QCD for B Physics
description
Transcript of QCD for B Physics
H. Kawamura, “QCD for B physics”
QCD for B Physics
KEK Theory meeting “Toward the New Era of Particle Physics ”
Dec.12 2007
Hiroyuki Kawamura (RIKEN)
H. Kawamura, “QCD for B physics”
B Physics
• NP search by (over)constraining “unitarity triangle”
• Flavor mixing + CP violation via weak interaction
HFAG: LP07
H. Kawamura, “QCD for B physics”
ex. (semi-leptonic decay)
QCD for B Physics• Extraction of |VCKM| and φCP from hadronic weak decays requires a good understanding of QCD effects.
• QCD effects are even necessary for “direct CP violation” — phase is detected through quantum interference
+
ex. (hadronic decay)
or B B
T (tree) P (penguin)
(*)B D l
B
H. Kawamura, “QCD for B physics”
Theoretical tools
• Light flavor symmetry: isospin, SU(3) symmetry, …
• Heavy quark effective theory (HQET)
• Λ/mb expansion ↔ separation of scales (factorization)
ex. isospin analysis for B → ππ etc.
• QCD factorization for inclusive semi-leptonic decay
• Lattice simulation
(Observable) ( , ( ), ) ( , ) ( )
p
iji W NP b i bi j b
C M M m H m O Om
• Light-cone sum rule (quark hadron duality, spectral function,OPE,…)
This talkMw
mb
Λ
μ
,cB X l
, ,B D • Soft-Collinear effective theory
• QCD factorization for exclusive hadronic decay
MNP
perturbative
H. Kawamura, “QCD for B physics”
HQET
• Can be described by an effective field theory which includes only soft modes of “large component “of Q + soft quarks + soft gluon
Heavy-light meson system
HQET field:
• Perturbative matching with full QCD (αs(mb) small) :
Wilson coeff.
Leading term : SU(2Nf) Spin-Flavor symmetry
mb
Λ
Mw
μ
QCD
HQET
H. Kawamura, “QCD for B physics”
Meson spectrum
•
•
H. Kawamura, “QCD for B physics”
Exclusive semi-leptonic decays
B (*)D
l
(*)B D l
• heavy-heavy form factorIsgur-Wise function
At the “zero-recoil limit” :
H. Kawamura, “QCD for B physics”
Experimental result
LP07
⇓
Extrapolation of the data to ω=1
2007 WA
H. Kawamura, “QCD for B physics”
Inclusive semi-leptonic decays
cB X l• total rate
OPE (short distance expansion)
⇒ ( ( ))i s bi
C m
iO
propagator1
↔
H. Kawamura, “QCD for B physics”
Moments vs. |Vcb| & HQET parameters
Moment → Vcb & HQET parameters
(kinetic energy)
⇓
Buchmuller & Flacher (‘05)
H. Kawamura, “QCD for B physics”
• differential rateuB X l
B→ Xulν
kinematical cuts to avoid Xc background. ex.
propagator
→ outgoing jet has low virtuality (sensitive to soft physics)
scale of outgoing jet :
non-local for b-quark residual momentum: shape function
Factorization Korchemsky, Sterman (’94)
H. Kawamura, “QCD for B physics”
• Shape function: new non-perturbative object
• Strategies for extracting |Vub| from B → Xulν
— ME of Light-cone non-local operator (similar to parton distribution)
1. Fit S(ω) from B → Xsγ, use it for B → Xulν
2. Use “shape-function free ” relation between B → Xsγand B → πlν
Lange, Neubert ,Paz (’05)
ex. Lange, Neubert ,Paz (’05)
: weight function (calculated at 2-loop)
: residual hadronic power corrections
Leibovich,Low,Rothstein (‘99)
B→ Xulν
H. Kawamura, “QCD for B physics”
LLR: Leibovich,Low,Rothstein (’99) ↔ 1-loop, without rhc LNP: Lange, Neubert ,Paz (’05)
|Vub| from BaBar data • ”SF free” analysis by Golubev, Skovpen, Luth : hep-ph/0702072v2
error: exp.(Xulν) +exp. (Xsγ) + th.
