# Higgs Boson – How Particles Acquire Mass

In response to a 1993 challenge from the UK Science Minister to produce a one-page simple explanation of the Higgs boson, the following entries were submitted.  (Quoted from “Physics World”, Volume 6 Number 9). As we all know, the Higgs has been found in July 2012 by the Large Hadron Collider.

### 1. How Particles Acquire Mass

By Mary and Ian Butterworth, Imperial College London, and Doris and Vigdor Teplitz, Southern Methodist University, Dallas, Texas, USA.

Matter is made of molecules; molecules of atoms; atoms of a cloud of electrons about one-hundred-millionth of a centimeter and a nucleus about one-hundred-thousandth the size of the electron cloud. The nucleus is made of protons and neutrons. Each proton (or neutron) has about two thousand times the mass of an electron. We know a good deal about why the nucleus is so small. We do not know, however, how the particles get their masses. Why are the masses what they are? Why are the ratios of masses what they are? We can’t be said to understand the constituents of matter if we don’t have a satisfactory answer to this question.

Peter Higgs has a model in which particle masses arise in a beautiful, but complex, progression. He starts with a particle that has only mass, and no other characteristics, such as charge, that distinguish particles from empty space. We can call his particle Higgs, or H. H interacts with other particles; for example, if H is near an electron, there is a force between the two. H is of a class of particles called “bosons”.

In the mathematics of quantum mechanics describing creation and annihilation of elementary particles, as observed at accelerators, particles at particular points arise from “fields” spread over space and time. Higgs found that parameters in the equations for the field associated with the particle H can be chosen in such a way that the lowest energy state of that field (empty space) is one with the field not zero. It is surprising that the field is not zero in empty space, but the result is that all particles that can interact with H gain mass from the interaction, even in empty space.

Mathematics links the existence of H to the mass of all particles with which H interacts. We can picture this possibility as a force field that, at its lowest energy state, “empty” space, is being filled with H particles which have no energy of their own. Other particles get their masses by interacting with this collection of zero-energy H particles. The mass (or inertia or resistance to change in motion) of a particle comes from its interaction with the Higgs field. As particles move through space they travel through this field, and if they interact with it they acquire what appears to be mass. This is similar to the action of viscous forces felt by particles moving through any thick liquid. the larger the interaction of the particles with the field, the more mass they appear to have.

If particles get their masses from interacting with the empty-space Higgs field, then the Higgs particle must exist; and we can find it. It is one of the main goals of the Large Hadron Collider at CERN to discover evidence of the Higgs boson, the force particle that creates mass for every other particle. If it can be proven that the Higgs particle does not exist,  scientists would know that the whole theory was flawed, and they have to look elsewhere in order to explain mass in the universe. There are also other hints about the Higgs: for example, if it exists, it plays a role in “unifying” different forces.

These questions, the mechanisms by which particles get their masses, and the relationship among different forces of nature, are major ones and so basic to having an understanding of the constituents of matter and the forces among them, that it is hard to see how we can make significant progress in our understanding of the stuff of which the earth is made without answering them.

### 2. The Need to Understand Mass

By Roger Cashmore Department of Physics, University of Oxford, UK.

What determines the size of objects that we see around us or indeed even the size of ourselves? The answer is the size of the molecules and in turn the atoms that compose these molecules. But what determines the size of the atoms themselves? Quantum theory and atomic physics provide an answer. The size of the atom is determined by the paths of the electrons orbiting the nucleus. The size of those orbits, however, is determined by the mass of the electron. Were the electron’s mass smaller, the orbits (and hence all atoms) would be smaller, and consequently everything we see would be smaller. So understanding the mass of the electron is essential to understanding the size and dimensions of everything around us.

It might be hard to understand the origin of one quantity, that quantity being the mass of the electron. Fortunately nature has given us more than one elementary particle and they come with a wide variety of masses. The lightest particle is the electron and the heaviest particle is believed to be the particle called the top quark, which weighs at least 200,000 times as much as an electron. With this variety of particles and masses we should have a clue to the individual masses of the particles.

Unfortunately, if you try and write down a theory of particles and their interactions then the simplest version requires all the masses of the particles to be zero. So, on one hand, we have a whole variety of masses and on the other a theory in which all masses should be zero. Such conundrums provide the excitement and challenges of science.

