Äîêóìåíò âçÿò èç êýøà ïîèñêîâîé ìàøèíû. Àäðåñ îðèãèíàëüíîãî äîêóìåíòà : http://qfthep.sinp.msu.ru/talks2011/2011QFTHEP-MS4.pdf Äàòà èçìåíåíèÿ: Wed Oct 5 14:19:38 2011 Äàòà èíäåêñèðîâàíèÿ: Mon Oct 1 19:46:57 2012 Êîäèðîâêà: ISO8859-5

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Main Ingredients of Spectral Density
We denote (Q2 , s) = (0) (Q2 , s) + as(1) (Q2 , s) + a2 (2) (Q2 , s) s NLO Spectral Density -- in [Mikhailov&Stefanis(2009)], partially corrected in [ABOP(2011)]: Im (1) 2 (Q , s) = (T1 ) (Q2 , -s - i) , s 0

QFTHEP'2011@Sochi (Russia)

TFF in LCSRs and DA: Global data fit

- p. 12


Main Ingredients of Spectral Density
We denote (Q2 , s) = (0) (Q2 , s) + as(1) (Q2 , s) + a2 (2) (Q2 , s) s NLO Spectral Density -- in [Mikhailov&Stefanis(2009)], partially corrected in [ABOP(2011)]: Im (1) 2 (Q , s) = (T1 ) (Q2 , -s - i) , s 0 NNLO0 Spectral Density -- in [M&S(2009)] Im (2,) 2 (T2 ) (Q2 , -s - i) , s 0 (Q , s) = 0 Both (1) and (2,) are obtained for arbitrary Gegenbauer harmonic.

QFTHEP'2011@Sochi (Russia)

TFF in LCSRs and DA: Global data fit

- p. 12


Main Ingredients of Spectral Density
We denote (Q2 , s) = (0) (Q2 , s) + as(1) (Q2 , s) + a2 (2) (Q2 , s) s NLO Spectral Density -- in [Mikhailov&Stefanis(2009)], partially corrected in [ABOP(2011)]: Im (1) 2 (Q , s) = (T1 ) (Q2 , -s - i) , s 0 NNLO0 Spectral Density -- in [M&S(2009)] Im (2,) 2 (T2 ) (Q2 , -s - i) , s 0 (Q , s) = 0 Both (1) and (2,) are obtained for arbitrary Gegenbauer harmonic. "Tw-6" contribution -- in [ABOP-PRD83(2011)0540020] s q q 2 x2 1 2 2xlnxx - x + 2 (x) - (Q , x) = 8 CF 2 Q6 Ncf 1-x

tw6

+
- p. 12

QFTHEP'2011@Sochi (Russia)

TFF in LCSRs and DA: Global data fit


High order corrections result
Twist-6 and NNLO0 contributions to the Q F
2

(Q2 )

with BMS-like Pion DA They practically cancel out each other [BMPS(2011)]

QF
0.02

2



0.01

tw6(Q2 )

0.00

0.01

NNLO0 (Q2 ) Q2 [GeV2 ]
10 20 30 40

0.02

We use this residual as theoretical uncertainty of our prediction, that provides us with an additional 3%-uncertainty.
QFTHEP'2011@Sochi (Russia)

TFF in LCSRs and DA: Global data fit

- p. 13


Pie chart for Pion-Photon TFF at Q = 8 GeV
Result is dominated by Hard Part of Twist-2 LO contribution.

2

2

FF 100

Tw2 100.8 Tw4 6.5 Tw6 5.7

LO 120.5 NLO 13.8

NNLO 5.9

Blue = negative terms Red = positive terms
QFTHEP'2011@Sochi (Russia)

TFF in LCSRs and DA: Global data fit

- p. 14


Pie chart for Pion-Photon TFF at Q = 8 GeV
Result is dominated by Hard Part of Twist-2 LO contribution. Twist-6 contribution is taken into account together with NNLO0 one -- they has close absolute values and opposite signs.

2

2

FF 100

Tw2 100.8 Tw4 6.5 Tw6 5.7

LO 120.5 NLO 13.8

NNLO 5.9

Blue = negative terms Red = positive terms
QFTHEP'2011@Sochi (Russia)

TFF in LCSRs and DA: Global data fit

- p. 14


Parameters of LCSRs
From PDG:
s(m2 ) Z

From QCD SR:
2 Borel parameter MLC
SR

Masses m, m

Vector Chan. Threshold s0 Twist-4 2 Á 20% Twist-6 (S q q ) ?

