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