There is, however, one very clever and very elegant solution to this problem, a solution first proposed by Peter Higgs. He proposed that the whole of space is permeated by a field, similar in some ways to the electromagnetic field. As particles move through space they travel through this field, and if they interact with it they acquire what appears to be mass. This is similar to the action of viscous forces felt by particles moving through any thick liquid. the larger the interaction of the particles with the field, the more mass they appear to have. Thus the existence of this field is essential in Higg’s hypothesis for the production of the mass of particles.

We know from quantum theory that fields have particles associated with them, the particle for the electromagnetic field being the photon. So there must be a particle associated with the Higg’s field, and this is the Higgs boson. Finding the Higgs boson is thus the key to discovering whether the Higgs field does exist and whether our best hypothesis for the origin of mass is indeed correct.

### 3. Politics, Solid State and the Higgs

By David Miller Department of Physics and Astronomy, University College, London, UK.

#### A. The Higgs Mechanism

Imagine a cocktail party of political party workers who are uniformly distributed across the floor, all talking to their nearest neighbors. The ex-Prime Minister enters and crosses the room. All of the workers in her neighborhood are strongly attracted to her and cluster around her. As she moves she attracts the people she comes close to, while the ones she has left return to their even spacing. Because of the knot of people always clustered around her she acquires a greater mass than normal, that is she has more momentum for the same speed of movement across the room. Once moving she is hard to stop, and once stopped she is harder to get moving again because the clustering process has to be restarted.

In three dimensions, and with the complications of relativity, this is the Higgs mechanism. In order to give particles mass, a background field is invented which becomes locally distorted whenever a particle moves through it. The distortion – the clustering of the field around the particle – generates the particle’s mass. The idea comes directly from the physics of solids. Instead of a field spread throughout all space, a solid contains a lattice of positively charged crystal atoms. When an electron moves through the lattice the atoms are attracted to it, causing the electron’s effective mass to be as much as 40 times bigger than the mass of a free electron.

The postulated Higgs field in the vacuum is a sort of hypothetical lattice which fills our Universe. We need it because otherwise, we cannot explain why the Z and W particles which carry the weak interactions are so heavy while the photon which carries electromagnetic forces is massless.

#### B. The Higgs Boson

Now consider a rumor passing through our room full of uniformly spread political workers. Those near the door hear of it first and cluster together to get the details, then they turn and move closer to their next neighbors who want to know about it too. A wave of clustering passes through the room. It may spread to all the corners or it may form a compact bunch which carries the news along with a line of workers from the door to some dignitary at the other side of the room. Since the information is carried by clusters of people, and since it was clustering that gave extra mass to the ex-Prime Minister, then the rumor-carrying clusters also have mass.

The Higgs boson is predicted to be just such a clustering in the Higgs field. We will find it much easier to believe that the field exists and that the mechanism for giving other particles is true if we actually see the Higgs particle itself. Again, there are analogies in the physics of solids. A crystal lattice can carry waves of clustering without needing an electron to move and attract the atoms. These waves can behave as if they are particles. They are called phonons and they too are bosons.

There could be a Higgs mechanism, and a Higgs field throughout our Universe, without there being a Higgs boson. The next generation of colliders will sort this out.

### 4. Of Particles, Pencils, and Unification

By Tom Kibble Department of Physics, Imperial College, London, UK.

Theoretical physicists always aim for unification. Newton recognized that the fall of an apple, the tides and the orbits of the planets as aspects of a single phenomenon, gravity. Maxwell unified electricity, magnetism, and light. Each synthesis extends our understanding and leads eventually to new applications.

In the 1960s the time was ripe for a further step. We had a marvelously accurate theory of electromagnetic forces, quantum electrodynamics, or QED, a quantum version of Maxwell’s theory. In it, electromagnetic forces are seen as due to the exchange between electrically charged particles of photons, packets (or quanta) of electromagnetic waves. (The distinction between particle and wave has disappeared in quantum theory.) The “weak” forces, involved in radioactivity and in the Sun’s power generation, are in many ways very similar, save for being much weaker and restricted in range. A beautiful unified theory of weak and electromagnetic forces was proposed in 1967 by Steven Weinberg and Abdus Salam (independently). The weak forces are due to the exchange of W and Z particles. Their short range, and apparent weakness at ordinary ranges is because, unlike the photon, the W and Z are, by our standards, very massive particles, 100 times heavier than a hydrogen atom.