Decay Widths , (for quasireal real )

Light-Cone Sum Rules: LO + NLO + Tw-4 + (NNLO0 +Tw-6)
-DA model

Data on FF Fitting -DA (an)
TFF in LCSRs and DA: Global data fit
- p. 15

FF Prediction
QFTHEP'2011@Sochi (Russia)


Direct Problem: LCSRs Results for Pion-Gamma Transition FF

QFTHEP'2011@Sochi (Russia)

TFF in LCSRs and DA: Global data fit

- p. 16


Pion-gamma FF vs Experimental Data
Comparison with all data: CELLO, CLEO and BaBar
0.35 0.30 0.25 0.20 0.15 0.10 0.05 0.00 1 10
BaBar 0

Q2 F (Q2 ) [GeV2 ]

curve

DA Asymp.QCD BMS bunch

CLEO CELLO



0 0

Q2 [GeV2 ]
100

BMS bunch describes very good all data for Q2 9 GeV2 .

QFTHEP'2011@Sochi (Russia)

TFF in LCSRs and DA: Global data fit

- p. 17


Pion-gamma FF vs Experimental Data
Comparison with all data: CELLO, CLEO and BaBar
0.35 0.30 0.25 0.20 0.15 0.10 0.05 0.00 1 10
BaBar 0 BaBar , BaBar e+ e- , CLEO 0 CELLO 0

Q2 F (Q2 ) [GeV2 ]

curve

DA Asymp.QCD BMS bunch

Q2 [GeV2 ]
100

BMS bunch describes very good all data for Q2 9 GeV2 . Note added BaBar , and e+ e- , data (1101.1142[hep-ex]): All they are inside BMS strip !

QFTHEP'2011@Sochi (Russia)

TFF in LCSRs and DA: Global data fit

- p. 17


Pion-gamma FF vs Experimental Data
Comparison with all data: CELLO, CLEO and BaBar
0.35 0.30 0.25 0.20 0.15 0.10 0.05 0.00 1 10
BaBar 0 BaBar , BaBar e+ e- , CLEO 0 CELLO 0

Q2 F (Q2 ) [GeV2 ]

curve

Agaev et al
Q2 [GeV2 ]
100

DA Asymp.QCD BMS bunch ABOP-1,3 PRD83-054020

BMS bunch describes very good all data for Q2 9 GeV2 . Note added BaBar , and e+ e- , data (1101.1142[hep-ex]): All they are inside BMS strip ! ABOP models are in between two sets of BaBar data.
QFTHEP'2011@Sochi (Russia)

TFF in LCSRs and DA: Global data fit

- p. 17


Inverse Problem: Fitting Pion DA from experimental data -- Confidential Regions
QFTHEP'2011@Sochi (Russia)

TFF in LCSRs and DA: Global data fit

- p. 18


Fitting pion DA under LCSR
We fitted experimental data on TFF by varying Gegenbauer coefficients of Pion DA.

QFTHEP'2011@Sochi (Russia)

TFF in LCSRs and DA: Global data fit

- p. 19


Fitting pion DA under LCSR
We fitted experimental data on TFF by varying Gegenbauer coefficients of Pion DA. Two sets of experim. data (1 - 9 GeV2 & 1-40 GeV2 ) were analyzed to show the influence of BaBar Data on Pion DA.

QFTHEP'2011@Sochi (Russia)

TFF in LCSRs and DA: Global data fit

- p. 19


Fitting pion DA under LCSR
We fitted experimental data on TFF by varying Gegenbauer coefficients of Pion DA. Two sets of experim. data (1 - 9 GeV2 & 1-40 GeV2 ) were analyzed to show the influence of BaBar Data on Pion DA.
0.30 0.25 0.20 0.15 0.10 0.05

F Q2

fit

Q2
0.00 1 10

Fit based on LCSRs with NLO+Tw4+3 Gegenbauers
QFTHEP'2011@Sochi (Russia)

