# Homework Help: [Solved] Derive the eightfold way

1. Dec 1, 2008

### catkin

1. The problem statement, all variables and given/known data
This is from Advanced Physics by Adams and Allday, section 9.11, question 3.

I am posting hints for the solution because it took me so painfully long to understand what the text and the question were and weren't saying and hence to find the necessary extra information.

Question: Write down in a sequence along one line all the possible combinations of the u and d quarks that give rise to baryons. On the line beneath, write down all the baryon combinations of u, d, and s quarks using one s quark only. On the next line do the same thing including two s quarks. Now, for each combination write down the charge and strangeness of the particle. Compare the result with the baryon pattern in the eightfold way diagram move. What is the quark content of the Ώ-?

Answering this question requires information that is not given in the spread and is hard to find, especially when you don't know what you are looking for. It also requires being aware of spin, despite spin being out-of-scope for A-level Physics. Thus spin is mentioned (but not explained) below.

The question is about the "eightfold way". What is the key difference between the eightfold way and the decuplet diagram? The spread mentions, in the note to the diagrams, that some of the particles have the same quark combinations but different masses. That's true but not enough information to assign baryons made of only d, s and u particles to one or other diagram. The key difference is that the eightfold way is for particles with 1/2 spin and the decuplet for particles with 3/2 spin (see http://www.nationmaster.com/encyclopedia/List-of-baryons").

Now knowing that only particles with 1/2 spin need be included in "all the possible combinations of the u and d quarks that give rise to baryons" etc., the required list can be created from information at http://hyperphysics.phy-astr.gsu.edu/Hbase/Particles/baryon.html#c1". It helps if you order them in ascending charge, too.

2. Relevant equations
None, only tables of data as in the above links.

3. The attempt at a solution
Not applicable (unless somebody asks).

Last edited by a moderator: Apr 24, 2017