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### All on the Higgs for (nearly) everyone

Like most of my colleagues, the most frequently asked question I get from friends and family these days is: what is this Higgs boson business? Here is what I hope will help not only family members but also struggling physicists. It is not the simplest but it is complete and accurate.

First of all, let’s clarify one point: it has nothing to do with God. This “God’s particle” business has got to go. It was just a bad joke to start with and like any joke, it gets stale fast.

And we need to talk about three separate aspects: the Higgs mechanism, the Higgs field and the Higgs boson.

Currently, there is a theoretical model describing just about everything observed so far in particle physics, called the Standard Model. It rests on two simple principles: 1) all matter is made of particles, namely quarks and leptons and 2) all interactions between particles are mediated by exchange particles associated to the fundamental forces.

The current equations from the Standard Model only produce massless particles when we know these particles all have a mass, as witnessed countless times in our particle detectors.

The “Higgs” mechanism is the mathematical representation of what happens. It is a way to remix the Standard Model equations for the electromagnetic and weak nuclear forces. It brings into the equations three particles called “Goldstone bosons”, that mathematically “absorb” the three massless bosons associated with these forces. Then, out of the new equations pop three massive particles, the W+, the W and the Z0 bosons, plus the massless photon. These are the four particles we know to be associated with the electromagnetic and weak nuclear forces.

In all fairness, it should be named after all the physicists who contributed to the idea but so many did, it is referred to as “Higgs mechanism” for short.

The mechanism is a mathematical description of a physical entity, the “Higgs field” that permeates all space, just like a gravitational field affects the space around a massive object. Although we cannot see this field, particles feel its effects by acquiring a mass, just like we feel the gravitational attraction du to the Earth’s field.

The Higgs field is what is needed to provide mass to all elementary particles such as the electrons, the quarks, the W and Z bosons. The fact that we have found the W and Z bosons with exactly the mass predicted by the theory is a strong indication that the Higgs mechanism takes place and the Higgs field exists, but there is of course no guarantee until we find the Higgs boson to prove it all.

The Higgs boson is just an excitation of the Higgs field. Ok, I admit, this one is harder to swallow. But think of a hydrogen atom. In its ground state, the hydrogen atom lives eternally. It will never decay into anything more stable. But it becomes “excited” after absorbing energy. Its electron then jumps to a higher level making the atom unstable. In just picoseconds (millionth of millionth of a second), the hydrogen atom will come back to its ground state by emitting a photon, spitting back the excess energy to return to its stable state.

The Higgs field, like a hydrogen atom, can be excited, also only in discrete values of energy corresponding to the Higgs boson mass. The energy released when protons collide in the Large Hadron Collider can excite the Higgs field. The excited state is just the Higgs boson itself. And just like the hydrogen atom in its excited state, it will try to return to its ground state. The Higgs boson is therefore very unstable and will decay into other particles instants after appearing.

What we need to establish now at CERN is exactly if the Higgs field exists and how it operates, how it can be excited, how it all works. This is what all our research around the Higgs boson is about. We want to know the specificities of the Higgs field. The simplest thing is that the first excited state is a single particle, the Higgs boson. That’s what the Standard Model favors. Some other theories bet on many different types of excitations, i.e. many different Higgs bosons or composite objects.

Now, last but not least, how does the Higgs field provide the mass to other particles? Imagine a completely empty pool table, with a perfectly smooth marble surface and perfectly straight marble sides. Toss a billiard ball across the table and it will travel on a straight line. Now glue many rigid posts to form two rows, leaving a narrow path for the ball. This time, the ball will hit the posts, bouncing back and forth along the way. If the table is perfectly smooth and the ball perfectly rigid, it will just bounce back without losing energy. It will eventually make it across the table, taking more time but keeping the same energy. If you measure its speed from how long it took to cross the table, it will appear like it is now travelling slower.

A particle moving in a space filled with the Higgs field would no longer be able to travel in a straight line because of its interaction with the field. It would progress more slowly overall, like a billiard ball interacting with small pegs would take more time to reach the other side of the table.

A physicist would say: there is now dispersion, the tossed ball no longer travels along a straight line but without dissipation, i.e. no energy loss.

The Higgs field acts like the posts glued to the table. It prevents the moving ball from traveling in a straight line but without it losing any energy.

In relativity, the mass is seen as a form of energy. This is expressed by the well-known equation:  E = mc2 where c2 is just like the exchange rate between mass m and energy E. Look at it as having money in your pocket: if you are at CERN, it would be in two currencies, Swiss francs and euro. The sum is the total money you have. For a moving particle, both its movement and its mass contribute to its energy as illustrated below:

For a moving particle, the energy comes from two sources: having speed and having mass. This is a bit like having money in two different currencies. One can convert them into each other.

Ok, let’s stretch our imagination one bit further and now imagine a massless billiard ball, a ball with absolutely no mass. If we toss that massless billiard ball across the table, all its energy comes from its motion since it has no mass. Its effective speed is lower since it no longer travels on a straight line. A physicist would talk of the group velocity here, the speed at which the ball seems to progress in the right direction.

For a massless particle, i.e a particle without any mass, all the energy comes from its motion. It’s like having only one currency in one’s wallet.

So, here is the million Swiss franc question: If it is slower, the energy share coming from its velocity is smaller, then how comes the ball still has the same energy? Simple: this ball has acquired mass through its interaction with the Higgs field. The contribution to the total energy from its mass is no longer zero and it adds up to the reduced contribution associated with movement to give the same total energy value.

A particle interacting with the Higgs field moves more slowly but its total energy is unchanged. It therefore has less energy in the form of motion and some now coming from the newly acquired mass just as if one had converted some Swiss francs into euro.

To summarize: The Higgs field provides the mass and the Higgs boson is just an excited state of this field. All particles that interact with the Higgs field acquire mass since they travel less rapidly but still have the same energy. The Higgs mechanism expresses all that mathematically.

Sleep tight.

Pauline Gagnon

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