TFF in LCSRs and DA: Global data fit

- p. 19


How many harmonics take into account?
The goodness-of-fit

0.6
2 ndf

2

ndf

-criterion vs conventional error (68.3% CL) as a function on
4

number n of fit parameters
n
100 Fstat n FB
F

6

1
3 5 4 2 3 2 1 1

2 0.4 3 4 5 6

0.2

n

n

1 - 9 Gev2 data region

Goodness - stable, while the error grows with n The compromise at
2
ndf

0.5 and n = 2, 3 is enough.

p. 6

BLTP JINR


How many harmonics take into account?
The goodness-of-fit

2.0
2 ndf

2

ndf

-criterion vs conventional error (68.3% CL) as a function on
100 Fstat n FB

number n of fit parameters
n
2
8 5 6
F

1

6

1.5
4

1.0 3 4 0.5 5 6
2 2 4 3

n

1

n

1 - 40 Gev2 data region

For fitting 1 - 40 Gev2 data region one should take n 3 parameters.

p. 6

BLTP JINR


NLC SR Results vs 3D Constraints
BMPS [PRD84(2011)034014]: 3D 1 -error ellipsoid at ÅSY = 2.4 GeV scale without t2 4 uncertainty w
0.4

a

6

0.3

Data Set 1 - 9 GeV

2

0.2

0.1

a
0.0 0.1 0.2 0.1

2

2D projection of 1 -error ellipsoid w 2df 0.4 n " BMS model with 2df 0.5 n

0.2

Best-fit = (0.17, -0.14, 0.12 Á 0.14) BMS = (0.14, -0.09)

a

4

Good agreement of all data at Q2 9 GeV2 At 68.3% CL we have good intersection 2D3D4D=
QFTHEP'2011@Sochi (Russia)

TFF in LCSRs and DA: Global data fit

- p. 20


NLC SR Results vs 3D Constraints
BMPS [PRD84(2011)034014]: 3D 1 -error ellipsoid at ÅSY = 2.4 GeV scale without t2 4 uncertainty w Data Set 1 - 9 GeV
2

2D projection of 1 -error ellipsoid w 2df 0.4 n " BMS model with 2df 0.5 n

Best-fit = (0.17, -0.14, 0.12 Á 0.14) BMS = (0.14, -0.09) Good agreement of all data at Q2 9 GeV2 At 68.3% CL we have good intersection 2D3D4D=
QFTHEP'2011@Sochi (Russia)

TFF in LCSRs and DA: Global data fit

- p. 20


NLC SR Results vs 3D Constraints
BMPS [PRD84(2011)034014]: 3D 1 -error ellipsoid at ÅSY = 2.4 GeV scale without t2 4 uncertainty w
0.4

a

6

0.3

Data Set 1 - 40 GeV

2

0.2

0.1

a
0.0 0.1 0.2 0.1

2

2D projection of 1 -error ellipsoid w 2df 1.0 n " BMS model with 2df 3.1 n

0.2

Best-fit = (0.18, -0.17, 0.31 Á 0.1) BMS = (0.14, -0.09)

a

4

Bad agreement of all data at Q2 40 GeV2 At 68.3% CL we have no intersection 2D3D=
QFTHEP'2011@Sochi (Russia)

, 3D4D=

.
- p. 20

TFF in LCSRs and DA: Global data fit


NLC SR Results vs 2D Constraints
NLC-bunch and lattice prediction at ÅSY = 2.4 GeV scale with accounting for t2 4 uncertainty. w DAs: x Asymp., v ABOP-3, " BMS, s CZ Lattice'10 estimate of a2 are shown by vertical lines.
0.2 0.1 0.0 0.1 0.2 0.3 0.0 0.1 0.2 0.3

a

4

Data Set 1 - 9 GeV

2

a

2
0.4

BMS bunch agrees well with the lattice data

QFTHEP'2011@Sochi (Russia)

TFF in LCSRs and DA: Global data fit

- p. 21


NLC SR Results vs 2D Constraints
2D-Analysis of the data at ÅSY = 2.4 GeV scale with accounting for t2 4 uncertainty. w DAs: x Asymp., v ABOP-3, " BMS, s CZ Lattice'10 estimate of a2 are shown by vertical lines.
0.2 0.1 0.0 0.1 0.2 0.3 0.0 0.1 0.2 0.3

a

4

Data Set 1 - 9 GeV

2

2D 1 -error ellipse

a

2
0.4

BMS bunch agrees well with the lattice data BMS bunch has better agreement with data up 9 GeV2 than with CLEO data only.
QFTHEP'2011@Sochi (Russia)

