Fundamental principles of particle physics

G.Ross, CERN, July08

Fundamental principles of particle physics

G.Ross, CERN, July07

• 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, July07

Fundamental Interactions

† Short range

2

2

4

14 137

2 5†

36

†

2

1

10

10

sg

s c

eem c

F p

N p

Strength

Strong

Electromagnetic

Weak G m

Gravitational G m

!

!

"

"

#

#

=

=

!

!

"

"

"

"

Fundamental principles of particle physics

G.Ross, CERN, July07

Fundamental Particles

2

2

4

14 137

2 5†

36

†

2

1

10

10

sg

s c

eem c

F p

N p

Strength

Strong

Electromagnetic

Weak G m

Gravitational G m

!

!

"

"

#

#

=

=

!

!

"

"

"

"

Fundamental Interactions

Fundamental principles of particle physics

G.Ross, CERN, July07

Fundamental Particles

2

2

4

14 137

2 5†

36

†

2

1

10

10

sg

s c

eem c

F p

N p

Strength

Strong

Electromagnetic

Weak G m

Gravitational G m

!

!

"

"

#

#

=

=

!

!

"

"

"

"

Fundamental Interactions

Fundamental principles of particle physics

G.Ross, CERN, July07

Fundamental Particles

2

2

4

14 137

2 5†

36

†

2

1

10

10

sg

s c

eem c

F p

N p

Strength

Strong

Electromagnetic

Weak G m

Gravitational G m

!

!

"

"

#

#

=

=

!

!

"

"

"

"

Fundamental Interactions

Strength Size

22e4 r 2

Energy PE + KE = - e

p

mE

!= +

Heisenberg's

Uncertainty principle

p. r! ! " !

2 2

2

e

4 r 2-

em r

E!

" +!

1 2 3 4 5

-25

-20

-15

-10

-5

E

r

2 2

2 3

e

4 r0

em r!

" # =!

2

4e

e

em c m rc!" # $

!

!

0E

r

!

!=

pr r

p! " # " "#

! !

Units

8

34 2

3.10 m/sec

10 kg m /sec

c

!

=

=!

Natural Units

Length : LTime : T

Energy : Eor Mass : m

Choose units such that :

2

1 /

1 . ( . / )

c L T

E 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/sec

1 10 kg m /sec = 10 J/sec GeV fm

c

!

= =

= =! "

-10

-27

1

1 24

1 1.6 10

1 1.8 10

1 0.2

1 0.710 sec

energy of GeV J

mass of GeV kg

length of GeV fm

time of GeV

!

! !

!

!

!

!

...typical of elementary particles

2

4

1

e e

e

em c m rc m r!" = =

!

!"

10 5

3

10 10

0.510

atom

e

r m fm

m GeV

!

!

! "

"

2 2

410

e

em !"

#= !

†

†

Dimensionless-same in any units

Fundamental Interactions and sizes

1

m r! =

2 2

410

e

em !"

#= $

10 5

3

10 10

0.510

atom

e

r m fm

m GeV

!

!

! "

"

1510 1

1

nucleus

p

r m fm

m GeV

!! "

"

2

41

g

strong !" = #

Atomic binding :

Nuclear binding :

2

2

4

1

4 137

2 5

2 36

1

10

10

sg

s c

eem c

F p

N p

Strength

Strong

Electromagnetic

Weak G m

Gravitational G m

!

!

"

"

#

#

=

=

!

!

"

"

"

"

Elementary particles

, ,e µ !" " "

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

1/3 1/3 1/3, ,d s b

! ! !

Leptons :

Quarks :

, ,e µ !

" " "

Isador Rabi 1937 “Who ordered the muon?”

Elementary particles

, ,e µ !" " "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 !

" " "

Elementary forces

√α

√α The strength of the forceγ

Nucleus

Exchange forces

1 2 14

( )e e

em rV r

!=

Experiments conducted in momentum space :

V

em( q ) ! V

em( r )e! ik .r

" d3r ! #

k2

e!

Electromagnetism

Photon “propagator”

Feynman diagram

√α

√α

γ

Nucleus

1 2 14

( )e e

em rV r

!=

Experiments conducted in momentum space :

2

. 3( ) ( ) i

em emV V e d !"

#k r

kq r r! !

e!

2 2

" "

Q

virtual photon

! "k

2( )Q

1Q

R!

Exchange forces

Electromagnetism

µ !

2

2 2

1

64CM

dM

d E

!

"=

#

e+

e!

µ ! µ+

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

HQM

| | | |I I

M H H e e!

!µ µ " "+ # + #$ < > < >

| | (0,1, ,0)I

H e e e i!" + #

< > $

| | (0,cos , ,sin )I

H e i!µ µ " # #+ $

< > %

2( ) (1 cos )M RL RL e !" = +

!

e+

e!

µ+

LH

LH

RH

RH

LHRH

!

Application to a scattering processes e e µ µ+ ! + !"

!

e+

e!

µ+

µ !

( )2 2

2

2

1| 1 cos

4 4 137unpolarised

CM

d e

d E

! "# "

$= + = =

%

cos!

21

4( ) sg

strong rV r

!= (Q2)

q

√α

√α

q

2 2

" "

Q

virtual gluon

! "k

In momentum space :

g

2

. 3( ) ( ) si

s sV V e d

!"

#k r

kq r r! !

Exchange forces

Strong interactions

1 2 14

( ) Zg g M r

weak rV r e

!

"=

2 2

. 3( ) ( ) weak

Z

i

weak weakM

V V e d!"

+#k r

k

k r r! !

(Q2)

q

√α

√α

e!

" "virtual Z boson

In momentum space :

Z

2

1

ZF MG !

Exchange forces

Weak force

Yukawa interaction

1 2( )m m

gravity N rV r G=

(Q2)

2m

√α

√α

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!

!

= =

"

=

"

=

!

!Planckor maybeM not fundamental

(Q2)

2m

√α

√α

1m

G1 2( )m m

gravity N rV r G=

Exchange forces

Gravitational force