285 10 Finding the Higgs The Standard Model has been very successful. All the detailed couplings and particles needed for the cancellations between the diagrams have been found, and the more complicated quantum mechanical corrections that can be calculated theoretically agree with the observed data. The most spectacular of these is the quantum correction to the ρ parameter and the mass of the top quark; it might be helpful to remind the reader in simple terms of this most remarkable incident. We will be repeating some of the arguments of Chapter 9, but it is from a slightly different point of view, and also such that it is not necessary to understand all of the sometimes difficult arguments of that Chapter. First of all there is the issue of the number of Higgs particles. While the theoretical difficulties that the Higgs particle(s) must cure are well defined, it is quite possible to cure those problems using one, two, or in fact any number of Higgs particles. So here is the first question: how many Higgs particles are there? Here we have some idea about the answer. The theory by itself has nothing to say about the values of the masses of the vector bosons. They must be established by measuring them. However, it so happens that if all theoretical problems mentioned in the previous Chapter are to be solved using one and only one Higgs particle then the ratio of the mass + of the charged vector bosons ( W or W ) to the mass of the neutral one ( Z 0) must have a very specific value. Thus by measuring the masses of the vector bosons we have an indication of the possible number of Higgs particles. Here experiment tells us
286 Peter Higgs (1929). This is the man whose name is associated with the big mystery of the Standard Model: the Higgs particle. He developed his work after an important piece of work by Anderson, who investigated the penetration of electromagnetic fields in a superconductor. He found that they penetrated only over a small distance, and he produced a theoretical understanding. The same mechanism was then used by Higgs (and Brout and Englert) to make a theory of photons with mass, thus with a limited range for the associated force. That became an ingredient of the Standard Model, not for the photons (that have zero mass), but for the homologues, the vector bosons W and Z. That turned out to be just what was needed to make the model mathematically viable (renormalizable). I met Higgs for the first time at a summer school in Edinburgh in 1959, where he was part of the organization, in particular he had the key to the wine cellar. Cabibbo and I, among others, profited greatly from his gracious understanding of our needs. Polkinghorne, a professor at that same summer school, writes in a book (Rochester Roundabout ): Higgs was a competent theorist, but of no great distinction, while in that same book he writes about X (admittedly a very good physicist): X is a very deep thinker with a marked reluctance to publish his ideas, and of the same X with respect to Higgs s idea: Perhaps one of the most surprising aspects of the story is that this idea did not occur to the acute and fertile mind of X himself. In 1979 Polkinghorne became an Anglican priest, instantly becoming the best physicist among Anglican priests. Recently he received the enormous Templeton prize. I think it was for something indeed not that easy: bridging the gap between sense and nonsense.
287 Robert Brout (1928, left) and François Englert (1932). These two must be credited, together with Higgs, for introducing the Higgs system. They are not well known to the general public, the name of Higgs alone has stuck in association with the subject. Brout and Englert were perhaps the first to suspect that their work would make vector boson theories renormalizable. Englert said so in a discussion remark at a talk by Weinberg at the 1967 Solvay conference. Weinberg did have a handwritten version of his 1967 paper with him, in which the same is said. However, I do not think that any of them had any inkling about the complexities of the theory. I feel a bit guilty with respect to Brout and Englert, because in 1971 I heard about Higgs s work, but only later of their work, and I thus did not cite them in the beginning. That was one of the reasons that they did not become as well-known as Higgs. They got full recognition in 1997, when they were awarded (together with Higgs) the High-Energy and Particle Physics prize of the European Physical Society. I met Brout in Utrecht around 1958. He impressed us all, but I did not meet him for a long time after that because he worked mainly in another field of physics, more related to the domain in which Anderson was active. At a dinner where Englert was also present I proposed a conjecture based on the statistics of one person (myself), namely that being born in the summer, preferably June, is the best with respect to intelligence. Englert, born in November, replied by saying that he was a Jew, and did not need this. Then he laughed so hard that I started to be worried for his life. For your information: my conjecture holds on the average for Nobel prize winners; Einstein, however, was born in March.
