Fundamental principles of particle physics G.Ross, CERN, July08.

Fundamental principles of particle physics

G.Ross, CERN, July08



• 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 Interactions

† Short range

2

2

4

14 137

2 5†

36

†

2

1

10

10

sgs c

eem c

F p

N p

Strength

Strong

Electromagnetic

Weak G m

Gravitational G m

π

π

αα

−

−

==

h

h

:

:

:

:



Fundamental Particles

2

2

4

14 137

2 5†

36

†

2

1

10

10

sgs c

eem c

F p

N p

Strength

Strong

Electromagnetic

Weak G m

Gravitational G m

π

π

αα

−

−

==

h

h

:

:

:

:




Fundamental Particles

2

2

4

14 137

2 5†

36

†

2

1

10

10

sgs c

eem c

F p

N p

Strength

Strong

Electromagnetic

Weak G m

Gravitational G m

π

π

αα

−

−

==

h

h

:

:

:

:


Strength Size

22e4 r 2Energy PE + KE = -

e

pmE π= +

Heisenberg's

Uncertainty principle

p. rΔ Δ ≥h

2 2

2e

4 r 2-

em rE π≈ + h

1 2 3 4 5

-25

-20

-15

-10

-5

E

r

2 2

2 3e

4 r0

em rπ⇒ − =h

2

4 e

eem c m rcπα ≡ ≈ h

h

0Er

∂∂ =

pr r

p⇒ ≥Δ ≥ ≥Δh h

Units

8

34 2

3.10 m/sec

10 kg m /sec

c−

=

=h

Natural Units

Length : LTime : T

Energy : Eor Mass : m

Choose units such that :

2

1 /

1 . ( . / )

c L T

E T M L T

=

= ≡h

1 unit left : choose9 -101 ( 10 electron volts = 1.6 10 J)E GeV= =

Natural Units

-10

-27

1

1 24

1 1.6 10

1 1.8 10

1 0.2

1 0.7 10 sec

energy of GeV J

mass of GeV kg

length of GeV fm

time of GeV

−

− −

;

;

;

;

...typical of elementary particles

2

41

e e

eem c m rc m rπα = =h

h ;

10 5

3

10 10

0.510

atom

e

r m fm

m 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

0.510

atom

e

r m fm

m GeV

−

−

: ;

;

1510 1

1nucleus

p

r m fm

m GeV

−: ;

;

2

4 1gstrong πα = ≈

Atomic binding :

Nuclear binding :

2

2

4

14 137

2 5

2 36

1

10

10

sgs c

eem c

F p

N p

Strength

Strong

Electromagnetic

Weak G m

Gravitational G m

π

π

αα

−

−

==

h

h

:

:

:

:

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 :

V

em( q ) : V

em( r )e−ik .r∫ d3r : 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( ) ( ) iem emV V e d α−∫ k r

kq r r: :

e−

2 2

" "

Q

virtual photon

≡−k

2( )Q

1Q

R:

Exchange forces

Electromagnetism

e2

e1

γ

μ−

2

2 2

1

64 CM

dM

d E

σπ

=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 cos

4 4 137unpolarisedCM

d e

d E

σ αθ 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( ) ( ) sis sV V e d α−∫ k r

kq 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 M

V V e d α−

+∫ k r

kk r r: :

(Q2)

q

e−

" "virtual Z boson

In momentum space :

Z

21

ZF M

G ∝

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

0

N Planck

N

Planck

fundamental

ma

G m kg could pr

ss c G GeV M

lengt

ovide scale

h cm l−

−

= =

≡

=

≡

=

h

!Planckor maybe M not fundamental

(Q2)

m2

1m

G1 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]

Fundamental principles of particle physics G.Ross, CERN, July08.

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