TFF in LCSRs and DA: Global data fit

- p. 21


NLC SR Results vs 2D Constraints
2D-Analysis of the data at ÅSY = 2.4 GeV scale with accounting for t2 4 uncertainty. w DAs: x Asymp., v ABOP-3, " BMS, s CZ Lattice'10 estimate of a2 are shown by vertical lines.
0.2 0.1 0.0 0.1 0.2 0.3 0.0 0.1 0.2 0.3

a

4

Data Set 1 - 9 GeV

2

a

2
0.4

2D 1 -error ellipse 2D-Proj. 3D-ellipsoid a6 = 0 cut of 3Dellipsoid

BMS bunch agrees well with the lattice data BMS bunch has better agreement with data up 9 GeV2 than with CLEO data only.
QFTHEP'2011@Sochi (Russia)

TFF in LCSRs and DA: Global data fit

- p. 21


NLC SR Results vs 2D Constraints
BMPS [arXiv:1105.2753 [hep-ph]]: 2D 1 -error ellipses at ÅSY = 2.4 GeV scale with accounting for t2 4 uncertainty. w DAs: x Asymp., v ABOP-3, " BMS, s CZ Lattice'10 estimate of a2 are shown by vertical lines.
0.2 0.1 0.0 0.1 0.2 0.3 0.0 0.1 0.2 0.3

a

4

Data Set 1 - 40 GeV

2

2D 1 -error ellipse 2D-Proj. 3D-ellipsoid
a
2
0.4

Bad agreement with 2D 1 -error ellipse No cross-section with a6 = 0 plane.
QFTHEP'2011@Sochi (Russia)

TFF in LCSRs and DA: Global data fit

- p. 22


3D Data Fit of Pion DA vs BMS (QCD SR)
:= BMS, := 1 - 9 GeV2 , at ÅSY = 2.4 GeV scale.
3

:= 1 - 40 GeV
3

2

x

x

2

2

1

1

0

0

1 0.0

3D

1, 9 GeV2 vs. BMS 0.2 0.4 0.6 0.8

x
1.0

1 0.0

3D

1, 40 GeV2 vs. BMS 0.2 0.4 0.6 0.8

x
1.0

BMS bunch agrees well with Data Set 1 - 9 GeV2 ;

QFTHEP'2011@Sochi (Russia)

TFF in LCSRs and DA: Global data fit

- p. 23


3D Data Fit of Pion DA vs BMS (QCD SR)
:= BMS, := 1 - 9 GeV2 , at ÅSY = 2.4 GeV scale.
3

:= 1 - 40 GeV
3

2

x

x

2

2

1

1

0

0

1 0.0

3D

1, 9 GeV2 vs. BMS 0.2 0.4 0.6 0.8

x
1.0

1 0.0

3D

1, 40 GeV2 vs. BMS 0.2 0.4 0.6 0.8

x
1.0

BMS bunch agrees well with Data Set 1 - 9 GeV2 ; New BaBar Data do not agree with BMS bunch based on NLC QCD SRs.

QFTHEP'2011@Sochi (Russia)

TFF in LCSRs and DA: Global data fit

- p. 23


3D Data Fit of Pion DA vs BMS (QCD SR)
:= BMS, := 1 - 9 GeV2 , at ÅSY = 2.4 GeV scale.
3

:= 1 - 40 GeV
3

2

x

x

2

2

1

1

0

0

1 0.0

3D

1, 9 GeV2 vs. BMS 0.2 0.4 0.6 0.8

x
1.0

1 0.0

3D

1, 40 GeV2 vs. BMS 0.2 0.4 0.6 0.8

x
1.0

B N NLC B

MS bunch agrees well with Data Set 1 - 9 GeV2 ; ew BaBar Data do not agree with BMS bunch based on QCD SRs. oth data sets does not match each other.
TFF in LCSRs and DA: Global data fit

QFTHEP'2011@Sochi (Russia)

- p. 23


End-point Bechavior of Pion DA
Integral derivative D
(2)

(x) =

1 x

x (y) 0y

dy

is an average derivative (x) near the end-point x = 0. Important property: lim D
x0 (2)

(x) = (0).

