## History of Electroweak Symmetry Breaking

The first post about DICE2014 is about Tom Kibble's keynote lecture about electroweak theory.

Physics in the 50s had great success with quantum electrodynamics and its perturbative methods because the coupling constant was smaller than 1: 1/137. However, for other interactions, perturbation theory was not working due to interaction strength and people looked at alternative theories, like S-matrix and Regge poles which ultimately lead to dead ends in physics.

If you look at strong interactions, the proton and the neutron are very similar and people naturally looked at the SU(2) symmetry. However this symmetry is broken by electromagnetism and people started thinking about how to break symmetries. Also from strong interactions the SU(3) symmetry was developed by Gell-Mann's eightfold way which made a successful prediction for a new particle. Today we know this is an approximate symmetry which comes from up, down, and strange quarks.

In 1954 Yang and Mills had their seminal paper in gauge theory. The same result was obtained by Ronald Show, a grad student under Abdus Salam, but he only wrote it in his PhD thesis and was not taken seriously. The problem of Yang-Mills theory is that it predicts a new infinite range interaction which does not exist in nature. Adding mass to the interaction restricts the range due to uncertainty principle, but adding a mass term makes the theory non-renormalizable.

Around the same time, Fermi developed his weak interaction V-A 4-point interaction theory and Schwinger suggested in 1957 what is now called the W+, W- weak bosons.

It was known that the weak interaction violates parity and was short range and the search was on for how to introduce this into the theory.

In 1961 Glashow proposed a solution to the parity problem by mixing Z0 with W0 and proposing the SU(2)xU(1) symmetry. Salam and Windberg independently proposed the same thing in 1964, and the W mass was put in by hand.

For the mass problem responsible for the short range of the interaction, Nambu proposed spontaneous symmetry breaking in 1960. Condensed matter physics were very familiar with spontaneous symmetry breaking as the explanation for plasmons in superconductivity.

The basic idea of spontaneous symmetry breaking is that the ground state does not share the system symmetry. A typical example is a ball of water which freezes: during crystallization the rotational symmetry is lost. In quantum field theory there was the Goldstone theory with its Mexican hat potential:

In 1964 Gerald Guralnik at Imperial College, collaborated with Walk Gilbert - a student of Abdus Salam, and a US visitor: Richard Hagen came with the idea of the Higgs mechanism to combine the massless gauge theory with the massive Goldstone boson. The same mechanism was proposed also independently by Peter Higgs/ Guralnik, Hagen, and Kibble/, and by Englert and Brout.

The problem was how to avoid the unobserved Goldstone boson. If you impose a continuity equation you get a charge by integrating the current density. However you need to consider the surface at infinity and due to relativity and microcausality in Coulomb gauge charge does not exists as a self-adjoint operator and this avoids the presence of the Goldstone boson. The key is the presence or absence of long range forces which interfere with the Goldstone theorem.

Then the electroweak unification and successes followed: Weinberg in 1967 and Salam in 1967 and 1968 proposed the electroweak theory, in 1971 't Hooft proved its renormalizability. In 1973 Z0 neutral currents were observed in CERN, and in 1983 W and Z bosons were observed in CERN as well.

70's and 80's saw the development of quantum chromodynamic based on SU(3) and the Standard model based on SU(3)xSU(2)xU(1) emerged.

After 1983 the only missing piece of the puzzle was the Higgs boson. Originally this played a minor role, the big deal was the Higgs mechanics. In 2012 the Higgs boson was confirmed experimentally and Englert and Higgs were awarded the Nobel Prize.

So what next? Grand unification of electroweak and strong force and supersymmetry (SUSY)? With SUSY the three coupling constants for electromagnetism, weak and strong force converge exactly and this is very powerful evidence. Unfortunately there is no current experimental evidence for SUSY.

Then there is a big gap between the Standard Model and M-theory/quantum gravity. To put it in perspective, strings to Standard Model is like atoms to our Solar System. Or if an atom is blown to the size of the observable universe, a string in string theory is the size of a tree on Earth.

In 1954 Yang and Mills had their seminal paper in gauge theory. The same result was obtained by Ronald Show, a grad student under Abdus Salam, but he only wrote it in his PhD thesis and was not taken seriously. The problem of Yang-Mills theory is that it predicts a new infinite range interaction which does not exist in nature. Adding mass to the interaction restricts the range due to uncertainty principle, but adding a mass term makes the theory non-renormalizable.

Around the same time, Fermi developed his weak interaction V-A 4-point interaction theory and Schwinger suggested in 1957 what is now called the W+, W- weak bosons.

It was known that the weak interaction violates parity and was short range and the search was on for how to introduce this into the theory.

In 1961 Glashow proposed a solution to the parity problem by mixing Z0 with W0 and proposing the SU(2)xU(1) symmetry. Salam and Windberg independently proposed the same thing in 1964, and the W mass was put in by hand.

For the mass problem responsible for the short range of the interaction, Nambu proposed spontaneous symmetry breaking in 1960. Condensed matter physics were very familiar with spontaneous symmetry breaking as the explanation for plasmons in superconductivity.

The basic idea of spontaneous symmetry breaking is that the ground state does not share the system symmetry. A typical example is a ball of water which freezes: during crystallization the rotational symmetry is lost. In quantum field theory there was the Goldstone theory with its Mexican hat potential:

The radial motion generate an effective mass term (because locally one approximate the radial motion with a parabola), but the motion around the center corresponds to a zero mass particle: the Goldstone boson. Since the Goldstone boson was not observed in nature, this was a major roadblock to adding mass to non-abelian gauge theories.

In 1964 Gerald Guralnik at Imperial College, collaborated with Walk Gilbert - a student of Abdus Salam, and a US visitor: Richard Hagen came with the idea of the Higgs mechanism to combine the massless gauge theory with the massive Goldstone boson. The same mechanism was proposed also independently by Peter Higgs/ Guralnik, Hagen, and Kibble/, and by Englert and Brout.

The problem was how to avoid the unobserved Goldstone boson. If you impose a continuity equation you get a charge by integrating the current density. However you need to consider the surface at infinity and due to relativity and microcausality in Coulomb gauge charge does not exists as a self-adjoint operator and this avoids the presence of the Goldstone boson. The key is the presence or absence of long range forces which interfere with the Goldstone theorem.

Then the electroweak unification and successes followed: Weinberg in 1967 and Salam in 1967 and 1968 proposed the electroweak theory, in 1971 't Hooft proved its renormalizability. In 1973 Z0 neutral currents were observed in CERN, and in 1983 W and Z bosons were observed in CERN as well.

70's and 80's saw the development of quantum chromodynamic based on SU(3) and the Standard model based on SU(3)xSU(2)xU(1) emerged.

After 1983 the only missing piece of the puzzle was the Higgs boson. Originally this played a minor role, the big deal was the Higgs mechanics. In 2012 the Higgs boson was confirmed experimentally and Englert and Higgs were awarded the Nobel Prize.

So what next? Grand unification of electroweak and strong force and supersymmetry (SUSY)? With SUSY the three coupling constants for electromagnetism, weak and strong force converge exactly and this is very powerful evidence. Unfortunately there is no current experimental evidence for SUSY.

Then there is a big gap between the Standard Model and M-theory/quantum gravity. To put it in perspective, strings to Standard Model is like atoms to our Solar System. Or if an atom is blown to the size of the observable universe, a string in string theory is the size of a tree on Earth.

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