Higgs Mechanism Described by an Engineer

[Alan Folmsbee]

Dear Physics Enthusiast,

The Higgs Mechanism for mass and other stuff has been mentioned in the lay press a thousand times. The press release has celebrated a great success at a collider which has found The Higgs Boson. This essay is based on a book, "Modern Particle Physics" by Mark Thomson. It was published in 2013 by Cambridge University Press.


Essay by Alan, quoting Mark, and author:

The Standard Model now has its "final element". This standard model claims that quarks are real things and that the Higgs Boson is just as real. The Higgs boson is "The final element of the Standard Model" on page 6. The mass of The Higgs Boson is measured at a mass energy of 125 GeV. That is like 133 proton masses.

Chapter 17 gives details. Here is some jargon that you are expected to already know before reading Chapter 17:

"acquire mass without breaking the local gauge symmetry" pp 460

"understanding requires... Lagrangians" (kinetic and potential E)

"The unitarity violation of the W... can be cancelled by... Higgs boson."

"if the photon has mass.. the Lagrangian... would be modified" pp 466

"Noether's theorem relates a symmetry of the Lagrangian to a conserved current" pp 467

"local gauge symmetry of the electroweak" pp 470

"A familiar example of spontaneous symmetry breaking is a ferromagnet" pp 471

"V... potential for a complex scalar field" pp 473

"The term that is quartic in the field (eta) can be identified as a mass" pp 474

eta is a perturbation of a field phi

phi is v or -v

v is a non-zero vacuum expectation value

"gauge invariance can be achieved by replacing the derivatives in the Lagrangian with the corresponding covariant derivatives."

"the Goldstone field"

SU(2)L (Unitary matrix symmetry group)

"massive gauge boson B"

h higgs


$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$

Now that the vocabulary is introduced, this essay is continued:

Equation 17.34 has a subtext describing L, a Lagrangian for Higgs

L = massive h scalar - massive gauge boson + h,B interactions - h self interactions

"The mass of the W boson is therefore determined by the coupling constant of the SU(2)L gauge interaction and the vacuum expectation value of the Higgs field."

"M is the non-diagonal mass matrix"

"parameters of the Higgs potential, mu and lambda, are related to the vacuum expectation value of the Higgs field v and the mass of the Higgs boson (m) by

v^2 = -mu^2 / lambda

m^2 = 2 lambda v^2 "

lambda is from collider data. pp 483

paraphrasing...
Electron masses arise from the couplings of the right handed and left handed massless chiral fermions through the interaction with the non-zero expectation value of the Higgs field. pp 485

"SUMMARY

"The Higgs mechanism... is based on a doublet of complex scalar fields of the Higgs potential V(phi)... where (mu)^2 < 0." See Figure 17.7 for double dip bucket shape.

The spontaneous breaking of this symmetry, when combined with SU(2) X U(1) gauge symmetry of the electroweak model, provides masses to W and Z gauge bosons with mw = mz cos(theta).

The interaction between the fermion fields and the non-zero expectation value of the Higgs field provides a gauge invariant mechanism for generating the masses of the Standard Model fermions."

The End

[Ross A. Finlayson]

"Higgs" isn't a field, it's an interface,
and has boundaries. So, any vacuum
expectation is in a sense "attenuated",
or rather, the vacuum is unbounded.