1. The Zoo of Subatomic Particles
ParticleZoo
The Zoo of Subatomic Particles
The Standard Model of Quarks and Leptons

2. Nucleons Are Not Elementary Particles!
Scatter high-energy electrons off protons. If there is no internal structure of e- or p, then well-defined “elastic” e- energy for each angle. See structure!! p e-
hadron jet
excited states of the proton
Each line in the energy spectrum of scattered electrons
corresponds to a different energy state of the proton.
Bartel etal. PL28B, 148 (1968)
scatter probability
energy of scattered electron
ground state of the proton
elastic
x1/8.5

3. The Quark Model
The quark model represents a relatively simple picture of the internal structure of subatomic particles and makes predictions of their production and decay. It uses a minimum of adjusted quark parameters and has great predictive power, e.g., for the composite-particle masses, magnetic moments, and lifetimes.
There are no contradictions to this model known so far, (but many questions remain).

4. Internal Nucleonic Structurep e-
The proton has internal structure, so-called quarks (u,u,d).
Quarks combine to nucleon states of different excitations.
Proton is the (u,u,d) ground state N D
S=½
S=3/2
1200 MeV
N: one doublet with a splitting of only Dm = 1.3 MeV
D: one quadruplet with a splitting of only Dm = 8 MeV
938 MeV
p S=0 Mesons
135 MeV

5. The Quark-Lepton Model of Matter
Explains the consistency of the known particles in all of their states. 3
families of quarks (3 “colors” each) and associated leptons.
All are spin-1/2 particles, quarks have non-integer charges
Mesons (q, q-bar)
q-bar:anti-quark
Nucleons (q,q,q)

6. 1 2 3 4
Spin ½ ½ 3/
Leptons
Baryons
Mesons
Hadrons m t X S L N
W X*Y* D hK p
K*w r 8 10
J/Y Y'
Y'’
Mass (GeV/c2)
n, e
Particle Spectrum
Simplified scheme of stable or unstable subatomic particles.
Families have different interactions, Leptons: weak+elm, Hadrons: weak+elm+strong
Each particle also has an anti-particle, with inverse quantum numbers.
“strange”

7. Quark Quantum Numbers All: spin=1/2, baryon number B=1/3 Q/e M/GeVc-2
Flavor
Q/e
M/GeVc-2 T T3 S C B*
Top u
+2/3
0.005 d
-1/3
0.009
- ½ s
0.175 -1 c
1.5 1 b
4.9 t
162
T,T3: isospin; S: strangeness; C: charm; B*: bottom qu.#, Top: top qu.#

8. Structure of Composite Particles
There are only 3-quark (q,q,q)  Baryons and quark-antiquark
configurations. No free quarks or higher quark multiplicities. _d _u _s u d s
quarks antiquarks
s= 1/2
Baryon Octet
s= 0
Meson Nonet _s d _u s u _d T3 d u s d n p S- S0 L0 S+ X- X0 p- K0 K+ K-
_K0 p0 h h’ p+ S

9. Baryon Decuplet
s = 3/2 d u s D- D0 D+
D++
S*-
S*0
S*+
X*-
X*0 W- S T3

10. Meson Wave Functions
Examples to interpret the graphic shorthand in these figures:
Meson spins are integer, vector sum of half-integer quark and anti-quark spins, and their integer orbital angular momentum l. In ground state, mostly l =0.

11. Baryon Wave Functions Examples to interpret the graphic shorthand:
These Baryon and Meson wave functions are schematic, do not have proper (anti-)symmetry property required by Pauli Principle: The total particle wave function
must be antisymmetric under quark exchange (quarks are fermions)

12. Pauli Principle and Color Coordinate
Quarks are Fermions  no two same quarks can be in the same state d D- u
D++
s3,T3
have both 3 identical fermions (same quarks) with same spins (S=3/2) and isospin (T3=+3/2) states
Violates Pauli Principle !?
Conclusion: There must be an additional quantum number (degree of freedom), “color”. Need 3 colors and their anti-colors
Color and complementary color (anti-color) add up to color-less (white) d _d
d quarks anti-d quarks

13. Color Wave Function d _d
d quarks anti-d quarks
D++ : Flavor and spin configurations symmetric, spatial configuration symmetric (no orbital angular momentum, l =0)
 color configuration must be antisymmetric. All colors are present with equal weights. All physical particles are “white.”
Necessity of color rules out combinations such as
There are no free quarks  Confinement

14. Gluons Bound quark systems (physical particles) by q-q interactions.
Field quanta: 8 Gluons (not actually pions!)
Spin and parity 1- like a photon.
Gluons carry color and the corresponding anticolor.
Color can be transferred but particle remains colorless. _q
qc’ q qc
gluon emission q-qbar creation self coupling changes color of the color charges
Usual conservation laws apply to reactions between quarks.

