The weak interaction is said to be responsible for beta decay, where a neutron decays into a proton, an electron, and an antineutrino. All four of these particles are said to be fermions. Fermions are of course named after Enrico Fermi, who proposed what’s now known as the Fermi interaction. That was in his 1933 paper Attempt at a theory of β rays. It was famously rejected by Nature, then published in both Italian and German in 1934.
The Fermi Interaction
The Fermi Interaction is “the precursor to the theory for the weak interaction, where the interaction between the proton-neutron and electron-antineutrino is mediated by a virtual Wˉ boson”. See Fermi and the theory of the weak interactions by Guruswamy Rajasekaran for some history:
Based on an image from Fermi and the theory of the weak interactions by G Rajasekaran
Rajesekaren says “Fermi based his intuition on electromagnetism which involves a vector current and we shall see in the context of later developments how sound this intuition proved to be”. Fermi treated beta decay like photon emission. The neutron emits an electron and an antineutrino and changes into a proton. Since its charge changes, there’s surely some electromagnetism involved. So Fermi’s intuition looks good. But not good enough. Look closely at the English translation of Fermi’s paper prefaced by Fred Wilson. He says “Fermi proposed his clear and simple description of β decay”, but there isn’t any description of beta decay. Fermi said “a quantitative theory of β decay is proposed”, but that’s quantitative, not qualitative. He talked about the proton and the neutron as two states of the same particle, about the Hamiltonian function of the system, and about creation operators and probability amplitudes. He proposed a mathematical model to fit experimental results rather than an explanation of what actually happens in beta decay. And rather ominously, Fermi said this: “should one encounter contradictions in a closer comparison of theory and experiment it might be possible to alter the theory without disturbing its conceptual fundamentals”. Even though there weren’t any conceptual fundamentals. However he did say the rest mass of the neutrino is either zero or very small. He also said this at the bottom of page 7: “In a notice appearing recently in Compt. Rend. 197 1625 (1933), F. Perrin comes to the same conclusion by qualitative considerations”.
Francis Perrin’s qualitative considerations
He was referring to a 1933 paper by Francis Perrin on the possibilité d’émission de particules neutres de masse intrinsèque nulle dans les radioactivités β. That translates to the possibility of emission of neutral particles with zero intrinsic mass in beta radioactivity. Perrin said one can try to deduce the neutrino mass from the beta decay spectrum. He said if the neutrino mass was equal to the electron mass you’d expect the kinetic energy to be equally shared, but that the maximum intensity was always less than half the total beta decay energy E0. He said it seemed simple to explain this by saying the neutrino mass was less than the electron mass, and that the most probable eventuality corresponded with the electron and the neutrino having the same momentum. Then he gave expressions for their momenta and kinetic energies, plus another expression for neutrino energy:
Then he referred to the beta decay spectrum of radium and said we can’t approximate the neutrino energy Em to the electron energy Ē “unless we take μ = 0, that is to say if we suppose the intrinsic mass of the neutrino to be zero”. Then he said a zero intrinsic mass for the neutrino would mean its speed was equal to the speed of light c, and that its momentum is obtained, as for a photon, by dividing its energy by c. He also said the neutrino would thus be more analogous to a photon than to an electron or neutron, but would be distinguished by the absence of an associated electromagnetic field determining its interaction with electrons. He finished up by saying that if the neutrino has a zero mass it should be created during the emission, and it must have a spin ½ for conservation of spin. See the translation on David Delphenich’s website for more. (Many thanks David). It’s good stuff. However Perrin didn’t describe what actually happens in beta decay either. This is perhaps understandable, since the neutron had only just been discovered by James Chadwick in 1932 and was not well understood. Nor was the neutrino. Or the proton. Or the electron.
