Fermi and the Theory of Weak Interactions

GENERAL ARTICLE Fermi and the Theory of Weak Interactions G Rajasekaran The history of weak interactions starting with Fermi's creation of the beta decay theory and culminating in its modern avatar in the form of the electroweak gauge theory is described. Dis- coveries of parity violation, matter{antimatter G Rajasekaran is a asymmetry, W and Z bosons and neutrino mass theoretical physicist at the are highlighted. Institute of Mathematical Sciences, Chennai and Introduction Chennai Mathematical Institute, Siruseri (near Sun gives us light and heat that makes life possible on Chennai). His field of the Earth. How do the Sun and stars produce energy research is quantum field and continue to shine for billions of years? Thermonu- theory and high energy clear fusion is the answer as Eddington proposed in 1920 physics. and Bethe demonstrated explicitly in 1939. Through a series of nuclear reactions, four protons (which are hy- drogen nuclei) in the core of the Sun combine to form a helium nucleus emitting two positrons and two neutrinos and releasing 27 MeV of energy: 4 + + p + p + p + p He + e + e + ºe + ºe + 27MeV: ! This can be regarded as the most important reaction for all life, for without it there can be no life on Earth! The above reaction is caused by one of the basic forces of Nature, called weak interaction. Beta decays of nuclei and in fact the decays of most of the elementary particles are now known to be due to weak interaction. Enrico Fermi formulated the theory of weak interactions in 1934 and his theory has stood the ground very suc- Keywords cessfully with appropriate amendments and generaliza- Fermi, beta decay, parity violation, electroweak theory, neutral tions and ¯nally served as a core part of the Standard current, quarks and leptons, Model of High Energy Physics, which is now known as neutrino mass. the basis of almost all of physics, except for gravitation. 18 RESONANCE January 2014 GENERAL ARTICLE In this article we trace the historical evolution of the theoretical ideas punctuated by the landmark experimental discoveries. This history can be divided into two parts separated by the year 1972 which marks the watershed year since the gauge theoretic revolution that converted Fermi's theory into the modern electroweak theory oc- curred roughly around that year. Discovery of P and CP violation as well as the discovery of neutrino oscilla- tion and neutrino mass are woven into this tapestry as integral parts of weak interaction physics and its history. Early History: Weak Interactions upto 1972 The story of weak interactions starts with Henri Bec- querel's discovery of radioactivity in 1896 and its subse- quent classi¯cation into alpha, beta and gamma decays of the nucleus by Ernest Rutherford and others. But the real understanding of beta decay in the sense we know it now came only after Enrico Fermi invented a physical mechanism for the beta decay process in 1934. The basic ingredient for Fermi's theory had been pro- vided by Wolfgang Pauli. To solve the puzzle of the continuous energy spectrum of the electrons emitted in the beta decay of the nuclei, Pauli had suggested that along with the electron, an almost massless neutral particle also was emitted. Fermi succeeded in incorporating Pauli's suggestion and thus was born the theory of weak interactions. Fermi also named the particle as neutrino. Drawing an analogy with electromagnetic interaction which at the quantum level is the emission of a photon by an electron, Fermi pictured the weak interaction responsible for the beta decay of the neutron as the emis- Pauli proposed the sion of an electron{neutrino pair, the neutron converting neutrino and Fermi itself into a proton in the process (Figure 1). created his theory of weak By initiating Quantum Electrodynamics, Dirac had laid interactions the foundation for Quantum Field Theory (QFT) in incorporating the 1927. Within a few years Fermi made the ¯rst non- neutrino. RESONANCE January 2014 19 GENERAL ARTICLE Figure 1. Fermi’s analogy. trivial application of QFT to weak interactions in which material particles are created. Either because of the neutrino which most people at that time did not believe in, or because of QFT which most people did not understand at that time or because of both, Fermi's note on beta decay theory was rejected by Nature with the comment \it contained speculations too remote from reality to be of interest to the reader". Fermi then sent the paper to Nuovo Cimento which ac- cepted it; another version was published in Zeitschrift [1,2]. (A vivid picture of those times is given in [3]). In Quantum Electrodynamics (QED) the electromagnetic current JE of the charged particle like the electron interacts with A, the electromagnetic vector potential