A la recherche de TPP
Sometime in the summer of 1964, the Civil Rights summer in the USA, I received a preprint request card from one "Roger Blin-Stoyle"of the "School of Mathematical and Physical Sciences, University of Sussex, Falmer, Brighton. (In those days, long before the advent of the internet or the arXiv, papers were typed by secretaries on to "onion skins, one for each page. These were then wrapped around an ink drum and typically one to two hundred copies of each page were printed. After collation, usually by press-ganged graduate students, the preprints were posted to the main groups around the world and to selected individuals whom the author adjudged might have a particular interest in the topic.) That was my first contact with Roger; I thought what a funny name he had and wondered about its origin. I'd never previously heard of the University of Sussex. The following year I was a postdoc in Oxford and by then the new University of Sussex was infamous if not famous: the social antics of the Jay twins, the daughters of the Labour Government's minister Douglas Jay, and their contemporaries meant that the University was often featured by the tabloid press, and deplored by the Daily Telegraph.With such credentials, clearly the place couldn't be all bad, so I had little hesitation in applying for one when I read an advertisement in The Guardian for "Lectureships in Theoretical Physics" at Sussex; in any case, I needed a job. There was no M25 in those days so the drive to Brighton for my interview was lengthy, but enjoyable; I was impressed to be given overnight accommodation in The Old Ship hotel on the seafront which was, I was later assured by Gabriel Barton, if not the best, certainly the most distinguished hotel in Brighton. The interview was conducted by Roger (apparently perfectly normal, notwithstanding the name), Ken Smith and Gabriel; the latter gave me a walking tour of the campus and the teacher training college (now Brighton University Falmer campus) then under construction on the other side of the railway tracks. A month or two after I had accepted the job offer, in the summer of 1965, I received a letter from Roger informing me that they had admitted a research student for me to supervise, a Miss Anjali Medhi, recently graduated from Imperial College's DIC programme. For these reasons, I have observed that Roger organised my whole life! He gave me my first permanent job and arranged my introduction to the woman who later became my wife. In Oxford, Lady Peierls, the wife of Prof Peierls, then Head of the Department of Theoretical Physics, was often ascribed similar powers, even telling young faculty members which house they should buy. Roger never did that, but he did volunteer to be the godfather of our first child, an offer that I now regret that we declined; I assumed that he was religious, and it was only many years later, at his humanist funeral in 2007, that I discovered he was not.
As Dean of MAPS, Roger had a nice office in Physics I, now Pevensey I 2C1 and currently used as a seminar room. There were then three of us who regarded ourselves as particle theorists: Gabriel, Norman Dombey and me. (We didn't use the abbreviation "TPP" in those days.) We had offices in the "Terrapin, a prefabricated temporary building situated alongside the service road, now called the North-South Road, and overlooking what is now Sussex House. The windows were totally opaque due to the mud thrown up by the interminable stream of construction traffic. There was little insulation, so we were freezing in winter and frying in summer; one could easily hear conversations, or worse, in the adjacent offices.
Roger regarded himself more as a nuclear theorist interested in the manifestation of particle physics effects in nuclei, rather than a particle theorist. He was interested in things like the charge dependence of nuclear forces, and meson exchange effects. The observation by Madame Wu in 1956 of parity violation in the beta decays of polarised cobalt nuclei led to the reformulation in 1958 by Feynman and Gell-Mann of Fermi's 1934 current-current theory of the weak interactions. In the modern version, the leptonic and hadronic (charged) weak currents both had vector and axial vector pieces; the vector and axial vector components of the weak nucleon current lead respectively to Fermi and Gamow-Teller beta decay transitions. Further, the purely hadronic (weak) Hamiltonian is also parity-violating. Since the strong part of the Hamiltonian is parity-conserving, it follows that the nuclear eigenstates have small admixtures of the "wrong paritycomponents. This in turn means that transitions that would otherwise be forbidden may actually occur but at a much slower rate than the allowed transitions. Roger was particularly active in persuading the experimentalists, Dennis Hamilton and Jim Byrne, to devise experiments to study these transitions. The discovery by Fitch and Cronin in 1964 of CP-violation (charge-conjugation C times parity reversal P) in the (weak) neutral kaon decays was strong evidence, later confirmed, of T-violation, i.e.violation of time-reversal T-symmetry, although the precise origin of the interaction responsible was not (and is still not) known. If it is in the weak interactions, then, as for parity, the nuclear eigenstates have (presumably small) admixtures of the "wrong T-parity. So later on, Roger was again active in urging experimental searches for T-violation in nuclear transitions. I particularly recall the arrival in 1968 of Roger's student Peter Herczeg, a dear friend, now retired from the Theory Division at Los Alamos National Laboratory. Peter fled Czechoslovakia during the Prague Spring in which the Soviet army invaded the country to halt reforms introduced by Alexander Dubcek. Peter worked on the effects of "irregular" components of the weak hadronic current, i.e. components having the "wrong or opposite G-parity to the standard components in the Feynman and Gell-Mann theory. One day, at tea on the Bridge, now the Bridge Cafe, I joined Peter talking to Gabriel. While waiting to ascertain the topic of their discussion, I realised that they were conversing in a foreign tongue, Hungarian, in fact. Until that day, I had had no inkling that Gabriel was anything other than an archetypal English gentleman - tweed sports jacket, woolen tie, Westminster and Christ Church: you can't get much more English establishment than that - nor of his flight from the Nazis in Budapest.
