ParticleZoo

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Nucleons Are Not Elementary Nucleons Are Not Elementary Particles!Particles!

p

e-

e-

hadron jet

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!!

elasticx1/8.5

Each line in the energy spectrum of scattered electrons

corresponds to a different energy state of the proton.

Bartel etal. PL28B, 148 (1968)

scatt

er

pro

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ility

energy of scattered electron

ground state of the proton

excited states of the proton

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The Quark ModelThe 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).

September 01

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Internal Nucleonic StructureInternal Nucleonic Structure

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

p

e-e-

(1232)

(1450)

(1688)

e

e p e

e

938 MeV

1200 MeV

N

S=½

S=3/2

135 MeV

S=0 Mesons

N: one doublet with a splitting of onlym = 1.3 MeV

: one quadruplet with a splitting of only m = 8 MeV

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The Quark-Lepton Model of MatterThe Quark-Lepton Model of Matter

Nucleons (q,q,q) Mesons (q, q-bar)

q-bar:anti-quark

families of quarks (3 “colors” each) and associated leptons.

All are spin-1/2 particles, quarks have non-integer charges

Explains the consistency of the known particles in all of their states.

3

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Particle SpectrumParticle Spectrum

0

1

2

3

4

Spin ½ ½ 3/2 0 1

Leptons

Baryons

Mesons

Hadrons

Y*

8

10

8

J

'

'’

Mass (

GeV

/c2)

e

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.

, .

e e

p p

n n

K K etc

“strange”

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7Quark Quantum NumbersQuark Quantum Numbers

Flavor Q/e M/GeVc-

2T T3 S C B* Top

u +2/3 0.005 ½ ½ 0 0 0 0

d -1/3 0.009 ½ - ½ 0 0 0 0

s -1/3 0.175 0 0 -1 0 0 0

c +2/3 1.5 0 0 0 1 0 0

b -1/3 4.9 0 0 0 0 -1 0

t +2/3 162 0 0 0 0 0 1

T,T3: isospin; S: strangeness; C: charm; B*: bottom qu.#, Top: top qu.#

All: spin=1/2, baryon number B=1/3

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0 T3

Structure of Composite ParticlesStructure of Composite ParticlesThere are only 3-quark (q,q,q) Baryons and quark-antiquark configurations. No free quarks or higher quark multiplicities.

( , )q q

_d

_u

_su d s quarks

antiquarks

d du

u ud

ds

u us

s us

dss

dus

_s d

d_u d

_u

_u s

_u s

_s u

d_du

_u

s_s

d

n p

- 0

0

+

- 0

+-

K0

K+

K-

_K0

0

’

S

s= 1/2 s= 0

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0

S

T3d dd

u uu

ddu

udu

ds d

ds u

us u

dss

u ss

s ss

s = 3/2

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Meson Wave FunctionsMeson Wave Functions

Examples to interpret the graphic shorthand in these figures:

0 1

2

Mesons

ud ud simple qq structure

uu dd mixed qq state

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.

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Baryon Wave FunctionsBaryon Wave Functions

Examples to interpret the graphic shorthand:

0

1/ 2

3/ 2

s Baryons

p u u d n d d u qqq structure

s Baryons

u d d u u d aligned qqq state

These Baryon and Meson wave functions are schematic, do not have proper (anti-)symmetry property required by Pauli Principle: The total particle wave function( ) ( ) ( ) ( )all coordinates space flavor spin

must be antisymmetric under quark exchange (quarks are fermions)

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Pauli Principle and Color CoordinatePauli Principle and Color Coordinate

have both 3 identical fermions (same quarks) with same spins (S=3/2) and isospin (T3=+3/2) states

Quarks are Fermions no two same quarks can be in the same state

dd d

uu u

s3,T3 s3,T3

Conclusion: There must be an additional quantum number (degree of freedom), “color”. Need 3 colors and their anti-colors

, ,

Red Green Blue

Red Cyan Green Magenta Blue Yellow

Color and complementary color (anti-color) add up to color-less (white)d dd

_d

_d

_dd quarks anti-d

quarks

Violates Pauli Principle !?

September 01

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Color Wave FunctionColor Wave Function

++ : 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.”All physical particles are “white.”

rr

d dd_d

_d

_dd quarks anti-d

quarks

, ,

, , ,...

r r b g gb

r b g b r g r g b

Mesons

mix of u d u d u d

Baryons

p mix of u u d u u d u u d

Necessity of color rules out combinations such as

There are no free quarks ConfinementConfinement

( ),( , , ),.....q q q q

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14GluonsGluons

Bound quark systems (physical particles) by q-q interactions. Field quanta: 8 GluonsGluons (not actually pions!)Spin and parity 1- like a photon.

qc

qc’ q

_q

gluon emission q-qbar creation self coupling changes color of the color charges

Usual conservation laws apply to reactions between quarks.

