### The Higgs Boson

```The Higgs boson
What it is:
1) barroom explanation
2) more, with some pictures
3) yet more, with some formulas
Plus pictures related to the discovery
John Donoghue
July 10, 2012
1) A Higgs boson walk into a bar…
1) A Higgs boson walk into a bar…
Basic points:
- In fundamental theory without Higgs, all particles
travel at speed of light
- Higgs is like “molasses” filling space – slows them down
- gives them mass
Significance – completes our fundamental theory (SM)
- without Higgs – no atoms, no stars …..
1) A Higgs boson walk into a bar…
And the atmosphere gets heavy…
He walks out and everyone falls apart…
“What are we trying to explain?
2MASS =UMass +
The reductionist’s Universe:
The Standard Model
=
with gauge group SU(3)xSU(2)LxU(1) and 3 generations
Basic features in words:
1) Fundamental particles:
World AtomsNuclei Quarks and Leptons

2) Fundamental forces/fields:
Strong – holds nuclei together
Electroweak – Electricity, Magnetism
+ atomic forces, light,....
Gravity – structure of universe at large scales
Relevant fact: 26 parameters
me =ev = 0.511 MeV
m =v = 105 MeV
m =v =1750 MeV
mu =uv = 4 MeV
md =dv = 7 MeV
ms =sv = 150 MeV
mc =cv = 1500 MeV
mb =bv = 5000 MeV
mt =tv = 175,000 MeV
etc.
 = e2/ħc = 1/137
w= 1/25
s = 1
MPL= 1/G1/2 = 1022 MeV
v = 246,000 MeV
=(10-9 MeV)4
MW =gw2v= 81,000 MeV
mH2 =  v2 = 125,000 MeV
Vus =0.22
Vcb = 0.04
Vub= 0.002
Also tied to “symmetry breaking”
Symmetry in the fundamental interactions:
Early on, evidence of hidden symmetry found:
- electron related to neutrino
- up quark and down quark related
- W, Z related
- but masses break the symmetry
There is mathematics of “group theory” at work
- SM = SU(3) x SU(2) x U(1)
But symmetry seems broken or hidden
- all equivalent due to symmetry
The Higgs “vacuum expectation value”
Standard Model relies on symmetry breaking of Higgs scalar
By 1960s, people had found approximate symmetries
in the interactions
- would be exact symmetries if masses were zero
Higgs mechanism – energetics to break symmetry
V(H)
Logic of symmetry breaking and mass generation
Basic theory has symmetry and massless particles
Higgs sector shares these properties, but
Energetics favor solution with a constant field everywhere
This then breaks symmetry
In this background field, particles have mass
Including Higgs itself
Now some equations:
Electricity and magnetism and photons:
Particle with mass:
Particle with Higgs
The Higgs mechanism:
Minimize energy
Source term now becomes mass term
Excitation around constant field is Higgs particle
Finding the Higgs
Large Hadron Collider (LHC) at CERN:
UMass participates on the ATLAS experiment
How one sees a Higgs boson:
Another decay process:
Discovery significance
Is it really the SM Higgs?
The Nobel dilemma:
My bet: Higgs, Englert and Brout
```