A working model

The last page of a presentation on July 4 at a seminar on the latest update on the search for the Higgs boson at CERN near Geneva.-AFP

The Standard Model has been shown to work extremely well for the range of energy currently accessible.

At present the so-called Standard Model is the best mathematical framework that physicists have been able to construct to describe the building blocks of matter and the fundamental forces of nature except gravity. It is one of the biggest achievements of 20th century physics, one of the major goals of which has been to unify the forces that are widely disparate in their strengths of interaction and range of influence in a single mathematical framework. The forces of gravity and electromagnetism are, of course, familiar.

Electromagnetism is responsible for electricity in our homes. It also drives chemical reactions and enables the formation of molecules by the binding of various atoms. The other two are the strong nuclear force, which binds atomic nuclei together and makes them stable, and the weak nuclear force, which causes radioactivity and nuclear fusion in stars like the sun to shine. While gravity and the electromagnetic force have infinite range, strong and weak nuclear forces have short ranges of interaction.

This unification was the result of generalising the mathematical symmetry inherent in the highly successive equations of electrodynamics formulated by James Clerk Maxwell towards the end of the 19th century. The equations remained unchanged under a certain mathematical operation called gauge invariance. Now, this symmetry principle, for example, immediately gave an explanation for charge conservation, which we know is the reality. Physicists generalised this principle and developed a framework that possessed symmetry under this enlarged mathematical operation, in which the fields of known forces and the fundamental particles of matter could be incorporated as a unified theory.

The forces that the theory describes include the electromagnetic force mediated by the massless photon, the weak nuclear force mediated by the massive particles called W and Z vector bosons and the strong nuclear force mediated by the eight massless particles called gluons. The particles included in this framework are leptons (the light ones), which are elementary themselves, and quarks, whose bound states are particles like protons and neutrons called hadrons (the heavy ones).

Particles of the universe can be classified into to two: bosons and fermions. The former class includes particles that have integral value for the quantum property called spin and obey what is called Bose-Einstein Statistics, named after Albert Einstein and Satyendra Nath Bose, the Indian physicist who in 1924-25 worked out the statistical distribution that an assembly of photons would obey. Einstein extended his derivation for photons to all particles elementary as well as composite such as atoms and predicted a phenomenon called Bose-Einstein Condensation, which took nearly 70 years to be verified experimentally. The latter class of particles has half-integral value for quantum spin and the particles obey what is called Fermi-Dirac Statistics.

The Japanese physicist Hideki Yukawa told us in the 1930s that the ranges of forces are inversely proportional to the masses of the respective force carriers, which are essentially quantum excitations of the all-pervasive force fields. This means that, unlike the case of the massless photon which transmits the electromagnetic force, the carriers of strong and weak nuclear forces should be massive particles. However, just as the simple symmetry of electrodynamics makes photon massless which is why the electromagnetic force has an infinite range this enlarged symmetry operation too required that the excitations of the other force fields included in the theory should also be massless. The symmetry also required that the matter particles in the theory namely, quarks and leptons should also be massless.

Now this is not the world we know. Particles have a range of masses. In 1962 the American physicist P.W. Anderson introduced a concept in the context of condensed matter physics that endowed certain energy excitations in solids, such as metals and superconductors, with mass-like attributes. He, in fact, visualised the relativistic extension of this idea and even speculated on its application to high-energy physics. Peter Higgs and others seized upon this remark and worked out the details of such a relativistic extension of the model and demonstrated that by introducing a scalar field (whose particles have zero value for quantum spin) and incorporating the mechanism of spontaneous symmetry breaking in the model, the problem of massless particles could be solved in theories with gauge invariance as the underlying mathematical symmetry.

What is spontaneous symmetry breaking? The concept can be simply explained by a popular analogy with the Mexican hat (see Figure). A ball balanced on the point of the hat has equal possibility to fall down any side of the hat. The hat has rotational symmetry about the vertical axis and as long as the ball is perched on top, the rotational symmetry is respected. But as soon as the ball falls, the symmetry is broken. This is called spontaneous symmetry breaking because the ball has equal probability of falling in any direction and this direction of falling is chosen spontaneously. Higgs and others used this idea to generate mass in models of Quantum Field Theory.

To incorporate this idea into a field theory with some inherent mathematical symmetry, a scalar field, which is now called the Higgs field after Peter Higgs, is introduced, which has potential energy in the shape of the Mexican hat. Like the ball falling, the ground state of the Higgs field spontaneously breaks the symmetry. But what is interesting is that in a theory with generalised gauge invariance not only the symmetry of the theory is maintained but the massless particles also gain masses (the Higgs mechanism). In particular, in the Standard Model, the mediators of the electroweak force, W and Z bosons, get mass. However, there is a price to pay; that is, we have to contend with the particle associated with the Higgs field, which is the Higgs boson (see story by G. Rajasekaran on page 124 for a more insightful description).

The foundations of the Standard Model, as we know today, were first laid in the late 1960s when Steven Weinberg, Abdus Salam and Sheldon Glashow showed that by incorporating a Higgs field into a field theory with generalised gauge invariance one could unify electromagnetism and the weak nuclear force in a single mathematical framework and with appropriate masses for the weak force carriers (W and Z bosons) and the fermions in the theory in accordance with the observations.

Such a theory described electromagnetism and the weak force as manifestations of a single force called the electroweak force. The theory later evolved to include the strong nuclear force mediated by the eight massless particles called gluons, as well. But gluons formed a separate sector in the theory and, unlike the electroweak sector, were not described as the manifestations of a single grand unified field. That grand unification is likely to manifest itself at a higher energy scale than the tera energy scale of the Higgs boson and perhaps requires a model with higher symmetry such as supersymmetry, for which such a simple Higgs boson will not suffice, and some of whose ramifications the Large Haldron Collider itself is expected to reveal as its energy is gradually ramped up to its design level of 7 tera electron Volt (TeV) per beam.

For the range of energy currently accessible, the Standard Model has been shown to work extremely well. The discovery of a boson, announced on July 4 by CERN (the European Organisation for Nuclear Research) in Geneva, which physicists believe to be the Higgs boson, has provided the only missing link that was bothering scientists for the past four decades.