Gluons carry color and the corresponding anticolor. Color can be transferred but particle remains colorless.

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Gluon ExchangeGluon Exchange

u_d

r

b

g

b

_r

_b

_g

_b

_

r,b

_

b,g

_ b,g

u

r

b

g b

_

b,g

_

b,g

_ r,g

g

g

g

r

b

u 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

tim

e

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Baryon Production with Strong InteractionsBaryon 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

uu

u

d_d

uu

u

s_s

p

Example

p K

annihilation creation d, d-bar s, s-bar

time

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Baryon ResonancesBaryon Resonances

Typically: Energetic projectile hits nucleon/nucleus, intermediate particle is produced and decays into other particles.

Example

p p

u u u ++

u u d

_ d u

tim

e

u u d

_ d u

p +

p +

++ produced as short-lived intermediate state, = 0.5·10-23s

corresp. width of state: = ħ/ = 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

September 01

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Confinement and StringsConfinement and StringsWhy 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!

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LeptonsLeptons

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.

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Conservation LawsConservation LawsQuantum numbers are additive.

Anti-quarks have all signs of quark quantum numbers reversed, except spin and isospin.Derived quantities:

3 (1 2) *Charge Q e T B S C B Top

Hypercharge Y B S

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

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Conservation Laws in DecaysConservation Laws in Decays

Decay A B + C possible, if mAc2 ≥ mBc2 + mCc2

Otherwise, balance must be supplied as kinetic energy.

22 2 2

, :

kin

Relativistic energy of particle

with rest massm momentum p

E pc mc E mc

Example: Conservation of charge, baryon number, lepton number in neutron decay.

1 1 0 0 1 1 0 1 0

0 0 1 1 0 0 1 0 1

0 0 0 0 0

e

e

n p e n decay p n capture

B

L L

Q e e e e

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Weak InteractionsWeak Interactions10-5 weaker than strong interaction, small probabilities for reaction/decays. Mediated by heavy (mass ~100GeV) intermediate bosons W± ,Z0. Weak bosons can change quark flavor

u

d

W+ W- Z0

u

s

u

u

up-down strange-non-strange no flavor change conversion conversion carries +e carries –e carries no charge

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Decays of WDecays of W± ± and Zand Z0 0 BosonsBosons

0

, , , , , ,

, '

, , , , , , ), ( , ,

, ), ( ,

, ( , ), ( , ), , ), ( , , ( ,

, , ,

), ( ,

, , , ,

, , ,

, , , , ,

,

,

e e

e

el eW

q q d u s c b

l e leptonic decaysW

q q d u s c b t hadronic decay

l l e e

Z

q q d d u u s s c c b b t t

t

s

)

Hadronic decays to quark pair are dominant (>90%), leptonic decays are weak. All possible couplings:

September 01

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Examples of Weak DecaysExamples of Weak Decays

Can you predict, which (if any) weak boson effects the change?

n

? ??

p

pe-

_e

p

e-

e

tim

e

n-decay? neutrino scattering neutrino-induced

off protons? reaction off e-?

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Examples of Weak DecaysExamples of Weak DecaysAnswer: Yes, all processes are possible. These are the bosons,

n

W- W+Z0

p

p e- _e

p

e-

e

tim

e

n-decay neutrino scattering neutrino-induced

off protons reaction off e-

Method:Method:

•Balance conserved quantities at the vortex, where boson originates. Remember W± carries away charge ±|e|.

•Balance conserved quantities at lepton vortex.

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Particle ProductionParticle Production

e- e+

- +

e- e+

fermion

e- e+

- +

anti-fermion

electromagnetic weak example

In electron-positron collisions, particle-anti-particle pairs can be created out of collision energy, either via electromagnetic or weak interaction.

collision energy (GeV)

pro

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The Standard ModelThe Standard ModelThe body of currently accepted views of structure and interactions of subatomic particles.

Interaction

Coupling Charge

Field Boson

Mass/GeVc-

2

J

strong color gluons (8) 0 1-

elmgn electric (e) photon () 0 1-

weak weak W+, W-, Z0 100 1

Interactions

Fermions

Family Q/e Color SpinWeak

Isospin

Quarksu c td s b

+2/3-1/3

r, b, g ½ ½

Leptons

e e

0-1

none ½ ½

Particles

Weak interactions violate certain symmetries (parity, helicity) see later

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The Standard Model ct’dThe Standard Model ct’d

Combine weak and elm interactions “electro-weak”Type of isospin-symmetry: same particles carry weak and elm charge.

Force range

Electromagnetic: ∞

Weak: 10-3fm

Strong qq force increases with distance

2mqc2

Vqq

r1 fm

0

There are no free quarks. All free physical particles are colorless.

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The EndThe End