Duke University

The Higgs Boson

Christine O’ConnellMath in the Universe- 89S

Hubert Bray22 February 2016

IntroductionThe Higgs boson, confirmed on March 14, 2013 was predicted by English physicist Peter

Higgs, who in 1964 proposed that an energy field gives particles mass. It relays and generates

mass to W and Z bosons through its interactions with them known as the Higgs mechanism

(Lincoln, Don. “The Higgs Boson”). W and Z bosons transmit quantified amounts of energy

through their admission and absorption, allowing for the weak force. The weak force enables

decay and allows for the transformation of a neuron into a proton and an electron into a neutrino.

It is one of the four fundamental forces in the Standard Model, which contain elementary

particles that make up the universe. One of these particles is the boson. Both the Higgs boson

and W and Z bosons are a part of the larger group of bosons which also include the gluon and the

photon, but the Higgs boson is the only scalar one. In general, a boson is a particle of matter that

transmits quantified amounts of energy through its interactions (Lucas). This essay is primarily

concerned with the Higgs boson and it explains the reason why the Higgs boson was predicted,

how it was discovered, its properties, and its possible future derivatives.

The Standard ModelIn order to understand the Higgs boson, the Standard Model and the Standard Model

Higgs particle must be understood. The Standard Model states that “everything in the universe

is found to be made from a few basic building blocks called fundamental particles, governed by

four fundamental forces (CERN The Standard Model).” The four forces include the strong force,

the weak force, the electromagnetic force, and the gravitational force. With the exception of the

gravitational force, the forces developed from bosons, and each force has their own boson. The

gluon is responsible for the strong force, the photon is responsible for the electromagnetic force,

and as mentioned above, the W and Z bosons are responsible for the weak force. The Standard

Model suggests that gravitation should be responsible for the gravitational force, but this has not

been discovered yet. However, the force of gravity is so small that it is almost negligible. Since

the Standard Model explains the three strongest fundamental forces, it is the most accurate

depiction of the subatomic world (CERN The Standard Model).

The theory behind the Higgs bosonUp until now, physicists have been unable to explain how particles gain mass. In order to

explain the notion of mass, the photon has been looked at. However, it mathematically does not

make sense that a photon could be able to gain mass because it would break the gauge

invariance. Wave functions and their charged particles are invariant under local gauge

transformations, meaning that they “change their phase by an amount that may vary from one

space-time point to another” in a field (Gauge 371). Mass cannot be included in the gauge

theory because it breaks the invariance. This is not important for photons because they are

massless; however, the gauge invariance would be broken in the electroweak model when W and

Z bosons gain mass. In order to solve this problem, symmetry was proposed as a potential

solution (Part 4).

The prediction for the Higgs boson involves calculations that break symmetry of a scalar

field in a vacuum. The Higgs mechanism was proposed as a way to keep the local gauge mainly

invariant by only breaking invariance in a vacuum. Under the Higgs mechanism, a new potential

(this potential is V(∅ ¿where (∅ ¿ is a weak spin ½ particle) is added to the Lagrangian(a

function that relates an event in spacetime to the value of the field at that particular point in

spacetime) such that the Lagrangian remains invariant, but the vacuum breaks invariance. This

added term is seen as a scalar particle with mass. Inside of the vacuum, the W and Z boson’s

symmetries are broken, signifying that the Higgs mechanism is responsible for giving them mass

(Part 4- 16). The exact calculations can be found here:

https://www.nikhef.nl/~ivov/HiggsLectureNote.pdf.

The mass of a Higgs bosonAs mentioned above, the Higgs boson relates to the Standard Model because it explains

the concept of mass. The Standard Model alludes to the notion that all particles should be

massless; however, this is in contradiction to what is observed in the world. The Higgs boson

has a mass of approximately 125 GeV, which is only about 130 times the size of a proton. This

mass was determined by accounting for all of the transformations of the Higgs boson as shown

below:

This figure shows the different subatomic particles that the Higgs boson converts into

The mass is further broken down into its “theoretical” mass, which is the actual mass of

the Higgs boson, and the mass of its transformations. The mass of the transformations is the the

mass of the sum of the effect of the bosons (particles with integer spins) minus the sum of the

effect of the fermions (particles with half-integer spins) multiplied by 1038GeV2. In order to get

the mass of the boson to be only 125Gev, there has to be an extremely small fermion/boson sum,

which is very unlikely. The more likely prediction is that there are other particles that have yet

to be discovered that offset the mass (Lincoln, Don why).

Testing the Higgs bosonThe Higgs boson was tested at the Large Hadron Collider (LHC). These detectors

examined 4000 billion proton collisions and made pictures of the particles immediately

following the collisions. The picture below shows how the particles retract from the energy

generated.

