Particle Phenomenology

7/29/2019 Particle Phenomenology

1/193

S e l e c t e d t o p i c s i n

P h e n o m e n o l o g y

S t e f a n o M o r e t t i

S c h o o l o f P h y s i c s a n d A s t r o n o m y

U n i v e r s i t y o f S o u t h a m p t o n

S o u t h a m p t o n S O 1 7 1 B J , U K

a n d

P a r t i c l e P h y s i c s D e p a r t m e n t

R u t h e r f o r d A p p l e t o n L a b o r a t o r y

C h i l t o n , D i d c o t , O x o n O X 1 1 0 Q X


2/193

F o r e w o r d

T h e t r a d i t i o n i s t h a t t h i s c o u r s e i s g i v e n u s i n g t r a n s p a r e n c i e s ,

u n l i k e t h e o t h e r c o u r s e s i n t h e s c h o o l a n d t h a t t h e t r a n s p a r e n -

c i e s a r e s i m p l y r e p r o d u c e d i n t h e p r o c e e d i n g s . T h i s y e a r I

h a v e u s e d a m i x t u r e o f s l i d e s a n d w h i t e b o a r d . T h e s e n o t e s a t -

t e m p t t o c o m b i n e a l l t h e m a t e r i a l I u s e d t h r o u g h o u t t h e c o u r s e

a n d a l s o c o n t a i n s o m e w h i c h I c o u l d n o t t r e a t e x t e n s i v e l y i n

t h e l e c t u r e t h e a t e r . I n p r e p a r i n g m y c o u r s e I u s e d m a t e r i a l

f r o m N i g e l G l o v e r , M i k e S e y m o u r a n d M i c h a e l K r a m e r , w h o

p r e c e d e d m e a s l e c t u r e r s o f t h e P h e n o m e n o l o g y c o u r s e . I a m

g r e a t l y i n d e b t e d t o t h e m f o r l e t t i n g m e u s i n g i t . I h a v e a l s o

r i p p e d o s o m e s l i d e s f r o m G a v i n S a l a m ' s t a l k s a n d p r e s e n t a -

t i o n s f o r s o m e o f t h e Q C D t o p i c s a n d f r o m L a u r a R e i n a i n t h e

c a s e o f H i g g s p h y s i c s . A s p e c i a l t h a n k g o e s t o D a n T o v e y f o r

l e t t i n g m e u s e m a n y s l i d e s f r o m o n e o f h i s t a l k s f o r t h a t v e r y

l a s t l e c t u r e t h e d a y a f t e r t h e s c h o o l d i n n e r ( a n d a f t e r m a t h ! ) .

T h e r e f e r e n c e s I h a v e u s e d t o p r e p a r e t h e c o u r s e a r e c o l l e c t e d

a t t h e e n d a n d s h o u l d i d e a l l y p r o v i d e a g o o d s t a r t i n g p o i n t

f o r t h o s e w h o w a n t t o l e a r n m o r e a b o u t s o m e o f t h e t o p i c s . I

w o u l d l i k e t o t h a n k T i m G r e e n s h a w f o r o r g a n i s i n g t h e s c h o o l

s o w e l l a n d f o r h i s s u p p o r t t h r o u g h o u t . L o t s o f t h a n k s a l s o

g o t o t h e o t h e r l e c t u r e r s , t o t h e t u t o r s a n d p r i m a r i l y t o t h e

s t u d e n t s . F i n a l l y , I a m g r a t e f u l t o M a r g a r e t E v a n s f o r a l l t h e

p r a c t i c a l a r r a n g e m e n t s a n d f o r c o p i n g w i t h m y e x t r e m e l a t e -

n e s s i n p r e p a r i n g t h e s e n o t e s : I w a s a g a i n t h e l a s t o n e . . .


3/193

I n t r o d u c t i o n

K a n t ' s C r i t i q u e o f P u r e R e a s o n ( a s i n t e r p r e t e d b y W i k i p e d i a ) :

1 . P h e n o m e n o n : P h e n o m e n a c o n s t i t u t e t h e w o r l d a s w e e x -

p e r i e n c e i t , a s o p p o s e d t o t h e w o r l d a s i t e x i s t s i n d e -

p e n d e n t l y o f o u r e x p e r i e n c e s ( t h i n g - i n - t h e m s e l v e s , ' d a s

d i n g a n s i c h ' ) . H u m a n s c a n n o t , a c c o r d i n g t o K a n t , k n o w

t h i n g s - i n - t h e m s e l v e s , o n l y t h i n g s a s w e e x p e r i e n c e t h e m .

2 . N o u m e n o n : \ T h i n g i n i t s e l f ( D i n g a n s i c h ) " i s a n a l -

l e g e d l y u n k n o w a b l e , u n d e s c r i b a b l e r e a l i t y t h a t , i n s o m e

w a y , l i e s " b e h i n d " o b s e r v e d p h e n o m e n a . N o u m e n a a r e

s o m e t i m e s s p o k e n o f , t h o u g h t h e v e r y n o t i o n o f i n d i v i d -

u a t i n g i t e m s i n " t h e n o u m e n a l w o r l d " i s p r o b l e m a t i c ,

s i n c e t h e v e r y n o t i o n s o f n u m b e r a n d i n d i v i d u a l i t y a r e

a m o n g t h e c a t e g o r i e s o f t h e u n d e r s t a n d i n g , w h i c h a r e

s u p p o s e d t o a p p l y o n l y t o p h e n o m e n a , n o t n o u m e n a .

( T h e c o n c e p t o f ' P h e n o m e n a ' l e d t o a t r a d i t i o n o f p h i l o s -

o p h y k n o w n a s P h e n o m e n o l o g y : H e g e l , H e i d e g g e r , e t c . {

w h i c h w e w i l l i g n o r e h e r e ! )

P h e n o m e n o n i n t h e g e n e r a l s e n s e : s t a n d s f o r a n y o b s e r v a b l e

e v e n t ; p h e n o m e n a m a k e u p t h e r a w d a t a o f s c i e n c e .

F a m o u s q u o t e s : " N o p h e n o m e n o n i s a p h e n o m e n o n u n t i l i t

i s a n o b s e r v e d p h e n o m e n o n " ( N i e l s B o h r ) .

( I w i l l n o n e t h e l e s s d i s c u s s S u p e r s y m m e t r y . . . )


4/193

M y d e n i t i o n o f ( h i g h e n e r g y ) p h e n o m e n o l o g y

B r a n c h o f h i g h - e n e r g y p h y s i c s t h a t s e e k s k n o w l e d g e b y :

1 E x p l o i t i n g t h e h i n t s a n d c l u e s a v a i l a b l e i n o b s e r v a b l e p h e -

n o m e n a ( a k a e x p e r i m e n t a l d a t a ) , w i t h o u t a n y p r e c o n c e p t i o n

o n t h e t h e o r y g o v e r n i n g t h e l a t t e r .

2 P a r a m e t r i s e t h e o r i e s i n t o a s e t o f o b s e r v a b l e s ( p r e d i c t i o n s )

t h a t c a n d i r e c t l y b e t e s t e d b y e x p e r i m e n t , t h u s c o n r m i n g o r

d i s p r o v i n g t h e f o r m e r .

P h e n o m e n o l o g y : b r i d g e b e t w e e n t h e o r y a n d e x p e r i m e n t !


5/193

O u t l i n e

I n t r o d u c t i o n : T h e S t a n d a r d M o d e l & B e y o n d

T e s t s o f t h e S t a n d a r d M o d e l

{ Q C D : r u n n i n g c o u p l i n g ; i n f r a r e d s a f e t y ; f a c t o r i s a t i o n ; p a r t o n d i s -

t r i b u t i o n f u n c t i o n s ; j e t p r o d u c t i o n ; s e a r c h e s f o r n e w p h y s i c s

{ E l e c t r o - W e a k ( E W ) P h y s i c s : w e a k i n t e r a c t i o n s f r o m u n i -

t a r i t y ; Z l i n e - s h a p e ; p r e c i s i o n t e s t s ; W b o s o n p r o d u c t i o n ; i n d i r e c t

s e a r c h f o r t h e H i g g s b o s o n

H i g g s B o s o n H u n t i n g

{ T h e H i g g s m e c h a n i s m

{ T h e H i g g s p i c t u r e

{ T h e H i g g s p r o l e

{ C o l l i d e r s e a r c h e s

S u p e r s y m m e t r y ( S U S Y )

{ W h y s u p e r s y m m e t r y

{ T h e h i e r a r c h y p r o b l e m a n d g a u g e c o u p l i n g u n i c a t i o n

{ T h e M i n i m a l S u p e r s y m m e t r i c S t a n d a r d M o d e l ( M S S M )

{ I n d i r e c t s e a r c h e s : g ? 2

{ C o l l i d e r s e a r c h e s

E p i l o g u e


6/193

I n t r o d u c t i o n

C u r r e n t t h e o r e t i c a l f r a m e w o r k o f p a r t i c l e p h y s i c s i s

S t a n d a r d M o d e l ( S M )

S M i s S U ( 3 ) S U ( 2 ) U ( 1 ) g a u g e t h e o r y w i t h

M a t t e r e l d s :

u

d

L

s

c

L

b

t

L

d

R

u

R

s

R

c

R

b

R

t

R

( q u a r k s )

e

e

L

L

L

e

R

R

R

( l e p t o n s )

F o r c e e l d s :

; W

; Z ; g ( V e c t o r b o s o n s )

a n d a

H ( H i g g s s c a l a r )

Q : W h y d o w e b e l i e v e i n t h e S t a n d a r d M o d e l ?

A : B e c a u s e c o n r m e d b y e x p e r i m e n t !

Q : W h y l o o k B e y o n d t h e S t a n d a r d M o d e l ( B S M ) ?

A : B e c a u s e S M l a c k s e x p l a n a t i o n o f f u n d a m e n t a l q u a n t i t i e s

!


7/193

S M F l a w s

S M d o e s n o t e x p l a i n q u a n t u m n u m b e r s :

! E M c h a r g e , w e a k i s o s p i n , h y p e r c h a r g e a n d c o l o u r

C o n t a i n s ( a t l e a s t ) 1 9 a r b i t r a r y p a r a m e t e r s :

3 g a u g e c o u p l i n g s

1 C P - v i o l a t i n g v a c u u m a n g l e

6 q u a r k m a s s e s

3 c h a r g e d l e p t o n m a s s e s

3 w e a k m i x i n g a n g l e s

1 C P - v i o l a t i n g C K M p h a s e

1 W m a s s

1 H i g g s m a s s

a n d ( p o s s i b l y ) 9 m o r e p a r a m e t e r s i n t h e n e u t r i n o s e c t o r :

3 n e u t r i n o m a s s e s

3 n e u t r i n o m i x i n g a n g l e s

3 C P - v i o l a t i n g p h a s e s

M o r e c r u c i a l l y : i t d o e s n o t i n c o r p o r a t e g r a v i t y !


8/193

B e y o n d t h e S t a n d a r d M o d e l

T h r e e k i n d o f p r o b l e m s :

1 . M a s s :

W h a t i s t h e o r i g i n o f p a r t i c l e m a s s e s

A r e t h e m a s s e s d u e t o a H i g g s b o s o n

W h a t s e t s t h e s c a l e o f f e r m i o n m a s s e s

2 . U n i c a t i o n :

I s t h e r e a t h e o r y u n i f y i n g a l l p a r t i c l e i n t e r a c t i o n s

3 . F l a v o u r :

W h y a r e t h e r e s o m a n y t y p e s o f q u a r k s a n d l e p t o n s

W h a t i s t h e o r i g i n o f C P - v i o l a t i o n

S o l u t i o n s s h o u l d i n c o r p o r a t e g r a v i t y ( s p a c e - t i m e o r i g i n / s t r u c t u r e

S t r i n g t h e o r y b e s t ( o n l y ) c a n d i d a t e , b u t n o t y e t p r e d i c t i v e !

