GELL MANN NISHIJIMA FORMULA RELATING CHARGE TO ISOSPIN Q I 3 ½ B S B baryon number S strangeness Q charge in units of e the electronic charge ID: 278136
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Slide1
Eightfold Way (old model)
GELL MANN - NISHIJIMA FORMULA
RELATING
CHARGE TO
ISOSPIN
Q = I
3
+
½(
B
+
S
)
B
= baryon number,
S
= strangeness
Q
= charge (in units of e, the electronic charge
)
Y = B + S
was called hypercharge.
I
3
= “z component” of
ISOSPINSlide2
Iso-SpinIt was discovered that particles with
approximately the same mass, and the same
(ordinary) spin existed in “charge
multiplets
”:
p
and
n
I
3
= ½, - ½ (a doublet)
∏
+
∏
-
∏
0
I
3
= 1, -1, 0
(a triplet)
number of states = 2I +1 Slide3
quark tripletsGell-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
I
3
along the horizontal axis.
The quark triplet is shown on the next slide.Slide4
The Quark Triplet
I
3
Y=B+S
-1/3
- -2/3
-
Q = I
3
+
½(
B + S
)Slide5
8-fold way plotsOne 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. Slide6
You can build 10 particles out of three quarks. Note I
3
symmetry.
I
3Slide7
Try it yourself!Slide8
baryon decupletSlide9
Real, physical particles were found to match the baryon decuplet
properties: all have spin = 3/2
and about the same massSlide10
baryon octetSlide11
Experimentally discovered particles “matched” the baryon octet properties: all have spin = ½ and about the same massSlide12
building mesonsOne 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.Slide13
meson octet: 8-fold way plotSlide14
Experimentally discovered particles “matched” the meson octet properties: all have spin = 0and about the same massSlide15
CommentsThe 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.