In the early 1960s data from the new particle accelerators dominated the particle physics scene.The Bevatron, built at Berkeley in 1954 but upgraded to about 25 GeV in 1960, the 33 GeV Alternating Gradient Synchrotron at Brookhaven, built in 1960, and the 25 GeV Proton Synchroton that began operating at CERN in 1959, all produced large volumes of strong interaction data on the scattering of pions and kaons on (fixed target) nucleons. Quantum field theory was not much use for these processes at these energies; it still isn't, although "chiral perturbation theory, developed later, has had a measure of success. Instead, theorists attempted to make quantitative predictions from general considerations. The scattering amplitude is constrained by the unitarity of the S-matrix, and, for 2-particle<math>\rightarrow</math> 2-particle processes, it was assumed that it had certain analyticity and crossing properties when regarded as a function of the { complexified} energy and scattering angle. The analyticity means that the scattering amplitude satisfies a dispersion relation involving its imaginary part, which is in turn determined by unitarity. The golden boy and arch evangelist of this era was Geoffrey Chew, a Californian based at Berkeley. He was alleged to have observed that ``Every time I hear of a young man [sic] working on quantum field theory my heart bleeds and I think: there goes another lost soul. His collaborator, Henry Stapp, in a similar vein, quipped that ``The contribution of quantum field theory to particle physics is less than epsilon, a dig at the axiomatic field theorists led by Arthur Wightman at Princeton and Rudolf Haag in Zurich. It's not that this approach is now known to be wrong or misguided, it's just that for the most part it wasn't very fruitful when applied to purely hadronic processes. It was much more successful when the hadronic interactions were probed by electromagnetic or weak interactions. The combination of (perturbative) quantum field theory to describe the probes and dispersion relations for the hadronic interactions {\em was} quite productive. In 1966 Gabriel was working on one of the most spectacular predictions that had been obtained using this technique, {\it viz} the claim by Dashen \& Frautschi to have explained the neutron-proton mass difference as being due to electromagnetic radiative corrections. In the absence of electromagnetic interactions, it was believed that the neutron and proton would have equal masses, and indeed that the $SU(2)$ isospin symmetry would also be exact. The ``democratic zeitgeist averred that all hadrons are equal, so that, for dispersion relation purposes, and using just pions and nucleons, a neutron can be regarded as a bound state of a proton and a negative pion, whereas the proton can be regarded as a bound state of a neutron and a positive pion. In the former, there is an attractive ({\it i.e.} negative) Coulomb contribution to the self energy deriving from single photon exchange, but not in the latter; magnetic effects are small. It follows that the neutron is lighter than the proton, in contradiction to the result of Dashen \& Frautschi and, unfortunately, to the experimental data; the neutron is heavier than the proton by about 1.29 MeV/c$^2$. Gabriel identified the error in their work - the incorrect treatment of an infrared divergence - but amazingly they declined to correspond and, so far as I know, never recanted. These days it is believed that the mass difference of the nucleons derives from the mass difference between the up $u$ and down $d$ quarks (see below) which constitute the nucleons, proton ($uud$) and neutron ($udd$). The origin of this latter difference is unknown, but is not now thought to have an electromagnetic origin. Another of Gabriel's projects used sidewise dispersion relations to calculate the electric dipole moment (EDM) of the neutron, a quantity whose measurement has been an enduring and continuing theme of the EPP group's research here. Both the magnetic dipole moment ${\bf \mu}_n$ and electric dipole moment ${\bf d}_n$, if there is one, must be proportional to the spin ${\bf s}_n$ of the neutron, which is an axial vector, since at rest there is no other vector available. However the former is coupled to the magnetic flux ${\bf B}$, also an axial vector, whereas the latter is coupled to the electric field ${\bf E}$, a vector. The magnetic coupling is therefore parity-conserving, whereas the latter is parity-violating. Further, the spin changes sign under time-reversal $T$, as does ${\bf B}$, whereas ${\bf E} $ is invariant. Thus the magnetic coupling is also $T$-conserving and the latter is $T$-violating. The known existence of both parity-violation and $T$-violation in the weak interactions indicates that there {\em must} be a non-zero EDM (of the neutron, in particular) at some level. In 1969 Gabriel, with his student Eddy White, published an upper bound on the EDM $|{\bf d}_n| \lesssim 10^{-23}$ e cm, and this result was refined the following year by another of Gabriel's students, David Broadhurst. Interestingly, although I was unaware of it until recently, Gabriel must have been thinking about this since at least 1965, barely one year after the discovery of $CP$-violation. His student Saime Goksu wrote her MPhil thesis that year on the topic; it is in the list of DPhil and MPhil theses that appears on another page of this site.
