, they need the extra fields associated with the Sz = 0 components.  These are provided by the three Higgs states as shown in the following table.  The Higgs field was designed as a Weak Isospin doublet (H+, Hº), where H+ has T3 = +1/2, and Hº has T3 = -1/2.  Its anti-doublet is (Hº*, H¯), where Hº* is the anti-particle of the H° and has T3 = +1/2, and H¯ has T3 = − 1/2.

.                                                                               Spin Component Sz

.                                                                   Sz = -1                   Sz = 0                      Sz = +1

Weak Isospin                 T3 = +1               W+                     W+(H+)                       W+

Component T3               T3 =   0    Wº+Bº→Zº+γ      Zº(Hº − Hº*)    Wº+Bº→Zº+γ

.                                         T3 = −1               W¯                    W¯(H¯)                         W¯

The Higgs Boson Field that has the constant vacuum part v and excitable field h is

1/√2(Hº+Hº*) = v + h.

The field h shows up as the Higgs particle found at the Large Hadron Collider (LHC) with a mass of 125 GeV.

The mixture of Wº and Bº fields is a rotation by the Weinberg angle to get the neutral weak boson Zº and the massless photon γ.

About Dennis SILVERMAN

I am a retired Professor of Physics and Astronomy at U C Irvine. For a decade I have been active in learning about energy and the environment, and in lecturing and attending classes at the Osher Lifelong Learning Institute (OLLI) at UC Irvine.
This entry was posted in Higgs Boson. Bookmark the permalink.

Leave a Reply