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### Genesis of electroweaksymmetry breaking - 1

Tom Kibble

Imperial College

13 Sep 2012

Electroweak symmetry breaking Sep 2012

Outline — Part 1

Story of idea of spontaneous symmetry breaking in gauge theories and electroweak unification

— from my viewpoint at Imperial College

• Physics after WW2: QED, renormalization theory

• Abdus Salam

• Models of strong interactions:

gauge theory, symmetry breaking

• The idea of weak-electromagnetic unification

• Obstacles to unification — the Goldstone theorem

Part 2:

• Overcoming the obstacles — the Higgs mechanism

Electroweak symmetry breaking Sep 2012

Physics after WW2

• During the war, physicists had been working on atomic weapons, radar, operational research, etc.

• After 1945, they went back to fundamental physics, leading to very rapid developments, initially in the simplest quantum field theory, Quantum Electrodynamics (QED) — the theory of interacting electrons and photons.

• Perturbation theory gave excellent results to lowest order in the fine structure constant

• But — higher order corrections were infinite.

Electroweak symmetry breaking Sep 2012

Renormalization

• Solution was found in 1947, independently by Richard Feynman,

Julian Schwinger and (in 1943) by Sin-Itiro Tomonaga

— all the infinities could be collected into infinite renormalization

constants, relating m and e to m0 and e0. For this work, they shared

the Nobel Prize for Physics in 1965.

• In 1948 Freeman Dysonshowed that all three approaches were

equivalent, and gave a proof that renormalization worked to all orders.

• Innovative experiments on the Lamb shift and the magnetic moment of the electron confirmed the results were correct to unprecedented accuracy.

• There was a gap in Dyson’s proof, however ...

Electroweak symmetry breaking Sep 2012

Abdus Salam at 14

• Abdus Salam was born in 1926, the son of a minor civil servant living in Jhang near

Lahore in what

is now Pakistan.

• At 14, he won

a scholarship to

Government

College, Lahore

with the highest marks ever recorded, making the front page of the local paper.

• He published his first paper at 17 — an improved solution to an algebraic problem solved by Srinivas Ramanujan.

• At 20 he won a scholarship to Cambridge.

Electroweak symmetry breaking Sep 2012

Salam in Cambridge

• Salam went to Cambridge in 1946 — an outstanding undergraduate.

• He was excited by recent developments in theoretical physics, and asked to be taken on as a PhD student by Nicholas Kemmer.

• Kemmer had no specific project for him, but suggested an older student of Kemmer’s, Paul Matthews, might have ideas for a project. Matthews suggested he try to fill an outstanding gap in Dyson’s proof that renormalization works to all orders in perturbation theory; it did not directly deal with the case of

overlapping divergences, e.g. in

• Matthews returned from a brief holiday to find Salam had completely solved the problem! This work gained him an instant international reputation, with an invitation to Princeton.

Electroweak symmetry breaking Sep 2012

Strong interaction models

• The success of QED inspired physicists to look for similar theories of

strong and weak interactions.

— or even better, a unified theory of all of them.

• Initially, strong interactions attracted most interest.

• The best guess as field theory of strong interactions was Hideki Yukawa’s meson theory: pions as force carriers

— Salam and Matthews (at Princeton) showed that too could be renormalized.

• But there was a big problem

— no one could make any calculations for a model with g ~ 1.

Electroweak symmetry breaking Sep 2012

Field theory vs S-matrix theory

• Problem with a field theory of strong interactions: perturbation theory calculations are impossible with a coupling constant ~1.

• During 1950s, many people concluded that field theory had had its day

— the new rage was S-matrix theory, based on analytic properties of

scattering amplitudes, especially Regge poles.

• Many people thought there were no elementary hadrons

— all were bound states of each other – the self-consistent bootstrap.

• But in a few places, the flag of field theory was kept flying

— Imperial College, Harvard, ... .

Electroweak symmetry breaking Sep 2012

Imperial College ca. 1960

Imperial College theoretical physics group was founded in 1956 by Abdus Salam — in 1959 he became the youngest FRS at age 33

• I arrived in 1959

• 3 permanent faculty:

— Abdus Salam

— Paul Matthews

— John C Taylor

• I joined faculty in 1961

• Numerous visitors:

Murray Gell-Mann,

Stanley Mandelstam,

Steven Weinberg,

Kenneth Johnson, Art Rosenfeld, ...

Electroweak symmetry breaking Sep 2012

Gauge theories

• First example of a gauge theory beyond QED was the Yang-Mills theory (1954), gauged SU(2)

— intended as a theory of strong interactions, with SU(2)

representing isospin

— same theory also proposed by Salam’s student Ronald Shaw, but

unpublished except as a Cambridge University PhD thesis.

• Although this ultimately proved not to be the correct theory of strong interactions, it was the model for all subsequent gauge theories.

Electroweak symmetry breaking Sep 2012

Gauge theories at Imperial

• Salam was convinced from an early stage that a unified theory of all interactions should be a gauge theory.

• There was a lot of interest in gauge theories at Imperial College

— my own first involvement in 1961 was to show how gravity could be

viewed as a gauge theory of the Poincaré group

— but not a renormalizable one.