This picture is from an LHC detector and shows the particle tracks after the decay of the Higgs

boson (O’Neill).

The force caused by these collisions agitated the surrounding field, and if there was the

correct amount of agitation, a Higgs particle could break off from the field. When this particle

breaks of, it has no spin, which aligns with the Standard Model prediction. As the billions of

protons retracted, they clumped together, but eventually they decayed into other particles. This

was in direct accordion with the theorized Higgs boson which was calculated to be very unstable

(Greene).

Fermion Decay of the Higgs bosonThe Higgs boson was first observed to decay into bosons and photons, but CERN

researches in the summer of 2014 found evidence for the decay into fermions. Fermion decay

has also been predicted by the Standard Model, which states that the most prominent fermion

decay of the Higgs boson is to the bottom quark, and the Higgs boson mass of approximately 125

GeV will prohibit it from decaying into top quarks (Evidence found). Therefore, in order to link

the Standard Model with the Higgs boson, the decay to the bottom quark-antiquark pairs and to

tau lepton-antilepton pairs, both of which are parts of fermions) must be observed. The

probability related to signal strength and expectation for the production and decay of a standard

model Higgs boson is shown below:

This figure shows the probability of Higgs boson decay for a mass of 125 GeV into fermions.

The red line represents decay into bottom quark-antiquark pairs, the blue line represents decay

into tau lepton-antilepton pairs, and the black line represents into these combined pairs (Evidence

for). The sigmas represent standard deviation, and “a discovery is deemed confirmed from a

significance of five sigma”(Evidence Found). Thus, this graph suggests that there is evidence for

decay of the Higgs boson into fermions.

SupersymmetryWhile the Higgs boson coincides with the Standard Model, the Standard Model still has

loop holes. In addition to not being able to explain gravity, it also does not account for dark

matter. In order to help explain this phenomena, some physicists have looked to supersymmetry.

Supersymmetry has been used by physicist to try to find a way to merge quantum mechanics

with general relativity, which has incompatibilities that include mathematical inconsistencies,

meaningless infinities, and negative probabilities (Murayama). Supersymmertry is a theory that

relates time with space translation and space rotation (An introduction). It states that for every

particle there is a super-partner that allows for the rotation of one particle into the other particle.

For example, the boson’s super-partner is the fermion which are both particles that spin, but the

fermions have a half-integer spin while bosons have an integer spin. Additionally, every fermion

occupies its own state while multiple bosons can occupy a single state (CERN Supersymmetry).

Some physicists have used supersymmetry to propose new hypothesis behind the nature

of the Higgs boson. Dr. Christoffer Petersson from Chalmers University of Technology has

proposed that the Higgs boson can disintegrate both into a photon (a particle of light) and

particles of dark matter. He is currently testing his hypothesis at two experimental stations

within the LHC, the Atlas and CMS (. If supersymmetry exists, the LHC should be able to

detect supersymmetric particles. Furthermore, supersymmetry also predicts up to five Higgs

particles in which case the lightest one of the Higgs bosons has been discovered. While this is

still being tested by producing more Higgs bosons, supersymmetry has gained support because

the Standard Model predicted for a larger Higgs boson (Folger).

End of the UniverseThe Higgs boson is still being studied to determine if it has significance outside of

explaining the foundation of the weak force in the Standard Model. Stephen Hawking, an

English theoretical physicist, cosmologist, author and Director of Research at the Centre of

Theoretical Cosmology within the University of Cambridge has suggested that the Higgs boson

could lead to the end of the universe. He published his theory in Starmus. The Higgs boson has

led scientists to believe that the universe exists in a metastable state. While the universe exists in

a low energy state, it still is not the lowest state (Dickerson). The Higgs boson could cause the

universe to transition to a lower state, which is known as “vacuum decay.” If the particle reaches

energies above 100 billion gigaelectronvolts, it could make the universe unstable. As a result,

the universe could decay into a vacuum, and the bubble of the vacuum would expand at the

speed of light, making it undetectable to the human eye. Energies that would allow for this

transition could occur through cosmic ray collisions, but there is not enough technology to build

a particle collider with that amount of power to detect whether or not the universe could fall into

a lower energy state (Palmer).

ConclusionIn conclusion, the Higgs boson is one of the few scientific discoveries that had been

predicted before it was observed. It was predicted by the Standard Model because it explained

how particles acquired mass. After 4.9 billion dollars, the Higgs boson was detected in the LHC

lab. As of right now, it has only confirmed the belief that this particle is responsible for the weak

force. However, the LHC is still funding proton collisions and the formation of Higgs bosons in

order to determine if it has any other importance.

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