Dipion Spectrum : e e- annihilations and t decays

1
Dipion Spectrum ee-
annihilations and t decays

• M. Benayoun
• LPNHE Paris 6/7

2
The Pion Form factor in ee- and t Data

• Since the advent of t data, disagreement with
  ee- data
• Large activity in identifying isospin symmetry
  breaking in both ee- annihilation and t decay
• Disagreement survived accounting for identified
  isospin breaking corrections!
• Is there a missing piece, a systematic effect (in
  ee- or t data) or new physics?

3
The Latest Account

• Inv. Mass dependent
• missing effect

M. Davier NP Proc. Supp. 169 (2007) 288
4
The Latest Account

• Inv. Mass dependent
• missing effect !
• Is it isospin breaking?

M. Davier NP Proc. Supp. 169 (2007) 288
5
Possible Missing Effect (?-?-f) Mixing
FFs New Data
Isospin 1 part of ?
Isospin 1 part of f
6
Possible Missing Effect (?-?-f) Mixing
FFs New Data
Isospin 1 part of ?
Isospin 1 part of f
Isospin 0 part of ?0 ? Can it be s-dependent?
7
OUTLINE

• A VMD-like Model HLS Model (briefly)
• Breaking of U(3)/SU(3) Symmetries (briefly)
• The Anomalous Sector (briefly)
• The Pion Form Factor in ee- Annihilation and t
  Decay (Isospin Breaking)
• Loop Transition Effects in ee- Physical ?0,
  ?, ?
• Extended Data Sample submitted to fit, Why?
• Fit results Plots
• Conclusions

8
OUTLINE

• A VMD-like Model HLS Model (briefly)
• Breaking of U(3)/SU(3) Symmetries (briefly)
• The Anomalous Sector (briefly)
• The Pion Form Factor in ee- Annihilation and t
  Decay (Isospin Brk)
• Loop Transition Effects in ee- Physical ?0,
  ?, ?
• Extended Data Sample submitted to fit, Why?
• Fit results Plots
• Conclusions

9
The Pion form Factor in ee- and t Physics

• Without Symmetry Breaking
• Isospin symmetry breaking mass splittings

W. Marciano A. Sirlin PRL 71 (1993) 3629
V. Cirigliano G. Ecker H. Neufeld PL B 513
(2001) 361
10
The Pion form Factor in ee- and t Physics

• Without Symmetry Breaking
• Isospin symmetry breaking mass splittings

HLS
W. Marciano A. Sirlin PRL 71 (1993) 3629
V. Cirigliano G. Ecker H. Neufeld PL B 513
(2001) 361
11
The Pion form Factor in ee- and t Physics

• With Symmetry Breaking
• Isospin symmetry breaking mass splittings

(?/W)V ?
?pp?
dm2
W. Marciano A. Sirlin PRL 71 (1993) 3629
V. Cirigliano G. Ecker H. Neufeld PL B 513
(2001) 361
12
?/W- ? Transitions

• No isospin breaking
• Isospin symmetry breaking
• 
  ? component
• 
  
• 
  

?I and ?I components
?I component
13
Transitions among vector fields at one loop

• At tree level ideal fields mass eigenstates
• At one loop, the HLS Lagrangian piece
• induces transitions among ideal fields
• ideal fields mass eigenstates
• isospin symmetry breaking

14
Transitions among vector fields at one loop

• Define the loops
• K K- , K0 K0
• Then, beside self-masses
• 
  e2(s) ? 0 always
• 
  
• -
• 
  ? 0 by isospin brk
• -
  e1(s)

VVP Lagrangian KK loops // Yang-Mills
KKloops
f(s)
15
The Modified Vector Mass Matrix
?I ?I fI
With m2 a g2 fp2 and µ zV No
SU(3) Brk , No SU(2) Brk
Blue Loop effects magenta SU(3) breaking
red isospin breaking
16
Loop Corrections (? , ?) Mixing
?I ?I fI
Blue Loop effects magenta SU(3) breaking
red isospin breaking
17
Isospin Breaking (?, ? , ?) Mixing
?I ?I fI
Blue Loop effects magenta SU(3) breaking
red isospin breaking
18
The Mass Matrix Eigen System

• Expect
• Then solve for the eigensystem perturbatively
• and

19
From Ideal To Physical Fields I
Real analytic matrix function
fulfills Unitarity Condition
20
From Ideal To Physical Fields II

• Mass term derived from the eigenvalues of M2(s)
  
• 
  

(Self masses include subtraction polynomials)
Leading order propagators become
21
V p p Couplings
At leading order ? term unchanged
s-dependent ? and f couplings generated
22
V p p Couplings
Orsay Phase 900 at peak
At leading order ? term unchanged
s-dependent ? and f couplings generated
23
? V Couplings

