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Quarks

• 100’s of hadrons (baryons and mesons) are
known

• Classified in terms of their properties
(mass, spin, parity, baryon number,
Particle Physics strangeness, isospin ….)

• Development of a schematic classification
scheme allowed one to predict the
Quarks properties of particles

• (a Periodic Table for particles)

• Eventually showed that all hadrons can be
constructed from fundamental, point-like
particles called quarks (and anti-quarks)
1 2

Hadrons The Eightfold Way
• 1961: Gell-Mann, Ne’eman et al.
• Particles having the same spin-parity (Jπ)
tend to have similar masses • Plot the known particles on Strangeness vs
Isospin plots
Same charge

3 4

Rohlf 17.7 Krane 18.11

The Eightfold Way The Eightfold Way

Successful in predicting particles
A building block ?
Are quarks real or just nice maths ?

5 6

Krane 18.12 & 13

Quarks Mesons
• All quarks are spin-1/2 fermions • A quark-antiquark pair qq
• Fractional charge + 2 e or
3 −1e
3 • Mesons have B = 0. {+ 1 − 1 = 0}
3 3

• Baryon number = +1
3
• 9 bound states (mesons) from the 3 basic
quarks:
• Intrinsic parity is +1
uu ud us du dd ds su sd ss
+ + − −
η π K π π 0
K 0
K K 0
η′
• Initially, 3 quark “flavours”

Flavour Name Charge (e) • (The , ,π 0 η η ′ are in fact admixtures
of qq pairs)
u Up +2/3
• “Pseudoscalar Mesons”
d Down −1/3

s Strange − 1/3

7 8

Mesons Mesons

• These 9 mesons form an Octet (8) and a • Lowest energy state has the quark and anti-
Singlet (1 – the η′). with l = 0
quark spins
↑↓
• Interchange quarks e.g.

d↔s & d ↔s π (q ) = −π (q ) fermions

∴ π (q q ) = π (q ) ⋅ π (q ) ⋅ (−1) l = −1
η ′ ⇒ (uu , dd , ss )

η′ → η′ • The lowest energy state of a meson has
π −
Same particle J =0

K0 = d s → K 0 = ds • Excited energy state has the quark and
with l = 0
anti-quark spins
↑↑
Different particles
J π = 1−

9 10

Baryons Baryons

• A quark triplet • Lowest energy state has the quark spins
with
↑↓↑
l =0
• Baryons have B = +1. qqq
π (q ) = −π (q ) fermions

• Antiparticles have B = −1 qqq ∴ π (q qq ) = π (q ) = +1
p = uud , n = udd π ( q q q ) = π ( q ) = −1
Λ0 = uds, Λ0 = u d s

Proton u u d uud • The lowest energy state of a baryon has
π 1+
Q +2/3 +2/3 −1/3 +1 J = 2

Spin +1/2 +1/2 +1/2 +1/2
• Excited energy state has the quark spins
with
↑↑↑
B 1/3 1/3 1/3 +1
l =0
3+
T +1/2 +1/2 +1/2 +1/2 Jπ = 2
T3 +1/2 +1/2 −1/2 +1/2
11 12

Colour Charm
• 19** Discovery of the Ω−
• 1974 Stanford and Brookhaven:
• Strangeness: S = −3 ⇒ sss Discovery of the J / ψ meson

• Spin = 3/2 so ↑↑↑ • Cannot be constructed from the u, d, and s
quarks and anti-quarks.
• 3 ‘s’ quarks, in the same quantum state –
violates Exclusion Principle.
• Must be a fourth quark --- “Charm (c)”.
• Introduce another property “Colour” or
“Colour Charge”
q=+2e
3
• NOTHING to do with visual colour
• So, we have 3 quarks with the same • Yet another introduced property, u, d and s
‘flavour’ i.e. ‘s’ but different ‘colours’. quarks have charm = 0. The c quark has
• Red, Green & Blue so when they’re charm = +1
combined, the resulting baryon is White
i.e. ‘Colour Neutral’.
• Mesons are also ‘Colour Neutral’ e.g. Red
& Anti-Red
13 14

Bottom (“Beauty”) Quarks
• 1977 Fermilab: Discovery of the Υ
• Cannot be constructed from the u, d, s and Flavour Name Charge (e)
c quarks and anti-quarks.
• Must be a fifth quark --- “Bottom (b) or u Up +2/3
Beauty”.
d Down −1/3
q=−1e
3
s Strange −1/3
Top (“Truth”) c Charm +2/3

• Reason to suspect there are 3 families of b Bottom −1/3
quark pairs, just like the 3 generations of
leptons t Top +2/3
• 1997 Fermilab: Evidence for the top quark

q=+2e
3

15 16

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Quarks

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