The Yukawa interaction
Fermi’s interaction features four fermions interacting at a single vertex, but Hideki Yukawa came up with a suggestion. His 1935 paper on the interaction of elementary particles started by talking about Fermi’s paper. Yukawa said this: “Recently Fermi treated the problem of β-disintegration on the hypothesis of ‘neutrino’. According to this theory, the neutron and the proton can interact by emitting and absorbing a pair of neutrino and electron”. Then he said the interaction energy is much too small to account for the binding energies of neutrons and protons, and “to remove this defect, it seems natural to modify the theory of Heisenberg and Fermi in the following way”. Then he talked about a U-field that could be likened to the scalar potential of the electromagnetic field, but which decreased more rapidly with distance. He said “this field should be accompanied by a new sort of quantum, just as the electromagnetic field is accompanied by the photon”. He also said this quantum has never been seen because in the ordinary nuclear transformation it can’t be emitted into outer space. That sounds rather odd. He also said the quantum “can be absorbed by a light particle which will then in consequence of energy absorption rise from a neutrino state of negative energy to an electron state of positive energy”. That sounds rather odd too. Do you know of any negative-energy particles? Me neither. But even so, Yukawa introduced the idea of beta decay wherein a neutron emits a short-lived particle which then decays into an electron and an antineutrino, and the idea caught on:
Based on an image in Fermi and the theory of the weak interactions by G Rajasekaran
Nowadays we think of the Yukawa interaction as something to do with the nuclear force and pions. But Yukawa did say “we obtain for mu a value 2 × 102 times as large as the electron mass”. And a year later in 1936 the muon was discovered. The muon has a mass that’s 206.77 times the electron mass. That’s very close to Yukawa’s prediction. Moreover muon decay is rather similar to neutron decay: the muon emits an electron and an antineutrino, and changes into a muon neutrino. So back then what Yukawa was saying looked promising. No wonder his idea caught on.
1936 was also the year that George Gamow and Edward Teller came up with their paper on the Selection Rules for the β-Disintegration. Gamow had previously written a paper on the Nuclear Spin of Radioactive Elements. That’s where he talked about alpha radiation where “the disintegrating and the product-nuclei possess different spins”. With Teller he moved from alpha decay to beta decay. They said this: “According to the theory of β disintegration given by Fermi no change of the total nuclear spin should occur in the most probable transformations, ie, in transformations located on the first Sargent curve. The transformations corresponding to the second Sargent curve approximately 100 times less probable should correspond to changes +1 or 0 of the angular momentum of the nucleus”. They were referring to Bernice Sargent who had laboriously tabulated The Maximum Energy of the β-Rays from Uranium X and Other Bodies. They demonstrated that there were at least two types of beta decay. The Fermi transition is where the electron and neutrino are emitted in similar directions and there’s no change in nucleon spin. The Gamow-Teller transition is where the electron and the antineutrino are emitted in opposite directions and there is a change in nucleon spin.
Proca’s massive spin-1 bosons
1936 was also the year when Alexandru Proca showed that a vector field can be used to describe not just massless bosons like the photon, but massive bosons too. His paper was Sur la theorie ondulatoire des electrons positifs et negatifs. Again there’s an English translation by David Delphenich on his website. It’s On the undulatory theory of positive and negative electrons. Proca’s paper is rather mathematical, but there’s a noticeable focus on electro-magnetism. It’s similar in Proca’s 1938 paper Théorie non relativiste des particules à spin entier. Again there’s an English translation by David Delphenich: Non-relativistic theory of particles with integral spin. I think Proca’s conclusion delivers the message well: “The preceding analysis shows that one can describe a particle with positive energy and integer spin by a function with three components that each satisfy a Schrödinger equation. The fact that the spin must be an integer is manifested in relativistic theory by the vectorial character of the wave function”. See the Wikipedia Proca action article where you can read that the Proca action “describes a massive spin-1 field”. Note that “the Proca equation is involved in the Standard model and describes there the three massive vector bosons, i.e. the Z and W bosons”.
Bhabha makes a proposal
Also see the Nature looking back article where you can read the 1938 paper Nuclear Forces, Heavy Electrons, and the β-Decay by Homi Bhabha. He talked about a neutron emitting a negative U-particle to become a proton. He said “in other cases the emission or absorption is merely virtual, as an intermediate state, as is the case in the quantum theory of radiation”. He also said a positive U-particle could decay into a positive electron and a neutrino, and he referred to neutral N-particles. Change the U to a W and the N to a Z, and it’s very close to the modern concept. Hence it might feel like electroweak theory was all over bar the shouting in 1938. It wasn’t. There are clues to this. For example when Bhabha talked about a positive U-particle decaying into a positron and a neutrino, he said “this disintegration being spontaneous” and “the U-particle may be described as a ‘clock’, and hence it follows merely from considerations of relativity that the time of disintegration is longer when the particle is in motion”. The tautological flaw with that is that he’s trying to explain spontaneous beta decay with an intermediary particle that itself decays spontaneously. The truth is that that there was considerable confusion, and it went on for years.
