1

QCD Radiative Corrections to Form Factors

Nan Zhu Yan tai University

Workshop of HFCPV, 2012.10.25-28

,B K

2

Outline

form factor and the extraction

of .

form factors.

Summary

lB lv

ubV

B Kl l

3

form factor and the extraction of .

● Experimental observations

BABAR , PRD 83 (2011) 052011

● Partial rate for

lB lv 2( )Bf q

ubV

lB lv

BABAR ,PRD 83 (2011) 032007

4

● BABAR, PRD 83 (2011) 052011

form factor and the extraction of .

2( )Bf q

ubV

2 2 2( ) ( ) 2 ( ) ( ( ) ( ))B B Bp u b B p q f q p f q f q q

● transition is parameterized as

lB lv

lB lv

5

●

●

form factor and the extraction of .

lB lv 2( )Bf q

ubV

6

form factor and the extraction of .

lB lv 2( )Bf q

ubV

7

One-loop Feynman diagrams contributing to the correction function

form factor and the extraction of .

lB lv 2( )Bf q

ubV

8

form factor and the extraction of .

lB lv 2( )Bf q

ubV

9

form factor and the extraction of .

lB lv 2( )Bf q

ubV

form factor and the extraction of .

lB lv 2( )Bf q

ubV

form factor and the extraction of .

● Central values and respective uncertainties due to each of inputs

lB lv 2( )Bf q

ubV

● Comparison of theoretical predictions

Approach[Ref.]

LCSR Phys.Rev.D83(2011)094031

Phys.Rev.D71(2005)014015

JHEP 04(2008)014

This work

form factor and the extraction of .

lB lv 2( )Bf q

ubV

form factor and the extraction of .

lB lv 2( )Bf q

ubV

Zuo.Hong.Li, Nan Zhu,Xiaojiao Fan,Tao Huang,JHEP 1205(2012)160.

Accessing the large region with z-parameterization

This parameterization ensures general analytic properties

of the form factor

form factor and the extraction of .

lB lv 2( )Bf q

ubV

To obey the expected near –threshod behavior ,the following relation

Is introduced

form factor and the extraction of .

lB lv 2( )Bf q

ubV

We fitted the numerical LCSR prediction for the form factor with

N=2

form factor and the extraction of .

lB lv 2( )Bf q

ubV

(0)Bk kb f b

So that

Finally, we have

1

0 0 0

1

1 [ (0, ) ( 1) (0, ) ]N

k k N N

k

k

kb b z t z t

N

form factor and the extraction of .

lB lv 2( )Bf q

ubV

18

2 2 2( ) ( ) 2 ( ) ( ( ) ( ))B K B K B KK p s b B p q f q p f q f q q

22 2 2 ( )

( ) ( ) [ (2 ) ( ) ]B K

TB K

B K

if qK p s q b B p q q p q m m q

m m

form factors B K2 2 2

0( ) , ( ) , ( )B K B K B K

Tf q f q f q

19

form factors

2 2/,2 2 2 ,4 2 2 ,2 2 2

0 0 0 0 1 02(0) ( , , ) ( , , ) ( , , )

2 4

Bm MB K K B K B K Bs F

B B

Cef F q M s F q M s F q M s

f m

2 2 2

2

0

1

,2 2 2 2

0 0( , , ) 2 ( )b Km q u m uu

K B uMb K K

u

duF q M s m f e u

u

2 2 2

2

0

1

,4 2 2 2

0 0( , , ) 2b Km q u m uu

K D uMb K

u

duF q M s m f e •

u

2 2

2 2 2 2 4 42 2 2 2

0

1 2( ) (1 ) ( )

u

KK K

b K b K

u mu u dv v

m q m u m q m u

2 2 42

2 2 2 2 42 2 2 2 2 2 2 2 2 2

6 12( )

4( ) ( )

b K KK

b K b K b K

m u um umd du

m q m u dudu m q m u m q m u

B K2 2 2

0( ) , ( ) , ( )B K B K B K

Tf q f q f q

2 2 42

2 2 2 2 42 2 2 2 2 2 2 2 2 2

6 12( )

4( ) ( )

b K KK

b K b K b K

m u um umd du

m q m u dudu m q m u m q m u

24

42 2 2 2

2 ( )( )K K

K

b K

um d udu

du dum q m u

2 2 2

42 2 2 2 2 2 2 2

2 41 ( )K K

K

b K b K

um u mdu u

m q u m du m q u m

2 2 2 2 2 21

42 2 2 2 2 2 2 2 2

2 ( ) 6( )

( )

K b K KK

ub K b K

um m q u m umdd

m q u m du m q u m

2

24

4

2 2 2 2 2

1

( )

4( )

cm

WWMb K K

b K u

m f e d u

m q u m du

B K2 2 2

0( ) , ( ) , ( )B K B K B K

Tf q f q f q

form factors

B K2 2 2

0( ) , ( ) , ( )B K B K B K

Tf q f q f q

form factors

02

2

1,2 2 2 /

1 00

( , , ) Im ( )

B

b

s

K B s M

s K

m

fF q M s dse du T u

B K2 2 2

0( ) , ( ) , ( )B K B K B K

Tf q f q f q

form factors

Form factors at 2 0q

23

Summary

● Form factor for is

calculated in a revised LCSR to twist-5

accuracy.

● Providing two methods to extract

● Giving the form factors.

lB lv2( )Bf q

ubV

B K l l