QFTHEP'2011@Sochi (Russia)

TFF in LCSRs and DA: Global data fit

- p. 24


End-point Bechavior of Pion DA
Integral derivative D
(2)

(x) =

1 x

x (y) 0y

dy

at ÅSY = 2.4 GeV scale.
1.0 0.8 0.6 0.4 0.2 0.0 3D: 1, 9 vs. 1, 40 GeV 0.2 0.00 0.05 0.10 0.15
2

60

x
50 40 30 20 10

D 2 x

3D

1 40 GeV

2

Asy 1 9 GeV 0.05 0.10
2

x
0.20 0 0.00

x
0.15 0.20

DA

1-9 GeV

2

and DA

1-40 GeV2

are separated near the origin.

BaBar Data demands End-Point Enhanced Pion DA.
QFTHEP'2011@Sochi (Russia)

TFF in LCSRs and DA: Global data fit

- p. 24


Confidential Region for Pion DA Moments vs. Lattice QCD

QFTHEP'2011@Sochi (Russia)

TFF in LCSRs and DA: Global data fit

- p. 25


2D Constraints and Lattice QCD
1 region in ( 2 , 4 ) plane from 2D(1 - 9 GeV2 ) analysis vs QCDSF&UKQCD Lattice Data [PRD74(2006)074501] at Ålat = 2 GeV scale:
0.13

curve

meaning 2D-1 -ellipse Lattice'06
0.12 0.11



4



0.10

0.09

0.08 0.20 0.22 0.24 0.26 0.28 0.30



2


0.32

Our 2D-1 region is almost completely inside Lattice'06 constraint.

QFTHEP'2011@Sochi (Russia)

TFF in LCSRs and DA: Global data fit

- p. 26


2D Constraints and Lattice QCD
1 region in ( 2 , 4 ) plane from 2D(1 - 9 GeV2 ) analysis vs RBC&UKQCD Lattice Data [PRD83(2011)074505] at Ålat = 2 GeV scale:
0.13

curve

meaning 2D-1 -ellipse Lattice'06 Lattice'10
0.12 0.11



4



0.10

0.09

0.08 0.20 0.22 0.24 0.26 0.28 0.30



2


0.32

Our 2D-1 region is one-half inside Lattice'10 constraint.

QFTHEP'2011@Sochi (Russia)

TFF in LCSRs and DA: Global data fit

- p. 26


2D Constraints and Lattice QCD
1 region in ( 2 , 4 ) plane from 2D(1 - 9 GeV2 ) analysis vs RBC&UKQCD Lattice Data [PRD83(2011)074505] at Ålat = 2 GeV scale:
0.13

curve

meaning 2D
0.7


0.12

4



-1 -ellipse

Lattice'06 Lattice'10 2D
1.5

0.11

0.10

-1 -ellipse

0.09

0.08 0.20 0.22 0.24 0.26 0.28 0.30



2


0.32

Our 2D-1 region with (M 2 0.7 GeV2 ) is one-half inside Lattice'10 constraint, whereas the 2D-1 region with ABOP value (M 2 = 1.5 GeV2 ) is completely out of Lattice'10 constraint!
QFTHEP'2011@Sochi (Russia)

TFF in LCSRs and DA: Global data fit

- p. 26


2D Constraints and Lattice QCD
1 region in ( 2 , 4 ) plane from 2D(1 - 9 GeV2 ) analysis vs RBC&UKQCD Lattice Data [PRD83(2011)074505] at Ålat = 2 GeV scale:
0.13

curve

meaning 2D-1 -ellipse Lattice'06 Lattice'10
0.12 0.11



4



0.10

0.09


0.08 0.20 0.22 0.24 0.26 0.28 0.30

2


0.32

Intersection of Lattice and 2D-1 region leads to prediction:

4 4

[0.11, 0.122] -- in a good agreement with estimation [0.095, 0.134] in [Stefanis, NPB.PS.181(2008)199].

