So where does the Higgs boson come from?

(Before we begin: all uses of the term "vacuum" in this discussion do not denote the absolute nothingness we know it colloquially to be. In quantum field theory, a vacuum is a space that contains "fleeting electromagnetic waves, within which things pop in and out of existence.")

[caption id="attachment_23450" align="alignright" width="300"] "Noob! I am your father!"[/caption]

When Alderaan was annihilated by the Death Star, Obi-Wan Kenobi sensed it even though he was not in the vicinity of the Empire's fleet. He said, "I feel a great disturbance in the Force, as if millions of voices suddenly cried out in terror, and were suddenly silenced." Now, imagine a place of absolute nothingness, also called a zero-point field, within such a Force, that contains no physical particles or energy quantizations. The best way to characterize this system would be in terms of its symmetry: that, in any direction starting from the centre of this vacuum, the probability of an event occurring is equal and zero. Now, imagine sticking your finger into such a system.

The first thing that happens is the symmetry breaks. A mass excitation is said to have been introduced in the zero-point field and that, starting from the centre and moving in any direction, the chances of finding a finger in one particular direction are going to be very good. Therefore, in anticipation of the finger being introduced into the system, the equations that define the system in the beginning must be able to account for symmetry-breaking. Now, eliminate any fingers and imagine that instead of a zero-point field, there is a continuous sea of particles with an unbroken energy symmetry, i.e., the chances of finding a perturbation in any direction is zero and that there is no mass excitation in the spectrum of possible excitations.

[caption id="attachment_23452" align="aligncenter" width="305"] A radial probability-cloud showing the probability decreasing from 1 (at the centre) to 0 (moving outward)[/caption]

While the system is in this phase, instantaneously expose it to an extremely high-temperature surrounding (t→10¹⁵ K, or approaching a thousand-trillion degrees Celsius). The sea of particles begins to vibrate because of the excess energy that has been imparted to their system, but the symmetry isn't yet broken. Suddenly, at 10¹⁵ K, the symmetry breaks spontaneously—which is thermodynamic lingo for "irreversibly"—but there is still no mass excitation.

That is because of Goldstone's theorem, formulated by Jeffrey Goldstone, which states that spontaneous symmetry breaking will occur only with massless excitations. The loss of symmetry can be interpreted as a gain of perturbations, as if a long-wavelength wave has been introduced as a disturbance into the system, giving rise to a field that acquires a non-invariant expectation value, and not necessarily corresponding to a vacuum expectation.

[caption id="attachment_23453" align="aligncenter" width="600"] Illustration of a standing wave, with amplitude described along the y-axis and its frequency, along the x-axis[/caption]

Simply put, the sea of particles can be thought of as a quantum fluid, or an infinite fabric. Beyond the critical temperature, the energy excitations of the particles pushes them to fall out of order, like a group of prisoners in a prison where the conditions are steadily getting worse: there will be a riot at some point, and the condition that precipitates the riot will have induced criticality in the system of prisoners. Just like the universe started to cool a few fractions-of-a-second after the Big Bang, a rollback of the adverse conditions will induce a gradual return to normalcy in the prison—a long-wavelength, low-frequency return to square one. At the same time, the guards remain on alert for small and localized disruptions because there is a non-zero expectation value (of an event).

[caption id="attachment_23454" align="aligncenter" width="640"] A history of the Big Bang: after one-hundred-billionth of a second, the symmetry has been broken to differentiate the electromagnetic and weak forces at an energy of 1 Tev. The LHC has been recreating just this situation by smashing together two beams of protons, each of 3.5 TeV, to reunify them as the electroweak force and look for the Higgs boson.[/caption]

For order to have resulted after the symmetry is broken, an order parameter is introduced. This is because, when the system was symmetric, the uniform probability eliminated the need to characterize any variations simply because the variations weren't there. After the spontaneous symmetry breaking, the system is said to be ordered in terms of the order parameter, although this is a different kind of order: one where subsystems can interact with excitations in the background field—the Force—to give rise to frames of reference (FoR). FoRs are localizations of activity that are logical enough to become something against which other such activities can be compared. (Notice now that the variations of the order parameter in the system are symmetric.)

The gain of perturbations in the system is understood in terms of the exchange of massless particles called the Nambu-Goldstone bosons, whose existence was postulated by Goldstone and Yoichiro Nambu, and the system is said to be in the Nambu-Goldstone mode. Such bosons arise out of the perturbing energy of the surrounding heat-reservoir to mediate the perturbing force. At the same time, the symmetry-breaking should've resulted in the formation of two "pieces" from one. These are two of the four fundamental forces of nature: the electromagnetic force and the weak force, the latter being responsible for radioactivity and beta decay. They are forces that are long-term manifestations of energy-transfer.

(The other two fundamental forces are gravitation and the strong nuclear force. Gravitational forces are mediated by the Higgs boson, whose origins we're exploring, and the strong force is mediated by gluons, which bind to quarks, other gluons and anti-gluons. The strong force holds the protons and neutrons in a nucleus together.)

[caption id="attachment_23455" align="aligncenter" width="275"] Jeffrey Goldstone and Yoichiro Nambu[/caption]

Just like the Nambu-Goldstone bosons are carriers of the perturbing force, two other kinds of bosons are brought into existence to carry the electromagnetic and weak forces: these are the massless photons (for the Em force) and the initially-massless W^±/Z bosons (for the weak force). The debut of massiveness, or the possession of mass, happens when the W^± and Z bosons "eat" the Nambu-Goldstone bosons and become extremely massive, in the process largely reducing the range of the weak force (hence, the name). The mass they acquire is of the non-vanishing sort, which means they can't lose it: the consumption is permanent. The process as a whole is known as the Higgs mechanism, and here we finally come to the Higgs boson, or the God particle.

Just as the original Nambu-Goldstone bosons arose out of an interaction between the high temperature and the background vacuum—again, the Force—so did the W^± and Z bosons arise out of the interaction between the Nambu-Goldstone bosons and what is called the Higgs field: a quantum field that pervades the entire universe and could be imagined to be the Force itself. Mathematically, the Higgs field has four components, two neutral and two charged just like an electric field has two components, its strength at a point and its direction at that point. The four Higgs components are all Nambu-Goldstone bosons: the two charged ones are consumed by the W⁺ and W^- bosons and one of the neutral ones is consumed by a Z boson. The remaining neutral boson had to have been consumed by a fourth boson or the quantum field would've exhibited a disturbance quite unlike what we've ever experienced.

This fourth boson is the Higgs boson—which means the fourth fundamental force is the gravitational force. The particle's existence means the presence of a Higgs field, and the presence of a Higgs field means the consumption by W^± and Z bosons of the Nambu-Goldstone bosons, and the consumption means the occurrence of a Higgs mechanism. Ultimately, the occurrence of a Higgs mechanism means its present formulation, along with that of the electroweak symmetry, holds true, firmly attesting to the Standard Model's ability to explain the dynamics of all the known subatomic particles.

[caption id="attachment_23456" align="aligncenter" width="640"] A schematic view of the LHC[/caption]