288 ELEMENTARY PARTICLE PHYSICS that the answer is that the values of the masses are indeed precisely such that one Higgs particle is enough to do the job. However, there are subtleties here. The mass of a vector boson such as the Z 0 is affected by quantum corrections (often called radiative corrections). The fact that a vector boson such as the Z0 may, for a short time, split into a pair of particles of different mass, changes slightly the value measured for the Z 0 mass. The particles that may intervene here are any of those that the Z 0 is coupled to, and that includes the top and bottom quark. The figure below shows the two possibilities. b Z 0 Z 0 b t Z 0 Z 0 The same story holds for the charged vector bosons. The + measured value of the mass of the W is also influenced by the occurrence of virtual pairs, but they occur differently as compared to the Z 0 case. In fact, there is only one possible diagram. The reader may observe that this is so because of conservation of charge. See the next figure, and remember that the antibottom quark has a charge of + 1 while the top quark has a charge of + 2. 3 b W + W + + The masses of the W and W are the same, and so are the corrections due to quantum effects. However, the corrections to the Z 0 + mass are not equal to those of the W mass, and the ratio of charged and neutral vector boson masses changes slightly. This rather small effect has been evaluated theoretically and measured experimentally, and as its value depends on the masses of top and bottom quark, the measurement can be used to determine the t t 3
FINDING THE HIGGS 289 top mass (the mass of the bottom quark is of course known since its discovery in the seventies). This then led to a prediction for the top mass, and indeed the top was found with precisely that value for its mass. It in fact helped the experimenters to find the top in 1995, since they had at least some idea about its mass before they started looking for it. At that moment the Nobel committee started worrying about what became the 1999 Nobel prize. Predicting and experimentally confirming the mass of an elementary particle is the sort of thing they look for. It is here that we resume our discussion of the Higgs particle. It too may influence the vector boson mass measurements, and possibly also the ratio of the masses. See the figure below. There is a strange new type of diagram that ought to tickle the imagination of the reader. H Z 0 Z 0 Z 0 Z 0 As the Higgs couples with different strength to the Z 0 and + the W the mass ratio is indeed affected, although very much less so than through the corrections due to bottom and top quark. So, the prediction for the top quark mass is unsure since we do not know the mass of the Higgs particle and thereby the magnitude of the correction (except that its magnitude is quite small). In practice this led to an uncertainty of about 5% in the prediction of the top quark mass. Once however the top quark was discovered and its mass measured, the mass of the Higgs could be estimated from this very small effect. The prediction for the Higgs mass from this is not very precise, and today stands at somewhere above 110 GeV with a very large error margin. So, what is the situation? Most likely there is only one Higgs (if any!) and there is a vague prediction for its mass. However, there is trouble brewing and it is not at all sure that the Higgs actually exists. Here are the complicating issues. H Z 0
290 ELEMENTARY PARTICLE PHYSICS Introducing the Higgs with certain couplings to the known particles (all of which have to be verified when the Higgs is actually found) leads also to the necessity of coupling the Higgs to itself. So two Higgs bosons may attract each other, etc. This turns out to have some really surprising consequences. There may be bound states of Higgs particles, depending on the strength of the Higgs self-coupling. The reader may recall the important feature of a bound state, namely that it is a state of negative energy as compared to the non-bound state. This is obvious if one realizes that it costs energy to tear the bound state apart. For example, in a hydrogen atom the electron is bound to the proton with an energy of 13.6 ev. You need 13.6 ev of energy to pull the electron from a hydrogen atom. Thus in a bound state there is some amount of negative energy, binding energy, in addition to the usual mass-energy. The total energy of one hydrogen atom is equal to the sum of electron and proton mass minus the binding energy. Thus a bound state of Higgs particles involves negative energy. It now happens that it is possible to have bound states of two, three, etc., Higgs particles, and there is a bound state of an infinite number of Higgs particles whose binding energy is actually larger than the sum of all the Higgs masses! Thus the total energy of that state is negative, and if you start with nothing then you can create energy by making such a bound state. This is a most curious and disturbing fact, because it is obvious that such a state (it actually has an infinite spatial extension) would be created immediately in the beginning of our universe. But such a bound state cannot go undetected. Having a system of Higgs particles all over the universe is something that would be sensed by gravitation, and calculation reveals that such a system would lead to a curved universe with the size of a football. Theoretically it must be cured in a most horrid way: one assumes that the universe was initially curved in a negative sense and in precisely the same amount before this Higgs bound state came along. The result then would be a flat universe. Quite unbelievable, unless there is a principle that forces these two a priori unrelated curvatures to be
FINDING THE HIGGS 291 the same. Recent observations by astronomers have shown that the universe is really very flat and even the expected curvature due to the masses of galaxies etc. has not been seen. There is a big puzzle here. Evidently there is some relation between the Higgs system and gravitation. How strange. All this indicates that there is more to the Higgs than meets the eye, and one may well expect to see something quite different from the simple picture of a particle of some 150 GeV with certain interactions with the known particles and itself. Even so the Higgs particle has a task to fulfill: it must be such that it cancels out certain unwanted effects in scattering processes. There are certain things that must be there with certainty, and therefore the hunt for the Higgs is not open-ended. There is an important theoretical fact: the strength of the self coupling of the Higgs is related to the mass of the Higgs. So, a heavy Higgs couples stronger to itself than a light Higgs. If the Higgs is sufficiently heavy these self-couplings become so large that perturbation theory breaks down. Diagrams with an ever increasing number of self-couplings are not smaller than diagrams with no or only a few such couplings. Under those circumstances the theorists cannot make precise quantitative predictions. Here is then the state of affairs. Higgs or Higgs related effects become large and visible (but actually unpredictable in precise magnitude) if the Higgs itself has a mass exceeding 500 GeV. The ominous fact that already now the Higgs, from an experimental point of view, seems heavier than any other particle we know seems to point in this direction. Of course, if the Higgs is that heavy the prediction from the vector boson mass ratio becomes worthless also, and cannot be used to predict the Higgs mass. So the Higgs mass prediction from present data may be a joke. We must go hunt for the thing itself, or inspect closely those situations where it has a job to do, cancelling undesirable behaviour for example in vector boson scattering. The theory ends here. We need help. Experiments must clear up this mess.
292 ELEMENTARY PARTICLE PHYSICS There are a few light points here. It is virtually sure that the Large Hadron Collider at CERN will come into operation in the first decade of this century. Very likely that will establish at least some as yet unanswered questions. The Higgs itself may actually be discovered if its mass is not too high (somewhere below 400 GeV). This machine does not cover, however, the complete spectrum of manifestations of the Higgs particle. Much more in that sense can be expected from a high-energy electron-positron collider, of which there are some on the drawing board. They may actually measure the Higgs self-interactions. But there is no question about it: we may well run into something totally unexpected!