Chaos and confusion
Visvapriya Mukherji gets it across in his short history of the meson theory from 1935 to 1943. He says this: “In 1938 Yukawa et al, Bhabha and Kemmer together with Fröhlich and Heitler came to the conclusion that the sign and spin dependence of nuclear forces can best be understood by assuming that the meson has a spin one, and obeys the Proca equations. But as Serber pointed out, the beta-decay lifetime on this theory would be connected to the upper limit of the beta spectrum by the seventh power of the momentum, while experimental evidence demands a fifth power law. ‘The only escape’, wrote Serber, ‘is to deny the mesotron any role in beta-decay, and return to direct emission of the light particle by the heavy ones”. Not everybody was happy about that. Hans Bethe found the idea of a connection between the nuclear force and beta decay to be so attractive that he was “very reluctant to give it up”. Bethe was an important player, he brought Yukawa to the attention of the American Physical Society. He wasn’t the only player of course. Mukherji’s short history refers to Møller and Rosenfeld and their mixed meson fields, to Schwinger and his mixture, to Sakata and Marshak and their two-meson hypotheses, to Uhlenbeck and Konopinski’s modified form of the Fermi field, and to Camp saying “this attempt to reconcile beta decay and heavy particle interaction has been abandoned”. There was confusion between the strong force and the weak interaction. Between the neutral theory and the symmetrical theory. Between pions and muons. Between vector mesons and pseudoscalar mesons. The second world war didn’t help. Many nuclear physicists were preoccupied with weapons as opposed to the weak interaction. Physics wasn’t functioning as normal. Mukherji says in 1943 Sakata and Inoue proposed their two-meson theory, but publication was delayed until the end of 1946 owing to war circumstances. He also refers to a 1943 paper by Pauli and Kusaka which concluded “there is no reason now to consider the strong coupling theory, we should go back to the weak coupling theory”. Physicists were giving up on the attractive connection between the nuclear force and beta decay because it didn’t fit with their intermediary particles.
Lee and Yang and non-conservation of parity
The next significant development came with the discovery that the weak interaction didn’t conserve parity. Tsung-Dao Lee told the story in the 1987 CERN Courier article History of the weak interactions. He described how in 1946 the pion was not known, and he attended a seminar by Fermi who said the mesotron could not possibly be the carrier of strong forces hypothesized by Yukawa. Lee said Jack Steinberger told him the muon decays into an electron plus two neutrinos, making it look like any other beta decay. Lee said this “stimulated M Rosenbluth, C N Yang, and myself to launch a systematic investigation”. He also said they went on to speculate that, in analogy with electromagnetic forces, the basic weak interaction could be carried by a universal coupling through “an intermediate heavy boson which I later called W ± for weak”. He referred to Fermi being very encouraging in 1948. He talked of establishing the universal Fermi interaction. And he said the same universal Fermi coupling observations “were made independently by at least three other groups, O Klein, G Puppi, and J Tiomno and J A Wheeler”. He also said Fermi’s thinking was profound, but unfortunately for physics Fermi’s proposal was never published. And that “a 1953 experiment on helium-6 decay seemed to rule out the theoretical idea of the intermediate boson, and I became quite depressed”. Lee then talked about the theta-tau puzzle and how parity non-conservation flickered through his mind in 1955. He told of his breakthrough in 1956 when he realized how non-conservation of parity might be revealed, and how he and Chen-Ning Yang discovered that there was no evidence of parity conservation in any weak interaction. Their paper was on the Question of Parity Conservation in Weak Interactions. In their introduction they said existing experiments “indicate parity conservation in strong and electromagnetic interactions to a high degree of accuracy”. But for the weak interactions “parity conservation is so far only an extrapolated hypothesis”. They said a simple possibility was to measure the angular distribution of the electrons coming from β decays of oriented nuclei. They gave Cobalt60 as an example, and spoke of the magnetic field used for orienting the nuclei.
