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Some notes on Nicola Cabibbo

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1. Universal Weak Interactions

In a famous book of 1961, Richard Feynman1 vividly described his and Murray Gell-Mann’s satisfaction at explaining the close equality of the muon and neutron beta decay Fermi constants. They and, independently, the russian physicists S. Gershtein and Y. Zeldovich had discovered the universality of the weak interactions, closely similar to the universality of the electric charge and a tantalising hint of a common origin of the two interactions. But Feynman recorded also his disconcert following the discovery that the Fermi constants of the strange particles, e.g. the β-decay constant of the Λ baryon, turned out to be smaller by a factor of 4-5. It was up to Nicola Cabibbo2 to reconcile strange particle decays with the universality of weak interactions, paving the way to modern electroweak unification.

2. Nicola Cabibbo: The beginning

  • laurea in 1958, tutor Bruno Touschek;
  • hired by G. Salvini, was the first theoretical physicist in Frascati;
  • meets there Raoul Gatto (5 years elder) who was coming back from Berkeley and begins an extremely fruitful collaboration;
  • these were exciting times in Frascati: the first e+e − collider, AdA (Anello di Accumulazione = storage ring), to be followed, later, by larger machine, Adone (= larger AdA), reaching up to 3 GeV in the center of mass (= laboratory) frame; new particles (the η meson) studied at the electro-synchrotron, related to the newly discovered SU(3) symmetry, etc.;
  • Cabibbo and Gatto author an important article on e+e − physics (the Bible);
  • in 1961, they investigated the weak interactions of hadrons in the framework of the newly discovered SU(3) symmetry.

3. The angle

Gatto and Cabibbo, in Frascati, and S. Coleman and S. Glashow, in the US, observed that the currents associated to the newly discovered SU(3) symmetry include a strangeness changing current that could be associated with strangeness changing decays, in addition to the isospin current that Feynman and Gell-Mann had identified as responsible for strangeness-non-changing beta decays.

The identification, however, was in conflict with the event Σ +→ µ+ + ν + n reported in an emulsion experiment. Nicola decided to ignore this evidence. He was a good friend of Paolo Franzini, then at Columbia University, and the fact that Paolo had a larger statistics of baryon decays without any such event was crucial.

Second, while semi-leptonic decays of strange particles are evidently suppressed with respect to nuclear β-decays, no such a suppression seem to be operative in the non-leptonic K S decays. Nicola ignored also this problem, later shown to be due to the effect of the strong interactions (among others, by Guido Altarelli and myself, in 1974).

Cabibbo formulated a notion of universality between the leptonic currents and one, and only one, hadronic current, a combination of the SU(3) currents responsible for the neutron and for the strange particles beta decay. The balance between the two components was described by two numerical parameters which could be written as the cosine and the sine of an angle, θ. This angle is a new constant of Nature, since known as the Cabibbo angle.

4. Cabibbo theory with quarks

The Cabibbo theory took a simple and inspiring form in the context of the quark model. If quarks and flavor-singlet gluons are the fundamental particles, as we know today, β-decays of baryons and mesons simply reflect the two transitions: d → u and s → u. Note that this is similar to Fermi’s idea that β-decays of nuclei are simply the manifestation of the n → p transition.Cabibbo’s weak current, in the quark picture, leads to the concept of quark mixing: there is only one transition, namely that which relates the quark u to a linear superposition of the quarks d and s determined by the Cabibbo angle.

This linearsuperposition, cos θd + sin θs = d C , defines the quark which participates in the weak interactions of the nuclear particles. The Cabibbo angle, θ, is seen as the mixing angle expressing the weakly interacting down-quark, d C , in terms of the fields with definite mass: d, s.

5. An outstanding success

The agreement of the Cabibbo theory with experiments, already remarkable at the time he wrote the article, has been reinforced by the most recent data from Frascati, FermiLab and CERN and his today out of question.

From its very publication, the Cabibbo theory has been seen as a crucial development. It indicated the correct way to embody lepton-hadron universality and it enjoyed a heartening phenomenological success, which in turns indicated that we could be on the right track towards a fundamental theory of the weak interactions.
The authoritative book by A. Pais,3 in its chronology, quotes the Cabibbo theory among the most important developments in after-war Particle Physics.

