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The Higgs Field and Observation of Higgs Bosons

By Christopher Lau

The Higgs Field

Fundamental particles gain what is described as mass when they interact with the Higgs Field. This interaction is called the ‘Brout-Englert-Higgs Mechanism.’ As the strength of this interaction increases, the more massive fundamental particles become. Some fundamental particles (such as photons) do not interact with the Higgs Field and therefore do not have mass.

Fundamental particles, as described by quantum field theory, are ‘excitations’ (quanta) of an associated quantum field (e.g., photons are quanta of the electromagnetic field) that exists ubiquitously in all of space. The Higgs Boson is the fundamental particle associated with the Higgs Field.

Contents

The Higgs Field

Theory and Origin of the Higgs Field

Effective Range of a Fundamental Interaction

Broken Symmetry and the Masses of Gauge Bosons

Brout-Englert-Higgs Mechanism and SSB

Observation of the Higgs Boson

Production and Detection of the Higgs Boson

Identifying the Higgs Boson

Future of Higgs Boson Research

Theory and Origin of the Higgs Field

Effective Range of a Fundamental Interaction

Fundamental particles include bosons, which can be described as ‘force-carriers.’ Force-carrier particles mediate interactions (or forces) between particles; for example, photons mediate the electromagnetic interaction. Force-carrier particles are emitted and exchanged between particles when they interact. There are four known fundamental interactions: electromagnetic, gravity, strong, and weak interactions, each with an effective range and an associated force-carrier particle. In general, the effective range of a fundamental interaction is inversely proportional to the mass of its associated force-carrier particle.

Example Feynman diagram (time, t = y; position, x = x) of the interaction between 2 positive charges. A photon, a force carrier particle, is exchanged between the positive charges and so the direction of travel of both positive charges change.

Broken Symmetry and the Masses of Gauge Bosons

Symmetry forms the basis of relativity and many quantum mechanics theories. For instance, take X as a symmetry group (group of invariant transformations) of equations of a theory that describe a given physical system, such as the ‘electroweak’ fundamental interaction. Let A1 be one state of the system (sets of variables that describe the system) and let A2 be another. A1 could be the electromagnetic interaction and A2 could be the weak interaction, where both are representations of an 'electroweak' interaction Generally, as part of the symmetry group X: equations relative to A1, A2 will be invariant transformations of one another, both as representations of X. This means different quantum states can be defined through simple transformations of one another if both (quantum states) are representations of an overall symmetry group.

The foundation of a successful description of the electromagnetic interaction had already been established by the existing quantum field theory. The theory would only be viable when the force-carrier particles associated with the interaction being described were massless (where photons, of the electromagnetic interaction, are indeed massless).

The weak interaction has an effective range of 10^-18 meters and is mediated by the W and Z bosons, with measured masses of about 80.4 GeV and 90.2 GeV, respectively (GeV is a unit of energy used for convenience in calculations due to its relativity to mass; E=mc^2).

As expressed previously, the range of a fundamental interaction is dependent on the mass of its associated force-carrier particles. The W and Z bosons, force-carriers of the weak interaction, were known to have mass due to their limited effective range. In the attempt to define the electromagnetic and weak interactions under a single unified theory, the application of the same description as the electromagnetic interaction to the weak interaction was not possible; the general equations related to the theory modeled the emitted force-carrier particles to be massless. The basic symmetry of the theory would be broken if the W and Z bosons were massive, consistent with the effective range of the weak interaction.

Brout-Englert-Higgs Mechanism and SSB

The Brout-Englert-Higgs mechanism was proposed as the solution to this problem. The first component of the mechanism was the introduction of a new quantum field and associated particle: the Higgs field and the Higgs boson. The second component of the mechanism was the concept of ‘spontaneous symmetry breaking,’ or ‘SSB.’ With respect to the prior example, SSB refers to the occasion when equations relative to A1 and A2 remain invariant transformations of one another. The solutions to the equations relative to A1 and A2 are, however, not invariant, hence symmetry breaking occurs spontaneously. SSB was applied to the Brout-Englert-Higgs mechanism such that Goldstone bosons ‘disappeared’ to give the relative gauge bosons (in this case, the W and Z bosons) a mass. Goldstone bosons are initially massless, scalar particles introduced by the Goldstone theorem, which states: if there is a spontaneously broken symmetry in the set of equations relative to a theory, there must be at least one massless, scalar particle (the Goldstone boson). The disappearance of the Goldstone boson occurs without explicitly breaking the symmetry of the equations of the theory.

Shown above is a model representing SSB depicting a uniform 'Mexican hat.' A ball is initially positioned at the exact center of the hat, in which case, perfect symmetry is present in the system. The ball then immediately falls to a random point around the brim of the hat, in which case breaks the symmetry of the system. The event of the ball falling, however, does not defy any laws of physics; the physical equations that define the system remain symmetrical.

It is known now that fundamental particles other than gauge bosons also gained masses through the Brout-Englert-Higgs mechanism.

Observation of the Higgs Boson

Production and Detection of the Higgs Boson

Higgs bosons were first discovered in the Large Hadron Collider (LHC) at CERN. Before this, Higgs bosons were only theoretical fundamental particles. The experiment at CERN confirmed the existence of the Higgs boson.