S u p e r s y m m e t r y ( S U S Y ) t o p l a y a r o l e i n s o l v i n g p r o b l e m s :

1 . ( G a u g e ) c o u p l i n g u n i c a t i o n b e s t w i t h l i g h t s p a r t i c l e s ;

2 . M a s s h i e r a r c h y n e e d s l i g h t s p a r t i c l e s f o r s t a b i l i s a t i o n ;

3 . S U S Y s e e m s e s s e n t i a l f o r t h e c o n s i s t e n c y o f s t r i n g t h e o r y .

J a r g o n : a s p a r t i c l e i s a S U S Y p a r t i c l e !


9/193

W h a t N e w P h y s i c s ( N P ) ?

W h i c h w a y t o g o a b o u t

1 . C o m e u p w i t h t h e o r y , d e v i s e m o d e l f o r i t , g e t o u t p r e -

d i c t i o n s , c o m p a r e w i t h e x p e r i m e n t !

2 . T r e a t S M a s e e c t i v e t h e o r y b e l o w s o m e h i g h s c a l e :

N P d e s c r i b e d b y o p e r a t o r s o f d i m e n s i o n 6 s u p p r e s s e d

b y p o w e r s o f E

2

=

2

( E ! r e l e v a n t e n e r g y ) .

H i s t o r i c e x a m p l e : F e r m i ' s t h e o r y o f w e a k i n t e r a c t i o n s ,

?

! e

?

e

d e c a y d e s c r i b e d b y e e c t i v e L a g r a n g i a n :

L =

G

F

p

2

( 1 ?

5

) ] e

( 1 ?

5

)

e

]

F r o m e x p e r i m e n t G

F

1 1 7 1 0

? 5

G e V

? 2

( F e r m i c o u p l i n g ) .

A s M

W

, W a p p e a r s a s d e v i a t i o n s f r o m e e c t i v e t h e o r y .

H e n c e , p r e c i s i o n t e s t s o f t h e S M c a n r e v e a l N P !

C r u c i a l q u e s t i o n f o r p h e n o m e n o l o g y i s :

W h a t i s t h e s c a l e o f n e w p h y s i c s


10/193

T e s t o f t h e S M : Q C D

O u t l i n e

I m p o r t a n c e o f Q C D

T h e Q C D c o u p l i n g

e

+

e

?

! h a d r o n s

I n f r a r e d s a f e q u a n t i t i e s

J e t s

P a r t o n s h o w e r

H a d r o n i s a t i o n

D e e p l y i n e l a s t i c s c a t t e r i n g

H a d r o n - H a d r o n c o l l i s i o n s

N e w p h y s i c s s e a r c h e s


11/193

I m p o r t a n c e o f Q C D

Q C D i s t h e c o r r e c t

t h e o r y o f s t r o n g i n t e r a c t i o n s

(

i n t h e d e s c r i b e d s e n s e o f a l o w - e n e r g y e e c t i v e t h e o r y )

! W h y Q C D s t u d i e s ?

1 ) A Q u a n t u m F i e l d T h e o r y ( Q F T ) w i t h u n i q u e f e a t u r e s :

{ a s y m p t o t i c f r e e d o m

{ i n f r a r e d s l a v e r y ( c o n n e m e n t )

2 ) W e n e e d t o u n d e r s t a n d Q C D a l s o t o s e a r c h f o r N P :

{ f o r n e w p a r t i c l e s h a d r o - p r o d u c t i o n ( T e v a t r o n a n d L H C )

{ t o p r e d i c t t h e S M b a c k g r o u n d s t o N P s i g n a l s

Q C D d e g r e e s o f f r e e d o m : q u a r k s & g l u o n s ( a k a p a r t o n s ) .

W i l l s t u d y t h e i r i n t e r a c t i o n s i n e

+

e

?

, e

p , p p a n d p p

( S e e N i c k ' s c o u r s e f o r L a g r a n g i a n & F e y n m a n r u l e s )


12/193

T h e Q C D L a g r a n g i a n i s g i v e n b y :

L = ?

1

4

F

A

F

A

+

X

a v o u r s

q

a

( i D = ? m )

a b

q

b

+ L

g a u g e ? x i n g

+ L

g h o s t

w h e r e F

A

i s t h e e l d s t r e n g t h t e n s o r d e r i v e d f r o m t h e g l u o n

e l d A

a

,

F

A

= @

A

A

? @

A

A

? g f

A B C

A

B

A

a n d t h e i n d i c e s A ; B ; C r u n o v e r t h e e i g h t c o l o u r d e g r e e s o f

f r e e d o m o f t h e g l u o n e l d . T h e q u a r k e l d s q

a

a r e i n t h e

t r i p l e t r e p r e s e n t a t i o n o f t h e S U ( 3 ) c o l o u r g r o u p a n d D i s t h e

c o v a r i a n t d e r i v a t i v e :

( D

)

a b

= @

a b

+ i g ( t

c

A

c

)

a b

T h e t a r e m a t r i c e s i n t h e f u n d a m e n t a l r e p r e s e n t a t i o n o f S U ( 3 )

a n d s a t i s f y :

t

A

; t

B

] = i f

A B C

t

C

F o r a d i s c u s s i o n o f t h e g a u g e - x i n g a n d g h o s t t e r m s o f t h e

Q C D L a g r a n g i a n s e e N i c k ' s c o u r s e .


13/193

T h e F e y n m a n r u l e s c a n b e d e r i v e d f r o m t h e Q C D L a -

g r a n g i a n :

? ? ? ? ? ? ? ? ? ? ?

A ; p B ;

A B

"

? g

+ ( 1 ? )

p

p

p

2

+ i "

#

i

p

2

+ i "

A p B

-

A B

i

p

2

+ i "

a ; i p b ; j

-

a b

i

( 6 p ? m + i " )

j i

?

?

?

B ;

A ; C ;

q

rp

?

?

?

?

?

? g f

A B C

h

g

( p ? q )

+ g

( q ? r )

+ g

( r ? p )

i

( a l l m o m e n t a i n c o m i n g )

?

?

?

?

?

?

?

?

?

?

A ; B ;

C ; D ;

? i g

2

f

X A C

f

X B D

( g

g

? g

g

)

? i g

2

f

X A D

f

X B C

( g

g

? g

g

)

? i g

2

f

X A B

f

X C D

( g

g

? g

g

)

A ;

B C

q

g f

A B C

q

?

?

?

?

?

? @

@

@

@

@

@

R

?

?

?

A ;

b ; i c ; j

?

?

?

?

?

?

@

@

@

@

@

@R

? i g

t

A

c b

(

)

j i

?

?

?


14/193

Tr(tAtB) = TRAB , TR =

1

2

A

AtAabt

Abc = CFac , CF =

N2c 1

2Nc=

4

3a

C,D f

ACDfBCD = CAAB , CA = Nc = 3

A

tAabtAcd =

1

2bcad

1

2Ncabcd (Fierz)

b a

c d

=


15/193

T h e Q C D c o u p l i n g

. . . i s r u n n i n g !

Q u a n t u m c o r r e c t i o n s a l t e r p a r t i c l e m a s s e s a n d c o u p l i n g s .

U l t r a v i o l e t d i v e r g e n c e s r e m o v e d b y r e n o r m a l i s a t i o n .

R e n o r m a l i s a t i o n i n t r o d u c e s a m a s s s c a l e { t h e s u b t r a c t i o n

p o i n t o f U V d i v e r g e n c e s { a n d t h e r e n o r m a l i s e d c o u p l i n g

s

d e p e n d s o n :

s

!

s

( ) =

1

0

l n (

2

=

2

)

;

0

= ( 1 1 N

C

? 2 n

f

) = 1 2 ; N

C

= 3 ; n

f

= # o f a c t i v e a v o u r s

Q C D

( 2 0 0 M e V ) i s a n i n t e g r a t i o n c o n s t a n t :

2

d

s

d

2

(

s

) = ?

0

2

s

+

A s y m p t o t i c f r e e d o m :

s

! 0 a s ! 1

! w e c a n u s e p e r t u r b a t i o n t h e o r y f o r p r o c e s s e s i n v o l v i n g

l a r g e m o m e n t u m s c a l e s ( s m a l l d i s t a n c e s ) .

S i g n o f i s c r u c i a l : i n Q E D ,


16/193

R u n n i n g o f

s

h a s b e e n e s t a b l i s h e d e x p e r i m e n t a l l y !

QCD

O( )

251 MeV

178 MeV

MS(5)

( )s Z

0.1215

0.1153

0.1

0.2

0.3

0.4

0.5

s(Q)

1 10 100

Q [GeV]

Heavy QuarkoniaHadron Collisions

e+e- AnnihilationDeep Inelastic Scattering

NLO

NNLO

TheoryData

Lattice

213 MeV 0.1184s4 {

M e a s u r e m e n t s o f

S

a r e r e v i e w e d i n E S W . T h e m o r e

r e c e n t c o m p i l a t i o n o f B e t h k e i s s h o w n a b o v e . E v i d e n c e

t h a t

S

( Q )h a s a l o g a r i t h m i c f a l l - o w i t h

Qi s p e r s u a s i v e .

{ T y p e s e t b y F o i l T

E

X { 1 9

( C o m p i l a t i o n o f d a t a b y S i g g i B e t h k e )

B u t h o w d o w e m e a s u r e

s


17/193

e

+

e

?

! h a d r o n s

B u t Q C D F e y n m a n r u l e s t e l l u s o n l y a b o u t p a r t o n s !

H a d r o n f o r m a t i o n ( l o n g d i s t a n c e ) i s n o t p e r t u r b a t i v e !

! h o w t o c a l c u l a t e e

+

e

?

! h a d r o n s

P l e n t y o f p h y s i c s b e t w e e n p a r t o n s a n d h a d r o n s !

e+

e-

Hadronization

Resonance

Decays

Parton Shower

O(s2) Leading-Log QCD

/Z

electro-weak

E a c h e v e n t h a s d i e r e n t h a d r o n i c n a l s t a t e !

! h o w t o s u m o v e r a l l o f t h e s e


18/193

S y m m e t r i e s c a n h e l p u s !

! M a t r i x E l e m e n t ( M E ) t o p r o d u c e n h a d r o n s h

1

: : : h

n

:

M f v ( p

e

+

) e

u ( p

e

?

) g

? g

q

2

T

( n ; q ; f p

h

1

: : : p

h

n

g ) ;

w i t h T

p a r a m e t r i s a t i o n o f t h e u n k n o w n p a r t .

! G i v e s t o t a l c r o s s s e c t i o n :

=

1

2 s

1

4

e

2

s

2

T r ( 6 p

e

+

6 p

e

?

)

X

n

Z

d P S

n

T

( n ; q ; f p

h

1

: : : p

h

n

g ) T

( n ; q ; f p

h

1

: : : p

h

n

g )

! D e n e : H

( q )

P

n

R

d P S

n

T

T

! I m p o s e L o r e n t z c o v a r i a n c e :

H

= A g

+ B q

q

; ( A ; B f u n c t i o n s o n l y o f q

2

)

! I m p o s e g a u g e i n v a r i a n c e :

q

H

= q

H

= 0 ) A = ? q

2

B

! H e n c e , =

e

2

2 s

B ( s ) a n d B ( s ) d i m e n s i o n l e s s .

