Nobelist Steven Weinberg Praises Professor Carl Hagen and Collaborators for Higgs Boson Theory

March 3, 2008

Carl HagenIn October 2007, Nobel Prize Winner Steven Weinberg reminded a new generation of physicists about the crucial contribution regarding the Higgs boson theory made by Professor Carl Hagen of the University of Rochester and his collaborators. Weinberg's comments were part of his invited presentation at a conference celebrating the fiftieth anniversary of John Bardeen, Leon Cooper, and J. Robert Schrieffer's (BCS) theory of superconductivity.

Three independently formulated papers describing the theoretical mechanism appeared in Volume 13 of Physical Review Letters in 1964. They were by Gerald Guralnik, Carl Hagen, and Tom Kibble; by Peter Higgs; and by Francois Englert and Robert Brout. All three papers were written from different perspectives, and each made a distinct contribution.

The Higgs boson is a hypothetical particle and the only fundamental piece of the Standard Model that has not yet been validated experimentally. It is massive and has no spin. To create the particle requires huge amounts of energy on the scale of that produced by the much anticipated Large Hadron Collider that is expected to be operational this year in Geneva, Switzerland.

It is this particle that many physicists believe will explain the origin of mass in other particles. If discovered, it will explain why the photon is massless and why the W and Z bosons are so heavy. In Glashow-Salam-Weinberg electroweak theory, this theoretical mechanism is also responsible for the heavy masses of the quarks, as well as of leptons: electrons, muons, and taus.


Of the four known fundamental forces, The Standard Model of matter includes three: electromagnetism and the strong and weak interactions. At present, gravity does not play an integral role in our theories about fundamental particles. The current model also has two categories of particles, quarks and leptons. The quarks are affected by all three forces and are the components that make up all protons and neutrons. Leptons generate and are affected by electromagnetism and weak interactions, and include the electron. The main difference between the quarks and leptons is something called color, and has nothing to do with colors that we see such as orange, yellow, or green. Rather, color in this case refers to a property that is somewhat like an electric charge. Leptons don't have color, while quarks have three colors. The color force leads to the strong interaction that is responsible for holding the proton and neutron bound in the nuclei.

In the Standard Model, the equations remain symmetric no matter how perspective shifts in space and time. Particles known as bosons transmit forces and ensure that the symmetries are maintained. Eight bosons called gluons carry the strong force.

Both the weak nuclear force and electromagnetism are thought of broadly as electroweak forces, and they have a different symmetry from the strong nuclear force. In the electroweak case, the forces are carried by four particles: the photon, the W+ boson, the W- boson, and the Z boson.

This unified electroweak theory is, in essence, the basis of Glashow, Salam, and Weinberg's Nobel Prize. Before the landmark Nobel work, theorists predicted four long-range mediators of force called the gauge bosons. In actuality, there is one long-range force particle, the photon, and the other three gauge bosons have short ranges that are less than one percent of the proton's radius, leading to the conclusion that the gauge bosons each have a mass of approximately 100 billion electron volts (GeV). And prior to Weinberg's work, it was not known why quarks and leptons have masses.

In Weinberg’s 1979 Nobel Lecture, he described the impasse faced by scientists who were seriously thinking about developing a gauge theory of fundamental particles. To avoid the appearance of massless particles other than the photon, he sought to invoke the broken symmetry ideas in the BCS work.

In simple terms, broken symmetry refers to the notion that, while the laws of nature may be symmetric, the outcome of those laws need not be symmetric. In superconductivity, electromagnetism has symmetric laws, yet in superconductive materials, the behavior of electromagnetism is not symmetric. Put another way, while the field equations are all covariant with respect to the underlying symmetry, the sole agent of symmetry breaking was the vacuum of space. Given the choice of completely equivalent or symmetric vacuum states, nature picked one, thus breaking the symmetry.

This intuitively appealing answer immediately seemed incorrect when confronted with the problem presented by the appearance of massless bosons. A theorem associated with Jeffrey Goldstone asserts that, any time a continuous symmetry group is broken, there is an accompanying effect that requires the appearance of massless particles. There is no room in the particle zoo for massless bosons in addition to the photon, and Weinberg in his Nobel Lecture describes his state of utter discouragement at the time of his 1962 paper.

Three Independent Teams Discover the Answer

As noted, it was in 1964 that the problem was resolved by three separate papers, all of which were in Volume 13 of Physical Review Letters. Each paper independently solved the problem of a physically sensible broken symmetry theory of elementary particles by noting that the Goldstone theorem includes relativistic invariance in its core of underlying assumptions. Since particle physics experimentalists have yet to detect the slightest breakdown of relativistic invariance, this hardly seemed to offer escape from the deadening hand of the Goldstone theorem. However, the three papers observed that, in dealing with gauge theories, there was an exception.

When symmetry is broken by a two-component scalar field, the photon-like gauge field, which has two transverse modes, combines with one of the scalar field components, hence providing the missing longitudinal mode required for a gauge field with mass. The leftover scalar field is a particle, and it is this particle that was first called the "Higgs" by Ben Lee in his talk at the 1966 Rochester Conference held at Berkeley.

Many physicists believe that the W and Z bosons, as well as quarks and leptons, all obtain their masses because they interact with the Higgs field. Rather than having mass to begin with, they obtain it, and thus the particles conform to the symmetry that the weak force requires.

The unification of vector gauge fields with scalar fields to form vector particles led to the detection of the W and Z vector bosons, and it also led to the 1979 Nobel Prize. The contributions made by all three papers -- Gerald Guralnik, Carl Hagen, and Tom Kibble; by Peter Higgs; and by Francois Englert and Robert Brout -- cannot be underestimated. They formed the basis of unified electroweak theory, and they predicted what scientists believe is the origin of mass. (lhg)


G.S. Guralnik, C.R. Hagen, and T.W.B. Kibble, "Global Conservation Laws and Massless Particles," Physical Review Letters, Volume 13, p. 585, 1964. See:

Peter W. Higgs, "Broken Symmetries and the Masses of Gauge Bosons," Physical Review Letters, Volume 13, p. 508, 1964. See:

F. Englert and R. Brout, "Broken Symmetry and the Mass of Gauge Vector Mesons," Physical Review Letters, Volume 13, p. 321, 1964. See: