Isr cross sections in e e and implications on muon g 2
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ISR cross sections in e + e - and implications on muon g-2. Bogdan MALAESCU ( LAL – Orsay ) ( Representing the BaBar Collaboration ). Outlook. The muon magnetic anomaly The BaBar ISR (Initial State Radiation) analysis Test of the method: e + e   +   ()

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ISR cross sections in e + e - and implications on muon g-2

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Isr cross sections in e e and implications on muon g 2

ISR cross sections in e+e- and implications on muon g-2

Bogdan MALAESCU

( LAL – Orsay )

( Representing the BaBar Collaboration )

HEP 2010


Outlook

Outlook

  • The muon magnetic anomaly

  • The BaBar ISR (Initial State Radiation) analysis

  • Test of the method: e+e+()

  • Results on e+e+ () (PRL 103, 231801  (2009))

  • Combination of all e+e data

  • Discussion and conclusion

HEP 2010


Isr cross sections in e e and implications on muon g 2

Lepton Magnetic Anomaly: from Dirac to QED

Dirac (1928) ge=2 ae=0

anomaly discovered:

Kusch-Foley (1948) ae= (1.19  0.05) 103

and explained by O() QED contribution:

Schwinger (1948) ae = /2 = 1.16 103

first triumph of QED

 ae sensitive to quantum fluctuations of fields

HEP 2010


Isr cross sections in e e and implications on muon g 2

More Quantum Fluctuations

+ ? a new physics ?

typical contributions:

QED up to O(4), 5 in progress (Kinoshita et al.)

Hadronsvacuum polarizationlight-by-light (models)

Electroweak new physics at high mass scale

 a much more sensitive to high scales

HEP 2010


Isr cross sections in e e and implications on muon g 2

Hadronic Vacuum Polarization and Muon (g–2)

Dominant uncertainty from lowest-order HVP piece

Cannot be calculated from QCD (low mass scale), but one can use experimental

data on e+e hadrons cross section

Im[ ]  | hadrons |2

had

Dispersion relation

HEP 2010


Isr cross sections in e e and implications on muon g 2

The E-821 Direct a Measurement at BNL*

Storage ring technique pioneered at CERN (Farley-Picasso…, 1970s), with μ+ and μ- data

a obtained from a ratio of frequencies

result updated with new value for /p (+0.9 1010)

(see new review in RPP2009 (Hoecker-Marciano))

aexp = (11 659 208.9  5.4  3.3) 1010

( 6.3) (0.54 ppm)

precessionrotation

*Bennet et al., 2006, Phys. Rev. D 73, 072003

HEP 2010


Isr cross sections in e e and implications on muon g 2

Goals of the BaBar Analysis

  • Measure [e+ e +  (FSR)] with high accuracy for vacuum polarization calculations, using the ISR method e+ e +  ISR (add.)

  •  channel contributes 73% of ahad

  • Dominant uncertainty also from 

  • Present systematic precision of ee experiments

    CMD-2 0.8% SND 1.5% in agreement

    KLOE (ISR from 1.02 GeV) 2005 1.3% some deviation in shape

    2008 0.9% better agreement

  • Big advantage of ISR: all mass spectrum covered at once (from threshold to 3 GeV in BABAR), with same detector and analysis

  • The ISR method needs a very large amount of data at an energy larger than the one at which we measure the cross section

  • Measure simultaneously +  ISR (add.) and +  ISR (add.)

  • Compare the measured +  ISR (add.) spectrum with QED prediction

  • Compare to spectral functions from previous e+ e data and  decays

     aim for a measurement with <1% accuracy (syst. errors at per mil level)

great interest to clarify the situation as magnitude of possible discrepancy

with SM is of the order of SUSY contributions with masses of a few 100 GeV

HEP 2010


Isr cross sections in e e and implications on muon g 2

The Relevant Processes

e+ e +  ISR (add.) and +  ISR (add.) measured simultaneously

ISR

FSR

LO FSR negligible for pp

at s(10.6 GeV)2

ISR + add. ISR

ISR + add. FSR

HEP 2010


Isr cross sections in e e and implications on muon g 2

BaBar / PEP II

BaBar EMC:

  • 6580 CsI(Tl) crystals, resolution ~1-2 % high E.

  • PEP-II is an asymmetric e+ecollider operating at CM energy of (4S).

  • Integrated luminosity = 531 fb-1

BaBar IFR:

  • resistive plate chambers

  • BaBar DIRC

  • particle ID up to 4-5 GeV/c

  • BaBar SVT and DCH

  • precision tracking

HEP 2010


Isr cross sections in e e and implications on muon g 2

The Measurement

  • ISR photon at large angle, detected in the EMC

  • detected tracks of good quality: 1 (for efficiency) or 2 (for physics)

  • identification of the charged particles (DIRC, DCH)

  • separate pp/KK/mm event samples

  • kinematic fit (not using ISR photon energy) including 1 additional photon (discussed

    later)

  • obtain all efficiencies (trigger, filter, tracking, ID, fit) from same data

  • measure ratio of ppg(g) to mmg(g) cross sections to cancel

    ee luminosity

    additional ISR

    vacuum polarization

    ISR photon efficiency

  • correct for LO FSR (|FSR|2) contribution in mmg(g) (QED, <1% below 1 GeV)

  • additional FSR photons measured

otherwise ~2% syst error

HEP 2010


Isr cross sections in e e and implications on muon g 2

Analysis Steps

Used an integrated luminosity of 232 fb-1 (U(4S) on-peak & off peak)

  • Geometrical acceptance (using Monte Carlo simulation)

  • All efficiencies measured on data (data/MC corrections)

  • Triggers (L1 hardware, L3 software), background-filter efficiencies

  • Tracking efficiency

  • Particle ID matrix (ID and mis-ID efficiencies):   K

  • Kinematic fitting

    reduce non 2-body backgrounds

    2 cut efficiency

    additional radiation (ISR and FSR)

    secondary interactions

  • Unfolding of mass spectra

  • Consistency checks for  (QED test, ISR luminosity) and 

  • Unblinding R  partial (√s`>0.5 GeV) preliminary results (Tau08, Sept. 2008)

  • Additional studies and checks

  • Final results on  cross section and calculation of dispersion integral

    (PRL 103, 231801  (2009))

HEP 2010


Isr cross sections in e e and implications on muon g 2

MC Generators

  • Acceptance and efficiencies determined initially from simulation,

    with data/MC corrections applied

  • Large simulated samples, typically 10  data, using AfkQed generator

  • AfkQed: lowest-order (LO) QED with additional radiation:

    ISR with structure function method,  assumed collinear to the beams and

    with limited energy

    FSR using PHOTOS

  • Phokhara 4.0: (almost) exact second-order QED matrix element, limited to NLO

  • Studies comparing Phokhara and AfkQed at 4-vector level with fast simulation

  • QED test with    () cross section requires reliable NLO generator

  • (FSR) cross section obtained through () / () ratio, rather insensitive to

    detailed description of radiation in MC

HEP 2010


Isr cross sections in e e and implications on muon g 2

Particle-related Efficiency Measurements

tag particle (track, ID)

γISR

candidate (p, , φ)

  • benefit from pair production for tracking and particle ID

  • kinematically constrained events

  • efficiency automatically averaged over running periods

  • measurement in the same environment as for physics, in fact same events!

  • applied to particle ID with p/K/m samples, tracking…

  • assumes that efficiencies of the 2 particles are uncorrelated

  • in practice not true  study of 2-particle overlap in the detector

    (trigger,tracking, EMC, IFR) required a large effort to reach per mil accuracies

HEP 2010


Isr cross sections in e e and implications on muon g 2

Kinematic Fitting

  • First analysis to measure cross section

  • with additional photons (NLO)

  • Two kinematic fits to X X ISR add

    (ISR photon defined as highest energy)

    Add. ISR fit: add assumed along beams

    Add. ‘FSR’ if add detected

  • Loose 2 cut (outside BG region in plot)

    for  and  in central  region

  • Tight 2 cut (ln(2+1)add.ISR<3)

    for  in  tail region

  • q q and multi-hadronic ISR background

    from MC samples + normalization from

    data using signals from 0ISR (qq),

    and  and  (0)

ppg(g)

HEP 2010


Isr cross sections in e e and implications on muon g 2

QED Test with mmg sample

  • absolute comparison of mm mass spectra in data and in simulation

  • simulation corrected for data/MC efficiencies

  • AfkQed corrected for incomplete NLO using Phokhara

  • strong test (ISR probability drops out for  cross section)

BaBar

(0.2  3 GeV)

BaBar ee luminosity

ISR  efficiency 3.4 syst.

trig/track/PID 4.0

HEP 2010


Isr cross sections in e e and implications on muon g 2

Obtaining the (FSR) cross section

Acceptance from MC + data/MC corrections

Unfolded spectrum

Effective ISR luminosity from () analysis (similar equation + QED)

 mass spectrum unfolded (B. M. arXiv:0907.3791) for detector response

Additional ISR almost cancels in the procedure (() / () ratio)

Correction (2.5 1.0) 103  cross section does not rely on accurate

description of NLO in the MC generator

ISR luminosity from () in 50-MeV energy intervals

(small compared to variation of efficiency corrections)

HEP 2010


Isr cross sections in e e and implications on muon g 2

Systematic uncertainties

s` intervals (GeV) errors in 103

Dominated by particle ID (-ID, correlated ‘’, -ID in ISR luminosity)

HEP 2010


Isr cross sections in e e and implications on muon g 2

BaBar results (arXiv:0908.3589, PRL 103, 231801  (2009))

e+ e  +  (FSR) bare (no VP) cross section diagonal errors (stat+syst)

HEP 2010


Isr cross sections in e e and implications on muon g 2

BaBar results in  region

2-MeV energy intervals

HEP 2010


Isr cross sections in e e and implications on muon g 2

BaBar vs. other experiments at larger mass

HEP 2010


Isr cross sections in e e and implications on muon g 2

VDM fit of the pion form factor

 Running (VP)

add. FSR

BaBar Preliminary Fit

BaBar Preliminary Fit

BaBar Preliminary Fit

HEP 2010


Isr cross sections in e e and implications on muon g 2

BaBar vs.other ee data (0.5-1.0 GeV)

direct relative comparison of cross sections with BaBar fit (stat + syst errors included)

(green band)

BaBar

CMD-2

BaBar Preliminary Fit

BaBar Preliminary Fit

SND

KLOE

BaBar Preliminary Fit

BaBar Preliminary Fit

HEP 2010


Isr cross sections in e e and implications on muon g 2

BaBar vs. IB-corrected  data (0.5-1.0 GeV)

  • relative comparison w.r.t. BaBar of

  • spectral functions corrected for

    isospin-breaking(IB)

  • IB corrections: radiative corr.,  masses,

  • - interference,  masses/widths

  • each  data normalized to its own BR

ALEPH

BaBar Preliminary Fit

CLEO

Belle

BaBar Preliminary Fit

BaBar Preliminary Fit

HEP 2010


Isr cross sections in e e and implications on muon g 2

Computing ampp

0.281.8 (GeV)

BABAR 514.1  3.8

previous e +e combined 503.5  3.5 *

 combined 515.2  3.5 *

*

*

* arXiv:0906.5443 M. Davier et al.

HEP 2010


Isr cross sections in e e and implications on muon g 2

Including BaBar in the e+e Combination

arXiv: 0908.4300

Davier-Hoecker-BM-Yuan-Zhang

Improved procedure and software

(HVPTools) for combining cross

section data with arbitrary point

spacing/binning, with full covariance

matrices and error propagation

HEP 2010


Isr cross sections in e e and implications on muon g 2

Other hadronic contributions

from Davier-Eidelman-Hoecker-Zhang (2006)

 another large long-standing discrepancy in the +  20 channel !