• In terms of Ideal Fields
• Becomes
• With

24
Vector Meson Couplings to ?/W

• (?/W) V transitions constant (PP,VP) loops
• 
  
• loop term disp. relation (subtractions)
• tree terms

25
Vector Meson Coupling to ?/W

• (?/W) V transitions constant (PP,VP) loops
• 
  
• loop term disp. relation (subtractions)
• tree terms

?I and ?I components of ?0
26
Parameter Freedom

• If only using the pion form factor (ee-,t) the
  parameter freedom is far too large
• a (HLS), g , zA , dm2 (4)
• Subtraction polynomials in
• ( 8)
• Too many parameters, too few structures
• Solution extend the fitted data sample more
  information, less correlations

27
The Extended Data Sample

• Add anomalous decay modes VP?, P??
• Price x, zT, zV, zA for 14 modes
• for
  free
• for
  free 4 measured data Total 18 add. data

M.B.,L.D. ,S.E, V.I. H.OC, PR D 59 (1999)
114027
M.B, H.OC EPJ C22 (2001) 503
28
The Main Guess

• Main Guess Proof of Principle
• 18 Decay Modes Pion FF in ee- annihilation
• Fully reconstruct
• The Pion FF in t decay
• (improvement of parameter fit values)

29
The ?2 contributions to fits
Data Set (data points) Full Data Fit No t data No Spacelike Data
Decays (181) 11.13 11.52 11.48
New Timelike (1271) 128.1 122.0 125.8
Old Timelike (821) 59.1 54.7 55.2
Spacelike (592) 65.7 55.2 89.8/(59)
t ALEPH (33) 23.9 42.3/(33) 20.8
t CLEO (251) 26.1 26.2/(25) 29.7
?2/dof Probability 313.8/331 74 257.7/274 75 238.8/272 93
30
The ?2 contributions to fits
Data Set (data points) Full Data Fit No t data No Spacelike Data
Decays (181) 11.13 11.52 11.48
New Timelike (1271) 128.1 122.0 125.8
Old Timelike (821) 59.1 54.7 55.2
Spacelike (592) 65.7 55.2 89.8/(59)
t ALEPH (33) 23.9 42.3/(33) 20.8
t CLEO (251) 26.1 26.2/(25) 29.7
?2/dof Probability 313.8/331 74 257.7/274 75 238.8/272 93
31
The ?2 contributions to fits
t DATA OUTSIDE FIT ?2 distance to prediction
Data Set (data points) Full Data Fit No t data No Spacelike Data
Decays (181) 11.13 11.52 11.48
New Timelike (1271) 128.1 122.0 125.8
Old Timelike (821) 59.1 54.7 55.2
Spacelike (592) 65.7 55.2 89.8/(59)
t ALEPH (33) 23.9 42.3/(33) 20.8
t CLEO (251) 26.1 26.2/(25) 29.7
?2/dof Probability 313.8/331 74 257.7/274 75 238.8/272 93
32
The ?2 contributions to fits
Spacelike data OUTSIDE FIT
Data Set (data points) Full Data Fit No t data No Spacelike Data
Decays (181) 11.13 11.52 11.48
New Timelike (1271) 128.1 122.0 125.8
Old Timelike (821) 59.1 54.7 55.2
Spacelike (592) 65.7 55.2 89.8/(59)
t ALEPH (33) 23.9 42.3/(33) 20.8
t CLEO (251) 26.1 26.2/(25) 29.7
?2/dof Probability 313.8/331 74 257.7/274 75 238.8/272 93
33
Global Fit to ee- Data
FFs New Data
Cross Sections Old Data
34
Fits to t Data
CLEO Data
ALEPH Data
35
Spacelike Data pp Phase Shift
SpaceLike Data
I1 pp Phase shift NOT A FIT
36
Fit Residuals No Structure
CLEO
ALEPH
ee- Data
37
Isospin Symmetry Breaking ?0 VS ?
38
Isospin Symmetry Breaking ?0 VS ?
0 NO IS Brk
Threshold -6
? Peak 3
F Mass -2
39
Conclusions

• No mismatch between ee- and t data
• Radiative decays pion form factor in ee-
  annihilation predict the observed
  pion form factor in t decay
• Previously unaccounted for effects I0 (?I,
  ?I) components inside the ?0 meson.
• The 3.3 s discrepancy between prediction (using
  ee- data) and the BNL measurement for the muon
  anomalous moment is confirmed

