Eightfold Way old model GELL MANN NISHIJIMA FORMULA
- Slides: 15
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 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 I 3 = ½, - ½ (a doublet) ∏+ ∏- ∏ 0 I 3 = 1, -1, 0 (a triplet) number of states = 2 I +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 I 3 along the horizontal axis. • The quark triplet is shown on the next slide.
The Quark Triplet Q = I 3 + ½(B + S) Y=B+S -1/3 I 3 - -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.
I 3 You can build 10 particles out of three quarks. Note I 3 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.
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