Electroweak Theory

1. Electroweak Theory Mr. Gabriel Pendas Dr. Susan Blessing

2. The Standard Model • The Standard Model describes our current view of particle physics incorporating the leptons, hadrons, and bosons (the force carriers) • The four forces in the standard model are: • Strong – force between quarks in nuclei • Electromagnetic • Weak • Gravity – weakest force; between very large objects

3. Electromagnetic Force • It has an infinite range! • Its has a relative strength to the strong force of 10^-2 if the strong force is give a strength of one • Its mediator particle is the photon • It is what’s responsible for making sure you don’t fall through the ground

4. Quantum Electrodynamics • Quantum theory of the interaction of charged particles with the electromagnetic field • Rests on the idea that the charged particles interact by emitting and absorbing photons, the particles of light that transmit the electromagnetic force • QED is both renormalizable and gauge invariant

5. Renormalization • In QED when you have a virtual photon electron-positron pairs may be created with as high energy or momentum as can be allowed • These are quantum fluctuations because energy and momentum are not conserved locally • This creates infinities when doing any type of physical calculation, the most well known being cross-sections • You use the technique of renormalization which sort of sweeps these inifinities under the rug and is explained further in Quantum Field Theory A • Seriously, it’s a very advanced mathematical technique that is beyond the scope of this talk

6. Gauge Invariance • Physics has many globally invariant quantities like space, time, voltage, etc… • Can quantities be locally invariant as well? • Yes, begin with the Schrodinger equation of a particle moving in empty space, and introduce a complex phase • You will find that the probability of finding a particle in a state does not change even if we introduce a different complex phase at different points in space as long as we introduce a modification to our vector potential known as a gauge transformation • The gauge transformation requires the introduction of additional fields known as gauge fields. • The quantization of these fields produces the gauge boson

7. Gauge Invariance (cont.) • In the electromagnetic case our vector potential can be interpreted as the electromagnetic vector potential which leads to the introduction of the magnetic and electric field • Electromagnetic gauge invariance is a local symmetry called a U(1) gauge symmetry • The gauge boson for the electromagnetic force is the photon

8. Search for a Weak Theory • So a quantum theory of the weak theory must be two things, it must be gauge invariant and its must be renormalizable • Gauge invariance requires that the boson which carries the force be massless, which is okay in E&M but the weak force is short range which would imply that its boson would have mass

9. Symmetries • Physicists were trying to come up with numerous models that were symmetric to explain the weak force, this is the method Weinberg used when he introduced the symmetry for his and Salaams electroweak theory • If we look at leptons, there are two left-handed electron type leptons and one right handed electron type so we can start with the group U(2) x U(1) • Breaking up U(2) into unimodular transformations and phase transformations, one could say the group was SU(2)x U(1)x U(1) • But, since one of the U(1)s can be identified with lepton number and lepton number is conserved our new symmetry is SU(2) x U(1)

10. Symmetry Breaking • If this new symmetry is to uphold then all four particles must be massless, but the weak force is a short range force not an infinite one so its boson must have mass • The symmetry must be broken so the Higgs mechanism was introduced. • When a particle interacts with a Higgs potential they might begin at the origin at the maximum which will still conserve symmetry however the Higgs field pushes the particle to the minimum and symmetry is broken!

12. Symmetry Breaking (cont.) • In our case the SU(2)xU(1)is broken to the U(1) symmetry of ordinary electromagnetic gauge invariance. • Since we have four parameters or rather four particles this symmetry breaking would allow three of our four particles to have mass. • These four particles were found found to be our three weak bosons the, W+, W- and Z, and the massless particle that was left over is the photon of the electromagnetic force • Therefore, we had a unified theory of electroweak interactions

13. Weak Theory (cont.) • So we have shown how we can have massive bosons with gauge invariance, what about renormalization? • This wasn’t done till later by ‘t Hooft and Veltman who in 1971 introduced dimensional regularization which put the second to final nail in the coffin for electroweak theory and won them the Nobel prize in 1999. • The final nail in the coffin was made by the discovery of the W and Z bosons in 1983 by Carlo Rubbia and Simon Van der Meer which won them the Nobel prize in 1984. • For their contributions in the construction of the electroweak theory Weinberg, Salaam, and Glashow won the Nobel Prize in 1979.