*My colleague in philosophy at Va Tech, Ben Jantzen*, sent me this piece by Steven Weinberg on the Higgs. Even though it does not deal with the statistics, it manages to clarify some of the general theorizing more clearly than most of the other things I’ve read. (See also my previous post.)
*

**Why the Higgs?**

August 16, 2012

*Steven Weinberg*

The New York Times Review of Books

The following is part of an introduction to James Baggott’s new book *Higgs: The Invention and Discovery of the “God Particle,”* which will be published in August by Oxford University Press. Baggott wrote his book anticipating the recent announcement of the discovery at CERN near Geneva—with some corroboration from Fermilab—of a new particle that seems to be the long-sought Higgs particle. Much further research on its exact identity is to come.

It is often said that what was at stake in the search for the Higgs particle was the origin of mass. True enough, but this explanation needs some sharpening.

By the 1980s we had a good comprehensive theory of all observed elementary particles and the forces (other than gravitation) that they exert on one another. One of the essential elements of this theory is a symmetry, like a family relationship, between two of these forces, the electromagnetic force and the weak nuclear force. Electromagnetism is responsible for light; the weak nuclear force allows particles inside atomic nuclei to change their identity through processes of radioactive decay. The symmetry between the two forces brings them together in a single “electroweak” structure. The general features of the electroweak theory have been well tested; their validity is not what has been at stake in the recent experiments at CERN and Fermilab, and would not be seriously in doubt even if no Higgs particle had been discovered.

But one of the consequences of the electroweak symmetry is that, if nothing new is added to the theory, all elementary particles, including electrons and quarks, would be massless, which of course they are not. So, something has to be added to the electroweak theory, some new kind of matter or field, not yet observed in nature or in our laboratories. The search for the Higgs particle has been a search for the answer to the question: What is this new stuff we need?

The search for this new stuff has not been just a matter of noodling around at high-energy accelerators, waiting to see what turns up. Somehow the electroweak symmetry, an exact property of the underlying equations of elementary particle physics, must be broken; if we are to account for mass, the electroweak symmetry must not apply directly to the particles and forces we actually observe.^{[1]}

It has been known since the work of Yoichiro Nambu and Jeffrey Goldstone in 1960–1961 that symmetry-breaking of this sort is possible in various theories, but it had seemed that it would, as a matter of theory, necessarily entail new massless particles, which we knew did not exist in fact.

It was the independent work of Robert Brout and François Englert; Peter Higgs; and Gerald Guralnik, Carl Hagen, and Tom Kibble, all in 1964, that showed that in some kinds of theories these massless Nambu-Goldstone particles would disappear, serving only to give mass to particles carrying forces.^{[2]} This is what happens in the theory of weak and electromagnetic forces proposed in 1967–1968 by Abdus Salam and myself. But this still left open the question: What sort of new matter or field is actually breaking the electroweak symmetry?

There were two possibilities. One possibility was that there are hitherto unobserved fields that pervade empty space, and that just as the earth’s magnetic field distinguishes north from other directions, these new fields distinguish the weak force from electromagnetic forces, giving mass to the particles that carry the weak force and to other particles, but leaving photons (which carry the electromagnetic force) with zero mass. These are called “scalar” fields, meaning that unlike magnetic fields they do not have directions in ordinary space. Scalar fields of this general sort were introduced in the illustrative examples of symmetry-breaking used by Goldstone and later in the 1964 papers.

When Salam and I used this sort of symmetry-breaking in developing the modern “electroweak” theory of weak and electromagnetic forces, we assumed that the symmetry breaking was due to fields of this scalar type, pervading all space. (A symmetry of this sort had already been hypothesized by Sheldon Glashow and by Salam and John Ward, but not as an exact property of the equations of the theory, so these theorists were not led to introduce scalar fields.)

One of the consequences of theories in which symmetries are broken by scalar fields, including the models considered by Goldstone and the 1964 papers and the electroweak theory of Salam and me, is that although some of these fields serve only to give mass to the force-carrying particles, other scalar fields would be manifested in nature as new physical particles that could be created and observed in accelerators and particle colliders. Salam and I found we needed to put four scalar fields into our electroweak theory. Three of these scalar fields were used up in giving mass to the W+, W-, and Z0 particles—the “heavy photons”—that in our theory carry the weak force. These particles were discovered at CERN in 1983–1984, and found to have the masses predicted by our electroweak theory. One of the scalar fields was left over to be manifested as a physical particle, a bundle of the energy and momentum of this field. This is the “Higgs particle” for which physicists have been searching for nearly thirty years.

But there was always a second possibility. There might instead be no new scalar fields pervading space, and no Higgs particle. Instead, the electroweak symmetry might be broken by strong forces, known as “technicolor forces,” acting on a new class of particles too heavy to have been observed yet. Something like this happens in superconductivity, in which electrical current can be conducted with no electrical resistance through some metals such as alumimum cooled to very low temperatures. This kind of theory of elementary particles was independently proposed in the late 1970s by Leonard Susskind and myself, and would lead to a whole forest of new particles, held together by technicolor forces. So this is the alternative with which we have been faced: Scalar fields? Or technicolor?

The discovery of the new particle certainly casts a very strong vote in favor of the electroweak symmetry being broken by scalar fields, rather than by technicolor forces. This is why the discovery is important.

But much remains to be done to pin this down. The electroweak theory of 1967–1968 predicted all of the properties of the Higgs particle, except its mass. With the mass now known experimentally, we can calculate the probabilities for all the various ways that Higgs particles can decay, and see if these predictions are borne out by further experiment. This will take a while.

The discovery of a new particle that appears to be the Higgs also leaves theorists with a difficult task: to understand its mass. The Higgs is the one elementary particle whose mass does not arise from the breakdown of the electroweak symmetry. As far as the underlying principles of the electroweak theory are concerned, the Higgs mass could have any value. That is why neither Salam nor I could predict it.

In fact, there is something puzzling about the Higgs mass we now do observe. It is generally known as the “hierarchy problem.” Since it is the Higgs mass that sets the scale for the masses of all other known elementary particles, one might guess that it should be similar to another mass that plays a fundamental role in physics, the so-called Planck mass, which is the fundamental unit of mass in the theory of gravitation. (It is the mass of hypothetical particles whose gravitational attraction for one another would be as strong as the electric force between two electrons separated by the same distance.) But the Planck mass is about a hundred thousand trillion times larger than the Higgs mass. So, although the Higgs particle is so heavy that a giant particle collider was needed to create it, we still have to ask, why is the Higgs mass so small?

Copyright © 2012 by Steven Weinberg

^{[1]} For more on scientific symmetry and broken symmetries, see my “Symmetry: A ‘Key to Nature’s Secrets,’” The New York Review, October 27, 2011. BACK TO POST

^{[2]} For brevity, I will refer to this work as “the 1964 papers.” BACK TO POST

*And Jantzen really does understand the physics!