40
Fit Decay Modes Vs PDG
Decay Mode FIT/PDG Remark
?0 ? p0? 0.86 0.15
? ? p? 1.120.11
?0 ? ?? 1.040.11
K? K? 1.000.14
K0? K0? 0.980.09
? ? p0? 0.930.03
?? ?? 1.350.11
? ? p0? 0.990.08
? ? ?? 0.990.03
Decay Mode FIT/PDG Remark
?? ?0? 1.130.04
?? ?? 1.040.11
? ? ?? 0.970.12
?? ?? 0.900.02 !!!!!
?'? ?? 0.990.07
? ?ee- 1.000.02
? ?ee- 1.000.02
? ?pp- 0.980.29
Phase ??pp- 0.790.15
41
The ?0 - ? Mass Difference
ALEPH Data
The ?0-? Mass Difference 1/ Only visible in
ALEPH data 2/ 1 .2 s from ChPT

dm2 0 Fixed
J. Bijnens P. Gosdzinsky PL B 388 (1996) 203
? Peak Region
dm2 Fitted
High mass Vector mesons
42
Two New Results
Process FIT PDG
?0 ?ee- x105 5.560.06 4.700.08
? ?pp- () 1.130.08 1.700.27
?0 ?pp- MeV 144.50.6 149.41.0
43
Two New Results
Process FIT PDG
?0 ?ee- x105 5.560.06 4.700.08
? ?pp- () 1.130.08 1.700.27
?0 ?pp- MeV 144.50.6 149.41.0
15 s apart starting from the same data!
44
Two New Results
Process FIT PDG
?0 ?ee- x105 5.560.06 4.700.08
? ?pp- () 1.130.08 1.700.27
?0 ?pp- MeV 144.50.6 149.41.0
May change the global fit to ? branching ratios
45
Fit Of The ? Mass Region Perfect
FFs New Data
Cross Sections Old Data
46
Additional Information

• THE MIXING  ANGLES 
• The (?,?) and (?, ?) mixing angles are small
  (wrt 1) complex numbers
• The (?, ?) mixing angle is real and small (wrt
  1)

47
The (?, ?) Mixing Angle
-4
Real part
Imag. part
48
The (?, ?) Mixing Angle
Real Part
Imag. Part
49
The (?, ?) mixing angle
Real Part
Start non-zero imaginary part
Imag. Part
50
Hadronic Photon Vacuum Polarization
?
?
M. Davier et al.
H. Burkhardt
Photon Hadronic VP
s (GeV2)
Full Correction Factor (Hadr. Lept.)
s (GeV2)
51
The Pion Form Factor
e
p
? I0,1
p-
e-
?t
p
t
W I1
p0
52
The Hidden Local Symmetry Model

• Vector Mesons gauge bosons of a HL symmetry
• Define
• Define covariant derivatives
• Then and
• The HLS Lagrangian
• VMD a2 , Phenomenology a 2.4
• 
  

M.Bando, T. Kugo K. Yamawaki Phys. Rep. 164
(1988) 217 M. Harada K. Yamawaki Phys. Rep. 381
(2003) 1
Expanded form M.Benayoun H.OConnell PR D 58
(1998) 074006
53
The Hidden Local Symmetry Model

• Vector Mesons gauge bosons of a HL symmetry
• Define
• Define covariant derivatives
• Then and
• The HLS Lagrangian
• VMD a2 , Phenomenology a 2.4
• 
  

M.Bando, T. Kugo K. Yamawaki Phys. Rep. 164
(1988) 217 M. Harada K. Yamawaki Phys. Rep. 381
(2003) 1
PS field matrix
Expanded form M.Benayoun H.OConnell PR D 58
(1998) 074006
54
The Covariant Derivatives

• Covariant derivatives ? for left- right-? fields
  
• With

T is CKM matrix reduced to Vus and Vud terms
55
Breaking of SU(3) Flavor Symmetry
Several possible schemes
Benayoun OConnell op. cit.
With Breaking matrices
zV related to vector meson masses,
Bando Kugo Yamawaki op. cit.
56
Breaking of SU(3) Flavor Symmetry
Several possible schemes
Benayoun OConnell op. cit.
With Breaking matrices
zV related to vector meson masses,
Bando Kugo Yamawaki op. cit.
57
Nonet Symmetry Breaking in HLS Model

• Nonet Symmetry Breaking accounted for by adding
  determinant terms to HLS Lagrangian
• Effective way
• Radiative decays of light mesons vs glue
• no glue but

M. Benayoun L. DelBuono H. OConnell EPJ C 17
(2000) 593
P.J. ODonnell RMP 53 (1981) 673
M. Benayoun et al. PR D 59 (1999) 114027
58
Anomalous Sector of the HLS Model

• HLS Model has an anomalous sector for VP? and
  P?? couplings can be derived from
• XT allows for correct account of K rad. decays
• C - 3 /(4 p2 fp)
• mixing angle related with
  vanishes when no SU(3) breaking

M. Benayoun et al. PR D 59 (1999) 114027
A. Bramon, A. Grau G. Pancheri PL B 345 (1995)
263
G. Morpurgo PR D 42 (1990) 1497
MB, LD HO EPJ C 17 (2000) 593