! G i v e s f u n d a m e n t a l p r e d i c t i o n :

R R ( e

+

e

?

) =

( e

+

e

?

! h a d r o n s )

( e

+

e

?

!

+

?

)

= c o n s t a n t ;

w i t h o u t k n o w i n g a n y t h i n g a b o u t h a d r o n i n t e r a c t i o n s !


19/193

e

+

e

?

! h a d r o n s a t l e a d i n g o r d e r

0

=

4

2

3 s

N

C

X

q

e

2

q

( i f f = q )

) R

0

0

( e

+

e

?

! h a d r o n s )

0

( e

+

e

?

!

+

?

)

= N

C

X

q

e

2

Q

! r s t e v i d e n c e f o r c o l o u r ( N

C

= 3 ) !

K i n e m a t i c a l l y a l l o w e d i f

p

s > 2 m

q

, s t e p s a t

p

s = 2 m

q

R

Ecm (GeV)

TOPAZVENUS

1234

10 15 5510 20 25 30 35 40 45 50 602

3

4

5

R

2 3 4 5 6 71

2

3

4

5

6

MARK IMARK I/LGW

MEA

2

{

J/(1S) (2S)

(nS)n=

AMY

CELLO

CLEO

CRYSTAL BALL

CUSB

DASP II

JADE

LENA

MAC

MARK J

PLUTO

TASSO

( e . g .

p

s = 3 4 G e V , R =

1 1

3

, c f P E T R A d a t a : 3 8 8 0 0 3 )


20/193

R a t t h e Z p e a k

C a n a l s o t e l l u s a b o u t E W c o u p l i n g s :

R = N

C

P

q

A

q

A

= 2 0 0 9 5 ; A

f

= v

2

f

+ a

2

f

( c f L E P a v e r a g e : 2 0 7 7 5 0 0 2 7 )

I n g e n e r a l , s e n s i t i v e t o ? Z i n t e r f e r e n c e :

( i n f a c t , R = 1 9 . 9 8 4 o n Z p e a k )


21/193

e

+

e

?

! h a d r o n s b e y o n d l e a d i n g o r d e r

s

l a r g e s t c o u p l i n g : e x p e c t Q C D c o r r e c t i o n s l a r g e s t !

! s t a r t w i t h t h e m !

A t O (

s

) :

-

V i r t u a l c o r r e c t i o n s : i n t e r f e r e t r e e - l e v e l d i a g r a m s w i t h o n e -

l o o p o n e s i n ( a )

! c a n b e n e g a t i v e

R e a l c o r r e c t i o n s : s q u a r e t r e e - l e v e l d i a g r a m s i n ( b )

! p o s i t i v e d e n i t e


22/193

( b ) r e a l g l u o n e m i s s i o n

3 - b o d y p h a s e s p a c e : d

3

= ] d d d d x

1

d x

2

w h e r e ; ; a r e E u l e r a n g l e s a n d x

1

= 2 E

q

=

p

s a n d x

2

= 2 E

q

=

p

s

a r e e n e r g y f r a c t i o n s o f n a l - s t a t e q u a r k a n d a n t i q u a r k .

A p p l y i n g F e y n m a n r u l e s a n d i n t e g r a t i n g o v e r E u l e r a n g l e s :

q q g

= 3

0

C

F

s

2

Z

d x

1

d x

2

x

2

1

+ x

2

2

( 1 ? x

1

) ( 1 ? x

2

)

w i t h i n t e g r a t i o n r e g i o n 0 x

1

; x

2

1

I n t e g r a l i s d i v e r g e n t a t x

1

; x

2

= 1 :

1 ? x

1

= x

2

x

3

( 1 ? c o s

q g

) = 2 ;

1 ? x

2

= x

1

x

3

( 1 ? c o s

q g

) = 2 ;

w h e r e x

3

= 2 E

g

=

p

s ( E

g

g l u o n e n e r g y ) a n d

i g

( i = 1 ; 2 ) a r e a n g l e s

b e t w e e n g l u o n a n d q u a r k s .

! c o l l i n e a r d i v e r g e n c e :

q g

! 0 o r

q g

! 0

! s o f t d i v e r g e n c e : E

g

! 0

S i n g u l a r i t i e s i n d i c a t e b r e a k d o w n o f p e r t u r b a t i o n t h e o r y

w h e n m a s s s c a l e s a p p r o a c h .

F o r t u n a t e l y , c o l l i n e a r / s o f t r e g i o n s d o n o t m a k e i m p o r t a n t

c o n t r i b u t i o n s t o t o t a l c r o s s s e c t i o n :

! t h e y c a n c e l !


23/193

M a k e i n t e g r a l n i t e u s i n g e . g . d i m e n s i o n a l r e g u l a r i s a t i o n :

D = 4 ? 2 )

q q g

= 3

0

C

F

s

2

H ( )

Z

d x

1

d x

2

( 1 ? ) ( x

2

1

+ x

2

2

) + 2 ( 1 ? x

3

)

( 1 ? x

3

)

( 1 ? x

1

) ( 1 ? x

2

) ]

1 +

w h e r e H ( ) =

3 ( 1 ? ) ( 4 )

2

( 3 ? 2 ) ? ( 2 ? 2 )

= 1 + O ( )

H e n c e

q q g

= 3

0

C

F

s

2

H ( )

2

2

+

3

+

1 9

2

?

2

+ O ( )

! s o f t / c o l l i n e a r d i v e r g e n c e s a r e r e g u l a t e d , a p p e a r i n g a s p o l e s

a t D = 4 ( = 0 ) .

( b ) v i r t u a l g l u o n e x c h a n g e

q q

= 3

0

1 + C

F

s

2

H ( )

?

2

2

?

3

? 8 +

2

+ O ( )

) A d d i n g r e a l a n d v i r t u a l c o r r e c t i o n s , t h e i n f r a r e d / c o l l i n e a r

p o l e s c a n c e l a n d t h e r e s u l t i s n i t e a s ! 0 :

R = R

0

n

1 +

s

+ O (

2

s

)

o

O t h e r r e g u l a r i s a t i o n s c h e m e s a v a i l a b l e : e . g . n i t e g m a s s

m

g

s ( n o n - g a u g e i n v a r i a n t ! ) .

) R i s a n i n f r a r e d s a f e q u a n t i t y !

) R i s n i t e a n d r e g u l a r i s a t i o n s c h e m e - i n d e p e n d e n t !


24/193

e

+

e

?

! h a d r o n s c r o s s s e c t i o n a t N L O

1 F i r s t

s

m e a s u r e m e n t :

R ( L E P ) = 2 0 7 7 5 0 0 2 7

R

0

( M

Z

) = 1 9 9 8 4

!

s

( M

Z

) = 0 1 2 4 0 0 0 4

2 S e c o n d

s

m e a s u r e m e n t :

R ( P E T R A ) = 3 8 8 0 0 3

R

0

( 3 4 G e V ) = 3 6 9

!

s

= 0 1 6 2 0 0 2 6

!

s

( M

Z

) = 0 1 3 4 0 0 1 8 ( u p o n r u n n i n g )

P E T R A a g r e e s w i t h L E P :

) t e s t o f Q C D i n i n t e r v e n i n g e n e r g y r a n g e !

N o t e : - d e c a y s

R e l a t e d m e a s u r e m e n t : R R ( ) =

B R ( ! h a d r o n s )

B R ( ! e l e c t r o n s ; m u o n s )

! o n e o f b e s t

s

m e a s u r e m e n t s :

s

( m

= 1 7 7 G e V ) = 0 3 3 0 0 3

!

s

( M

Z

) = 0 1 1 8 0 0 0 4 ( u p o n r u n n i n g )

C r o s s s e c t i o n n o w k n o w n t h r o u g h N N N L O ! g

A n d t h e o r e t i c a l e r r o r s W h e r e a r e t h e y


25/193

Dependence of total cross section on only hard gluons is good behaviour of perturbation series:

tot = qq

1 + 1.045s(Q)

+ 0.94

s(Q)

2 15

(Coefficients gi


26/193

R e n o r m a l i s a t i o n s c a l e d e p e n d e n c e

R e c a l l

s

( ) , a r b i t r a r y : w o u l d d i s a p p e a r t o a l l o r d e r s . . .

) U s e d e p e n d e n c e a s e s t i m a t e o f u n c e r t a i n t y d u e t o t r u n -

c a t i n g p e r t u r b a t i v e s e r i e s ! s m a l l e r a t e a c h o r d e r

V a r y ( b y s o m e f a c t o r ) t o e s t i m a t e t h e o r e t i c a l u n c e r t a i n t y :

W h a t s c a l e t o u s e f o r c e n t r a l

s

v a l u e

1 . P h y s i c a l s c a l e , =

p

s

2 . P r i n c i p l e o f M i n i m a l S e n s i t i v i t y : w h e r e d = d = 0

3 . F a s t e s t A p p a r e n t C o n v e r g e n c e : w h e r e N L O = L O

! t h e o r e t i c a l p r e d i c t i o n s r a t h e r s u b j e c t i v e !


27/193

I n f r a r e d s a f e q u a n t i t i e s

R ( e

+

e

?

) a n d R ( ) a r e v e r y i n c l u s i v e q u a n t i t i e s : t o t a l c r o s s

s e c t i o n s o r d e c a y r a t e s !

I n f r a r e d s a f e t y g u a r a n t e e d b y ` t h e o r e m s ' , e . g . B l o c h a n d

N o r d s i e c k ( B N ) p l u s K i n o s h i t a , L e e a n d N a u e n b e r g ( K L N ) :

! s u i t a b l y d e n e d q u a n t i t i e s a r e f r e e o f s i n g u l a r i t i e s .

P h y s i c a l m e a n i n g : e v e n t s w i t h h a d r o n s g i v e a p p r o x i m a t e l y

t h e s a m e m e a s u r e m e n t a s p a r t o n o n e s .

C o m p u t a t i o n a l m e a n i n g : i n n i t i e s c a n c e l w h e n a d d i n g r e a l

g l u o n e m i s s i o n a n d v i r t u a l g l u o n e x c h a n g e .

B N & K L N a p p l y a l s o t o m o r e e x c l u s i v e q u a n t i t i e s : e . g .

1 n - j e t s c r o s s s e c t i o n , n = 2 ; 3 ; : : :

2 . E v e n t - s h a p e v a r i a b l e s l i k e t h r u s t


28/193

J e t s

N a i v e l y e x p e c t m o s t e v e n t s t o l o o k l i k e :

Y

XZ

200. cm.

Ce n t r e o f s c r e en i s ( 0 . 0 0 00 , 0 . 0 00 0 , 0 . 0 00 0 )

50 GeV20105

Run:even t 4093: 1000 Dat e 930527 T ime 20716

Eb eam 4 5 . 6 58 E v i s 9 9 . 9 Em i s s - 8 . 6 V t x ( - 0 . 0 7 , 0 . 0 6 , - 0 . 8 0 )

Bz=4. 350 Thrus t =0.9873 Aplan=0.0017 Obl a t =0.0248 Spher=0. 0073

Ct rk (N= 39 Sump= 73. 3) Eca l (N= 25 SumE= 32 .6 ) Hca l (N=22 SumE= 22.6 )

Muon(N= 0) Sec V t x (N= 3) Fdet (N= 0 SumE= 0. 0)


29/193

w i t h a f r a c t i o n

s

m o r e l i k e :

Y

XZ

200. cm.

