From ‘tau’ to ‘top’ – the man behind the Dalitz plot

1 March 2004

Richard (Dick) Dalitz has spent more than 50 years in the study of elementary particles, the quark model and quantum chromodynamics. Here he talks to Melanie O’Byrne.

Let’s start right at the beginning. Where were you born?


I was born in Dimboola, in the state of Victoria, Australia. Back then it was a town of about 2000 people, but it’s more like 1000 today. It is by the Wimmera River, which carries rainwater falling inside the Great Dividing Range of Australia northwards until it sinks into the sands. My mother, a schoolteacher, was very keen that her children should have an education in Melbourne, so we moved there when I was two years old; all of my schooling was in Melbourne. At Melbourne University I took a four-year course for a Bachelor of Arts (Honours Mathematics) and a Bachelor of Science (Physics), and then I took my PhD in Cambridge.

How did you become interested in science?

I was always interested in mathematics. Physics was a later interest, since it involved the use of mathematics.

What led you to Cambridge?

In 1946 I was awarded the Aitchison Travelling Scholarship of Melbourne University. I married at age 21 and took my wife with me [to Cambridge]. My supervisor there was Kemmer and my first aim was to learn how to use quantum mechanics. There wasn’t much knowledge of that in Melbourne in those days.

What sparked your interest in quantum mechanics?

Quantum mechanics was essential for research in physics. Paul Dirac’s The Principles of Quantum Mechanics was the book to study. Its first edition in 1930 was sparse in words and very difficult to read. The 1935 edition was rewritten but was unobtainable after the war. Dirac lectured from third-edition proofs in 1946 and I attended a second time in 1947, with my own copy. Mrs [Bertha Swirles] Jeffreys also gave very intelligible and useful lectures. Lectures were not required for postgraduate students, but we went along out of interest.

What was your PhD thesis work?

Its title was “Zero-zero transitions in nuclei”. Primarily it was a study of the transitions from the first level of oxygen, which has spin-parity 0+, to the ground state, which also has 0+, together with a number of other topics added as appendices.

Was your thesis entirely theoretical?

Yes, it was entirely theoretical but it stemmed from experiments by [Samuel] Devons at the Cavendish Laboratory. After two years at Cambridge, I ran out of money. We had a young child by that time so I took up a one-year post at the University of Bristol.

What came next?

I was a student assistant to Professor Mott. He began in nuclear physics in the early 1930s but many students at the Cavendish Laboratory consulted him (himself a student) about their solid-state physics research. He did this so well that he quickly became known as a solid-state physics expert. He never found time to take a PhD himself. However, he recognized the high quality of the research being done by the Cosmic Ray Group on the fourth floor of the Physics Department at Bristol University. He wished to know more about this work and perhaps even to take part in it. This was the group of C F Powell, who not long before had identified the pion as Yukawa’s nuclear-force meson. It was there that I learned about elementary particles first-hand, because they were the people finding them. Mott was in such demand in solid-state problems that I never managed to help him make the transition back to nuclear physics.

At Bristol I got involved in problems of cosmic-ray particles. I took a particular interest in the “tau meson”, which we call the K+ meson today. That tau meson decayed into three pions. I started collecting evidence about them and their decay configurations. Although I thought a lot about them, I did not do any work on them until I had completed my thesis in 1960, more than a year later.

This year at Bristol was vital for my development in many ways, a very important year for me, in my opinion. I was invited to join the department of Professor Peierls at Birmingham University. My first year there was mainly occupied with completing my thesis work. I was also learning how to use the quantum-electrodynamical methods of Feynman, which I used to generate a number of appendices to my thesis.

Did you stay at Birmingham after completing your thesis?

Yes, I wrote the thesis in the first year, then I was a research fellow and later a lecturer. It was a strong group, centred on Peierls. This was his style; Peierls supervised all of the students. He had a wide range of understanding in physics and in life.

I was very lucky. Dyson, who had worked in America showing that the theoretical formalisms of Feynman and Schwinger were equivalent, did so on a UK fellowship that required him to return to England for two years after his work there. He chose to work at Birmingham. He was in a fairly relaxed state then, because he’d done his most important work and so he had an amount of time to talk with me now and then. His presence, and my contact with him, was considerable and important for me.

I did my work then [in 1951] on the neutral pion decay, to a photon and an electron-positron pair [the “Dalitz pair”], before moving on to the tau-meson decay, for which I devised a convenient representation, the so-called “Dalitz plot”.

How did you come up with the Dalitz plot?

The Dalitz plot is a kind of map, summarizing all of the possible final configurations, each dot representing one event. I came at it from a geometrical perspective because I visualize geometry better than numbers. The idea was convenient then for all systems decaying into three particles. Tau-meson decay to three pions is particularly simple. With parity conservation (P), I used the plot to show that if the tau meson was also capable of decay to two pions, then the three-pion plot should show special features, which are absent in the data; and also to show that the tau meson had zero spin. If the K+ meson can decay to three-pion and two-pion states, then these two final states must have opposite parity. These facts were the first intimation that P might fail for weak decay interactions.


