*“Dear Dr. Hossenfelder,*

First, I love your blog. You provide a great insight into the world of physics for us laymen. I have read in popular science books that the bosons are the ‘force carriers.’ For example the photon carries the electromagnetic force, the gluon, the strong force, etc. How come we never hear of a force that the Higgs boson carries?

Ramiro Rodriguez”

First, I love your blog. You provide a great insight into the world of physics for us laymen. I have read in popular science books that the bosons are the ‘force carriers.’ For example the photon carries the electromagnetic force, the gluon, the strong force, etc. How come we never hear of a force that the Higgs boson carries?

Ramiro Rodriguez”

The short answer is that you never hear of a force that the Higgs boson carries because it doesn’t carry one. The longer answer is that not all bosons are alike. This of course begs the question just how the Higgs-boson is different, so let me explain.

The standard model of particle physics is based on gauge symmetries. This basically means that the laws of nature have to remain invariant under transformations in certain internal spaces, and these transformations can change from one place to the next and one moment to the next. They are what physics call “local” symmetries, as opposed to “global” symmetries whose transformations don’t change in space or time.

Amazingly enough, the requirement of gauge symmetry automatically explains how particles interact. It works like this. You start with fermions, that are particles of half-integer spin, like electrons, muons, quarks and so on. And you require that the fermions’ behavior must respect a gauge symmetry, which is classified by a symmetry group. Then you ask what equations you can possibly get that do this.Since the fermions can move around, the equations that describe what they do must contain derivatives both in space and in time. This causes a problem, because if you want to know how the fermions’ motion changes from one place to the next you’d also have to know what the gauge transformation does from one place to the next, otherwise you can’t tell apart the change in the fermions from the change in the gauge transformation. But if you’d need to know that transformation, then the equations wouldn’t be invariant.

From this you learn that the only way the fermions can respect the gauge symmetry is if you introduce additional fields – the gauge fields – which exactly cancel the contribution from the space-time dependence of the gauge transformation. In the standard model the gauge fields all have spin 1, which means they are bosons. That's because to cancel the terms that came from the space-time derivative, the fields need to have the same transformation behavior as the derivative, which is that of a vector, hence spin 1.

To really follow this chain of arguments – from the assumption of gauge symmetry to the presence of gauge-bosons – requires several years’ worth of lectures, but the upshot is that the bosons which exchange the forces aren’t added by hand to the standard model, they are a consequence of symmetry requirements. You don’t get to pick the gauge-bosons, neither their number nor their behavior – their properties are determined by the symmetry.

In the standard model, there are 12 such force-carrying bosons: the photon (γ), the W+, W-, Z, and 8 gluons. They belong to three gauge symmetries, U(1), SU(2) and SU(3). Whether a fermion does or doesn’t interact with a gauge-boson depends on whether the fermion is “gauged” under the respective symmetry, ie transforms under it. Only the quarks, for example, are gauged under the SU(3) symmetry of the strong interaction, hence only the quarks couple to gluons and participate in that interaction. The so-introduced bosons are sometimes specifically referred to as “gauge-bosons” to indicate their origin.

The Higgs-boson in contrast is not introduced by a symmetry requirement. It has an entirely different function, which is to break a symmetry (the electroweak one) and thereby give mass to particles. The Higgs doesn’t have spin 1 (like the gauge-bosons) but spin 0. Indeed, it is the only presently known elementary particle with spin zero. Sheldon Glashow has charmingly referred to the Higgs as the “flush toilet” of the standard model – it’s there for a purpose, not because we like the smell.

The distinction between fermions and bosons can be removed by postulating an exchange symmetry between these two types of particles, known as supersymmetry. It works basically by generalizing the concept of a space-time direction to not merely be bosonic, but also fermionic, so that there is now a derivative that behaves like a fermion.

In the supersymmetric extension of the standard model there are then partner particles to all already known particles, denoted either by adding an “s” before the particle’s name if it’s a boson (selectron, stop quark, and so on) or adding “ino” after the particle’s name if it’s a fermion (Wino, photino, and so on). There is then also Higgsino, which is the partner particle of the Higgs and has spin 1/2. It is gauged under the standard model symmetries, hence participates in the interactions, but still is not itself consequence of a gauge.

In the standard model most of the bosons are also force-carriers, but bosons and force-carriers just aren’t the same category. To use a crude analogy, just because most of the men you know (most of the bosons in the standard model) have short hair (are force-carriers) doesn’t mean that to be a man (to be a boson) you must have short hair (exchange a force). Bosons are defined by having integer spin, as opposed to the half-integer spin that fermions have, and not by their ability to exchange interactions.

In summary the answer to your question is that certain types of bosons – the gauge bosons – are a consequence of symmetry requirements from which it follows that these bosons do exchange forces. The Higgs isn’t one of them.

Thanks for an interesting question!

Peter Higgs receiving the Nobel Prize from the King of Sweden. [Img Credits: REUTERS/Claudio Bresciani/TT News Agency] |

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