1. Eightfold Way (old model)
GELL MANN - NISHIJIMA FORMULA
RELATING CHARGE TO ISOSPIN
Q = I3 + ½(B + S)
B = baryon number, S = strangeness
Q = charge (in units of e, the electronic charge)
Y = B + S was called hypercharge.
I3 = “z component” of ISOSPIN

2. Iso-Spin
It was discovered that particles with approximately the same mass, and the same (ordinary) spin existed in “charge multiplets”: p and n  I3 = ½, - ½ (a doublet) ∏+ ∏- ∏0  I3 = 1, -1, 0 (a triplet) number of states = 2I +1

3. Energy Levels (Masses) for the Zoo Mass (MeV/c2)
B = 1/3 q
10 3/2 + Baryons
1385
B = 1
qqq
8 1/2 + Baryons
B = 1
1100
qqq
800
Mesons
B = 0
q qbar
Mesons
550
Mesons
B = 0
q qbar
Strong force
I, S symmetry broken
Independent of charge, color, flavor,
( I , I3 and S )
Weak force -- I3
symmetry broken
Maximal Symmetry -- all particles in
multiplet have
same mass,
M = Mo.
Symmetry broken - multiplets split into
I sublevels
M = Mo.+ m
Symmetry broken, further – I sublevels split into
I3 sublevels
M = Mo.+ m +m

4. quark triplets
Gell-Mann and others proposed that one might build all the experimentally observed particles from just three quarks: the up, the down and the strange.
One way to “build” the particles is to think of the quarks as vectors in a two dimensional “imagined” space with Y along the vertical axis and I3 along the horizontal axis.
The quark triplet is shown on the next slide.

5. The Quark Triplet
Q = I3 + ½(B + S)
Y=B+S
-1/3 I3
- -2/3 -

6. 8-fold way plots
One can generate particle multiplets by adding the u, d and s vectors in this two dimensional space.
Adding three (e.g. u + d + s ) vectors will generate multiplets with 10, 8, 8 and 1 particles,
called decuplets, octets and singlets.
The decuplet is shown on the next slide.

7. I3 uuu uud udd ddd suu sdd ssu ssd sss uds 10
You can build 10 particles out of three quarks. Note I3 symmetry.

8. baryon decuplet

9. Real, physical particles were found to match the baryon decuplet properties: all have spin = 3/2 and about the same mass

10. baryon octet

11. Experimentally discovered particles “matched” the baryon octet properties: all have spin = ½ and about the same mass

12. building mesons
One can build mesons from quarks by adding quark and anti-quark vectors.
The anti-quark vector is just a vector pointing in the opposite direction.
Adding vectors in this way results in one octet (8 particles) and a singlet (one particle).
A plot of the meson octet is shown in the next slide.

13. meson (spin = 0) octet: 8-fold way plot

14. Experimentally discovered particles “matched” the meson octet properties: all have spin = 0 and about the same mass

15. Energy Levels (Masses) for the Zoo Mass (MeV/c2)
B = 1/3 q
10 3/2 + Baryons
1385
B = 1
qqq
8 1/2 + Baryons
B = 1
1100
qqq
800
Mesons
B = 0
q qbar
Mesons
550
Mesons
B = 0
q qbar
Strong force
I, S symmetry broken
Independent of charge, color, flavor,
( I , I3 and S )
Weak force -- I3
symmetry broken
Maximal Symmetry -- all particles in
multiplet have
same mass,
M = Mo.
Symmetry broken - multiplets split into
I sublevels
M = Mo.+ m
Symmetry broken, further – I sublevels split into
I3 sublevels
M = Mo.+ m +m

16. Comments
The 8-fold way “cataloged” for the first time the particles w.r.t. spin, mass, charge, using quarks as the constituent elementary particle.
While the physical SU(3) symmetry which generated the model is only approximate, mathematical SU(3) models later took on a special importance.
Gell-Mann won a Nobel Prize for his 8-fold way model and contributions to the classification of particles and their interactions.

18. Gell-Mann’s great contribution: quarks

20. Try it yourself!