Fundamental principles of particle physics

G.Ross, CERN, July09

Fundamental principles of particle physics

G.Ross, CERN, July09

• Introduction - Fundamental particles and interactions

• Symmetries I - Relativity

• Quantum field theory - Quantum Mechanics + relativity

• Theory confronts experiment - Cross sections and decay rates

• Symmetries II – Gauge symmetries, the Standard Model

• Fermions and the weak interactions

Outline

http://www.physics.ox.ac.uk/users/ross/cern_lectures.htm

Fundamental principles of particle physics

G.Ross, CERN, July09

Fundamental Interactions

† Short range

2

24

14 1372 5†

36

†

2

1

1010

sgs c

eem c

F p

N p

Strength

StrongElectromagnetic

Weak G mGravitational G m

π

π

αα

−

−

==

Fundamental principles of particle physics

G.Ross, CERN, July09

Fundamental Particles

2

24

14 1372 5†

36

†

2

1

1010

sgs c

eem c

F p

N p

Strength

StrongElectromagnetic

Weak G mGravitational G m

π

π

αα

−

−

==

Fundamental Interactions

Fundamental principles of particle physics

G.Ross, CERN, July09

Fundamental Particles

2

24

14 1372 5†

36

†

2

1

1010

sgs c

eem c

F p

N p

Strength

StrongElectromagnetic

Weak G mGravitational G m

π

π

αα

−

−

==

Fundamental Interactions

Strength Size

22e4 r 2Energy PE + KE = -

e

pmE π= +

Heisenberg'sUncertainty principle

p. rΔ Δ ≥

2 2

2e4 r 2-

em rE π≈ +

1 2 3 4 5

-25

-20

-15

-10

-5

E

r

2 2

2 3e4 r

0em rπ

⇒ − =

2

4 e

eem c m rcπα ≡ ≈

0Er

∂∂ =

pr r

p⇒ ≥ Δ ≥ ≥Δ

Units

8

34 2

3.10 m/sec10 kg m /sec

c−

==

Natural Units

Length : L Time : T

Energy : E or Mass : m

Choose units such that :

2

1 /1 . ( . / )

c L TE T M L T

== ≡

1 unit left : choose 9 -101 ( 10 electron volts = 1.6 10 J)E GeV= =

Natural Units

8 23

34 2 34 15

1 3.10 m/sec = 3.10 fm/sec1 10 kg m /sec = 10 J/sec GeV fmc

−

= == =

-10

-27

1

1 24

1 1.6 101 1.8 101 0.2

1 0.710 sec

energy of GeV Jmass of GeV kglength of GeV fmtime of GeV

−

− −

...typical of elementary particles

2

41

e e

eem c m rc m rπα = =

10 5

3

10 10

0.510atom

e

r m fmm GeV

−

−

2 24 10e

em πα −=

†

†

Dimensionless- same in any units

Fundamental Interactions and sizes

1m rα =

2 24 10e

em πα −= ≈10 5

3

10 10

0.510atom

e

r m fmm GeV

−

−

1510 11

nucleus

p

r m fmm GeV

−

2

4 1gstrong πα = ≈

Atomic binding :

Nuclear binding :

2

24

14 1372 5

2 36

1

1010

sgs c

eem c

F p

N p

Strength

StrongElectromagnetic

Weak G mGravitational G m

π

π

αα

−

−

==

Elementary particles

, ,e µ τ− − −

2/3 2 /3 2 /3, ,u c t

1/3 1/3 1/3, ,d s b− − −

Leptons :

Quarks :

, ,e µ τν ν ν

Isador Rabi 1937 “Who ordered the muon?”

Elementary particles

, ,e µ τ− − −Leptons :

Quarks : , ,u c t, ,u c t, ,u c t

, ,d s b, ,d s b, ,d s b

Hadrons : 3 strong “colour” charges

, ,e µ τν ν ν

Elementary forces

The strength of the force

Nucleus

Exchange forces

1 2 14( ) e e

em rV r π=

Experiments conducted in momentum space :

Vem( q ) Vem( r )e− ik .r∫ d 3r α

k2

e−

Electromagnetism

Photon “propagator”

Feynman diagram

e1

e2

γ

Nucleus

1 2 14( ) e e

em rV r π=

Experiments conducted in momentum space :

2. 3( ) ( ) i

em emV V e d α−∫ k rk

q r r

e−

2 2

" "Q

virtual photon≡ −k

2( )Q1QR

Exchange forces

Electromagnetism

e2

e1

γ

µ −

22 2

164 CM

d Md Eσ

π=

Ω

e+ e−

µ − µ+

Feynman diagram : Transition amplitude <final state| | initial state> IHQM

| | | |I IM H H e eααµ µ γ γ+ − + −∝ < > < >

| | (0,1, ,0)IH e e e iαγ + −< > ∝

| | (0,cos , ,sin )IH e iαµ µ γ θ θ+ −< > ∝

2( ) (1 cos )M RL RL e θ→ = +

θe+ e−

µ+

LH

LH

RH

RH

LH RH

γ

Application to a scattering processes e e µ µ+ − + −→

θe+ e−

µ+

µ −

( )2 2

22

1| 1 cos4 4 137unpolarised

CM

d ed Eσ α θ α

π= + = =

Ω

cosθ

21

4( ) sgstrong rV r π= (Q2)

q

q

2 2

" "Q

virtual gluon≡ −k

In momentum space :

g

2. 3( ) ( ) si

s sV V e d α−∫ k rk

q r r

Exchange forces

Strong interactions gs

gs

1 2 14( ) Zg g M r

weak rV r eπ−=

2 2. 3( ) ( ) weak

Z

iweak weak MV V e d α−

+∫ k rk

k r r

(Q2)

q

e−

" "virtual Z boson

In momentum space :

Z

21Z

F MG ∝

Exchange forces

Weak force

Yukawa interaction

g1

g2

1 2( ) m mgravity N rV r G=

(Q2)

2m

1m

" "virtual graviton

G

Exchange forces

Gravitational force

11 3 2

1/ 2 19

33

6.610 / .sec ..

( /

.

) 1

.

1

:

.210

0N Planck

N

Planck

fundamentalmaG m kg could prss c G GeV M

lengt

ovide scale

h cm l−

−

= =

≡

=

≡

=

!Planckor maybeM not fundamental

(Q2)

m2

1m

G 1 2( ) m m

gravity N rV r G=

Exchange forces

Gravitational force

References useful for future lectures:

Halzen & Martin, ‘Quarks & leptons’, Wiley, 1984

Aitchison & Hey, ‘Gauge Theories in Particle Physics’, Taylor and Francis, 2005

[Peskin & Schroeder, ‘Quantum Field Theory’, Addison-Wesley, 1995]