Ce n t r e o f s c r e en i s ( 0 . 0 0 00 , 0 . 0 00 0 , 0 . 0 00 0 )

50 GeV20105

Run:even t 2542: 63750 Dat e 911014 T ime 35925

Eb eam 4 5 . 6 09 E v i s 8 6 . 2 Em i s s 5 . 0 V t x ( - 0 . 0 5 , 0 . 1 2 , - 0 . 9 0 )

Bz=4. 350 Thrus t =0.8223 Aplan=0.0120 Obl a t =0.3338 Spher=0. 2463

Ct rk (N= 28 Sump= 42. 1) Eca l (N= 42 SumE= 59 .8 ) Hca l (N= 8 SumE= 12.7 )

Muon(N= 1) Sec V t x (N= 0) Fdet (N= 2 SumE= 0. 0)

( a n d e v e n a f r a c t i o n

2

s

f o u r - j e t l i k e , e t c )


30/193

J e t d e n i t i o n

I n t u i t i v e l y , j e t i s a s p r a y o f c o l l i m a t e d p a r t i c l e s .

N e e d a p r o c e d u r e : i n e

+

e

?

u s e c l u s t e r i n g a l g o r i t h m s .

S t a r t w i t h a l i s t o f m o m e n t a p

1

; p

2

; : : : ; p

n

( I n p e r t u r b a t i v e c a l c u l a t i o n s , t h e y a r e p a r t o n m o m e n t a . )

T h r e e i n g r e d i e n t s :

1 . A m e a s u r e o f i n t e r - j e t d i s t a n c e : y

i j

! f o r e a c h p a i r o f n a l s t a t e m o m e n t a c a l c u l a t e , e . g .

y

i j

= m

2

i j

= s ( I n v a r i a n t M a s s )

y

i j

= 2 E

i

E

j

( 1 ? c o s

i j

) = s ( J A D E )

y

i j

= 2 m i n f E

2

i

; E

2

j

g ( 1 ? c o s

i j

) = s ( D u r h a m )

2 . A r e s o l u t i o n f o r t h e l a t t e r : y

c u t

! m i n f y

i j

; : : : g < y

c u t

c o m b i n e i a n d j i n t o k

3 . A r e c o m b i n a t i o n p r o c e d u r e : e . g .

p

k

= p

i

+ p

j

( E - s c h e m e )

p

k

= ( j p

i

+ p

j

j ; p

i

+ p

j

) ( p - s c h e m e )

p

k

= ( j E

i

+ E

j

j ;

E

i

+ E

j

j p

i

+ p

j

j

p

i

+ p

j

) ( E 0 - s c h e m e )

R e p e a t t i l l m i n f y

k l

; : : : g > y

c u t

: r e m a i n i n g o b j e c t s a r e j e t s .

A n - p a r t o n n a l s t a t e c a n g i v e a n y n u m b e r o f j e t s b e t w e e n n

( a l l p a r t o n s w e l l - s e p a r a t e d ) a n d 2 ( e . g . t w o e n e r g e t i c q u a r k s

a c c o m p a n i e d b y s o f t a n d c o l l i n e a r g l u o n s ) .


31/193

J e t r a t e s

D e n e n - j e t f r a c t i o n f

n

( y ) b y ( y y

c u t

)

f

n

( y ) =

n

( y )

P

m

m

( y )

=

n

( y )

t o t

;

I f

t o t

=

0

( 1 +

s

= + ) , t h e n

X

n

f

n

( y ) = 1

F o r =

p

s a n d n = 2 ; 3 a n d 4 :

f

2

( y ) = 1 ?

s

2

A ( y ) +

s

2

2

( 2 A ( y ) ? B ( y ) ? C ( y ) ) + : : : ;

f

3

( y ) =

s

2

A ( y ) +

s

2

2

( B ( y ) ? 2 A ( y ) ) + : : : ;

f

4

( y ) =

s

2

2

C ( y ) + : : : ;

C o u p l i n g c o n s t a n t

s

a n d f u n c t i o n s A ( y ) ; B ( y ) a n d C ( y )

d e n e d i n s o m e r e n o r m a l i s a t i o n s c h e m e ( e . g . M S s c h e m e ) .

T e r m s o f o r d e r O (

2

s

) i n v o l v i n g A ( y ) t a k e a c c o u n t o f t h e

n o r m a l i s a t i o n t o

t o t

r a t h e r t h a n t o

0


32/193

E x a m p l e 1 o f n - j e t e v e n t r a t e s (

2

s

v s . O P A L )


33/193

T h e - d e p e n d e n c e o f t h e t h r e e - j e t r a t e i s i n t r o d u c e d b y

s

!

s

( ) ; B ( y ) ! B ( y ) ? A ( y )

0

l n

Q


34/193

E v e n t s h a p e v a r i a b l e s

A t t e m p t t o n d a m o r e g l o b a l m e a s u r e o f 2 / 3 - j e t s e p a r a t i o n

E . g . T h r u s t ( T ) :

T = m a x

n

P

j p

i

n j

P

j p

i

j

T h r o u g h o r d e r

2

s

:

1

0

d

d T

=

s

( )

2

A ( T )

+

s

( )

2

2

2

6

6

4

2 A ( T )

0

l o g

2

s

| { z }

r e n o r m a l i s a t i o n s c a l e d e p e n d e n c e

+ B ( T )

3

7

7

5

L O t e r m :

A ( T ) = C

F

2 ( 3 T

2

? 3 T + 2 )

T ( 1 ? T )

l o g

2 T ? 1

1 ? T

?

3 ( 3 T ? 2 ) ( 2 ? T )

1 ? T

T ! 1

C

F

4

1 ? T

l o g

1

1 ? T

?

3

1 ? T

N L O t e r m B ( T ) c o m p u t e d n u m e r i c a l l y !


35/193


36/193

s

( M

Z

) c o m p i l a t i o n s

O (

2

s

) !


37/193

P a r t o n s h o w e r

q

subprocess

underlying

event

p

jet jet

p

hard

q

+

0Z

ee

0 00 01 11 10 0 0 0 00 0 0 0 00 0 0 0 00 0 0 0 01 1 1 1 11 1 1 1 11 1 1 1 11 1 1 1 1 0 0 0 00 0 0 00 0 0 00 0 0 01 1 1 11 1 1 11 1 1 11 1 1 10 0 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 0 01 1 1 1 1 1 1 1 1 1 11 1 1 1 1 1 1 1 1 1 11 1 1 1 1 1 1 1 1 1 11 1 1 1 1 1 1 1 1 1 11 1 1 1 1 1 1 1 1 1 11 1 1 1 1 1 1 1 1 1 1 0 0 0 0 00 0 0 0 00 0 0 0 01 1 1 1 11 1 1 1 11 1 1 1 10 00 00 01 11 11 1 0 00 00 01 11 11 10 0 0 0 00 0 0 0 00 0 0 0 01 1 1 1 11 1 1 1 11 1 1 1 10 00 01 11 1 0011 0 00 00 01 11 11 1 00110 0 00 0 00 0 01 1 11 1 11 1 1

0 0 0 0 00 0 0 0 00 0 0 0 00 0 0 0 00 0 0 0 01 1 1 1 11 1 1 1 11 1 1 1 11 1 1 1 11 1 1 1 10 0 0 0 00 0 0 0 00 0 0 0 00 0 0 0 00 0 0 0 01 1 1 1 11 1 1 1 11 1 1 1 11 1 1 1 11 1 1 1 1010 01 10 01 1010101 0011


38/193

q

q

0 0 0 0 00 0 0 0 00 0 0 0 00 0 0 0 00 0 0 0 01 1 1 1 11 1 1 1 11 1 1 1 11 1 1 1 11 1 1 1 1 0 0 0 00 0 0 00 0 0 00 0 0 01 1 1 11 1 1 11 1 1 11 1 1 10 01 10 01 1 0 01 10 01 10 0 01 1 1 0 0 01 1 10 0 01 1 10 0 01 1 1 W/Zl lq

PS

ME

PS


39/193

q

D0

pp W

CDF

pp Z


40/193

H a d r o n i s a t i o n

T h e f o r m a t i o n o f h a d r o n s ( l o n g d i s t a n c e p h y s i c s ) i s n o t

d e s c r i b e d b y p e r t u r b a t i v e Q C D

S p a c e - t i m e p i c t u r e :

e

+

a n d e

?

f o r m ( o r Z ) w i t h v i r t u a l m a s s Q =

p

s ,

w h i c h u c t u a t e s i n t o q a n d q

{ B y t h e u n c e r t a i n t y p r i n c i p l e , u c t u a t i o n o c c u r s a t

s h o r t d i s t a n c e / t i m e s c a l e 1 = Q

{ A t l a r g e Q , t h e r a t e e

+

e

?

! q q ( g ) i s g i v e n b y p e r -

t u r b a t i o n t h e o r y .

A t m u c h l a t e r t i m e s 1 = , q u a r k s f o r m h a d r o n s .

{ H a d r o n i s a t i o n m o d i e s t h e o u t g o i n g s t a t e , b u t o c -

c u r s t o o l a t e t o c h a n g e t h e o r i g i n a l p r o b a b i l i t y f o r

t h e e v e n t t o h a p p e n .

) ( e

+

e

?

! h a d r o n s ) =

( e

+

e

?

! p a r t o n s ) ( 1 + O ( = Q )

n

) ( p o w e r c o r r e c t i o n s )

) ( e

+

e

?

! h a d r o n s ) c a n b e c a l c u l a t e d i n p e r t u r b a t i v e

Q C D f o r Q

) N e e d M o n t e C a r l o ( M C ) a p p r o a c h f o r Q


41/193

Q u a r k s a n d g l u o n s p r o d u c e d i n a s h o r t - d i s t a n c e p r o c e s s

f o r m t h e m s e l v e s i n t o h a d r o n s : h a d r o n i s a t i o n .

H a d r o n i s a t i o n m o d e l l e d t o d a t a i n M C p r o g r a m s l i k e

1 . H E R W I G ( c l u s t e r h a d r o n i s a t i o n )

2 . P Y T H I A , A R I A D N E ( s t r i n g h a d r o n i s a t i o n )

G e n e r a l a p p r o a c h t o h a d r o n i s a t i o n b a s e d o n \ p a r t o n - h a d r o n

d u a l i t y " : t h e o w o f m o m e n t u m a n d q u a n t u m n u m b e r s a t

h a d r o n l e v e l f o l l o w s t h a t e s t a b l i s h e d a t t h e p a r t o n i c s t a g e .

E . g . a v o u r o f q u a r k i n i t i a t i n g a j e t f o u n d i n h a d r o n n e a r

t h e j e t a x i s .

A p p r o a c h w o r k s b e c a u s e h a d r o n i s a t i o n i s l o n g - d i s t a n c e p r o c e s s

w h i c h o n l y i n v o l v e s s m a l l m o m e n t u m t r a n s f e r s .


42/193

D e e p l y I n e l a s t i c S c a t t e r i n g ( D I S )

F i r s t t e s t o f p e r t u r b a t i v e Q C D w a s b r e a k i n g o f B j o r k e n

s c a l i n g i n d e e p l y i n e l a s t i c l e p t o n h a d r o n - s c a t t e r i n g ( D I S ) .

D I S s t r u c t u r e f u n c t i o n s p r o v i d e a m o n g m o s t p r e c i s e t e s t s

o f Q C D & d e t e r m i n e P a r t o n D i s t r i b u t i o n F u n c t i o n s ( P D F s )

o f h a d r o n s :

! c a n b e u s e d i n p r e d i c t i n g h a d r o n i c c r o s s s e c t i o n s .