The “electro-weak” theory has been convincingly verified, in particular by the discovery of the W and Z at CERN in 1983, and by many tests of the properties. However, the origin of their masses remains mysterious. Our best guess is the “Higgs mechanism” – but that aspect of the theory remains untested.

The fundamental theory exhibits a beautiful symmetry between W, Z and photon. But this is a spontaneously broken symmetry. Spontaneous symmetry breaking is a ubiquitous phenomenon. For example, a pencil balanced on its tip shows complete rotational symmetry – it looks the same from every side. – but when it falls it must do in some particular direction, breaking the symmetry. We think the masses of the W and Z (and of the electron) arise through a similar mechanism. It is thought there are “pencils” throughout space, even in a vacuum. (of course, these are not real physical pencils – they represent the “Higgs field” – nor is their direction a direction in real physical space, but the analogy is fairly close.) The pencils are all coupled together so that they all tend to fall in the same direction. Their presence in the vacuum influences waves traveling through it. The waves have of course a direction in space, but they also have a “direction” in this conceptual space. In some “directions”, waves have to move the pencils too, so they are more sluggish; those waves are the W and Z quanta.

The theory can be tested because it suggests that there should be another kind of wave, a wave in the pencils alone, where they are bouncing up and down. That wave is the Higgs particle. Finding it would confirm that we really do understand the origin of mass, and allow us to put the capstone on the electro-weak theory, filling in the few remaining gaps.

Once the theory is complete, we can hope to build further on it: a longer-term goal is a unified theory involving also the “strong” interactions that bind protons and neutrons together in atomic nuclei – and if we are really optimistic, even gravity, seemingly the hardest force to bring into the unified scheme.

There are strong hints that a “grand unified” synthesis is possible, but the details are still very vague. Finding the Higgs would give us very significant clues to the nature of that greater synthesis.

### 5. Ripples at the Heart of Physics

By Simon Hands Theory Division, CERN, Geneva, Switzerland.

The Higgs boson is an undiscovered elementary particle, thought to be a vital piece of the closely fitting jigsaw of particle physics. Like all particles, it has wave properties akin to those ripples on the surface of a pond which has been disturbed; indeed, only when the ripples travel as a well-defined group is it sensible to speak of a particle at all. In quantum language, the analog of the water surface which carries the waves is called a field. Each type of particle has its own corresponding field.

The Higgs field is a particularly simple one – it has the same properties viewed from every direction, and in important respects in indistinguishable from empty space. Thus physicists conceive of the Higgs field being “switched on”, pervading all of space and endowing it with “grain” like that of a plank of wood. The direction of the grain in undetectable, and only becomes important once the Higgs’ interactions with other particles are taken into account. for instance, particles call vector bosons can travel with the grain, in which case they move easily for large distances and may be observed as photons – that is, particles of light that we can see or record using a camera; or against, in which case their effective range is much shorter, and we call them W or Z particles. These play a central role in the physics of nuclear reactions, such as those occurring in the core of the sun.

The Higgs field enables us to view this apparently unrelated phenomenon as two sides of the same coin; both may be described in terms of the properties of the same vector bosons. When particles of matter such as electrons or quarks (elementary constituents of protons and neutrons, which in turn constitute the atomic nucleus) travel through the grain, they are constantly flipped “head-over-heels”. this forces them to move more slowly than their natural speed, that of light, by making them heavy. We believe the Higgs field responsible for endowing virtually all the matter we know about with mass.

Like most analogies, the wood-grain one is persuasive but flawed: we should think of the grain as not defining a direction in everyday three-dimensional space, but rather in some abstract internal space populated by various kinds of vector boson, electron, and quark.

The Higgs’ ability to fill space with its mysterious presence makes it a vital component in more ambitious theories of how the Universe burst into existence out of some initial quantum fluctuation, and why the Universe prefers to be filled with matter rather than anti-matter; that is, why there is something rather than nothing. To constrain these ideas more rigorously, and indeed flesh out the whole picture, it is important to find evidence for the Higgs field at first hand – in other words, find the boson. there are unanswered questions: the Higgs’ very simplicity and versatility, beloved of theorists, makes it hard to pin down. How many Higgs particles are there? Might it/they be made from still more elementary components? Most crucial, how heavy is it? Our current knowledge can only put its mass roughly between that of an iron atom and three times that of a uranium atom. This is a completely new form of matter about whose nature we still have only vague hints and speculations and its discovery is the most exciting prospect in contemporary particle physics.

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