# Experimental confirmation of electroweak?

1. Aug 19, 2011

### Sparky_

Can you clear something up for me?

I see that the discovery of the W and Z boson in 1983 is described as confirming the electroweak unification theory.

I was thinking that the W and Z were carriers of just the weak force.

I don’t see how the experimental discovery of the W and Z show that electromagnetism and the weak force are really one force at higher energies.

Was it the experimental discovery of something else that confirms the electroweak unification?

Can you clear this up for me?

I have a follow-up also – has the strong force been experimentally verified as unified with the electroweak force yet? If so what particle or particles were discovered and when? I don’t recall this making the news (yet).

Thanks
-Sparky

2. Aug 19, 2011

### fzero

Experiments don't just detect new particles. They also measure cross sections for scattering processes and decay rates of the elementary particles that are produced. It is this wealth of data that can be used to statistically confirm the electroweak theory.

Electroweak unification is partly verified (it's also strongly tied to the charge assignments of the fundamental particles) by confirming the relationship between the $SU(2)\times U(1)$ coupling constants,

$\frac{1}{g_1^2} + \frac{1}{g_2^2} = \frac{1}{4\pi\alpha} ,$

where $\alpha$ is the fine structure constant. Some relationship of this form must hold if the electromagnetic $U(1)$ gauge group is nontrivially embedded in both factors of the electroweak group. Extracting the electroweak parameters like $g_1,g_2$ is done by comparing theoretical vs experimental results for many processes, not just the W and Z masses.

Unification of the strong and electroweak forces is what's referred to as a grand unified theory (GUT). Despite various theoretical motivations for grand unification, no GUT has been experimentally verified. It is worth pointing out that the most probable scale for grand unification is many orders of magnitude above what we can test at a collider experiment for the foreseeable future. Observational cosmology might have some chance to provide at least indirect tests of GUT ideas before we have the technology or funding to build a solar system scaled collider.

3. Aug 19, 2011

### Sparky_

I recall reading something - pretty sure it was in Discover years and years ago regarding the discovery of the W and / or Z boson and how that confirmed the electroweak unification.

The article (of course for the average person - like me) seemed to point to the success of I forget which accelerator in this discovery.

I now see that W and Z seem to be associated with just the weak force.

Am I correct that the W and Z are carriers of the weak force?

Am I correct in recalling that there was celebration with the experimental discovery of either or both the W and Z?

If the W and Z are carriers of the weak force how does their discovery do anything for the electromagnetic side?

Thanks again
-Sparky_

4. Aug 19, 2011

### fzero

What we mean by unification is that the electromagnetic force is not simply the $U(1)$ factor of the electroweak $SU(2)\times U(1)$. It's easy to roughly sketch a bit of how things work by considering how the W, Z and photon, $A_\mu$, embed into the EW group. For the $SU(2)$ factor, the 3 gauge boson are a Hermitian matrix that we can write as

$\begin{pmatrix} C^0_\mu & C^+_\mu \\ C^-_\mu & - C^0_\mu \end{pmatrix},$

while we'll denote the carrier of the $U(1)$ by $B_\mu$. Then we have the identifications

$W^\pm_\mu = \frac{1}{\sqrt{2}} C^\pm_\mu, ~~Z_\mu = C^0_\mu \cos\theta_W - B_\mu \sin\theta_W ,~~ A_\mu = C^0_\mu \cos\theta_W + B_\mu \sin\theta_W,$

where $\theta_W$ is called the weak mixing (or Weinberg) angle. Unification is the fact that the photon and Z are orthogonal linear combinations of the same neutral gauge bosons. The pattern of electroweak symmetry breaking through the Higgs mechanism gives the Z combination a mass, but leaves the photon massless.

This is to be contrasted with nonunification, where perhaps we try to identify $C^0$ with the Z and $B$ with the photon. Such an attempt would not be consistent with observation.

The W and Z are carriers of the weak force. Their large masses explain why the weak force is so much weaker than the electromagnetic force at scales well below the EW symmetry breaking scale. Observation of the W and Z was a great triumph, but the associated analysis of the rest of the data regarding electroweak interactions had a more profound effect on our understanding of physics.

5. Aug 20, 2011

### Parlyne

Sparky, I think what you're thinking of was the electroweak model's prediction of the mass of the Z. Basically, the nature of the electroweak unification means that you can predict the mass of the Z (well, ignoring small quantum corrections) knowing only three parameters - the electromagnetic coupling constant (e), the (charged current) weak coupling strength (usually given in terms of the Fermi constant, $G_F$), and the W mass ($m_W$). Given these, the Z mass should be
$$m_Z = \frac{m_W}{\sqrt{1-\frac{e^2}{4\sqrt{2}m_W^{\phantom{W}2}G_F}}}$$.
And, in fact, when the Z was found, its mass matched that prediction quite well.