My high school has a month long period where we spend all day studying one topic called Immersion. This year I'm doing Astronomy. We have been assigned to write a paper on some aspect of cosmology, and I chose the Higgs mechanism as my topic.

In my experience, this forum's collective IQ and interest in topics like theoretical particle physics is distinctly higher than that of most places on the internet, and its hard to find other high schoolers willing to take a quick look at any paper titled "Spontaneous Symmetry Breaking and the Higgs Mechanism".

Long story short, if any of you have any knowledge of this topic, and would be willing to take a quick look at this short paper on the topic and offer any type of criticism I would appreciate it. Also, I know that there's are no citations yet, I'll get around to it :) I also realize I didn't get into any of the mathematics. I'll be honest, I'm only a first year calc student and I don't understand any of it. Its filled with something called Lagrangian Field Transformations. Scary stuff.

https://docs.google.com/document/d/1V-yMfhFyksMU7471JLuez_RVcAn0AGs5o3U2a2Pndn8/edit

I'm having some issue getting into the page, specifically the internet can't find it and using the hotlink tosses me into a page saying my security settings are too strict.

I may be able to help a little bit. I'm not much of a writer, but I'm studying to be an Electrical Engineer, currently in Differential Equations and with a love of physics.

I'll copy the paper onto a post, hopefully it isn't too long. Should eliminate any issues with the link.

According to the Standard Model, elementary particles have various intrinsic attributes. Among these attributes are helicity, spin, and charge. All elementary particles have some value associated with each characteristic. It may seem illogical, but mass is not a property that every elementary particle has. A photon is an example of one such massless particle. Various explanations have been proposed for what gives some particles mass while leaving others massless. Philip Warren Anderson proposed the Higgs Mechanism in 1962 as one such explanation, and the theory was farther developed by Peter Higgs, Gerald Guralnik, C.R. Hagen, and Tom Kibble.

The first thing to establish is a need for a mechanism through which mass can be developed. There is no better example than that of the W and Z bosons, and the photon. The W and Z bosons are the carriers of the weak nuclear force, and have a mass. The photon is the carrier of the electromagnetic force, and has no associated value for mass. At extremely high temperatures the electromagnetic force and the weak nuclear force begin to function as two different aspects of the same force, known as the electroweak force. Another way of describing this relationship is that the electromagnetic and weak forces are symmetric. The carriers of the forces are inherently similar. A mechanism is needed to explain the differences in mass, to spontaneously break the symmetry of the forces with no outside interference, while remaining gauge invariant (gauge invariance is changing a aspect of a force, or field, without changing its overall properties). Without getting into the specific mathematics, the Higgs Mechanism is a mathematically appealing method for this generation of mass.

In quantum field theory, there is no such thing as a continuous force. All forces actually carried by various elementary particles, the photon carries the electromagnetic, the W and Z bosons the weak nuclear, the graviton gravity, etc. The strength of the forces is dependent on the quantity of force carriers there are, which increases as you approach the origin of the force. This “field” of force carriers is what constitutes all of the four forces. The Higgs Mechanism introduces another such field. The Higgs Field permeates all of space, and differs from the other forces in that it does not have a source, but is evenly spaced at every point in the universe. An interesting fact to note is that this eliminates the possibility of a true vacuum. The Higgs Field’s force carrier is the famous “god particle”, known as the Higgs boson. As a particle moves through this field, it interacts with the Higgs field. The Higgs bosons begin to latch onto the particle, creating almost a dragging effect on it. This dragging is what we perceive as mass. Some particles, such as the top quark, react very heavily with the Higgs field, very light particles such as the neutrino have very little interaction, and completely massless particles such as the photon do not interact with the Higgs field at all. The simplest version of the Higgs Mechanism has one type of Higgs field accompanied by one Higgs boson, while the most complex have up to five of each.

