#qcd

Introduction Quark-Gluon Plasma (QGP) is an extreme state of matter believed to have existed microseconds after the Big Bang. It’s a hot, dense phase of quantum chromodynamics (QCD) where quarks and gluons—fundamental particles of the strong interaction—roam free rather than being confined within hadrons (like protons and neutrons). The study of QGP provides crucial insights into the early…

The Strong Nuclear Force Made Easy: Without Colors Or Group Theory

“It’s true that the Universe obeys arcane and complicated rules, and that the best language for expressing those rules happens to be mathematics. But that doesn’t mean we shouldn’t endeavor to be translators, keeping the accuracy of the rules but making them accessible to far greater numbers of people. Every time we learn of a new way to present a scientific or mathematical phenomena, we gain a new tool in our arsenal for not only teaching it to others, but for better understanding it ourselves.

The strong interaction obeys all of the group theory rules associated with the special unitary group SU(3), but unless you’re an advanced graduate student in either physics or math, that’s probably not a language you speak. It can be described in terms of color, but the flaws in that analogy often leave long-lasting misconceptions even among physicists. The “triangle” analogy is more uncommon, but might help keep more of the mathematical intricacy of the theory while simultaneously eliminating numerous points of colorful confusion. However you slice it, there’s an entirely new set of nuclear forces at play inside atomic nuclei, and the strong force is what holds every nucleus in the Universe together. The better we understand it, the better we understand the physics at the literal core of our very existence.”

Equation (1) of www.math.ucla.edu/~wdduke/preprints/mocktheta.pdf reads ∏ 1 ÷ (1−qⁿ). I started expanding the denominator (in crayon) and found the pattern of + − + + − +’s easier to understand in colour.

Here is a sketch of the "combinatorial tetris" that results. I think the colours make the sources of the terms easier to track, and therefore to get a better intuitive feel for the algebra. (Anyone want to make a javascript app of this process?

Doodling with binomial expansion coefficients helped me understand the central limit theorem, Black-Scholes, and the Jones polynomial.

Quarks Don't Actually Have Colors

“We may call it color charge, but the strong nuclear force obeys rules that are unique among all the phenomena in the Universe. While we ascribe colors to quarks, anticolors to antiquarks, and color-anticolor combinations to gluons, it's only a limited analogy. In truth, none of the particles or antiparticles have a color at all, but merely obey the rules of an interaction that has three fundamental types of charge, and only combinations that have no net charge under this system are allowed to exist in nature.

This intricate interaction is the only known force that can overcome the electromagnetic force and keep two particles of like electric charge bound together into a single, stable structure: the atomic nucleus. Quarks don't actually have colors, but they do have charges as governed by the strong interaction. Only with these unique properties can the building blocks of matter combine to produce the Universe we inhabit today.”

At a fundamental level, forces like gravity are easy. There’s only one type of charge, mass/energy, and it’s always attractive. The electric force is a little more complex, with two types of fundamental electric charges, positive or negative, where like charges repel and opposite charges attract. But in the theory of the strong interactions, there are three fundamental types of charge, and that changes everything. We call this color charge because of a good analogy with how additive and subtractive colors work, but we can learn even more by investigating where the analogies break down.

Ask Ethan: Where Does A Proton's Mass Come From?

“What’s happening inside protons? Why does [its] mass so greatly exceed the combined masses of its constituent quarks and gluons?”

The whole is equal to the sum of its parts. That’s one of the first rules you learn, and it’s true about almost everything in the Universe. If you were to break a human being down into our constituent components, the cells in our body would add up to our entire selves. Same for the molecules in our cells and the atoms in our molecules.

But when you get down to atomic nuclei, something funny happens: the individual protons and neutrons are about 1% heavier than the atoms as a whole. That’s a clue as to what’s happening, but it cannot prepare us for the most mind-boggling fact: the quarks that make up the proton are only 0.2% of the proton’s actual mass!