K i n e m a t i c s o f D I S :

! C o n s i d e r l ( k ) + h ( p ) ! l

0

( k

0

) + X ( v i a , W o r Z ) :

S t a n d a r d D I S v a r i a b l e s a r e d e n e d b y

Q

2

= ? q

2

; x =

? q

2

2 p q

a n d y =

q p

k p

S c a t t e r i n g i s c a l l e d d e e p l y i n e l a s t i c i f Q

2

2


43/193

S t r u c t u r e f u n c t i o n s p a r a m e t r i s e t a r g e t a s ` s e e n ' b y ; W ; Z

C o n s i d e r p h o t o n o n l y :

! c r o s s s e c t i o n c a n b e w r i t t e n a s d / L

( k ; q ) W

( p ; q )

S t r u c t u r e o f l e p t o n t e n s o r i s d e t e r m i n e d b y Q E D :

L

= T r ( k

k

0

) = 2

H a d r o n i c t e n s o r W

c o n t a i n s i n s t e a d i n f o r m a t i o n a b o u t

p h o t o n i n t e r a c t i o n w i t h h a d r o n i c t a r g e t a n d c a n n o t b e c a l -

c u l a t e d i n p e r t u r b a t i o n t h e o r y !

S y m m e t r y p r o p e r t i e s g i v e r e s t r i c t i o n s o n W

f o r m .

D e n e t w o s c a l a r s t r u c t u r e f u n c t i o n s , F

1

a n d F

2

, d e p e n d e n t

o n l y o n ( i n v a r i a n t s ) x a n d Q

2

:

W

= ?

g

?

q

q

q

2

F

1

( x ; Q

2

)

+

p

? q

p q

q

2

p

? q

p q

q

2

1

p q

F

2

( x ; Q

2

)

N e g l e c t i n g h a d r o n m a s s w . r . t . Q

2

, D I S c r o s s s e c t i o n i s

d

d x d y

=

4

2

2 Q

2

y F

1

+

1 ? y

x y

F

2

I n p r i n c i p l e , c a n u s e y d e p e n d e n c e t o d e t e r m i n e s t r u c t u r e

f u n c t i o n s F

i

i n a D I S e x p e r i m e n t .

( A d d i t i o n a l s t r u c t u r e f u n c t i o n , F

3

, n e e d e d f o r W , Z )


44/193

B j o r k e n s c a l i n g l i m i t d e n e d a s Q

2

! 1 w i t h x x e d :

! s t r u c t u r e f u n c t i o n s o b e y a p p r o x i m a t e s c a l i n g l a w , i . e .

F

i

( x ; Q

2

) ! F

i

( x )

E v e n t h o u g h t h e Q

2

v a l u e s v a r y b y t h r e e o r d e r s o f m a g n i -

t u d e , d a t a a p p r o x i m a t e l y l i e o n u n i v e r s a l c u r v e .

S c a l i n g i m p l i e s

- s c a t t e r i n g o p o i n t - l i k e c o n s t i t u e n t s .

O t h e r w i s e ( d i m e n s i o n l e s s ) s t r u c t u r e f u n c t i o n s w o u l d d e p e n d

o n Q = Q

0

, w i t h 1 = Q

0

s o m e l e n g t h s c a l e c h a r a c t e r i s i n g s i z e o f

c o n s t i t u e n t s . ]

O b s e r v a t i o n o f s c a l i n g w a s t h e m o t i v a t i o n f o r p a r t o n m o d e l .


45/193

P a r t o n m o d e l : p m a d e o f p o i n t - l i k e c o n s t i t u e n t s ! p a r t o n s .

T h e i r i n t e r a c t i o n s a r e o v e r t i m e s c a l e s o f O ( 1 = ) : l o n g e r

w . r . t . t i m e i t t a k e s e

?

t o t r a v e r s e L o r e n t z c o n t r a c t e d p r o t o n .

C a n t h e r e f o r e c o n s i d e r p a r t o n s a s ( a p p r o x i m a t e l y ) f r e e p a r -

t i c l e s o v e r t h e v e r y s h o r t i n t e r a c t i o n t i m e .

M o d e l l e a d s t o i n t u i t i v e f o r m u l a :

d

( l h )

d x d Q

2

=

X

a

Z

1

0

d f

a = h

( )

d

( l a )

d x d Q

2

;

d

( l h

! i n c l u s i v e c r o s s s e c t i o n f o r l e p t o n - n u c l e o n s c a t t e r i n g ;

d

( l a )

t o p a r t o n - e l e c t r o n o n e ;

p , 0 <


46/193

H a r d s c a t t e r i n g c r o s s s e c t i o n s f r o m p e r t u r b a t i o n t h e o r y :

U s i n g Q E D F e y n m a n r u l e s :

d

d Q

2

=

2

2

e

2

q

Q

4

1 + ( 1 ? y )

2

M a s s - s h e l l c o n s t r a i n t f o r o u t g o i n g q u a r k

( p + q )

2

= q

2

+ 2 p q = ? 2 p q ( x ? ) = 0

i m p l i e s x =

W r i t e

R

1

0

d x ( x ? ) = 1 a n d o b t a i n

d

d x d Q

2

=

4

2

Q

4

1 + ( 1 ? y )

2

1

2

e

2

q

( x ? )

A t l o w e s t o r d e r , s t r u c t u r e f u n c t i o n s a r e g i v e n b y

F

2

( x ; Q

2

) =

X

q

e

2

q

x f

= h

( x ) = 2 x F

1

( x ; Q

2

)

! C a l l a n - G r o s s r e l a t i o n : f r o m s p i n o f p a r t o n s !

D o n o t c o n f u s e s t r u c t u r e f u n c t i o n s a n d P D F s !


47/193

I n h i g h e r o r d e r Q C D , s t r u c t u r e f u n c t i o n s F

i

a r e Q

2

- d e p e n d e n t

a n d s c a l i n g i s b r o k e n b y l o g a r i t h m s o f Q

2

T h r o u g h O (

s

) :

Q u a r k a c q u i r e s l a r g e t r a n s v e r s e m o m e n t u m k

T

w i t h p r o b -

a b i l i t y

s

d k

2

T

= k

2

T

a t l a r g e k

T

I n t e g r a l e x t e n d s u p t o t h e k i n e m a t i c l i m i t k

2

T

Q

2

a n d

g i v e s r i s e t o c o n t r i b u t i o n s /

s

l n Q

2

w h i c h b r e a k s c a l i n g .

A l s o , k

T

i n t e g r a l l o g a r i t h m i c a l l y d i v e r g e n t a s j k

T

j ! 0

I n t r o d u c i n g k

T

c u t - o :

F

2

( x ; Q

2

) = x

X

q

e

2

q

Z

1

x

d

f

q = h

( )

1 ?

x

+

s

P

q q

x

l n

Q

2

2

+ C

x

P

q q

( ) = C

F

( 1 +

2

) = ( 1 ? ) c a l l e d s p l i t t i n g f u n c t i o n a n d

C i s n i t e t e r m d u e t o v i r t u a l g l u o n e x c h a n g e .

L i m i t k

T

! 0 ( ! 0 ) c o r r e s p o n d s t o l o n g - r a n g e n o n -

p e r t u r b a t i v e Q C D : h o w e v e r ,

! f a c t o r i s a t i o n t h e o r e m : c a n s e p a r a t e f r o m h a r d s c a t t e r i n g .


48/193

Q C D f a c t o r i s a t i o n t h e o r e m

P e r t u r b a t i v e e x p a n s i o n c a n b e r e a r r a n g e d s u c h t h a t c o n -

t r i b u t i o n s f r o m l o n g - r a n g e p h y s i c s a p p e a r i n P D F s w h i l e

t h o s e s h o r t - d i s t a n c e a p p e a r i n t h e h a r d - s c a t t e r i n g c r o s s s e c -

t i o n ( C o l l i n s , S o p e r , S t e r m a n ) .

S e p a r a t i o n r e q u i r e s i n t r o d u c t i o n o f f a c t o r i s a t i o n s c a l e

F

E . g . g l u o n e m i s s i o n w i t h k

2

T

2

F

i s p a r t o f f

q = h

w h i l e

w i t h k

2

T

2

F

i s p a r t o f p e r t u r b a t i v e s c a t t e r i n g .

T h r o u g h O (

s

) :

F

2

( x ; Q

2

) = x

X

q

e

2

q

Z

1

x

d

f

q = h

( ;

2

F

)

1 ?

x

+

s

P

q q

x

l n

Q

2

2

F

+ C

F S

x

( C

F S

f a c t o r i s a t i o n - s c h e m e d e p e n d e n t n i t e c o r r e c t i o n ) .

A r b i t r a r i n e s s i n h o w m u c h o f C

F S

i s f a c t o r e d i n t o P D F s

d e n e s s o - c a l l e d ` f a c t o r i s a t i o n s c h e m e ' .

W h i l e P D F s a n d h a r d s c a t t e r i n g c r o s s s e c t i o n d e p e n d o n

F

, p h y s i c a l c r o s s s e c t i o n d o e s n o t .

T h e m o r e t e r m s i n c l u d e d i n t h e p e r t u r b a t i v e e x p a n s i o n t h e

w e a k e r t h e d e p e n d e n c e o n

F

F a c t o r i s a t i o n t u r n s Q C D i n t o a r e l i a b l e c a l c u l a t i o n a l t o o l !


49/193

Q C D s c a l i n g v i o l a t i o n o b s e r v e d e x p e r i m e n t a l l y :

0

2

4

6

8

10

12

14

16

1 10 102

103

104

105

Q2

(GeV2)

Fem

-log10x

2

ZEUS 96/97 Preliminary

H1 96/97 H1 94/00 Prel.

NMC, BCDMS, E665, SLAC

ZEUS QCD Fit (Prelim.)

H1 QCD Fit


50/193

P D F s c a n b e d e n e d i n t e r m s o f q u a r k - a n d g l u o n - e l d

o p e r a t o r s .

P D F s a p p e a r i n Q C D f o r m u l a e f o r a n y p r o c e s s w i t h n 1

h a d r o n s i n i n i t i a l s t a t e .

P D F s c o u l d ( i n p r i n c i p l e ) b e c a l c u l a t e d i n l a t t i c e Q C D , y e t

d e t e r m i n e d f r o m e x p e r i m e n t .

D e p e n d e n c e o f P D F s o n

F

d e t e r m i n e d b y R e n o r m a l i s a t i o n

G r o u p E q u a t i o n ( R G E ) D o k s h i t z e r - G r i b o v - L i p a t o v - A l t a r e l -

l i - P a r i s i ( D G L A P ) e q u a t i o n ] :

d

d l n

F

f

a = h

( x ;

F

) =

X

b

Z

1

x

d

P

a b

( x = ;

s

(

F

) ) f

b = h

( ;

F

)

S p l i t t i n g f u n c t i o n P

a b

h a s p e r t u r b a t i v e e x p a n s i o n :

P

a b

( x = ;

s

(

F

) ) = P

( 1 )

a b

( x = )

s

(

F

)

+ P

( 2 )

a b

( x = )

s

(

F

)

2

+

F i r s t t w o t e r m s k n o w n a n d u s e d i n n u m e r i c a l s o l u t i o n s .

D G L A P - e q u a t i o n :

! e n a b l e s t o r e l a t e P D F s m e a s u r e d a t o n e s c a l e t o o t h e r

s c a l e s a n d m a k e c o r r e s p o n d i n g p r e d i c t i o n s


51/193

P D F s

C o n s t r a i n P D F s b y u s i n g m a n y d i e r e n t b e a m s / t a r g e t s :

N o m e n c l a t u r e / i s o s p i n :

f

u = n

( x ; Q

2

) = f

d = p

( x ; Q

2

) = f

d = p

( x ; Q

2

) f

d

( x ; Q

2

) , e t c .