The Higgs Mechanism has long been theorized, but the Higgs field has yet to have been observed. We do however know how and where to look. If we could detect a Higgs boson, then we could say with certainty that the Higgs Mechanism is correct, providing further validation for the Standard Model (another interesting fact, the Higgs boson is the only elementary particle predicted by the Standard Model that is yet to be found). In order to find such a boson, protons are collided at extremely high speeds in machines such as the Large Hadron Collider. This should provide enough energy to produce a Higgs boson. However, there are a few complications that arise. Primarily, the exact weight of the Higgs boson has not been determined. The amount of energy required is directly proportional to the mass of the boson, so its a game of guess and check as to what energy is required. Many of the potential energy levels have been eliminated, giving researchers the idea that, within 95% certainty, if the boson exists it lies at around 115-130 GeV/C². Further testing at particle accelerators will confirm or nullify this conjecture. Another difficulty in finding the boson is that it is very unstable. As with various atoms, the larger the mass of the particle the less stable it is, and the Higgs boson is an extremely massive particle, around 133 proton masses. Thus, the particle instantaneously decays into other, more stable particles. The particles it decays to depends on what the actual mass of the boson is. If, as is most likely the case, the Higgs boson is between 115-130 GeV/C², then it will most likely decay into either bottom quarks, or W bosons. If the Higgs boson was to have a mass of 500 GeV/C², there is even a 20% chance it would decay into a pair of top quarks. As a rule of thumb, the heavier the boson, the heavier the particles it would decay into. The question remains, how can one detect a particle that instantly decays into something else? When the protons collide, the collider can detect the various elementary particles that are created. If a Higgs boson was created, it would decay into whatever particle is predicted, and there would be an excess of that type of particle. The Higgs boson can be detected by an abundance of elementary particles that cannot be accounted for by the standard model without the Higgs boson.

You've over stretched. Don't do that topic. While it's hot in the press, it's also volatile in the science, so not a good choice for a paper your currently writing (you may finish it to discover it's all wrong / changed). If you're doing an assessed course, pick the safe option.

I already wrote the paper for the most part, I'm not going to scrap everything.

Also, my teacher won't let me change topics. I tried the second I saw the math involved. He said he wanted me to stick through it so, not much of a choice.

Sounds like a hard run then. What's the title of the paper? Your link doesn't work.

Spontaneous Symmetry Breaking and The Higgs Mechanism. I copy and pasted the whole paper in the 3rd post because somebody else said my link was broken too.

What do you want to achieve? As in what will your conclusion cover?

It's just supposed to be a relatively brief explanation of what the Higgs Mechanism is. I suppose my conclusion will probably just restate what it does again, and talk a little about the implication of finding or not finding it.

Hi Skate,

I read your paper and thought it was very good. I'm a bit surprised that this counts as cosmology as the Higgs mechanism belongs to particle physics, which is a completely different field. Anyway, I wrote some comments on your paper below. If you have any questions about particle physics or cosmology, I'd be happy to answer them. Helicity is not an intrinsic property of a particle. It is defined as the projection of the spin onto the momentum, so the helicity of a particle depends on the frame of reference. Therefore you won't find helicity listed in any tables of particle properties. I wouldn't say it's illogical that some particles have mass while others don't. It could be surprising etc., but there's really nothing illogical about it. I would substitute "high energies" for "high temperatures," but the two things are essentially equivalent. I am not quite sure what you mean here. What is the origin of a force? How does the quantity of force carriers increase? This doesn't sound entirely correct to me. I don't understand what the last sentence means. What is a true vacuum and why is it eliminated by the Higgs field? Just about every physicist I know cringes when they hear the term "god particle." It's something that journalists love and scientists hate. Models with five physical Higgs bosons are not the most complex ones. In principle, one can construct arbitrarily complicated Higgs sectors. I assume you are referring to supersymmetry here, which requires a minimum of five Higgs bosons (some charged and some uncharged) for a technical reason called anomaly cancellation. If the particle discovered has the right properties (spin, couplings to other particles, ...) I would say "high energies" here instead of "high speeds." Particles at accelerators are always accelerated to essentially the same speed, the speed of light. I wouldn't say "most likely" but "most frequently" here. The Higgs boson decays differently each time, you can only predict the relative frequencies of the different decay modes. I would add here the one of the main difficulties is that there are large foregrounds from ordinary processes which can mask the Higgs decays. Essentially, the challenge is to identify the very small number of interesting events under an enormously large number of uninteresting ones.

Thank you for the feedback. I realize cosmology has been rather loosely defined, but its my topic nonetheless . I felt a little over my head, so I'm glad that somebody was able to clear up some of my misinformation.

By "continuous force" I meant that the Higgs field is evenly distributed everywhere, even where there is no matter. For example, gravitons theoretically come from particles what have mass, the quantity of which decreases exponentially as you move farther away from the mass. The Higgs field does have any "source" in this sense.

The part about the vacuum was something I picked up while reading a paper on the mechanism. A vacuum requires the absence of anything in the space, but the Higgs field is everywhere in the universe, so there is nowhere that is truly devoid of everything. At least that was my understanding.

Thanks again! You really helped me out here.