QFTHEP'2011@Sochi (Russia)

TFF in LCSRs and DA: Global data fit

- p. 26


Fit Results and Pion DA Models

QFTHEP'2011@Sochi (Russia)

TFF in LCSRs and DA: Global data fit

- p. 27


Comparing Fit Results with Pion DA models
Model/Fit
a2 , a4 , a6 Fit BMS Agaev et al Kroll AdS/QCD CZ Asympt.

Values of an
(0.18, -0.17, 0.31) (0.14, -0.09) (0.08, 0.14, 0.09) (0.21, 0.01) 0.15, 0.06, 0.03 (0.39) (0, 0)

2 /ndf (1 - 9 GeV2 ) 0.4 0.5 2.8 3.8 2.3 32.3 4.7

2 /ndf (1 - 40 GeV2 ) 1.0 3.1 2.4 4.4 2.8 25.5 7.9

All values given at ÅSY = 2.4 GeV scale.

BMS DA gives best LCSR Description of TFF for Q2 9 GeV2 . All-Data LCSR-Fit Result is far from All Considered Pion DA Models.
QFTHEP'2011@Sochi (Russia)

TFF in LCSRs and DA: Global data fit

- p. 28


Comparing Different Data Set Analyses
Q2 regions [1 - 9] GeV
2

[1 - 40] GeV

2

BMS bunch
and

Agreement Agreement
2, 3 0.53, 0.44 20.2 Á 19.8 Á 1.1 6.6 Á 1.1 Á 0.4

No! No!
3, 4 1.0, 0.77 48.5 Á 11.4 Á 0.4 8.1 Á 0.7 Á 0.3

Number of harmonics n Best 2df n Derivative (x)|x=0 Derivative D
(2)

(0.4)

QFTHEP'2011@Sochi (Russia)

TFF in LCSRs and DA: Global data fit

- p. 29


Conclusions
By fitting Transition FF Data in LCSR Approach we obtained Confidential Regions for Gegenbauer coefficients, Moments, and Derivatives of Pion DA.

QFTHEP'2011@Sochi (Russia)

TFF in LCSRs and DA: Global data fit

- p. 30


Conclusions
By fitting Transition FF Data in LCSR Approach we obtained Confidential Regions for Gegenbauer coefficients, Moments, and Derivatives of Pion DA. Result of fitting the CELLO, CLEO, and BaBar Data up to 9 GeV2 is in a good agreement with previous CLEO-based fit and prefers the End-Point Suppressed (BMS) Pion DA.

QFTHEP'2011@Sochi (Russia)

TFF in LCSRs and DA: Global data fit

- p. 30


Conclusions
By fitting Transition FF Data in LCSR Approach we obtained Confidential Regions for Gegenbauer coefficients, Moments, and Derivatives of Pion DA. Result of fitting the CELLO, CLEO, and BaBar Data up to 9 GeV2 is in a good agreement with previous CLEO-based fit and prefers the End-Point Suppressed (BMS) Pion DA. Taking into account all the data on F (Q2 ), including the new BaBar points with Q2 = 10 - 40 GeV2 , requires sizeable coefficient a6 , while a2 and a4 remain the same. All-Data-Fit prefers End-Point Enhanced Pion DA.

QFTHEP'2011@Sochi (Russia)

TFF in LCSRs and DA: Global data fit

- p. 30


Conclusions
By fitting Transition FF Data in LCSR Approach we obtained Confidential Regions for Gegenbauer coefficients, Moments, and Derivatives of Pion DA. Result of fitting the CELLO, CLEO, and BaBar Data up to 9 GeV2 is in a good agreement with previous CLEO-based fit and prefers the End-Point Suppressed (BMS) Pion DA. Taking into account all the data on F (Q2 ), including the new BaBar points with Q2 = 10 - 40 GeV2 , requires sizeable coefficient a6 , while a2 and a4 remain the same. All-Data-Fit prefers End-Point Enhanced Pion DA. Evident conflict between ( and ) and 0 BaBar Data may signal about strong isospin symmetry violation in pseudoscalar meson sector.