The Higgs boson has an extremely short lifetime of about 1.6 x 10^-22 seconds (before decaying into other fundamental particles) according to the Standard Model, and thus cannot be found ‘in nature.’ The Higgs boson must be produced artificially in order to be observed. The short lifetime of the Higgs boson poses a further issue: the Higgs bosons cannot be directly observed, as in the moment they are produced, the Higgs bosons nearly immediately decay into other fundamental particles. To remedy this issue, the particles emitted from the decay of the Higgs bosons must be detected and precisely measured. The process of producing Higgs bosons, or what could be Higgs bosons (‘candidate Higgs bosons’), in the LHC involves colliding large numbers of particles. Higgs bosons are only produced in approximately 1/10^9 (~0.0000001%) of such collisions. This then contributes to another complication, as particles emitted by the decay of Higgs bosons are generally the same as those typically produced in collisions between other particles.

There was no method of distinguishing between which of the detected particles were products of Higgs boson decay or otherwise. The approach to detecting the Higgs boson was to collect a substantial amount of data from a substantial number of collisions; such that there will be sufficient evidence to suggest Higgs bosons could have been produced among the collisions that have occurred.

A mass, specifically invariant mass or rest mass, is calculated using the decay products of the particles produced from the collisions. If, for example, particle B was a very unstable particle produced from a collision, and particle C was a final decay product of B: if B immediately decays (and so no longer exists to be detected) into a pair of C particles which are then instead detected, then the measured energy and momenta of the pair of C particles can be used to calculate the invariant mass of particle B.

A dataset in the form of a graph produced at CERN using collision data collected throughout 2011-2016 is as shown in the image below: the dataset concerns only the decay of candidate Higgs bosons into a pair of photons, as indicated by H→γγ in the top left corner of the graph.

The section at the bottom of the image displays the distribution of masses (energies) of the photon pairs, which will be relative to the masses of the sources of decay, candidate Higgs bosons. The peak at mγγ (x-axis) = 125.8 GeV represents the invariant mass of the Higgs boson determined from this set of data. (This dataset was combined with another for a more accurate mass later on)

This statistical method is used because, in general, the masses of decay products (particles) from a source other than the Higgs boson will be a random value within a given range of possible masses. In comparison, the masses of decay products from a Higgs boson source will always be constant (with uncertainty, but ideally exactly constant). The value of invariant mass calculated from a set of decay products will therefore have an increased probability of being correspondent to the invariant mass of the Higgs boson, hence the distribution displaying evident bias towards the mass of the Higgs boson.

Identifying the Higgs Boson

An additional question could be posed regarding the detection of the Higgs boson, as the invariant mass of (supposedly) the Higgs boson, that was found using the statistical method, could have been the mass of a particle other than the Higgs boson. As predicted by the equations of the Standard Model theory, a Higgs boson will decay into a Z boson and a photon (H→Zγ) at a 0.15% rate, if the Higgs boson has an invariant mass value of approximately 125 GeV. Some theories that add to the Standard Model, however, predict different decay rates (probabilities).

In the effort to verify such theories, after the discovery of Higgs boson in the LHC in 2012, ATLAS and CMS at CERN both used similar methods to search for Higgs boson decays into a Z boson and a photon. Z bosons decay further into pairs of electrons or muons (muons are like electrons, albeit much more massive), so the detection of pairs of electrons and muons was used to identify Z bosons. In a distribution graph of the combined masses of decay products, collision events relative to the signal of this (H→Zγ) decay mode of the Higgs boson would be represented by a narrow peak.

In a more recent study, collaborations between ATLAS and CMS combined the datasets collected from the past (2011<) and more recent (2015<) experiments at the LHC and have significantly increased the accuracy and statistical precision of their searches for the H→Zγ decay mode of the Higgs boson. The collaboration led to the first evidence of the decay into a Z boson and a photon from a Higgs boson. This result was found to have statistical significance of 3.9 standard deviations, which was less than the conventional minimum 5 standard deviations required to claim there is sufficient evidence to suggest a new physical phenomenon (in this case, the occurrence of H→Zγ) has been discovered.

5 standard deviations relate to normal distribution concepts where the result of an experiment lay at least 5 standard deviations away from a mean, and, in physics, implies that the probability of the result of an experiment occurring only by chance was below ~0.00003%.

Prototype magnets of the HL-LHC at CERN

Future of Higgs Boson Research

Research on the Higgs boson has not yet concluded. Further research on the decay modes and interactions of Higgs bosons may allow properties and interactions of particles other than just the Higgs boson to be better analyzed. More capable equipment such as the HL-LHC, the High-Luminosity Large Hadron Collider, operational approximately by the beginning of 2029, will likely enable the study of particles such as the Higgs boson in greater detail. Luminosity is proportional to the number of collisions that occur per given time, so experiments in the HL-LHC will progress at a much greater (about 5x) rate, thereby leading to, possibly, more spontaneous discoveries.

References

https://www.quantamagazine.org/what-is-a-particle-20201112/

https://home.cern/science/physics/standard-model

https://home.cern/news/news/physics/where-does-higgs-boson-come

https://lightcolourvision.org/dictionary/definition/excitation-of-quantum-fields/

https://home.cern/science/physics/origins-brout-englert-higgs-mechanism

https://home.cern/science/physics/higgs-boson/what

https://www.fnal.gov/pub/science/higgs/index.html

https://news.fnal.gov/wp-content/uploads/higgs-boson.pdf

https://www.energy.gov/science/doe-explainsquantum-mechanics

https://physicsmasterclasses.org/exercises/hands-on-cern/hoc_v21en/main_frame/sm_concl1.html

https://webhome.phy.duke.edu/~kolena/modern/forces.html