H. Kawamura, “QCD for B physics”
Exclusive hadronic decays
B D Effective Hamiltonian
• Naïve factorization
4-fermi operators
• QCD factorization holds for decays in which the spectator quark is absorbed into the final heavy meson.
from “color transparency” argument, but no μ dependence
B D
πT0,8
Фπ
FB→π
Beneke, Buchalla, Neubert, Sachrajda (’00)
H. Kawamura, “QCD for B physics”
B→Dπ• What must be shown?
— gluon exchange between (B,D) and π• Soft div. cancel among diagrams• Collinear div. absorbed into universal pion wave function
— shown up to 2-loop by BBNS (’00) All-order proof was given using SCET : Bauer et al. (‘01)
• SCET (Soft-Collinear effective theory)
HQET (soft) + collinear modes of quark & gluon + …
— systematic expansion in
— soft mode decouple with col. modes from power counting
→ Factorization proved at the leading power in operator language
light-like vector
H. Kawamura, “QCD for B physics”
, , B K • Key point: B → π form factor B
— end-point singularity ↔ soft nature of spectator quarks— “hard-collinear scale”
asymptotic form
• 3 formalisms have been developed in recent years
(1) QCDF (BBNS:’99 - )
• end-point singularity included in the form factor.• proof given by SCET.• power corrections partly included (parameterized)• NLO calculation completed
B → M1 M21
2 1 2
B M I IIM M M BF T T
B→ππ, Kπ
H. Kawamura, “QCD for B physics”
(2) SCET (BPSR ’04-) Bauer, Pirjol, Stewart, Rothstein
• end-point singularity included in the form factor• hard-collinear scale distinguished. → different formula from (1)• power correction neglected• modest → large number of fitted input
1
2 1 2
B M I IIM M M BF T T J
(3) PQCD (’01-) Li, Kuem, Sanda, Kurimoto, Mishima, Nagashima, , ,
• kT factorization + Sudakov →end-point suppressed• power counting different from (1) & (2).• more predictive power• NLO calculation has started
1 2
( ) ( , ) ( , ) ( , )S bM M BH e x b y b k b
b:impact parameter
B→ππ, Kπ
H. Kawamura, “QCD for B physics”
Theory (QCDF) vs. Data Beneke (Beauty06)
( )Br B PP ( )CPA B PP
• Good agreement with B → PP, PV data except “πK puzzle” and large direct CP of π+π- (input set S4: Beneke &Neubert (’03))
• BPRS, PQCD are also good.
• How can different formalism can give similar prediction?
H. Kawamura, “QCD for B physics”
CKM phase from data
123 8
0.58 0.09
65
S
63 6
0.03 0.09
69
S
123 8
0.13 0.19
65
S
Average:
3 (68 4)
3 (61 5)
UT fit
Beneke (Beauty06)
H. Kawamura, “QCD for B physics”
B meson LCWF
• Operator definition
=(1,0,0, 1) nm -light-cone vector:
momentum rep.
0
tn
k v momentum of light quark (at tree level)
Complicated object which contains soft + “hard” dynamics
• In SCET soft fieldscol. fields
• Hard radiative tail
( )lo(
g) sB iFaf
m
ww
w-:
0( )j
Bdwwf w¥
=- ¥ò
H. Kawamura, “QCD for B physics”
Operator relations Kodaira, Tanaka, Qiao, HK (’01)
HQ symmetry + EOM
→
3-body ops.
( ( )) ( ) ( )( ) BWWBB
gf f wwf w = +“Solution”
( )2
( ) (2 )2
WWB iF
wf w q w= L -
L“Wandzura-Wilczek approx.”
