Eightfold Way old model GELL MANN NISHIJIMA FORMULA

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

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

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.

uuu uud udd ddd suu sdd ssu ssd sss uds 10 I 3 You can build 10 particles out of three quarks. Note I 3 symmetry.

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

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

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

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.

Gell-Mann’s great contribution: quarks

Try it yourself!