15. Gluon Exchange Gluons are exchanged back and forth between q-q,
time u _d r b g _r _b _g p+
_ r,b
_ b,g u r b g
_ b,g
_ r,g d p
Gluons are exchanged back and forth between q-q,
changing q colors and momenta dynamically
r, g, and b are visited with equal probability

16. Baryon Production with Strong Interactions
Typically: Energetic projectile hits nucleon/nucleus, new particles are produced.
Rules for strong interactions:
Energy, momentum, s, charge, baryon numbers, etc., conserved
q existing in system are rearranged, no flavor is changed
q-q-bar pairs can be produced u d _d s _s
time  u p S+ p+ K+
annihilation creation d, d-bar s, s-bar

17. Baryon Resonances
Typically: Energetic projectile hits nucleon/nucleus, intermediate particle is produced and decays into other particles.
u u d
_ d u
time  p p+
D++ produced as short-lived intermediate state, t = 0.5·10-23s
corresp. width of state: G = ħ/t = 120 MeV
This happens with high probability when a nucleon of 300 MeV/c, or a relative energy of 1232 MeV penetrates into the medium of a nucleus.  Resonance
u u u D++

18. Confinement and Strings
Why are there no free quarks? Earlier: symmetry arguments.
Property of gluon interaction between color charges (“string-like character).
Q: Can one dissociate a qq pair?
energy in strings proportional to length 0.9GeV/fm
field lines: color strings
successive q/q-bar creation, always in pairs!

19. Leptons Leptons have their own quantum number, L, which is conserved.
It seems likely, but is not yet known, whether electronic, muonic and tau lepton numbers are independently conserved in reactions and decays.

20. Quantum numbers are additive.
Conservation Laws
Quantum numbers are additive.
Anti-quarks have all signs of quark quantum numbers reversed, except spin and isospin.
Derived quantities:
In a reaction/transmutation, decay, the following quantities are conserved (before=after):
The total energy, momentum, angular momentum (spin),
The total charge, baryon number, lepton number

21. Conservation Laws in Decays
A  B + C
possible, if
mAc2 ≥ mBc2 + mCc2
Otherwise, balance must be supplied as kinetic energy.
Example: Conservation of charge, baryon number, lepton number in neutron decay.

22. Weak Interactions Weak bosons can change quark flavor
10-5 weaker than strong interaction, small probabilities for reaction/decays. Mediated by heavy (mass ~100GeV) intermediate bosons W± ,Z0.
Weak bosons can change quark flavor d u u Z0 W+ W- u s u
up-down strange-non-strange no flavor change conversion conversion carries +e carries –e carries no charge

23. Decays of W± and Z0 Bosons
Hadronic decays to quark pair are dominant (>90%), leptonic decays are weak. All possible couplings:

24. Examples of Weak Decays
Can you predict, which (if any) weak boson effects the change? p
_ne p ne e- n m- ? ? ?
time n p n nm e-
n-decay? neutrino scattering neutrino-induced
off protons? reaction off e-?

25. Examples of Weak Decays
Answer: Yes, all processes are possible. These are the bosons, p
_ne ne e- p n m- W- Z0 W+
time n p n nm e-
n-decay neutrino scattering neutrino-induced
off protons reaction off e-
Method:
Balance conserved quantities at the vortex, where boson originates. Remember W± carries away charge ±|e|.
Balance conserved quantities at lepton vortex.

26. Particle Production
In electron-positron collisions, particle-anti-particle pairs can be created out of collision energy, either via electromagnetic or weak interaction.
probability
 collision energy (GeV)
anti-fermion
fermion m- m+ m- m+ Z0 g Z0 e- e- e+ e- e+ e+
electromagnetic weak example

27. The Standard Model Interactions
The body of currently accepted views of structure and interactions of subatomic particles.
Interactions
Interaction
Coupling Charge
Field Boson
Mass/GeVc-2 Jp
strong
color
gluons (8) 1-
elmgn
electric (e)
photon (g)
weak
W+, W-, Z0
100 1
Weak interactions violate certain symmetries (parity, helicity) see later
Particles
Fermions
Family
Q/e
Color
Spin
Weak Isospin
Quarks
u c t
d s b
+2/3
-1/3
r, b, g
Leptons
ne nm nt
e m t -1
none

28. The Standard Model ct’d
Combine weak and elm interactions “electro-weak”
Type of isospin-symmetry: same particles carry weak and elm charge.
Vqq r
1 fm
Force range
Electromagnetic: ∞
Weak: 10-3fm
Strong qq force increases with distance
2mqc2
There are no free quarks. All free physical particles are colorless.

29. The End