which becomes the ¯eld operator for the photon: LE = eJEA: Within a few years of the founding of The symbol e is the numerical value of the electrical Quantum Field charge of the electron and characterizes the strength Theory of the electromagnetic interaction. In Fermi's theory by Dirac, Fermi of weak interactions, the weak current of the proton{ made its first neutron pair written as p¹n interacts with the weak cur- nontrivial rent of the electron{neutrino pair denoted by e¹º: application to beta GF decay in which L = (p¹n e¹º + n¹p º¹e) ; F p material particles 2 are created. where the particle symbols p; n; e; º, etc., represent the 20 RESONANCE January 2014 GENERAL ARTICLE corresponding ¯eld operators. Detailed explanation of the language of QFT needed to understand QED and Fermi's theory is given in Box 1. The strength of the weak interaction is characterized by the Fermi coupling constant GF whose value is 10¡5 GF = 2 mp where mp is the proton mass. It is because of the small- ness of this number that this interaction is called `weak' in contrast to the nuclear force which is `strong'. Box 1. Quantum Field Theory (QFT) Quantum Field Theory created by Dirac and used by Fermi to describe weak interactions remains to this day as the correct basic language to understand all high energy physics. Here we give an elementary account of its symbolism and interpretation. We start with Quantum Electrodynamics. The electromagnetic force between two charged particles such as proton and electron can be represented by the diagram in Figure A. The wavy line denotes the photon which is the quantum of the electromagnetic ¯eld and it is exchanged between the proton and the electron. It is this exchange that leads to the electromagnetic force between the charged particles. This is the quantum version of the classical picture where the proton is considered to produce the electromagnetic ¯eld which then in°uences the electron placed in the ¯eld. In QFT, the range of a force is inversely proportional to the mass of the quantum that is exchanged. Since photon mass is zero, the electromagnetic force mediated by the exchange of photons is of in¯nite range. We shall make a rather liberal use of pictorial representations of interactions and processes such as in Figure A. These are called Feynman diagrams, after Feynman whose use of such diagrams in an intuitive interpretation of complex calculations in QFT was an important step in the elucidation of the fundamental processes of Nature. Figure A. Exchange of photon. Box 1. Continued... RESONANCE January 2014 21 GENERAL ARTICLE One can split up the above diagram into two parts, one describing the emission of the photon by the proton and the other describing the absorption of the photon by the electron. So the basic QED interaction in symbolic form is written as eJEA. Here A denotes the quantum ¯eld operator for the photon and JE denotes the electromagnetic current of the charged particles. The photon ¯eld operator A is actually the quantum version of the vector potential of classical electrodynamics (from which the electric ¯eld and magnetic ¯eld can be obtained by taking suitable space and time derivatives). So all the ¯elds become quantum operators whose main property is that they can either create or annihilate particles. In this case, A can create or annihilate a photon, thus explaining the emission or absorption of a photon. Further the current JE also is composed of ¯eld operators, but ¯eld operators of the charged particles like proton and electron. In QFT every particle is a quantum of the corresponding ¯eld; electron is a quantum of the electron ¯eld. Denoting the proton and electron ¯eld operators by p and e respectively, we write JE symbolically as a sum of terms p¹p; e¹e, etc. In general, a ¯eld operator such as p can either annihilate a particle or create the corresponding antiparticle while a ¯eld operator with a bar above such as p¹ can either annihilate an antiparticle or create a particle. The antielectron is the positron. In general the antiparticle is di®erent from particle. But for photon antiparticle is not di®erent; antiphoton is the same as photon and so A annihilates or creates the photon only. Hence the interaction described by the combined operator e¹eA actually describes the 8 processes given in Figure B. These describe the emission or absorption of a photon by an electron or positron and also the annihilation or creation of an electron{positron pair. Similar processes exist with proton and antiproton. In all Feynman diagrams time increases vertically upwards. Particles and antiparticles are distinguished by having their arrows in the upward and downward directions respectively. Figure B. The basic QED processes.

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