Electroweak symmetry breaking Sep 2012

The particle zoo

• Experimental particle physics grew fast

— cosmic ray observation with cloud chambers

— bubble chamber experiments with particle accelerators

• Discovered a huge number of new particles

— could they all be elementary?

• Search for symmetries

— particles arranged in multiplets, related by symmetries

— SU(2) isospin (Heisenberg, Kemmer)

— SU(3) eightfold way (Murray Gell-Mann, Yuval Ne’eman)

— ...

• Now understood in terms of quarks: SU(2) symmetry of (u,d),

SU(3) of (u,d,s)

Electroweak symmetry breaking Sep 2012

Broken symmetries

• These were approximate symmetries, therefore broken in some way

— spontaneously?

• Spontaneous breaking of gauge symmetry, giving mass to the plasmon, was known (not fully understood) in superconductivity. Nambu (1960) suggested a similar mechanism could give masses to elementary particles.

• Nambu and Jona-Lasinio (1961) proposed a specific model

— phase symmetry is exact

— chiral symmetry is spontaneously broken

Electroweak symmetry breaking Sep 2012

Unification

• Because of the difficulty of calculating with a theory with large coupling constant, interest began to shift towards the weak interactions.

• A very important step was the discovery that the weak four-fermion interactions involved V and A rather than S, T or P.

• V–A theory proposed by Marshak & Sudarshan (1957) and by Feynman & Gell-Mann (1958)

• This meant that the weak interactions could be seen as due to the exchange of spin-1 W± bosons. This made them seem very similar to electromagnetic interactions mediated by photons.

— So the question arose:

could there be a unified theory of weak and electromagnetic

interactions?

Electroweak symmetry breaking Sep 2012

Similarity and Dissimilarity

Weak

interaction

Electromagnetic

interaction

exchange of

spin-1 W±

exchange of

spin-1

But

short range

large

long range

parity violating

parity conserving

So: Can there be a symmetry relatingandW±?

If so it must be broken

Electroweak symmetry breaking Sep 2012

Early Unified Models

• The first suggestion of a gauge theory of weak interactions mediated by W+ and W– was by Schwinger (1956), who suggested there might be an underlying unified theory, incorporating also the photon.

• Glashow(1961) proposed a model with symmetry group SU(2) x U(1) and a fourth gauge boson Z0, showing that the parity problem could be solved by a mixing between the two neutral gauge bosons.

• Salam and Ward(1964), unaware of Glashow’s work, proposed a similar model, also based on SU(2) x U(1)

— though neither model used the correct representation of leptons.

• Butgauge bosons are naturally massless, and in all these models symmetry breaking, giving the W bosons masses, had to be inserted by hand.

Electroweak symmetry breaking Sep 2012

Massive vector bosons

• Gauge theories naturally predicted massless vector bosons.

• If masses were added by an explicit symmetry-breaking term, then the vector-meson propagator would not be

but rather

• Thus we have a much worse divergence, and the theory is clearly not renormalizable.

• So the question started to be asked: could the symmetry breaking that gives rise to vector boson masses be spontaneous symmetry breaking?

Electroweak symmetry breaking Sep 2012

Spontaneous Symmetry Breaking

• Particle physics exhibited many approximate symmetries

— it was natural to ask whether they could be spontaneously broken

• Spontaneous breaking of symmetry occurs when the ground state or vacuum state does not share the symmetry of the underlying theory. It is ubiquitous in condensed matter physics

• Often there is a high-temperature symmetric phase, and a critical temperature below which the symmetry is spontaneously broken

— crystallization of a liquid breaks rotational symmetry

— so does Curie-point transition in a ferromagnet

— gauge symmetry is broken in a superconductor

• Could this work in particle physics too?

Electroweak symmetry breaking Sep 2012

Nambu-Goldstone bosons

• Butthere was a big problem — the Goldstone theorem:

in many cases, spontaneous beaking of a continuous symmetry implies the existence of massless spin-0 bosons, none of which had ever been seen.

• This happens because of the existence of degenerate vacuum states,

labelled by a continuous parameter . We can consider an excitation in which this parameter varies spatially. Since the different vacuum states have the same energy, the only energy cost comes from the gradient terms, giving tending to zero in the long-wavelength limit . This implies a massless excitation.

• For example the Nambu–Jona-Lasinio model has a massless pseudoscalar, identified with the pion

— N & J-L suggested chiral symmetry was not quite exact even before spontaneous symmetry breaking, hence pion has a small mass

Electroweak symmetry breaking Sep 2012

Impasse

• Counter-examples to Goldstone were known in condensed matter

• When Steven Weinberg spent a sabbatical at Imperial in 1962, he and Salam constructed a proof for all relativistic theories (Goldstone, Salam & Weinberg 1962).

• In a relativistic theory, there seemed to be no escape

— spontaneous symmetry breaking implied the existence of

zero-mass spinless bosons

— since no such bosons had been seen, spontaneous symmetry

breaking was ruled out

— other models with explicit symmetry breaking were clearly

divergent, giving infinite results

• Weinberg commented:

‘Nothing will come of nothing; speak again!’ (King Lear)

Solution tomorrow!

Electroweak symmetry breaking Sep 2012

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