The Wu experiment
That was the recipe for the famous Wu Experiment. It was performed by Chien-Shiung Wu and Ernest Abler, Raymond Hayward, Dale Hoppes, and Ralph Hudson of the low temperature group at the National Bureau of Standards. Wu was also known as Madame Wu, and the National Bureau of Standard is now known as NIST. Their 1957 paper was an experimental test of parity conservation in beta decay. It led to Nobel prizes that very year for Yang and Lee, whose respective Nobel lectures make for interesting reading. Even more interesting is the way the Wu experiment is reminiscent of the magnetic field associated with a current loop:
CCASA image by nagualdesign, see Wikipedia Image by Sbyrnes321 see Pseudovector on Wikipedia
This says beta decay has a chiral attribute like the screw nature of electromagnetism. But parity violation came as some kind of great surprise to the likes of Wolfgang Pauli and Richard Feynman. See Symmetry Destroyed: The Failure of Parity by Krishna Myneni dating from 1984. That’s because parity was some sacred principle. Despite the fact that Fermi’s interaction was based on electromagnetism. Despite the fact that the Poynting vector and the right-hand rule were nothing new.
More chaos and confusion
Was it another period of chaos and confusion? Yes. See Appendix 8: The Articulation of Theory: Weak Interactions by Allan Franklin and Slobodan Perovic dating from 2015. They refer to a great variety of experiments such as Langer and Price (1949), Sherr Muether and White (1949), Langer Motz and Price (1950), Mayer Moszkowski and Nordheim (1951), Sherr and Gerhart (1952 page 619), and Rustad and Ruby (1953 and 1955). Some of the experiments turned out to be misleading, and most of have been lost in the wash. Experiments by Richard Garwin, Leon Lederman and Marcel Weinrich, and by Jerome Friedman and Valentine Telegdi tend to be forgotten. Even the 1956 Cowan–Reines neutrino experiment performed by Clyde Cowan and Frederick Reines along with Kiko Harrison, Herald Kruse, and Austin McGuire was overshadowed by the Wu experiment. Nobel recognition didn’t take a year, it took forty, way too late for Cowan. There’s yet more confusion in the way the Fermi interaction is portrayed in the light of the Wu experiment. See slide 17 of Susan Gardner’s 2009 presentation β-decay and the rise of the standard model. She says Fermi’s interaction can’t explain parity violation, or the Gamow-Teller transition. Also see Weak Interaction Before the Standard Model article by Samoil Bilenky dating from 2010. He says the Fermi and Gamow-Teller Hamiltonians are invariant under space inversion, and so conserve parity. Meanwhile the Wu experiment paper says this: “One might point out here that since the allowed beta decay of Co60 involves a change of spin of one unit and no change of parity, it can be given only by the Gamow-Teller interaction”. So the Wu experiment demonstrated that the Fermi interaction was doubly wrong. And yet in Rajasekaran’s Fermi and the theory of the weak interactions you can read that “the theory of weak interactions proposed by Fermi almost 80 years ago purely on an intuitive basis stood the test of time in spite of many amendments that were incorporated into Fermi’s theory successfully”. Rajasekaran also says the only modification “was to replace the vector current of Fermi by an equal mixture of vector(V) and axial vector(A) currents”. It would seem Fermi’s interaction was wrong on multiple counts, but infinitely elastic. I am reminded of the John von Neumann quote: “With four parameters I can fit an elephant, and with five I can make him wiggle his trunk”.
