Toughest trial of Weak Interaction

Abstract: How the riddle of beta decay was solved by Fermi? How weak interaction appeared in the realm of modern physics? Why weak interaction faced series of amendments and how the problem was solved? I would try to find answer to these questions.

It has been more than eighty years since Enrico Fermi informed the world that there exists a weak interaction by his famous nuclear beta decay theory, yet its importance has not faded. Various changes and modifications have been made to Fermi’s weak interaction theory during the process of formulation of Standard Model but still the fundamental idea of Fermi serves as a core part of this model. Now it is known that not only beta decay, most of the elementary particles such as muons, kaons, pions and hyperons decay via weak interaction.

Years of Conundrum

By the end of 1920, it was evident that there was something strange about beta decay. Alpha and gamma rays, which were also the nuclear byproduct like beta rays, had discrete energy but beta rays were observed to have continuous energy spectrum. When energy available for beta decay was calculated, as this can be easily done by calculating the difference of masses of parent and daughter nuclei, it seemed to violate energy conservation. If the beta decay was simply the emission of electron from the nucleus then from the energy momentum-conservation one would expect the well defined value of energy for emitted beta particle. However, the observed continuous beta decay spectrum suggested that there was something wrong with this assumption.

Many scientists were working on the theory of beta decay but it was a tough job to create an electron in the nucleus. Heisenberg uncertainty principle ruled out the existence of nuclear electron and there was not a clear idea how such particles can be bound within nuclear orbits. In 1930, to explain this anomaly Wolfgang Pauli proposed the third particle neutrino (originally called “neutron” by him) so that it would not violate the conservation of momentum and energy. On the basis of this assumption, in 1934 Fermi proposed the the theory of beta decay.

Assumptions and formulation of the theory

During the formulation of the theory of beta decay following assumptions were made by Fermi.

a) During the process of beta decay, along with the emission of beta particle, another quasi- particle called neutrino is also emitted. The mass of the neutrino is of the order of the electron or less than that and it is charge less.

b) In quantum theory of electromagnetic radiation, photons are absorbed or emitted by an atom so the total number of photon is not constant. Drawing an analogy from this one can assume that the electrons, as well as neutrinos, can be created or annihilated and hence the total number of electrons (or neutrinos) is not necessarily constant.

c) The nucleus consists of two heavy particles i.e neutron and proton and they may be treated as the two internal state of the same particle. One can assign intrinsic coordinate to the particle to differentiate one from another. The value of intrinsic coordinate is unity and takes positive sign if the particle is neutron and negative sign if the particle is proton.

d) To ensure the conservation of charge, the Hamiltonian function is chosen such that each transition from neutron to proton is associated with the creation of electron and neutrino and the reverse process is associated with the annihilation of an electron and a neutrino.

During the formulation of theory of beta decay, he made some major modification in the Lagrangian density of the proton. While doing so, he replaced electromagnetic current of proton by the term which described the transition of neutron into proton and in the place of spinor of the photon he used the term which described the production of electron and neutrino. These new terms were called Dirac currents. He also replaced the electronic charge ‘e’ by the new coupling constant ‘G’, now known as Fermi coupling constant. It is important to note that these Dirac currents are ‘charged’ unlike electromagnetic currents, leading one’s to think that beta decay was something completely new. In this way, long before the W and Z bosons were known and quark model formulated, he successfully discovered the new forces of nature.

Fermi first sent his work to the the Nature but the editorial board rejected his paper saying “it contained abstract speculations too remote from physical reality to be of interest to the reader”. They did not like four particle interactions that created an electron and neutrino out of nothing and more importantly they did not take neutrino seriously. Later he submitted slightly revised versions of the paper to less prestigious Italian and German journal, which published them quickly in their languages. Though Fermi’s weak interaction was a great intellectual leap and a significant step towards the right direction, it would face series of challenges and amendments with the passage of time.

Years of trial

1. Universal Fermi interaction

In the mid 1930’s, Japanese physicist Yukawa argued that nuclear strong force is mediated by particle with a mass of approximately 200 times that of electron. Yukawa also suggested that this particle might be responsible for the beta decay as it could decay into electron anti-neutrino pair. Few years later, Anderson and his colleague discovered the particle which had the similar properties as described by Yukawa but the problem with the detected particle was that it could traverse through thick layer of matter without any interaction. In fact, the particle was a fermion (muon) with half integer spin rather than a boson of integral spin, which would turn out to be a milestone in our story of the weak interaction.

