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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
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
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.
The Quark Triplet
Q = I3 + ½(B + S)
Y=B+S
-1/3
I3
- -2/3
-
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.
I3
You can build 10
particles out of
three quarks. Note
I3 symmetry.
Try it yourself!
baryon decuplet
Real, physical particles were found to
match the baryon decuplet
properties: all have spin = 3/2
and about the same mass
baryon octet
Experimentally discovered particles “matched”
the baryon octet properties: all have spin = ½
and about the same mass
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.
meson octet: 8-fold way plot
Experimentally discovered particles
“matched” the meson octet properties: all
have spin = 0
and about the same mass
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.