I understand that the excitation of the Higgs field itself is the Higgs boson, and not the Higgs field itself, which does fit somewhat into the little String theory I've read (The excitations of the strings are the particles, not the strings themselves). However, how does one actually get an excitation of the field? Since the mass of something is constant, changing it suddenly is not possible and even breaking it apart into other stuff conserves the net energy. So, how do we get the excitation? In my understanding, even if we smash two particles together really hard, and they break apart, the net energy remains conserved, and since mass and energy are kind of the same thing, what does it take to excite the field? How does the Higgs boson come into existence?

I don't know advanced particle physics though, this is just based on random article-reading.

  • $\begingroup$ How is this question specific to the Higgs boson? All other particles are likewise "excitations" in their corresponding fields. $\endgroup$ – ACuriousMind May 22 '20 at 22:21
  • $\begingroup$ @ACuriousMind Oops, I guess it isn't really specific to that. I was watching a Ted-ed video titled-"The Basics of the Higgs Boson", and I guess it was on my mind while writing the question. $\endgroup$ – VanshajVidyan May 23 '20 at 11:48

The word "excitation" embraces the concept of quantization of a field.

The first excitation of a field is one quantum (unit) of the field. The second excitation of a field are two quanta (units) of the field. It is valid for electromagnetic, weak, strong-interacting and possibly also the gravitational field (a consistent theory of the latter is still lacking). It is the concept to make compatible an a-priori continuous field with its actually discontinuous quanta.

The first excitation of a field is the smallest non-zero field (but there are exceptions, I come to that below) that can exist according to quantum field theory. A strong field, however, consists of a myriad of its quanta. It is this weird behaviour of nature that a field, for instance an electromagnetic field, when it is scattered for instance at a slit or even a double-slit behaves like a wave and when it impinges on the detector behind the slit it is registered as a series of quanta. The photon is the smallest unit of an electromagnetic field. It cannot be split in two parts to create an even smaller unit of the electromagnetic field. From the point of view of a classical continous field this cannot be understood, however, this is how nature really behaves, it has quantum properties. However, the quantum nature is not always noticable. Because one quantum, although being only one, can have different energies. So a slowly changing field will consist of low-energy quanta, whereas a fast changing field of high-energy quanta. The dectection, however, of single low-energy quanta is very difficult, so the overall behaviour of such a system will be observed as a continuous field. However, high energy quanta can be detected as a series of single quanta, because the energy change in the detector is large enough to be detectable.

Now let's come to the famous Higgs-boson. The concept is applied exactly in the same way, one Higgs-boson is first excitation of the Higgs field, two Higgs-bosons are the second excitation of the Higgs field and so on. A "strong" dynamical (changing in time) Higgs field consists of myriad of Higgs-bosons. It has, however, a property that distinguishes it from other quantum fields.

Whereas in the majority (for instance the electromagnetic/photon field) of fields if there are no quanta, the field value is zero. For instance if there are no photons, there is no electromagnetic field. Its field value is zero, i. e. electric and magnetic field strength are zero. This is not true for the Higgs-field. In space there might be no Higgs-boson at all, but the Higgs-field is non-zero. This non-zero field is not quantized. It cannot be considered as myriad of Higgs-bosons. This is what is meant with the vacuum expectation value of the Higgs field is non-zero. It cannot be "damped". It is always there. Higgs-quanta decay, they disappear, but the Higgs-field without any Higgs quanta persists.

Part of the question is "How do we get an excitation?". Everywhere where is an interaction. One of the simplest case is the light bulb. High temperature make the electrons in the wire get to higher energy levels from which they return to their original energy levels by the emission of light, or differently said, by the emission of light quanta, photons. It is an interaction of the electrons with the electromagnetic field. Photons have no mass, so there is no energy threshold necessary to create them, the interaction can be very weak.

For Higgs-quanta it needs at least 125GeV to produce them as they have a large mass. So particles with sufficient energies have to be smashed to create them.

  • $\begingroup$ I understand that to get a Higgs boson, particles with enough energy have to be smashed so as to get 125 GeV to sufficiently excite the Higgs field. Since there are tons of fields present in the universe just waiting to be 'excited' enough to emit their respective particles, how do we know we're only exciting the Higgs field? I mean, why is that energy be distributed into a bunch of other fields, instead of the Higgs field, so that we get a lot of other particles, instead of the Higgs boson? Again, I know nothing about particle physics, just building on what I inferred from your answer. $\endgroup$ – VanshajVidyan May 23 '20 at 17:01
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    $\begingroup$ @VanshajVidyan: this depends on the rules that govern particle physics. So it cannot be answered in just one post. But to give you an idea: It depends above all (+other rules) on the coupling (constant)to other fields. In particular the coupling of the H to other fermions is mainly determined by the mass of the fermion. So it is much easier to create a H by a t-anti-top collision than by electron-positron collision. $\endgroup$ – Frederic Thomas May 23 '20 at 17:30

The standard model of particle physics is a quantum field theoretical model and the Higgs boson is one of elementary particles axiomatically posited in this model, even before it was found experimentally.

Quantum field theory is a mathematical tool devised in order to be able to calculate particle interactions in quantum mechanics, when complex scattering problems appear, and the Feynman diagrams used to calculate decays and crossections are based on QFT.

In this theory, all the elementary particles in the table are assumed to have a mathematically defined field in all of space time, an electron field, a neutrino field a specific-quark field etc. It is like a Lorenz invariant aether on which interactions happen. The fields are defined as the plane wave solution of the corresponding quantum mechanical equation , Dirac, or Klein Gordon, or quantized Maxwell depending on the particle. Creation and annihilation operators acting on these fields, and propagate the particles and allow to write the Feynman diagrams to calculate the interactions.

How is the higgs field excited to give a Higgs boson?

By a creation operator, the same way that the electron field is excited to give an electron. It is a specific mathematical formalism that one has to study to really understand. If the energy available for an interaction is below the mass of the particle one has virtual particle creation.


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