The first semblance of order in the burgeoning hadronic zoo was brought by Murray Gell-Mann (Norman's supervisor) in 1961. He incorporated the SU(2) isospin group into the larger SU(3) symmetry group. (The word ``flavourwas a later addition to the lexicon.) He observed that the nine pseudoscalar mesons $(\pi^{\pm,0}, K^{\pm}, K0, \bar{K}0, \eta, \eta')$ all having spin $J$ and parity $ P$ with $J^P=0^-$, fitted neatly into the octet ${\bf 8}$ plus singlet ${\bf 1}$ representation of SU(3), as did the $J^P=1^-$ vector mesons $(\rho ^{\pm,0}, {K^*}^{\pm},{K^*}0, \bar{K^*}0, \omega, \phi)$. Similarly, the eight $J^P=\frac{1}{2}^+$ nucleons and hyperons $(p,n,\Sigma ^{\pm,0}, \Xi ^{-.0},\Lambda)$ also filled out an ${\bf 8}$, However, the nine $J^p=\frac{3}{2}^+$ baryons $(\Delta ^{++,+,0,-}, {\Sigma ^*}^{\pm,0},{\Xi ^*}^{0,-})$ left a single unfilled slot in the decuplet ${\bf 10}$ representation. A negatively charged isospin singlet state $\Omega ^-$ with strangeness -3 was missing. The source of the breaking of the SU(3) symmetry was unknown, although manifestly considerably larger than the presumed electromagnetic breaking of the isospin symmetry. However the breaking between $\Sigma ^*$ and $\Delta$ isospin multiplets is $m_{\Sigma^*}-m_{\Delta} \sim 150$ MeV/c$^2$, and that between the $\Xi^*$ and $\Sigma ^*$ multiplets is also $m_{\Xi^*}-m_{\Sigma ^*} \sim 150$ MeV/c$^2$. Thus the predicted mass of the $\Omega ^-$ was $m_{\Omega ^-} \sim m_{\Xi^*}+150$ MeV/c$^2 \sim 1680$ Mev/c$^2$. Its discovery with a mass a little below the predicted value, the first of a particle with -3 units of strangeness, at Brookhaven in 1964, was a welcome and rare triumph for theory. The above representations of SU(3) can of course all be constructed using the fundamental triplet $\bf 3$ representation and its complex conjugate $\bar{\bf 3}$. In particular ${\bf 3} \times \bar{\bf 3}={\bf 8} + {\bf 1}$, so the nine pseudoscalar mesons could be regarded as bound states constructed from a baryon triplet $(p,n,\Lambda)$ and their antiparticles. This was originally proposed by Sakata in 1956. However it does not explain the origin of the baryon octet and decuplet. In 1964 Gell-Mann made a further proposal. More generally the ${\bf 3}$ representation must consist of an isodoublet of ``quarks $(u,d)$ with electric charges (in units of $e$) of $(z+1,z)$ together with an isosinglet quark $s$ with charge $z$; the Sakata model corresponds to the choice $z=0$. (Presumably in deference to Sakata, the quarks were often denoted by $(p,n,\lambda)$ rather than the much better notation that we now use.) If we also demand that the electric charge $Q$ is a generator of $SU(3)$, then trace$(Q)=0$ and $z=-1/3$. The quark charges are then fractional $(Q_u,Q_d,Q_s)=(2/3,-1/3,-1/3)$, and the anti-quarks in the $\bar{\bf 3}$ representation have the negatives of these. The baryon octet and decuplet, with the correct charges, then arise in the product ${\bf 3} \times {\bf 3}\times {\bf 3}= {\bf 1}+{\bf 8} +{\bf 8} +{\bf 10}$. In this picture a baryon is a bound state of three quarks $(qqq)$, and a meson is a quark-anti-quark bound state $(q\bar{q})$.
Clearly the quarks had to be fermions, but initially the view was that they were only ``mathematical entitiesused to construct the weak hadronic current, which was the real quantity of physical interest. It was recognised too that Pauli's exclusion principle would forbid the $s$-wave ground state baryons, {\it e.g.} $\Delta^{++} = uuu$, and this was resolved by the invention of three ``colours: each quark flavour $q=u,d,s$ exists in three colours $q_i,( i=1,2,3)$ labelling the fundamental representation ${\bf 3}$ of a (different) SU(3)$_{\rm colour}$ symmetry. (Americans often preferred to use $i=$ `red', `white', and `blue'.) Then $s$-wave baryons are allowed in the totally antisymmetric, colour-singlet representation. The SU(3)$_{\rm colour}$ symmetry was eventually promoted to a local, gauge symmetry, and QCD was born. Note that the one-third integral charges of the quarks derived from the three then known flavours. This in turn requires baryons to be made of three quarks, and hence the need for three colours. Since then, three more quark flavours, `charm' $c$, `top' $t$ and `bottom' $b$, have been identified, but they all still have one-third integral charges. I have always found it remarkable that the discovery of the SU(3)$_{\rm colour}$ symmetry was based on what must be a fallacious argument.