When did you visit Cornell University, from Birmingham?

I was at Birmingham University from 1949 to 1953. Then I was given two years leave to work in America, primarily at Cornell University in Ithaca, upstate New York, in the group of Professor Bethe, at his invitation. He was a tremendous stimulation. Our names appear together on one paper, but our contributions were made at different places and different times. My work was mostly on pion-nucleon scattering and the production of pions. I was also very fortunate to be able to work at a number of places for short periods. I spent one summer at Stanford University, another at the Brookhaven National Laboratory and one semester at the Institute for Advanced Studies at Princeton.

And when did you go to the University of Chicago?

I joined the faculty of the University of Chicago and its Enrico Fermi Institute for Nuclear Studies in 1956. After Fermi died in 1954, a number of senior theoretical physicists left Chicago – Gell-Mann went to CalTech, Goldberger went to Princeton University, and there were others. Those appointed to senior posts at the University of Chicago then had a tremendous opportunity – to build up groups again and get things going, with the junior faculty still to be appointed. There were quite a number of good students there too, many from other countries.

My interest in hypernuclear events developed particularly well in Chicago because a young emulsion experimenter, Riccardo Levi-Setti, whose work I had known from his hypernuclear studies at Milan, came to the Institute for Nuclear Studies at this time. We each benefited from the other, I think, and we got quite a lot done.

Did all of this happen over just two years in Chicago?

No, I was connected to the University of Chicago for 10 years in all. I enjoyed Chicago. I thought it a very interesting place and a very fine university. I approved of the way the university did things, although the place wasn’t very fashionable with American physicists. At that time they tended to go to either the east coast or the west coast. Relatively few of them were interested in being in the middle of the country; perhaps more do these days.

After Chicago, you went to Oxford University

Peierls became the Wykeham professor of theoretical physics in Oxford, where there had not really been any central department for this. There were some individual theoretical physicists, but only a small number. Peierls brought all that together, and he was very keen for me to go back with him to Oxford.

I became a research professor of the Royal Society. They have no buildings for research, but they had funds and could appoint some researchers to be in various universities. I was responsible for organizing particle-physics theory in Oxford. Besides quark-model work, I still did work on hypernuclear physics, much of this with Avraham Gal of Jerusalem.

Life became increasingly busy as the years went by. I was attached to the Rutherford High-Energy Laboratory, as it was called in those days. They had their own accelerator and I was their adviser on theoretical matters. That was quite a happy arrangement, also.

I’ve heard scientists call you the “father of QCD”. Do you think that’s fair to say?

Oh, no. I wouldn’t claim that. I first heard quark colours mentioned in a seminar by Gell-Mann. I just picked up the ball very quickly since this concept immediately resolved some deep difficulties with the quark model that we had adopted in 1965. Of course, many people wouldn’t give any credence for the quark theory at that early stage, but I was always interested in it, and others came to Oxford to join in the work.

As time passed, heavier quarks, charm (c) and bottom (b), became established and we became interested in the spin correlations between the quark and antiquark jets from electron-positron annihilation events. Finally we came to the top quarks, for which these effects would probably be quite different.

What was your involvement in the discovery of the top quark?

Two groups at the Tevatron (Fermilab) were doing experiments at sufficiently high energies to find the top (t) quark, but little was known about their progress. We – myself and Gary Goldstein (at Tufts University) – thought about the problems of how one might identify tops and antitops from the decay processes that seemed most natural for them, and worked out a geometrical method by which experimental data could be used to deduce the top quark mass.

It was known that there was one event that seemed to have the features needed – this had been shown at a conference by the CDF group at Fermilab – but which the CDF experimenters would not accept as a possible top-antitop production and decay event. Since they wished to determine the top pair-production cross-section, they had laid down fiducial limits for such events. However, these limits were not always relevant for determining the existence and mass of the top quark. Knowledge of this one event made us think very hard about devising this method – empirical data drive the theoretical mind! We tried out our method, with the conclusion that, if this event were top-antitop production and decay, the top quark mass must be greater than about 130 GeV, an unexpectedly large value. But of course this one event might not have been a top-antitop event. This could only be decided on the basis of a large number of observed events, all of them being consistent with a unique mass, and this was the case when the two experimental groups came to conclude later that the top mass was about 180 GeV.

You’ve had a lot of good fortune and hard work along the way!

Yes, I know…I’m very aware of that. I have been lucky.

Melanie O’Byrne, Thomas Jefferson Laboratory, talked to Richard Dalitz during the 8th International Conference on Hypernuclear and Strange Particle Physics, held at Jefferson Lab in October 2003. This article is based on the interview published in Jefferson Lab’s newsletter, On Target, in March 2004, and is published with the laboratory’s permission.

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