In the History of CERN, J.Iliopoulos4 writes: There are very few articles in the scientific literature in which one does not feel the need to change a single word and Cabibbos is definitely one of them. With this work he established himself as one of the leading theorists in the domain of weak interactions.

6. Post-Cabibbo developments: a unified, renormalizable, electroweak theory

Eight Nobel Prizes have been given for the theory of the unified electroweak interactions pioneerd by S. L. Glashow, S. Weinberg and A. Salam. The Cabibbo theory has been the starting point for the formulation of a unified theory that could describe nuclear particles, besides electrons, muons and the corresponding neutrinos.
Here a brief description of the crucial steps that followed Nicola’s article.

  • The hypothesis of a fourth, charmed, quark by S. Glashow, J. Iliopoulos and L. Maiani made it possible to extend the Weinberg-Salam theory to hadrons, restoring lepton-quark symmetry; the suppression of the strangeness changing neutral currents fixes the mass scale of charmed particles, in agreement with experimental observation;
  • G. t’ Hooft and M. Veltman, 1972, proved the renormalizability of the spontaneously broken (via the Higgs mechanism) gauge theory;
  • filed theory anomalies, called the Adler-Bell-Jackiw anomalies, were the lastobstacle towards a renormalizable electroweak theory and they were proven to cancel between quark (fractionally charged and in three colors) and lepton doublets, by C. Bouchiat, J. Iliopoulos and P. Meyer in 1972.

These developments defined the consistency of an alectroweak theory based on two generations of lepton and quark doublets:


7. CP violation

1973. Kobayashi and Maskawa discovery: three left-handed quark doublets allow for one CP violating phase in the quark mixing matrix, since known as the CKM matrix;

1976. S. Pakvasa and H. Sugawara and L. Maiani, show that the phase agrees with the observed CP violation in K decays and (LM) leads to vanishing neutron electric dipole at one loop;

1986. I. Bigi and A. Sanda predict direct CP violation in B decay;

2001. The experimental collaborations Belle (in Japan) and BaBar (in the US) discover CP violating mixing effects in B-decays, in agreement with what we call now the Cabibbo-Kobayashi-Maskawa theory, CKM in brief.

8. Cabibbo: Leading the Roma school

Nicola settled in Roma La Sapienza in 1966, moved to Roma Tor Vergata for few years and came back to La Sapienza. Inspired by Nicola’s physical intuition, mathematical skill and personal carisma, the Rome school significantly contributed to establishing what we call today the Standard Theory of particle physics, which Nicola had greatly helped to build. A few results of these wonderful years (reference to the original papers can be found in my article on Rassegna del Nuovo Cimento).5

  • The parton-model description of e+e − annihilation into hadrons;
  • the first calculation of the electroweak contribution to the muon anomaly;
  • field theoretic description of the parton densities in hadrons;
  • QCD prediction of a phase transition from hadrons into deconfined quarks and gluons starting from the limiting temperature introduced by R. Hagedorn;• CP and T reversal violation in the oscillations of three flavored neutrinos;
  • upper and lower bounds to the Higgs boson and heavy fermion masses in Grand Unified theories;
  • parton analysis of the heavy quark β-decay spectrum (affording one of the most precise determinations of the CKM mixing parameters);
  • lattice QCD calculation of weak parameters with lattice QCD;
  • with G. Parisi, Cabibbo proposed and realised a parallel supercomputer for lattice QCD calculations. The APE supercomputers and their subsequent evolutions have played an important role in elucidating basic QCD in the nonperturbative regime

9. Nicola Cabibbo: Science Manager, teacher and friend

Nicola played an overall important role in the Italian scientific life of the turn of the century, as:

  • Member of Academia Nazionale dei Lincei and of the American Academy of Science;
  • President of Istituto Nazionale di Fisica Nucleare: 1983-1992;
  • President of Ente Nazionale Energie Alternative: 1993 -1998;
  • President of the Pontifical Academy of Science: from 1993;

He held these important positions with vision, managerial skill and universally appreciated integrity.

10. New Challenges

Problems which were on the table at the beginning of our story, the end of nineteen fifties, have all been solved by an extraordinary mix of theoretical inventions and experimental results. Some of the crucial steps have been described in this paper.