F

e p

2

( x ; Q

2

) =

1

9

x f

d

+

4

9

x f

u

+

1

9

x f

d

+

4

9

x f

u

+

1

9

x f

s

+

F

e n

2

( x ; Q

2

) =

4

9

x f

d

+

1

9

x f

u

+

4

9

x f

d

+

1

9

x f

u

+

1

9

x f

s

+

F

p

2

( x ; Q

2

) = 2 x f

d

+ 2 x f

u

+ 2 x f

s

+ 2 x f

c

+

F

p

3

( x ; Q

2

) = 2 x f

d

? 2 x f

u

+ 2 x f

s

? 2 x f

c

+

F

p

2

( x ; Q

2

) = 2 x f

u

+ 2 x f

d

+ 2 x f

c

+ 2 x f

s

+

F

p

3

( x ; Q

2

) = 2 x f

u

? 2 x f

d

+ 2 x f

c

? 2 x f

s

+

e t c

! g l o b a l t s ! g

E . g . M R S ( T ) , C T E Q , G R V , e t c . ,

! h t t p : / / d u r p d g . d u r . a c . u k / h e p d a t a / p d f . h t m l


52/193


53/193

H a d r o n - h a d r o n c o l l i s i o n s

C r o s s s e c t i o n f o r e . g . Z b o s o n p r o d u c t i o n

c a n b e f a c t o r e d :

d ( p

A

; p

B

) =

X

a ; b

Z

d

A

d

B

f

a = A

(

A

;

F

) f

b = B

(

B

;

F

)

d

a b

(

A

p

A

;

B

p

B

;

F

)

C h a r a c t e r i s t i c s c a l e o f h a r d s c a t t e r i n g Q

2

2

c o u l d b e

e . g . M

Z

o r p

T

Z

F a c t o r i s a t i o n f o r m u l a h o l d s u p t o

2

= Q

2

c o r r e c t i o n s .

T o p r o v e f a c t o r i s a t i o n o n e n e e d s t o s u m o v e r g r a p h s a n d

u s e u n i t a r i t y , c a u s a l i t y a n d g a u g e i n v a r i a n c e ( C o l l i n s , S o p e r

a n d S t e r m a n ) .


54/193

H i s t o r i c a l l y , c o n r m e d b y l e p t o n - p a i r h a d r o - p r o d u c t i o n ( A +

B ! l

+

l

?

+ X , o r ` D r e l l - Y a n ' p r o c e s s , D Y ) , u s i n g t h e p a r t o n

p i c t u r e a n d t h e P D F s f r o m D I S :

( D i s t r i b u t i o n i s l e p t o n p a i r i n v a r i a n t m a s s s q u a r e d . )


55/193

N P i n D Y p r o c e s s e s

( a ) d = d M d i s t r i b u t i o n o f e

+

e

?

( C D F a n d D O / ) a n d

+

?

( C D F ) . S M ( d a s h e d ) n o r m a l i z e d ( 1 1 1 ) t o C D F d a t a i n

Z m a s s r e g i o n . ( b ) C D F A

F B

v e r s u s m a s s c o m p a r e d t o

S M ( d a s h e d ) . A l s o s h o w n a r e t h e o r e t i c a l c u r v e s ( 1 1 1 ) f o r

d = d M a n d A

F B

f o r e x t r a E

6

b o s o n w i t h M

Z

0

= 3 5 0 G e V

a n d ?

Z

0

= 0 1 M

Z

0

, f o r = 6 0

0

( s o l i d ) a n d 1 7 3

o

( d o t t e d ) .


56/193

T o p m a s s

M e a s u r e d b y T e v a t r o n e x p e r i m e n t s ( C D F & D ) .

H a d r o - p r o d u c t i o n m o d e s :

g g ! t

t ( d o m i n a t e s a t L H C ) ;

q q ! t

t ( d o m i n a t e s a t T e v a t r o n )

T o p d e c a y s ( e . g . s e m i - l e p t o n i c , j = j e t & = e ; ) :

t

t ! ( b W

+

) (

b W

?

) ! ( b j j ) (

b `

) + C C

6 - j e t s i g n a t u r e s h a s w o r s e c o m b i n a t o r i c s !

R e c o n s t r u c t m

t

f r o m b j j i n v a r i a n t m a s s ( e . g . D ) :

Reconstructed Mass (GeV/c2)

Events/(10GeV/c2)

Mtop

(GeV/c2)

-log(L)

0

5

10

15

20

100 150 200 250 300 350

125 150 175 2000

5

10


57/193

T o p p a i r p r o d u c t i o n c r o s s s e c t i o n

M e a s u r e d b y b o t h T e v a t r o n e x p e r i m e n t s ( C D F & D ) .

A c h i e v e d c o n s i s t e n c y w i t h S M p r e d i c t i o n ( r e q u i r e d N L O

a n d r e s u m m a t i o n )

1 . M a n y d i e r e n t c h a n n e l s

2 . C o m p a r e t o l o o k f o r N P

3 . C u r r e n t l y s t a t i s t i c s l i m i t e d ( 7 5 0 p b

? 1

)

4 . A s s u m e m

t

= 1 7 5 G e V

) (pb)ttp(p0 2 4 6 8 10 12 14

0

8

Cacciari et al. JHEP 0404:068 (2004)

Kidonakis,Vogt PRD 68 114014 (2003)

2=175 GeV/ctAssume m

*CDF Preliminary

Combined*

0.40.60.57.3)

-1(L= 760 pb

(lumi)(syst)(stat)

All-hadronic: Vertex Tag*

0.52.2

3.31.78.0)

-1

(L= 311 pb

MET+Jets: Vertex Tag*

0.40.91.41.26.1

)-1

(L= 311 pb

Lepton+Jets: Soft Muon Tag 0.31.01.33.35.3

)-1

(L= 193 pb

Lepton+Jets: Vertex Tag*

0.50.90.68.2)

-1(L= 695 pb

Lepton+Jets: Kinematic ANN*

0.30.90.66.0)

-1

(L= 760 pb

Dilepton*

0.51.01.58.3)

-1(L= 750 pb

)2

Top Quark Mass (GeV/c160 162 164 166 168 170 172 174 176 178 180

)(pb)

tt

p

(p

0

2

4

6

8

10

12

Cacciari et al. JHEP 0404:068 (2004)

uncertaintyCacciari et al.

Kidonakis,Vogt PIM PRD 68 114014 (2003)

Kidonakis,Vogt 1PI

-1CDF II Preliminary 760 pb


58/193

T o p m a s s : T e v a t r o n S u m m a r y

R u n 2 i n i t i a l g o a l

w a s m

t

= 2 . 0 { 2 . 5 G e V

( p e r e x p e r i m e n t )

Integrated Luminosity (fb-1

)

Proje

ctedmt

(GeV)

Statistical uncertainty

JES systematic uncertainty (from MW

only)

Remaining systematic uncertantiesTotal uncertainty

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5

0 1 2 3 4 5 6 7 8

L a r g e s y s t e m a t i c s f r o m j e t e n e r g y s c a l e

)2

Top Quark Mass (GeV/c

150 160 170 180 190 2000

19

Tevatron Summer06*

1.81.2171.4(CDF+D0 Run I+II) (syst.)(stat.)

CDF Summer 2006*

1.91.4170.9)-1(L=1030 pb

All hadronic: Ideogram*

4.74.9177.1)-1(L= 310 pb

All hadronic: Template*

4.82.2174.0)-1

(L=1020 pb

jj+Wrecotop

Lepton+Jets: M*

2.21.7173.4)-1(L= 680 pb

Lepton+Jets: Matrix Element*

2.01.6170.9)-1(L= 940 pb

xyLepton+Jets: L*

5.613.915.7183.9)-1(L= 695 pb

Lepton+Jets: DLM 3.22.42.6173.2)-1(L= 318 pb

Dilepton: DLM*

3.26.77.3166.6)-1(L= 340 pb

ofDilepton: 4.09.08.9169.7)-1(L= 340 pb

)t(tzDilepton: P 4.07.27.7169.5)-1(L= 340 pb

weightingDilepton: 3.76.56.9170.7)-1(L= 360 pb

Dilepton: Combined 3.75.2167.9)-1(L= 360 pb

Dilepton: Matrix Element*

3.93.9164.5)-1(L=1030 pb

Dilepton: Matrix Element b-tag*

3.84.6167.3)-1(L= 955 pb

Run 1 All-hadronic 5.710.0186.0(Run 1 only)

Run 1 Lepton+Jets 5.35.1176.1(Run 1 only)

Run 1 Dilepton 4.910.3167.4(Run 1 only)

CDF (*Preliminary)

)2

Top Quark Mass (GeV/c

155 160 165 170 175 180 185 10

Tevatron July06* 1.81.2171.4(CDF+D0 Run I+II Average) (syst(stat)

CDF All hadronic* 4.82.2174.0)-1(L=1020 pb

CDF Lepton+Jets* 2.01.6170.9)

-1(L= 940 pb

CDF Dilepton* 3.93.9164.5)

-1(L=1030 pb

D0 Lepton+Jets* 3.82.5170.3)

-1(L= 370 pb

D0 Dilepton* 4.86.7178.1)

-1(L= 370 pb

Best Tevatron Run II (*Preliminary)


59/193

tt production at the LHC

s = 14TeV (pp tt) 800pb 8 106 events @ L

8 107 events @ L

g

g

x1

x2

t

t

g

g

x1

x2

q

q

x1

x2

t

t

90 %

10 %

Lars Sonnenschein Lehrstuhl B, III. Phys. Inst., RWTH Aachen


60/193

Systematical uncertainties of the top mass

(only hadronic decay in semileptonic channel)

mtop = 2.16 GeVmtop(GeV)

170 172 174 176

Simulated data (PYTHIA/CTEQ4M)

CTEQ5M

MRST99

_____________________________

mW

-100MeV

mW

+100MeV

_____________________________

Hadronic energy scale +2%

Hadronic energy scale -2%_____________________________

Minimum Bias (UA5), pmin=3GeV

M. B. (UA5), pmin=1,55GeV

M. B. (PYTHIA/default), pmin=3GeV

_____________________________

Qmin

(FSR)=0,5GeV

Qmin

(FSR)=2,0GeV

FSR off (soon)

ISR off (soon)

CMS 10fb

Lars Sonnenschein Lehrstuhl B, III. Phys. Inst., RWTH Aachen


61/193

'

&

$

%

At LHC it is possible to produce top quarks singly via the

weak interaction

q q

W

tb

Wglarge LHC x-sec 245 pbhigh rate, Vtb, polarized tops,etc.

b

g

b W

t

WtLHC x-sec 50 pbVtb, new theoretical results re-cently.....

q

q

W t

b

W

LHC x-sec 10 pblow th. errors, Vtb

New Physics can affect each rate differently

Single top provides the best opportunity to study W-t-bvertex:

- cross-section |Vtb|2

- source of polarized tops (precise prediction)

1


62/193

David Gerdes, University of Michigan Top/QCD at the Linear Collider: Experimental Aspects

Threshold Results

" Mass: mt = 16 MeV, s = 0.0011

Using cross section only: mt = 24 MeV, s = 0

t, g

tthfixed at SM values; assume m

h=120 GeV,

Theory error: ~100 MeV.

" Width: allow to vary in a 3parameter fit.

t= 32 MeV, mt = 18 MeV, s = 0

2% exp. uncertainty on width


63/193

David Gerdes, University of Michigan Top/QCD at the Linear Collider: Experimental Aspects

ttH production and the Top Yuk

Couplinge+e ttH WbWb bbVery complicted final state:

Up to 8 jets

4 bs

Many kinematic constraints

Tiny cross section (~2 fb), withbackgrounds ~3 orders of magnitude

higher.

