Precision Charmed Meson Spectroscopy and Decay Constants from Chiral Fermions
Model independent analysis of B meson light-cone wavefunction
description
Transcript of Model independent analysis of B meson light-cone wavefunction
Model independent analysis of B meson light-cone wavefunction
BNM08 in AtamiJan.24-26 2008
Hiroyuki Kawamura (RIKEN)
Work in collaboration with K.Tanaka (Juntendo Univ.)
Hiroyuki Kawamura (RIKEN) BMN2008
BBNS vs. data
QCD Factorization for Exclusive B decays: B →ππ, πlν, γlν…
→ systematic framework to calculate QCD effects in the mb →∞ limit
Beneke et al. (’99)Bauer, Pirjol, Stewart (’01)Keum, Li, Sanda (’01)
1 2B M M
• successful to describe the hadronic B decays.
• In some cases, the ignorance of B meson wavefunction gives a major theoretical uncertainty. ex. hard spectator interactions in B→π0π0
( )Br B PP
Beneke (Beauty06)
Introduction
etc.
Hiroyuki Kawamura (RIKEN) BMN2008
• B meson light-cone wavefunction in HQET
=(1,0,0, 1) nm - light-cone vector:
In momentum space
0
tn
k v momentum of light quark
• UV structure (radiative tail)
( )lo(
g) sB iFaf
m
ww
w-:
0( ) ( 0)j
Bd jww f w¥
=- ¥ ³ò
B meson LCWF
HQET field:
Radiative corrections generate a hard negative tail. ↔ pion LCWF
2 ( =1)Bp m v vm m=
Hiroyuki Kawamura (RIKEN) BMN2008
— Contributions from higher dim. Operators in the IR region.
Kodaira, Tanaka, Qiao, HK (’01)
HQ symmetry + E.O.M.
( ( )) ( ) ( )( ) BWWBB
gf f wwf w = +
( )
2( ) (2 )
2
0 (0)( ) ( )
WWB
nv
iF
q v D h B v
wf w q w= L -
L
« ×
“Wandzura-Wilczek” part
( ) 0 ( )gB vq hG B vf :
— “twist = dimension - spin” is not a good quantum number
v vvh h 0vq D v Dh � ��������������
IR structure
→
Hiroyuki Kawamura (RIKEN) BMN2008
• non-analytic at .
• cusp singularity → radiative tail
Lange & Neubert (’03), Braun et al. (03),Li & Liao (’04), Lee & Neubert (’05)
2log ( )it
log( ) it
0(0) exp ( ) ( )v vh P ig dsv A sv h v
MSlog( ), EL it egm m m= =
• UV & IR structures are different!
Radiative corrections
1-loo
21
5
p
2
50 2
( , )
5(1 ) 0 ( )
2 24 1
( ) (0)
( ) (
1
0
11
20 ) (
2
1
IR
IR
UV UVUV
B
sv
v
F LL
t
Cd B vq tn n h
q tnL h Bn
e ee
f m
a px g
x g
p xe
e
xx d x
+
éì üæ ö æ öé ùï ï÷ ÷ï ïê ç ç ê ú÷ ÷= - + + + - + -ç çí ý÷ ÷ê ç ç ê ú÷÷ï ç ïç -è øè ø ë ûêï ïî þëæ ö÷ç ÷- +ç ÷ç ÷çè ø
ò
%
5
2
) 2 1 0 ( )
( ) ( ,
1
IR po
( ) (0)
higher-dim ople .s )s
IRvqv t B v
O t
L Dn hvtnx x ge
æ ö÷ç ÷- -+ ×-ç ÷ç ÷çè ø
ù+ úû
su
RG evolution
CUSP0t
Hiroyuki Kawamura (RIKEN) BMN2008
• gives a natural scale to separate UV & IR behaviors ⇒ OPE
Operator product expansion
• B meson LCWF in terms of HQET parameters
RG evolution for LCWF2
1 1,
UV UVe e
1
IRe
OPE at
( , ) ( , (() 0 ))B ii
it C t B vOf m m m=å% %
expansion in
F bm
t
1/ t
UV
IR
µ( , ) ( , ) ( , )B F F Bt U tf m m m f m= Ä% %
with higher dim. ops.
1
t
1/ t
2log ( ), log( )it it 1/ t correlated
Hiroyuki Kawamura (RIKEN) BMN2008
• Lee & Neubert PRD72(’05)094028
OPE at NLO
vq hG vqD hG
UV UV( , , ) ( , , 0 ( ))) (B ii
it C t O B vf m m mL L=å% %
• This work
( , ) ( , (() 0 ))B ii
it C t B vOf m m m=å% %
MS-bar scheme, up to dim-5 ops. vq hG vqD hG
{ }, v vDq hD qG hG G+
cut-off scheme, up to dim-4 ops.
Hiroyuki Kawamura (RIKEN) BMN2008
Calculation
• 1-loop matching of the non-local operator for B meson LCDA with non-local ops. up to dim.5
many dim. 5 ops.
→ calculation in x-space keeping gauge invariance explicitly.
(C)
1(C) (C)
0 (
(
) (
0
)
)x A x
A x duux G uxrm r
m
m
m
Þ =
=
ò
{ }50
( )P exp ( ) (0) , , , t
v v v v vD Dq tn ig d n A n n h q h q h q h q hD Gmml l g
æ ö÷ç « G G G G÷ç ÷è øò
→ decouple from Wilson line
• Fock-Schwinger gauge forclA
cl qA A A
• Background field method
Hiroyuki Kawamura (RIKEN) BMN2008
dim.3
dim.4
dim.5
OPE up to dim.5 (NLO in MS-bar scheme)
MSEe= gm mlog( )L i tm=
Hiroyuki Kawamura (RIKEN) BMN2008
Matrix elements
dim.3
dim.4
dim.5 (covariant tensor formalism)
“Chromo-electronic”
“Chromo-magnetic”
← decay constant
Hiroyuki Kawamura (RIKEN) BMN2008
B meosn LCWF from OPE
• Dim.3&4 terms reproduce the results in cut-off scheme by Lee & Neubert (’05)
dim.3
dim.4
dim.5
• Expressed in terms of 3 HQET parameters:
• in on-shell scheme suffers IR renormalon ambiguities.
→ “distribution amplitude” scheme
Hiroyuki Kawamura (RIKEN) BMN2008
real part imaginary part
• Contributions from dim. 5 operators are important.• Effects from are very small. • Evolution effects must be included.
LCWF from OPE at 1GeV
Inputs:Grozin,Neubert (’97)
Lee,Neubert (’05)
, E H
(QCD sum rule)
Hiroyuki Kawamura (RIKEN) BMN2008
• expressed in terms of 3 HQET parameters at
Summary
• Knowledge of B meson LCWF is important to reduce the theory error for exclusive B decays.
• Radiative correction to B meson LCWF
• OPE for B meson LCWF — up to dim.5 — NLO corrections to Wilson coefficient
1/ t
— different UV & IR structures
, , E H
• Model-independent study including RG evolution is underway.
• Similar analysis for shape function is possible.
— 2log ( ), log(it )it →
( , )B t
( , )B t 1GeV
Hiroyuki Kawamura (RIKEN) BMN2008
LCWF with analytic continuation t i