The proliferation of nuclear particles and resonances, initiated with the discovery of strange particles, has found an explanation in terms of more fundamental fermion fields, quarks coming in six flavours, each with three colours. The muon has found its place in the second quark-lepton generation. The fifth and sixth quarks neatly pair with the (ν τ , τ) lepton doublet in a third generation, necessary to explain the CP violation initially observed with particles belonging to the first and second generations.

We understand the structure of the weak and electromagnetic currents, their renormalisation properties and the relation between leptonic, semi-leptonic and non-leptonic weak processes. The unified gauge theory of both interactions, electromagnetic and weak, has been experimentally confirmed in crucial instances, includingexistence and properties of the predicted, necessary, weak intermediaries. The mathematical consistency of the theory requires, by the way, precisely the lepton-quark simmetry which is so prominent in the spectrum of the elementary fermions.

Neutrino oscillations have been observed, in particular where they are required to support our understanding of the way the Sun works. We now know that neutrinos have masses, similarly to quarks and charged leptons, and that the phenomenon of fermion mixing, discovered by Cabibbo, is quite general, although we do not know yet how to predict its structure.

The description of the basic strong interactions with an asymptotically free gauge theory based on the colour symmetry is, perhaps, the most unexpected and most spectacular development of the second half of the last century. It has allowed for crucial quantitative tests of the strong interactions, in the short distance region where we can apply perturbative methods. Non-perturbative calculations based on the numerical simulation of QCD in a space-time lattice, have produced highly non trivial results in the large distance, strongly interacting, regime. One instance is the calculation of the axial couplings of the pseudo-scalar mesons, although, admittedly, we are still far from a systematic understanding of this domain. A gauge description of all fundamental interactions, including gravity, is a strong suggestion of a unified theory encompassing all interactions, realising the dream of Albert Einstein.

With the turn of the Century, we have a new panorama of problems and challenges and a new machine, the Large Hadron Collider at CERN, to explore a new energy domain, ranging from 100 to above 1000 GeV=1 TeV. A will list only a few of the challenges which may be attacked in the new round of experiments at the LHC. This is a personal list and may well turn out to be incomplete or even irrelevant: future will tell.

The first challenge is to find the Higgs boson. The Higgs boson is needed for the unified electro-weak theory to agree with Nature, validating the idea that symmetry breaking particle masses arise from the spontaneous breaking of the gauge symmetry.
At the same time, this mechanism gives a vision of the quantum vacuum which may help us to explain new phenomena in the universe at large: inflation, chaotic universe, etc..

Find the Supersymmetric Particles. The Unification of Forces requires a Symmetry to relate different spins: this is Supersymmetry, a fermion-boson symmetry discovered in 1974 at CERN by J. Wess and B. Zumino and in Russia by D. Akulov and V. Volkov.
There are arguments, related to the so-called hierarchy problem of fundamental scales, that suggest the presence of the supersymmetric partners of the known particles in the TeV range, possibly within reach of the LHC.

Indications for a form of stable matter other than we know, protons, electrons and neutrinos, come independently from the existence of non-luminous matter, gravitationally observed in the Universe. In fact, the data on the primordial abundance ofhelium and other light nuclei limit the abundance of baryonic matter to a few percent of the total mass and neutrinos are definitely too light. The origin of the dark matter is thus one of the most prominent puzzles of present physics. A neutral, very long lived, supersymmetric partner surviving from the hot Big Bang could be a natural candidate to be the constituent of the dark matter in the Universe.

Finally, the search for extra space-dimensions. String formulations of Quantum Gravity are not consistent in 3+1 dimensions. Curved extra-dimensions are needed.
How small is their radius ? Can LHC high energy particles get into and map for us the new dimensions?

11. Conclusions

Nicola liked to teach and he continued to do so until his very last months. Like all great minds, he could find simple arguments to explain the most difficult concepts.
His students were fascinated by his simplicity, gentle modes and sense of humour. So we did, all of us we who had the privilege to be his collaborators and friends.

1) R. P. Feynman, Theory of Fundamental Processes
2) N. Cabibbo, Phys. Rev. Lett., 10, 531 (1963).
3) A. Pais, Inward Bound Of Matter And Forces In The Physical World, Oxford, Uk: Clarendon ( 1986) 666 p. New York, Usa: Oxford Univ. Pr. (1986) 666p.
4) J. Iliopoulos in History of CERN, Elsevier 1996, Vol 3, p. 277.
5) L. Maiani, Rassegna del Nuovo Cimento, 34, 679 (2011).

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