The V-A interaction
Parity violation generated a great deal of interest in the weak interaction. Particularly from Ennackal Sudarshan. See his V-A: Universal Theory of Weak Interaction website or download the pdf. In 1956 he was a graduate student under Robert Marshak in Rochester. Marshak suggested he study the weak interaction, so Sudarshan did. He studied every paper going. He studied older papers by Sargent, Fermi, Yukawa, Gamow and Teller, Konopinski, and Wu. He also studied a “torrent” of new papers. On top of that he read the paper by Tiomno and Wheeler on the possibility of a universal Fermi interaction applying to more than just beta decay. Fermi had postulated a vector-vector interaction between four spinor fields, but this didn’t even cover Gamow-Teller beta decay. A more generalized interaction had been outlined back in 1933 by Wolfgang Pauli, who demonstrated that only five options were Lorentz covariant and so compatible with special relativity. These were the scalar, vector, tensor, axial vector, and pseudoscalar forms, known as S V T A and P. Sudarshan was convinced that the universal interaction had to include the axial vector interaction, because charged pion decay “may be viewed as if it were beta decay of a nucleus with zero atomic weight”. He was also convinced that there were experimental inconsistencies wherein Helium6 beta decay pointed to a T interaction, Argon35 beta decay pointed to a V interaction, Neon19 beta decay pointed to an S-T or a V-A interaction, and muon decay pointed to a V or A interaction. Sudarshan worked out that the experiments were contradictory, and that the universal interaction had to take the V-A form, which is chiral. An axial vector is also known as a pseudovector. In a loop of conducting wire the right-hand rule applies, and “the position of the wire and its current are vectors, but magnetic field B is a pseudovector”.
(a) spin vector (b) axial vector in right-screw oriented reference frame (c) axial vector in the left-screw oriented reference frame, images from Basic operations of tensor algebra by Konstantin Naumenko and Holm Altenbach
Sudarshan gives some more history in A Glance Back at Five Decades of Scientific Research. He tells how he couldn’t present his conclusions at the Rochester conference in spring 1957. He also tells how in the summer he was encouraged by Marshak to present the theory to Murray Gell-Mann and others over lunch in Santa Monica. Gell-Mann found it convincing, but said he didn’t plan to write a paper on these ideas. Marshak asked Sudarshan to write it up, which he did. The resultant paper, co-authored with Marshak, was The Nature of the Four-Fermion Interaction. It said “the only possible universal four-fermion interaction is an equal admixture of vector plus axial vector interaction. Several experiments appear to contradict this hypothesis and their status is re-examined”. However instead of sending it to a journal, Marshak said he’d present it at the Mesons and Newly Discovered Particles conference in Padua-Venice in September. So the paper “rested in peace”, and was only published in conference proceedings in May 1958.
Gell-Mann and Feynman and current x current
However Gell-Mann didn’t rest in peace. He wrote a paper with Richard Feynman “with no analysis but with the declaration that it was the V-A interaction”. It would seem that it was sent to Physical Review on September 16, precisely the date on which the Sudarshan-Marshak preprint was circulated. The Gell-Mann-Feynman paper was a Theory of the Fermi Interaction. It says this: “We have adopted the point of view that the weak interactions all arise from the interaction of a current Jμ with itself”. And this: “it is the simplest possibility from a certain point of view (that of two-component wave functions emphasized in this paper)”. There’s also “the interaction of the two ‘currents’”, and of course the phrases “our hypothesis” and “our theory”. They didn’t credit Marshak or Sudarshan with the V-A interaction, they merely thanked them for “important discussions”. Sudarshan later said “despite the clear evidence of our priority and the systematic analysis, everyone quoted our V-A theory, but ascribed it to Feynman and Gell-Mann”. Some people think this cost Sudarshan and Marshak a Nobel prize. See their 1994 Origin of the Universal V-A theory for some great historical detail. Like it seems clear that “the Feynman-Gell-Mann paper was written during the Summer of 1957 with the help of amateur radio between Rio de Janiero and Pasadena”.
