ParticleZoo

ParticleZoo

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)

scat

ter p

roba

bilit

y

energy of scattered electron

ground state of the proton

excited states of the proton

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).

Internal Nucleonic StructureInternal Nucleonic StructureThe 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)

ee 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

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

Particle SpectrumParticle Spectrum

0

1

2

3

4

Spin ½ ½ 3/2 0 1

Leptons Baryon

sMesons

Hadrons

Y*

8

10

8

J

'

'’

Mas

s (G

eV/c

2)

e

Simplified scheme of stable or unstable subatomic particles.Families have different interactions, Leptons: weak+elm, Hadrons: weak+elm+strongEach particle also has an anti-particle, with inverse quantum numbers.

, .

e ep pn nK K etc

“strange”

Quark Quantum NumbersQuark Quantum Numbers

Flavor Q/e M/GeVc-

2 T 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

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

0

S

T3d dd

u uu

ddu

udu

ds d

ds u

us u

dss

u ss

s ss

s = 3/2

Meson Wave FunctionsMeson Wave Functions

Examples to interpret the graphic shorthand in these figures:

0 12

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.

Baryon Wave FunctionsBaryon Wave FunctionsExamples 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)

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 !?

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 asThere are no free quarks ConfinementConfinement

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

GluonsGluonsBound 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.

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 dynamicallyr, g, and b are visited with equal probability

tim

e

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

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

time

u u d

_ d u

p +

p +

++ produced as short-lived intermediate state, = 0.5·10-23scorresp. width of state: = ħ/ = 120 MeVThis 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

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!

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.

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

Conservation Laws in DecaysConservation Laws in DecaysDecay A B + C possible, if mAc2 ≥ mBc2 + mCc2

Otherwise, balance must be supplied as kinetic energy.

22 2 2

, :

kin

Relativistic energy of particlewith 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 00 0 1 1 0 0 1 0 1

0 0 0 0 0

e

e

n p e n decay p n capture

BL L

Q e e e e

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

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:

Examples of Weak DecaysExamples of Weak DecaysCan you predict, which (if any) weak boson effects the change?

n

? ??

p

p e-_e

p

e-

e

tim

e

n-decay? neutrino scattering neutrino-inducedoff protons? reaction off e-?

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-inducedoff 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.

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)

prob

abilit

y

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

Interaction

Coupling Charge

Field Boson

Mass/GeVc-

2J

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 Spin Weak

Isospin

Quarks u 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

The Standard Model ct’dThe Standard Model ct’dCombine 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.

The EndThe End