What is beta function in physics? Can it be negative?

Question

Please explain to me as though I am a layman, I came across an article in which the noble laureates of last year had proved that beta function can be negative, but I didn't understand how.
P.S. I am a 16 year old studying in class 11.

Answer 1

The beta-function (usually written with a hyphen) is a function which arrises in quantum field theory to describe the interaction strength of particles. An example of this is the "charge". "Charge" tells how strongly charged particle, like protons and neutrons, attract and repel each other. It is a rather complex topic that I am not going to pretend to understand, but this should at least direct the answers here as the term "beta function" is very broad.

The nobel prize you are referring to is the physics nobel prize won in 2004 by Gross, Politzer, and Wilczek.

Answer 2

The beta function is the name used by Legendre and Whittaker and Watson (1990) for the beta integral (also called the Eulerian integral of the first kind). It is defined by

(1)

The beta function is implemented in Mathematica as Beta[a, b].

To derive the integral representation of the beta function, write the product of two factorials
The strong interaction – often called the colour interaction – is one of Nature’s four basic forces. It acts between the quarks, the constituents that build protons, neutrons and the nuclei. Progress in particle physics or its relevance for our daily life can sometimes appear hard to grasp for anyone without a knowledge of physics. However, when analysing an everyday phenomenon like a coin spinning on a table, its movements are in fact determined by the fundamental forces between the basic building blocks – protons, neutrons, electrons. In fact, about 80% of the coin’s weight is due to movements and processes in the interior of the protons and neutrons – the interaction between quarks. This year’s Nobel Prize is about this interaction, the strong or colour force.

Answer 3

Maybe there is more than one Beta function, in statistics the beta function assumes values from 0 to 1.