The Goldhaber Experiment
In their paper Sudarshan and Marshak said “The choice between AV and ST thus hinges essentially on the electron-neutrino angular correlations or equivalently on the determination of the spirality of the neutral particle emitted in the β decay”. This neutral particle was the antineutrino. Spirality was the word they used for helicity. They essentially said the antineutrino must be right-handed because of chirality invariance. They also said it was impossible to determine neutrino helicity directly. However it could be determined indirectly, and this is what the Goldhaber experiment did in Brookhaven in late 1957. The paper by Maurice Goldhaber, Lee Grodzins, and Andrew Sunyar was called Helicity of Neutrinos. It described how they used Europium152 which decays via electron capture, typically emitting an 840 keV neutrino and a 960 keV gamma photon. The neutrino and the photon are emitted in opposite directions with the same helicity, and measuring the photon circular polarization via samarium fluorescence effectively measures the neutrino helicity. What they found was that the gamma photons were 68±14% circularly polarized with a negative helicity. Negative helicity means left-handed helicity, ergo neutrinos are left-handed. For more details see The tabletop measurement of the helicity of the neutrino written by Lee Grodzins in 2009. He says the experiment settled the controversy of the nature weak interaction, and “Beta decay proceeds via axial vector and vector modes”. Later experiments measured antineutrino helicity to be right-handed.
The weak interaction is weak
Things seemed to be coming together by 1959. Especially since the charged current of the V-A interaction is still state of the art and survives to this day in the Standard Model as the low-energy description of weak interactions. It’s said to involve a W-boson exchange, the charged current being the motion of the W boson. See reference 8 in the Wikipedia weak interaction article. It’s a physnet weak interaction module by John Christman. It refers to The Weak Interactions by Steven Treiman which appeared in Scientific American in March 1959. Treiman said the nuclear forces had begun to share centre stage with the unimaginably weak forces associated with the decay of the various recently-discovered particles. He also said none of these late-comers had any part in the constitution of matter in the ordinary sense, and all of them were unstable. He then referred to Lee and Yang and Wu and co-workers, and said “we can get an idea of the significance of this finding if we try to imagine physics without the law of conservation of energy”. Treiman also explained just how weak the weak interaction was. He started by saying the strong forces reach across interparticle distances of no more than 10-13 cm, and with particles moving at nearly the speed of light 3 x 1010 cm, they’re interacting for circa 10-23 seconds. He then talked about a lambda particle decaying into a proton and a π meson in circa 3 x 10-10 seconds, and said from such observation we deduced that the weak interactions had only 10-14 the strength of the strong interactions.
The chaos and confusion carried on
It looks pretty good for 1959. Physics had come a long way in just over twenty-five years since the discovery of the neutron. See the history in Allan Franklin’s Are the Laws of Physics Inevitable? dating from 2008. Or in Alexander Lesov’s 2009 thesis on The Weak Force: from Fermi to Feynman. Or in the 1987 Weak Interaction Physics: from its birth to the electroweak model by José Lopes. In 1959 things weren’t perfect, but there’s a definite sense of progress. We have axial vector currents interacting. What’s a neutrino if not an axial vector current? What’s an electron if not an axial vector current too? Only this time it’s a two-component wave function because it goes around and around in a spin ½ Dirac’s-belt loop. That’s why there’s a Poynting vector, and why it has spin. The proton has spin too, as do other particles, and spin is real, as demonstrated by the Einstein-de Haas effect. Hence Frederik Belinfante’s 1939 paper On the spin angular momentum of mesons. As Hans Ohanian said, Belinfante established that the spin could be regarded as due to a circulating flow of energy. But Feynman and Gell-Mann’s current-current interaction wasn’t the weak interaction of two opposite chiral energy flows within the neutron. Nor was their current the motion of a particle like an electron. They said the interaction of the proton-neutron current and the muon-neutrino current would result from the exchange of a meson. They said current Jμv is the total current density of isotopic spin T+. But isotopic spin does not have the units of angular momentum and is not a type of spin. Despite what Cassen and Condon said in 1936, the proton is not an isospin-up neutron, and the neutron is not an isospin-down proton. But what did Feynman say in 1961? When he was talking about the Poynting vector? He said this: “So there is a circulation of energy in this so-called static condition. How absurd it gets”. He said that because physicists were still groping in the dark with no qualitative understanding of what the electron was, or the neutrino, or the neutron, or the weak interaction:
Fundamental forces image by xkcd
The sacred symmetry of parity had supposedly been slain, but the chaos and confusion carried on. That was nearly sixty years ago. As for the weak interaction today, try to explain it to your grandmother. When you can’t, try saying this instead: how absurd it gets.