QFTHEP'2011@Sochi (Russia)

TFF in LCSRs and DA: Global data fit

- p. 30


Conclusions
By fitting Transition FF Data in LCSR Approach we obtained Confidential Regions for Gegenbauer coefficients, Moments, and Derivatives of Pion DA. Result of fitting the CELLO, CLEO, and BaBar Data up to 9 GeV2 is in a good agreement with previous CLEO-based fit and prefers the End-Point Suppressed (BMS) Pion DA. Taking into account all the data on F (Q2 ), including the new BaBar points with Q2 = 10 - 40 GeV2 , requires sizeable coefficient a6 , while a2 and a4 remain the same. All-Data-Fit prefers End-Point Enhanced Pion DA. Evident conflict between ( and ) and 0 BaBar Data may signal about strong isospin symmetry violation in pseudoscalar meson sector. To resolve BaBar puzzle we need Belle verification of Transition FF Data.
QFTHEP'2011@Sochi (Russia)

TFF in LCSRs and DA: Global data fit

- p. 30


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? åå Î ì Î Í Îì àã ì + Îì àã ì - ì + Î(? ) - ? ì Î Ö Ù Í-ì

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a)


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b)


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c)







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d)



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BaBar Doubts about BaBar data?
BaBar Collaboration also measured FFs of and , see [Arxiv:1101.1142].

From and FFs they extracted hypothetical n FF using - mixing in the quark flavor basis:
1 |n = (|uu + |dd ), 2 | = cos |n - sin |s , | |s = |ss , = sin |n + cos |s ,

Take into account flavor structure and quark charges 5 5 2 2 2 2 eu + ed = Ç eu - ed factor . 3 3
FF and Pion DA - p. 18

with = 39.9 Á 2.9 .

Frontiers in Nuclear Physics @ Dubna, May. 16-19, 2011


BaBar Doubts about BaBar data?
BaBar Collaboration also measured FFs of and , see [Arxiv:1101.1142]. curve
DA

(3/5)Q Fn(Q ) (GeV)

0.3

CZ BMS
0.2

2

Asymp. BMS-curve goes just through the new BaBar data!
0 BaBar data are in contradiction with , BaBar data!
FF and Pion DA - p. 19

2

0.1

BABAR ( 0) CLEO ( ,/) CLEO (e+e- ,/) BABAR ( ,/) BABAR (e+e- ,/) 10
2

0 10

2

Q (GeV )
Frontiers in Nuclear Physics @ Dubna, May. 16-19, 2011

2


Attempts to solve the "pion puzzle"
A possible scenarios to explain the BaBar data A. Dorokhov [0905.3577] with constituent quark model 2 Q2 F (Q2 ) ln2 (Q2 /Mq ) with Mq 135 MeV.

Dorokhov QCD asymptotics [CELLO 91] [CLEO 98] [BaBar 09]

Note Mq

135 MeV< 300 MeV. No trace of QCD...
FF and Pion DA - p. 20

Frontiers in Nuclear Physics @ Dubna, May. 16-19, 2011


Attempts to solve the "pion puzzle"
A possible scenarios to explain the BaBar data A. Radyushkin [0906.0323] with "flat" DA (x) 1 and using Light-Front Gaussian model:
1

Q2 F

LFG

(Q2 )
0 2

(x) x

1 - exp -

xQ

2

2x ?

dx

Here

0.53 GeV .

Frontiers in Nuclear Physics @ Dubna, May. 16-19, 2011

FF and Pion DA - p. 20


Attempts to solve the "pion puzzle"
A possible scenarios to explain the BaBar data A. Radyushkin [0906.0323] with "flat" DA (x) 1: Q2 LFG Q2 F (Q2 , 0) ln , M 2 = 2 e-E 0.6 GeV2 . M2

&

LFG model QCD asymptotics [BaBar 09]

No Factorization. Rad. Corrs. removed by hand!
FF and Pion DA - p. 20

Frontiers in Nuclear Physics @ Dubna, May. 16-19, 2011


Attempts to solve the "pion puzzle"
A possible scenarios to explain the BaBar data M. Polyakov [0906.0538] with "flat" DA (x, Å0 = 0.6 GeV) = 1.3 - 0.3 Ç 6 x (1 - x) and using:
1

Q2 F

Pol

(Q2 )
0

(x, Q2 ) x + m /Q
2 2

dx

Here m

0.65 GeV from BaBar data fit.

Ç

Polyakov QCD asymptotics [BaBar 09]

QCD Evolution is here!

Frontiers in Nuclear Physics @ Dubna, May. 16-19, 2011

FF and Pion DA - p. 20