During the research on muon, Italian physicist Bruno Pontecorvo noticed that if the mass difference between the electron and muon is taken into account one could draw an analogy between the capture of muon by nuclei and capture of electron from the innermost atomic shell. In 1947, Pontecorvo proposed the theory of muon decay. A years later, Jack Steinberg in his Ph.D thesis found that the energy spectrum of such electron is continuous as like in beta decay, which led other theoretician to propose the so called Universal Fermi theory of weak interaction. Thus it became clear that beta decay, muon captures and muon decay were different aspect of the same interaction.

2. Parity violation

The serious observation on pionic decay of K-mesons forced Lee and Yang to rethink that parity might be violated in weak interaction. In 1956, when they made a detail analysis of all previous experiment on weak interaction, they realized that there was not a clear evidence for parity conservation in weak interaction. So they proposed to reconsider the validity of this principle and suggested experiments where the assumption could be tested. In 1957, Madame Wu and her team performed an experiment by taking cobalt nuclei and established the fact that fewer electrons were emitted in the forward hemisphere than in the backward hemisphere with respect to the spins of the decaying nuclei. This striking result was a watershed in the history of weak interaction and a complete shock to the physics world. The effect of this result can be put in the words of Isador Rabi who had said “A rather complete theoretical structure has been shattered at the base and we are not sure how the pieces will be put together.”

Fig 1: The Wu Experiment: the thick arrows indicate the direction of the spin of the ⁶⁰Co nucleus, while the thin arrows show the direction of the electron’s momentum.

Thus the result of Wu’s experiment demonstrated the fact that the weak force violates the reflection symmetry and hence the parity conservation. It also revealed that electrons are preferentially left handed. Later when the helicity of the neutrino was measured, it was found that all the neutrinos are also left handed. The consequence of these series of discovery was huge and of serious concern because an understanding of weak interaction was impossible If it was neglected.

3. A new lagrangian and V-A theory

While drawing an analogy from quantum theory of radiation, Fermi confined himself into Vector bilinear field (one of the five forms of Dirac bilinear covariant fields). In Dirac’s quantum field theory, these bilinear covariant fields are the different ways in which one can write a physical law so that it remains Lorentz invariant. If Fermi had not limited himself to the case of Vector field he would have written more general form of lagrangian. So one of the assumptions then on was to consider the general form of lagrangian. Now it was remained to modify this general form of lagrangian so that it would include the observed phenomena of parity violation.

It is impossible here to understand the whole theory without any mathematical expression but the main idea was to replace the full spinors of massive leptons with their left handed projection. After inserting these left handed projections into parity violating Hamiltonian, one would get a completely new Hamiltonian which would account both Fermi transitions and Gamow-Teller interaction. This general form of interaction is known as V-A theory. The V-A theory being itself a significant step towards a complete theory however possessed some serious mathematical difficulties. It would take an elegant touch of Glashow, Salam and Weinberg to lift weak interaction into completely new level.

Conclusion

Fermi’s theory is one of the greatest achievements in the history of modern physics. Although peculiarities had been observed many times in the path of beta decay, it endured the trial of truth keeping its spirit intact. Fermi theory even survived the fundamental revolution. His particular form of beta interaction laid the foundation for the systematic study of other types interaction. For the first time, it introduced the concept of creation and annihilation of material particles. The importance of Fermi theory can be put in the word of Fermi’s friend and associate Emilio Segre who once said, “Fermi was fully aware of the importance of his accomplishment and said that he thought he would be remembered for this paper, his best so far.”

References:

[1] F. L. Wilson, Fermi’s Theory of Beta Decay*, American Journal of Physics 36 1150 (1968)

[2] A. Lesov, The weak force: From Fermi to Feynman, University of South Carolina (2009)

[3] B. R. Martin, Nuclear and Particle Physics, Wiley, England (2006)

[4]J. Orear, Enrico Fermi: The Master Scientist, Cornell University (2003)