( ) 0 ( )vg
B q hG B vf :
— “Twist = Dimension - Spin” is not a good quantum number
B bm mL = -
— Higher dim. operators appear in IR region (at large tΛ)
v vvh h 0vq D v Dh �
“enhanced power correction” Lee,Neubert,Paz (’06) Shape Function
H. Kawamura, “QCD for B physics”
Radiative corrections
( )( )
( )
( )
211-loop
0
22
5
loglog
5( , ) (1 )
2 2
log
l
( ) (
4
0 ( )1
1
1
o
2
12
1
1
01
g
)
2 UVUV
IR IR
s
R
F
I
B
Uv
V
Ct d
B
itit
it
i
vq tn n
t
h
t
a pf m x d
x g
m
ex
pm
m
m
e e
x
e
e x
e
x
+
éì æ öï ÷ï çê ÷= - + + + -çí ÷ê ç ÷ï çè øêïîëüæ ö æ öé ù ï÷ ÷ïç çê ú÷ ÷+ - - +ç ç ý÷ ÷ç çê ú ÷÷ çç ï- è øè øë û ïþ
æ ö÷ç- - -çççè ø+
ò%
52( ) (00 ( ) ( ) (IR pole, higher-dim ps )) o .v B v Oq vt Dn tn hx g ù÷ +ú÷ ×
÷ û
su
Lange & Neubert (’03), Braun et al,(03),Li & Liao (’04), Lee & Neubert (’05)
• Cusp singularity2log ( )it
• non-analytic at t=0 1
( )t
→ hard radiative tail
0(0) exp ( ) ( )v vh P ig dsv A sv h v
1-loop
MSEe= gm m
• UV & IR structure different!
H. Kawamura, “QCD for B physics”
Evolution equation
Consistent with Lange & Neubert (’03)
H. Kawamura, “QCD for B physics”
Operator product expansion
• Separation of UV & IR behavior ⇒ OPE• Interpolate B meson LCWF to HQET parameters
RG evolution for LCWF
2
1 1,
UV UVe e
1
IRe
RG evolution for local ops.
( , ) ( , ) ( )( )0Bi
iiOt C t B vf m m m+ =å% %
many higher-dim. ops
expansion parameter
1-loop matching
H. Kawamura, “QCD for B physics”
• Lee & Neubert PRD72(’05)094028 : Cut-off scheme up to dim-4 ops.
Operator product expansion (cont’d)
vq hG vqD hGUV UV( , , ) ( , , 0 ( ))) (B ii
it C t O B vf m m mL L=å% %
• Our calculation (HK & K.Tanaka)
( , ) ( , (() 0 ))B ii
it C t B vOf m m m=å% %
→ OPE + exponential ansatz “hybrid model”
MS-bar scheme up to dim-5 ops. vq hG vqD hG
{ }, v vDq hD qG hG G+
H. Kawamura, “QCD for B physics”
Calculation
• 2-point + 3-point functions with non-local operators
• Operator identification calculation in x-space
• Keep gauge invariance explicitly background method + Fock-Schwinger gauge
(C)1
(C) (C)
0 (( ) (0 ))x A x A x duux G uxr
m rm mm Þ == ò
50
( )P exp ( ) (0)t
vq tn ig d n A n n hmml l g
æ ö÷ç ÷ç ÷è øò
→ decouple from Wilson line
H. Kawamura, “QCD for B physics”
dim.3
dim.4
dim.5
ResultMS
Ee= gm m
H. Kawamura, “QCD for B physics”
Matrix elements
dim.3
dim.4
B bm mL = -
dim.5 (covariant tensor formalism)
“Chromo-electronic”
“Chromo-magnetic”
: decay constant
H. Kawamura, “QCD for B physics”
LCWF from OPE
• Dim.3&4 terms reproduce the results in cut-off scheme by Lee & Neubert (’05)
dim.3
dim.4
dim.5
• Represented by HQET parameter: ↔ Lattice, QCD sum rule
Evolution & phenomenological studies underway!
H. Kawamura, “QCD for B physics”
Summary
• Understanding of QCD effects in B physics has been largely improved in recent years.
• B meson wave function for exclusive B decay is quite different from pion wave function.
• OPE for bilocal operator for B meson LCWF to dim.5 → expressed by 3 HQET parameters
1/ t different UV & IR structures
, , E H
• Model-independent study of B meson LCWF is underway.
• Similar analysis for shape function is ongoing.