Interfering backgrounds from EWK (ttZ),

QCD (gbb)

Noninterfering backgrounds

Dominantly e+e tt

Formally smaller number of partons, butcan enter the selection due to hard gluonradiation, detector effects, and their verylarge cross sections


64/193

Important to test coupling between Higgs and top q

Combine LHC and LC for model independent measu

LHC: pp ttH+X measure (ttH)xBR(H WW) t

ILC: e+e- ZH - measure BR(H WW) to 2%

Can do with 500 GeV Linear Collider

2462 ==GeVmg

top

ttH

K. DeschM. Schumacherhep-ph/0407159

SM prediction is

Top Yukawa Coup


65/193

N e w p h y s i c s s e a r c h e s

N P c a n i n t r o d u c e n e w t e r m s i n S M ( e e c t i v e ) L a g r a n g i a n .

I m a g i n e q u a r k s s c a t t e r i n g b y g l u o n e x c h a n g e t o p r o d u c e

t w o j e t s s u p p l e m e n t e d b y q u a r k s e x c h a n g i n g n e w o b j e c t w i t h

m a s s M O ( T e V ) :

A t

p

s M , N P d e t a i l s c a n n o t b e r e s o l v e d .

E e c t c a n b e e m u l a t e d b y n e w t e r m s i n Q C D L a g r a n g i a n :

L =

~g

2

M

2

( ~g

2

! s t r e n g t h o f c o u p l i n g b e t w e e n q a n d N P ) .

F a c t o r 1 = M

2

n e e d e d f o r d i m e n s i o n a l r e a s o n s a n d i m p l i e s

t h a t e e c t o f N P i s s m a l l .

T o o b s e r v e d e v i a t i o n f r o m S M n e e d :

1 . h i g h - p r e c i s i o n e x p e r i m e n t , o r

2 . e x p e r i m e n t l o o k i n g f o r s o m e e e c t f o r b i d d e n i n S M , o r

3 . a n e x p e r i m e n t a t

p

s M


66/193

E . g . c o n s i d e r p p ! j e t + X a s a f u n c t i o n o f E

j e t

T

o f j e t .

F o r E

j e t

T

M :

D a t a ? T h e o r y

T h e o r y

/ ~g

2

E

2

T

M

2

C o m p a r e e x p e r i m e n t a l j e t c r o s s s e c t i o n t o N L O Q C D :

Et (GeV)

-0.5

0

0.5

1

(Data-Theory)/

Theory

200 300 40010050

CTEQ3MCDF (Preliminary) * 1.03D0 (Preliminary) * 1.01

B e w a r e : o b s e r v e d e e c t c a n m o s t l i k e l y b e e x p l a i n e d b y

t h e o r e t i c a l u n c e r t a i n t y o n g l u o n P D F a t l a r g e x !


67/193

T e s t o f S M : E W P h y s i c s

O u t l i n e

W e a k i n t e r a c t i o n s f r o m u n i t a r i t y

S M r e n o r m a l i s a t i o n

e

+

e

?

a n n i h i l a t i o n n e a r Z p o l e

W p r o d u c t i o n

I n d i r e c t s e a r c h f o r t o p a n d H i g g s


68/193

W e a k i n t e r a c t i o n s f r o m u n i t a r i t y

W e a k i n t e r a c t i o n s d i s c o v e r e d i n - d e c a y a n d d e s c r i b e d b y

e e c t i v e L a g r a n g i a n ( F e r m i t h e o r y ) .

F o r

?

! e

?

e

, L a g r a n g i a n i s :

L =

G

F

p

2

( 1 ?

5

) ] e

( 1 ?

5

)

e

]

w i t h G

F

1 1 7 1 0

? 5

G e V

? 2

( F e r m i c o u p l i n g )

F e r m i t h e o r y a s a n e e c t i v e l o w - e n e r g y t h e o r y a n d c a n n o t b e

e x t e n d e d t o a r b i t r a r i l y h i g h e n e r g i e s .

A p p l y i n g e e c t i v e L a g r a n g i a n a t h i g h e n e r g i e s ,

M

e

?

!

?

e

]

G

F

s

2

p

2

S c a t t e r i n g a m p l i t u d e m u s t r e s p e c t u n i t a r i t y b o u n d

j R e M j 1 = 2

) T h e o r y c a n n o t b e a p p l i e d a t s

>

( 6 0 0 G e V )

2

) C a n d e d u c e s t r u c t u r e o f w e a k i n t e r a c t i o n s f r o m u n i t a r i t y c o n -

s t r a i n t s ( L l e w e l l y n S m i t h a n d C o r n w a l l , L e v i n a n d T i k t o p o u l o s ) .


69/193

U n i t a r i t y p r o b l e m i n

e

?

!

?

e

s o l v e d b y a s s u m i n g

w e a k i n t e r a c t i o n s m e d i a t e d b y h e a v y c h a r g e d v e c t o r b o s o n s :

W p r o p a g a t o r d a m p e n s r i s e o f s c a t t e r i n g a m p l i t u d e s a s

p

s ! 1 i f M

W

1 0 0 G e V

:

M

e

?

!

?

e

] !

G

F

s

2

p

2

M

2

W

M

2

W

? s

C o n s i d e r p r o d u c t i o n o f W

+

W

?

p a i r s i n e

+

e

?

a n n i h i l a t i o n .

N e u t r i n o t e r m g r o w s q u a d r a t i c a l l y a n d v i o l a t e s u n i t a r i t y .

B a d h i g h - e n e r g y b e h a v i o u r c u r e d b y e x c h a n g e o f a n e w

n e u t r a l v e c t o r b o s o n W

3

i n s - c h a n n e l !


70/193

A m p l i t u d e f o r W

L

W

L

! W

L

W

L

, a s m e d i a t e d b y v i r t u a l

W e x c h a n g e a n d q u a d r i l i n e a r W b o s o n c o u p l i n g ,

g r o w s q u a d r a t i c a l l y w i t h e n e r g y !

W W s c a t t e r i n g a m p l i t u d e c a n b e d a m p e d b y n e w i n t e r a c -

t i o n s b e t w e e n W b o s o n s a t h i g h - e n e r g y .

I f t h e o r y i s t o r e m a i n w e a k l y i n t e r a c t i n g u p t o h i g h e n e r g i e s ,

a n e w s c a l a r p a r t i c l e , H i g g s b o s o n , m u s t b e i n t r o d u c e d , w h i c h

c o u p l e s t o a p a r t i c l e w i t h a s t r e n g t h p r o p o r t i o n a l t o p a r t i c l e

m a s s .

H i g g s b o s o n e x c h a n g e c a n c e l s b a d h i g h - e n e r g y b e h a v i o u r s o

t h a t a m p l i t u d e f u l l l s u n i t a r i t y r e q u i r e m e n t i f M

H


71/193

S M r e n o r m a l i s a t i o n

S t r u c t u r e o f E W i n t e r a c t i o n s e m e r g e d f r o m r e q u i r e m e n t o f

u n i t a r i t y a t h i g h e n e r g i e s .

T h e o r e t i c a l l y , S M i s a n o n - A b e l i a n g a u g e e l d t h e o r y .

S M o b s e r v a b l e s c a n b e c a l c u l a t e d t o a r b i t r a r i l y h i g h p r e c i -

s i o n i n a s y s t e m a t i c e x p a n s i o n a f t e r a f e w b a s i c p a r a m e t e r s

a r e x e d e x p e r i m e n t a l l y .

Q u a n t u m c o r r e c t i o n s i n i n t e r a c t i n g e l d t h e o r i e s m o d i f y

p a r t i c l e m a s s e s a n d c o u p l i n g s , i . e . i n t e r a c t i o n s r e n o r m a l i s e

t h e f u n d a m e n t a l p a r a m e t e r s .

D e s c r i b e d b y F e y n m a n d i a g r a m s i n c l u d i n g l o o p s

Z

d

4

k

k

4

l n

2

c u t

S e l f - e n e r g y a n d v e r t e x c o r r e c t i o n s a r e l o g a r i t h m i c a l l y d i -

v e r g e n t f o r l a r g e l o o p m o m e n t a a n d l e a d t o c o n t r i b u t i o n s

l n

2

c u t

w h e r e

c u t

i s e n e r g y s c a l e u p t o w h i c h S M i s v a l i d .

Q u a n t u m c o r r e c t i o n s a d d t o u n o b s e r v a b l e b a r e m a s s m

0

a n d b a r e c o u p l i n g g

0

t o g e n e r a t e t h e o b s e r v a b l e p h y s i c a l m a s s

m a n d c o u p l i n g g , i . e . m

0

+ m = m a n d g

0

+ g = g

R e n o r m a l i s a t i o n i s s u c i e n t t o a b s o r b a l l d i v e r g e n c e s a n d

r e n d e r a l l o b s e r v a b l e s n i t e i f

c u t

! 1

S M i s r e n o r m a l i s a b l e ( ' t H o o f t a n d V e l t m a n ) .

O n c e m a s s e s / c o u p l i n g s a r e x e d e x p e r i m e n t a l l y , a l l o t h e r

o b s e r v a b l e s a r e c a l c u l a b l e t o a r b i t r a r i l y h i g h p r e c i s i o n .


72/193

e

+

e

?

a n n i h i l a t i o n n e a r Z p o l e

L E P 1 a n d S L C e x p e r i m e n t s a l l o w e d t e s t s o f E W t h e o r y a t

q u a n t u m l e v e l .

C o n s i d e r e

+

e

?

! f

f ( f = q ; ` ; ) i n S M :

-

( s ) =

4

2

3 s

Q

2

f

N

f

( N

q

= N

C

; N

` ;

= 1 )

Z

( s ) =

4

2

3 s

s

2

( s ? M

2

Z

)

2

+ M

2

Z

?

2

Z

A

f

A

e

N

f

w i t h

A

f

= v

2

f

+ a

2

f

=

( t

3 f

? 2 Q

f

s i n

2

W

)

2

+ t

2

3 f

4 s i n

2

W

c o s

2

W


73/193

I n c l u d e l e a d i n g l o g a r i t h m i c r a d i a t i v e c o r r e c t i o n s

! ( s ) ( i m p r o v e d B o r n a p p r o x i m a t i o n )

S M c r o s s s e c t i o n :

( s ) =

4

2

( s )

3 s

s

2

( s ? M

2

Z

)

2

+ ( s

2

= M

2

Z

) ?

2

Z

1 +

Z

| { z }

+

4

2

( s )

3 s

Q

2

f

N

f

? Z i n t e r f e r e n c e

( a l s o u s e r u n n i n g w i d t h ) .

M o s t i m p o r t a n t E W c o r r e c t i o n s n e a r Z r e s o n a n c e :

-

( L e a d t o u l t r a v i o l e t d i v e r g e n c e s w h i c h h a v e t o b e a b s o r b e d

i n t o r e n o r m a l i s e d m a s s e s a n d c o u p l i n g s . )

I n a d d i t i o n , Q C D c o r r e c t i o n s h a v e t o b e i n c l u d e d i n q q


74/193

Q E D c o r r e c t i o n s d u e t o p h o t o n I n i t i a l S t a t e R a d i a t i o n

( I S R ) a r e c r u c i a l n e a r r e s o n a n c e :

Ecm

[GeV]

had

[nb]

from fitQED unfolded

measurements, error barsincreased by factor 10

ALEPH

DELPHI

L3

OPAL

0

Z

MZ

10

20

30

40

86 88 90 92 94

F i r s t n o n - t r i v i a l S M t e s t :

! g i v e n m e a s u r e m e n t s o f ; M

Z

; G

F

a n d ?

