A Gauge Theory for the Weak and Electromagnetic Interactions

In this chapter we develop the Glashow–Weinberg–Salam theory of electromagnetic and weak interactions based on the gauge group SU(2) × U(1). We show that the apparent difference in strength between the two interactions is due to the Brout–Englert–Higgs phenomenon which results in heavy intermediate vector bosons. The model is presented first for the leptons, and then we argue that the extension to hadrons requires the introduction of a fourth quark. We show that the GIM mechanism guarantees the natural suppression of strangeness changing neutral currents. In the same spirit, the need to introduce a natural source of CP-violation leads to a six quark model with the Cabibbo–Kobayashi–Maskawa mass matrix.

Quark-hadron duality for heavy meson mixings in the ’t Hooft model

We study local quark-hadron duality and its violation for the $$ {D}^0-{\overline{D}}^0 $$ D 0 − D ¯ 0 , $$ {B}_d^0-{\overline{B}}_d^0 $$ B d 0 − B ¯ d 0 and $$ {B}_s^0-{\overline{B}}_s^0 $$ B s 0 − B ¯ s 0 mixings in the ’t Hooft model, offering a laboratory to test QCD in two-dimensional spacetime together with the large-Nc limit. With the ’t Hooft equation being numerically solved, the width difference is calculated as an exclusive sum over two-body decays. The obtained rate is compared to inclusive one that arises from four-quark operators to check the validity of the heavy quark expansion (HQE). In view of the observation in four-dimensions that the HQE prediction for the width difference in the $$ {D}^0-{\overline{D}}^0 $$ D 0 − D ¯ 0 mixing is four orders of magnitude smaller than the experimental data, in this work we investigate duality violation in the presence of the GIM mechanism. We show that the order of magnitude of the observable in the $$ {D}^0-{\overline{D}}^0 $$ D 0 − D ¯ 0 mixing is enhanced in the exclusive analysis relative to the inclusive counterpart, when the 4D-like phase space function is used for the inclusive analysis. By contrast, it is shown that for the $$ {B}_d^0-{\overline{B}}_d^0 $$ B d 0 − B ¯ d 0 and $$ {B}_s^0-{\overline{B}}_s^0 $$ B s 0 − B ¯ s 0 mixings, small yet non-negligible corrections to the inclusive result emerge, which are still consistent with what is currently indicated in four-dimensions.

My Life with Quarks

This is a personal, anecdotal and autobiographical account of my early endeavors in particle physics, emphasizing how they interwove with the conception and eventual acceptance of the quark hypothesis. I focus on the years from 1958, when my doctoral work at Harvard was completed, to 1970, when John Iliopoulos, Luciano Maiani and I introduced the GIM mechanism, thereby extending the electroweak model to include all known particles, and some that were not then known. I have not described the profound advances in quantum field theory and the many difficult and ingenious experimental efforts that undergird my story which is not intended to be an inclusive record of this exciting decade of my discipline. My tale begins almost two years before I met Murray and over five years before the invention of quarks.