Z

p r e d i c t s

S M

( M

Z

) =

4

2

3 ?

2

Z

A

f

A

e


75/193

T o t a l Z W i d t h

C o n s i d e r w i d t h t o g i v e n n a l s t a t e f e r m i o n :

?

f

=

1

3

M

Z

A

f

T o t a l w i d t h c o m e s a l l p o s s i b l e n a l s t a t e s :

?

Z

=

X

f

?

f

=

X

?

+

X

?

+

X

q

?

q

! ?

Z

= 2 4 9 5 2 0 0 0 2 3 G e V

! G i v e s f u r t h e r n o n - t r i v i a l t e s t o f S M !

G i v e s m e a s u r e m e n t o f n u m b e r o f n e u t r i n o s p e c i e s :

N

= 2 9 9 3 0 0 1 1

O r l i m i t o n w i d t h t o a d d i t i o n a l i n v i s i b l e p a r t i c l e s :

?

i n v

= 4 9 9 0 1 5 M e V


76/193

F o r w a r d - B a c k w a r d a s y m m e t r y

L i n e - s h a p e a n d w i d t h s o n l y s e n s i t i v e t o c o m b i n a t i o n s o f :

A

f

= v

2

f

+ a

2

f

c o s - d e p e n d e n c e a l s o c o n t a i n s

B

f

= 2 v

f

a

f

C o n s t r u c t f o r w a r d - b a c k w a r d a s y m m e t r y :

A

F B

S M

( 9 0

)

S M

( 9 0

)

=

3

4

B

e

B

f

A

e

A

f

! m o r e a n d c o m p l e m e n t a r y t e s t s !


77/193

L e f t - r i g h t a s y m m e t r y

S L C h a d u n i q u e f e a t u r e : h i g h l y p o l a r i z e d e l e c t r o n s

P

e

?

6 9 %

N e w a s y m m e t r y :

A

L R

S M

( e

+

e

?

L

) ?

S M

( e

+

e

?

R

)

S M

( e

+

e

?

L

) +

S M

( e

+

e

?

R

)

= ?

B

e

A

e

N o t e :

1 . i n d e p e n d e n t o f n a l s t a t e

2 . i n d e p e n d e n t o f a n g u l a r r a n g e

3 . m u c h l a r g e r t h a n A

F B

! a l m o s t s y s t e m a t i c a l l y e r r o r - f r e e !

J u s t n e e d t o m e a s u r e p o l a r i s a t i o n w e l l . . .

( S L D : w o r l d ' s b e s t s i n

2

W

)


78/193

W p r o d u c t i o n

C o n s i d e r e

+

e

?

! W

+

W

?

( L E P 2 ) :

-

L a r g e c a n c e l l a t i o n s a t h i g h e n e r g i e s ( d i t t o ) :

e a c h d i a g r a m

G

2

F

s

4 8

; s M

2

W

b u t s u m

G

2

F

m

4

w

s

l o g

s

M

2

W

; s M

2

W

V e r y s e n s i t i v e t o T r i p l e G a u g e C o u p l i n g s ( T G C s )

! o t h e r v e r y p o w e r f u l S M t e s t


79/193

W m a s s i n e

+

e

?

P r e d i c t e d b y S M o n c e ; G

F

a n d M

Z

m e a s u r e d

) a n o t h e r s t r o n g S M t e s t ( s y m m e t r y b r e a k i n g m e c h a n i s m )

N e a r t h r e s h o l d :

W W

G

2

F

M

2

W

2

r

1 ?

4 M

2

W

s

| { z }

v e l o c i t y o f W

r a p i d l y v a r y i n g f o r

p

s 2 M

W

V e r y c l e a n t h e o r e t i c a l l y , b u t f e w e v e n t s

) l a r g e s t a t i s t i c a l e r r o r s ! g

A b o v e t h r e s h o l d :

! M e a s u r e i n v a r i a n t m a s s o f W d e c a y p r o d u c t s ! g

L E P a v e r a g e :

M

W

= 8 0 4 1 2 0 0 4 2 G e V


80/193

0

10

20

30

160 180 200

s (GeV)

WW(

pb)

YFSWW/RacoonWWno ZWW vertex (Gentle)onlye exchange (Gentle)

LEPPRELIMINARY

11/07/2003

0

10

20

30

40

50

60

70

80

50 55 60 65 70 75 80 85 90 95

MW

(GeV/c2)

Eventsp

er1GeV/c2

ALEPH Preliminaryeqq selection

s = 188.6 GeV

Data (Luminosity = 174.2 pb-1

)

MC (mW = 80.35 GeV/c2)

Non-WW background


81/193

W m a s s i n h a d r o n - h a d r o n

W b o s o n m a s s m e a s u r e d a t h a d r o n c o l l i d e r s ( T e v a t r o n ) .

W

!

=

`

d e c a y s p r o v i d e s m a l l b u t c l e a n s a m p l e .

N e u t r i n o l o s t ) p

r e c o n s t r u c t e d f r o m r e s t o f e v e n t .

M a n y h a d r o n s l o s t i n b e a m d i r e c t i o n s .

) o n l y t r a n s v e r s e m o m e n t u m c o n s e r v a t i o n c a n b e u s e d

U s e :

1 . l e p t o n t r a n s v e r s e m o m e n t u m : p

T

( ) ! g

2 . t r a n s v e r s e m a s s : M

2

T

2 p

e

T

p

T

( 1 ? c o s ) ! g

( I n s e n s i t i v e t o W t r a n s v e r s e m o m e n t u m ! )

T e v a t r o n a v e r a g e :

M

W

= 8 0 4 5 2 0 0 5 9 G e V

W o r l d a v e r a g e :

M

W

= 8 0 4 2 5 0 0 3 4 G e V


82/193

pT(e) (GeV)

events/0.5

GeV

0

100

200

300

400

500

600

700

30 35 40 45 50 55

0

100

200

300

400

500

50 60 70 80 90 100 110 120

CDF(1B) Preliminary 2/df = 158/139 (50 < MT< 120)

2/df = 62/69 (65 < MT< 100)

Mw = 80.430 +/- 0.100 (stat) GeV

Fit region

Transverse Mass (GeV)

#Events


83/193

P r e c i s i o n o b s e r v a b l e s

S u m m e r 2 0 0 6

Measurement Fit |OmeasOfit|/meas0 1 2 3

0 1 2 3

had

(mZ)(5) 0.02758 0.00035 0.02766

mZ[GeV]mZ[GeV] 91.1875 0.0021 91.1874

Z[GeV]Z[GeV] 2.4952 0.0023 2.4957

had[nb]0

41.540 0.037 41.477

RlRl 20.767 0.025 20.744

AfbA0,l

0.01714 0.00095 0.01640

Al(P)Al(P) 0.1465 0.0032 0.1479

RbRb 0.21629 0.00066 0.21585RcRc 0.1721 0.0030 0.1722

AfbA0,b

0.0992 0.0016 0.1037

AfbA0,c

0.0707 0.0035 0.0741

AbAb 0.923 0.020 0.935

AcAc 0.670 0.027 0.668

Al(SLD)Al(SLD) 0.1513 0.0021 0.1479

sin2

effsin2lept(Qfb) 0.2324 0.0012 0.2314

mW

[GeV]mW

[GeV] 80.392 0.029 80.371

W[GeV]W[GeV] 2.147 0.060 2.091

mt[GeV]mt[GeV] 171.4 2.1 171.7

( P u l l i s d e n e d a s d e v i a t i o n f r o m t h e o r e t i c a l p r e d i c t i o n i n

u n i t s o f c o r r e s p o n d i n g o n e - s t a n d a r d d e v i a t i o n e x p e r i m e n t a l

u n c e r t a i n t y . )

I n c l u d e s l a t e s t t o p m a s s !


84/193

M

W

( a n d N u T e V a n o m a l y ? )

D i r e c t v s . i n d i r e c t M

W

d e t e r m i n a t i o n s :

W-Boson Mass [GeV]

mW [GeV]80 80.2 80.4 80.6

2/DoF: 1.3 / 1

TEVATRON 80.452 0.059

LEP2 80.376 0.033

Average 80.392 0.029

NuTeV 80.136 0.084

LEP1/SLD 80.363 0.032

LEP1/SLD/mt 80.361 0.020

N u T e V :

! r a t i o o f n e u t r a l t o c h a r g e d c u r r e n t s i n n e u t r i n o - n u c l e o n

M e a s u r e m e n t f r o m N u T e V c o l l a b o r a t i o n ( w h e n i n t e r p r e t e d

a s a m e a s u r e m e n t o f M

W

) s h o w s 2 . 6 { 2 . 8 d e v i a t i o n .

( S o m e s o r t o f ) S M i n c o n s i s t e n c y

( C a n b e v i e w e d a s P D F p r o b l e m , e t c . )


85/193

A l s o W w i d t h :

W-Boson Width [GeV]

W [GeV]2 2.2 2.4

2/DoF: 1.0 / 1

TEVATRON 2.078 0.087

LEP2 2.196 0.083

Average 2.147 0.060

pp

indirect 2.141 0.057

LEP1/SLD 2.091 0.003

LEP1/SLD/mt 2.091 0.002

C a n c o r r e l a t e m

t

a n d M

W

i n g l o b a l E W t :

80.3

80.4

80.5

150 175 200

mH[GeV]114 300 1000

mt [GeV]

mW

[GeV]

68% CL

LEP1 and SLD

LEP2 and Tevatron (prel.)

( S u m m e r 2 0 0 6 c o m b i n a t i o n f o r m

t

= 1 7 1 4 2 1 G e V )


86/193

I n d i r e c t s e a r c h f o r t o p a n d H i g g s

P r e c i s i o n o b s e r v a b l e s a r e a e c t e d b y q u a n t u m u c t u a t i o n s :

! g i v e a c c e s s t o t w o h i g h m a s s S M s c a l e s : m

t

a n d M

H

t ; H e n t e r i n l o o p c o r r e c t i o n s t o E W o b s e r v a b l e s .

E . g . r a d i a t i v e c o r r e c t i o n s t o M

W

, M

Z

v s . s i n

2

#

W

r e l a t i o n :

s i n

2

W

= 1 ?

M

2

W

M

2

Z

Q u a d r a t i c d e p e n d e n c e o n m

t

a n d l o g a r i t h m i c o n M

H

:

/ m

2

t

/ l o g M

H

( S e n s i t i v i t y a l s o t o B S M p h y s i c s . )


87/193

EW precision fits: perturbatively calculate observables in tparameters:

MZ, GF, (MZ), MW, mf, (s(MZ))

extracted from experiments with high accuracy.

SM needs Higgs boson to cancel infinities, e.g.

MW, MZ W,Z W,Z

H

Finite logarithmic contributions survive, e.g. radiativto = M2W/(M

2Z cos

2 W):

= 1 11g2

962 tan2 W lnMH

MW

Main effects in oblique radiative corrections (S,T-parame

New physics at the scale will appear as higher dimensioperators.


88/193

E W p r e c i s i o n o b s e r v a b l e s l e d t o m

t

p r e d i c t i o n !

D e t e r m i n a t i o n s o f m

t

f r o m

1 . t s t o E W o b s e r v a b l e s ( o p e n c i r c l e s )

2 . 9 5 % c o n d e n c e - l e v e l ( C L ) l o w e r b o u n d s o n m

t

Particle Phenomenology

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