HEP 2010


Isr cross sections in e e and implications on muon g 2

The Problematic +-20 Contribution

preliminary ISR BaBar data:

A. Petzold, EPS-HEP (2007)

e+e-  +20 data (CMD2 discarded)

only statistical errors

Preliminary

old contribution 16.8  1.3

update 17.6  1.7 probably still underestimated (BaBar)

 21.4  1.4

HEP 2010


Isr cross sections in e e and implications on muon g 2

BaBar Multi-hadronic Published Results

Statistical + systematic errors

Still more channels under analysis: K+K, KK with K0

HEP 2010


Isr cross sections in e e and implications on muon g 2

Where are we?

  • including BaBar 2 results in the e+e combination + estimate of hadronic

  • LBL contribution (Prades-de Rafael-Vainhstein, 2009) yields

  • aSM[e+e] = (11 659 183.4 4.1 2.6 0.2) 1010

  • HVP LBL EW (4.9)

  • E-821 updated result* (11 659 208.9 6.3) 1010

  • deviation (ee) (25.5  8.0) 1010

  • (3.2 )

  • updated  analysis

  • +Belle +revisited IB corrections

  • deviation () (15.7  8.2) 1010

  • (1.9 )

*new proposal submitted to Fermilab

to improve accuracy by a factor 4

HEP 2010


Isr cross sections in e e and implications on muon g 2

Conclusions

  • BaBar analysis of p+p-and m+m-ISR processes completed

  • Precision goal has been achieved: 0.5% in  region (0.6-0.9 GeV)

  • Absolute m+m- cross section agrees with NLO QED within 1.1%

  • eep+p-()cross section very insensitive to MC generator

  • full range of interest covered from 0.3 to 3 GeV

  • Comparison with data from earlier experiments

  • fair agreement with CMD-2 and SND, poor with KLOE

  • agreement with t data

  • Contribution to am from BaBar is (514.1 2.23.1)1010 in 0.28-1.8 GeV

  • BaBar result has an accuracy (0.7%) comparable to combined previous results

  • Contribution from multi-hadronic channels will continue to be updated with

  • more results forthcoming from BaBar, particularly +-20

  • Deviation between BNL measurement and theory prediction reduced using

    BaBar p+p- data

    a[exp] –a[SM] =(19.8 ±8.4)10–10+- from BaBar only

    25.5  8.0 combined e+e- including BaBar

HEP 2010


Isr cross sections in e e and implications on muon g 2

Backup Slides

HEP 2010


Isr cross sections in e e and implications on muon g 2

Data on e+e  hadrons

CMD-2 (2006)

CMD-2 (2004)

SND (2006)

KLOE (2009)

HEP 2010


Isr cross sections in e e and implications on muon g 2

The Role of Data through CVC – SU(2)

W: I=1 &V,A

CVC: I=1 &V

: I=0,1 &V



e+

hadrons

W

e–

hadrons

Hadronic physics factorizes (spectral Functions)

branching fractionsmass spectrum kinematic factor (PS)

HEP 2010


Isr cross sections in e e and implications on muon g 2

SU(2) Breaking

  • Corrections for SU(2) breaking applied to  data for dominant  – + contrib.:

    • Electroweak radiative corrections:

      • dominant contribution from short distance correction SEW

      • subleading corrections (small)

      • long distance radiative correction GEM(s)

    • Charged/neutral mass splitting:

      • m–  m0leads to phase space (cross sec.) and width (FF) corrections

      •  - mixing (EM    – + decay) corrected using FF model

      • m–  m0 *** and –  0 ***

    • Electromagnetic decays:      ***,    ,    ,   l+l –

    • Quark mass difference mu  md (negligible)

Marciano-Sirlin’ 88

Braaten-Li’ 90

Cirigliano-Ecker-Neufeld’ 02

Lopez Castro et al.’ 06

Alemany-Davier-Höcker’ 97, Czyż-Kühn’ 01

Flores-Baez-Lopez Castro’ 08

Davier et al.’09

HEP 2010


Isr cross sections in e e and implications on muon g 2

Situation at ICHEP’06 / 08

Hadronic HO – ( 9.8 ± 0.1) 10–10

Hadronic LBL + (12.0 ± 3.5) 10–10

Electroweak (15.4 ± 0.2) 10–10

QED (11 658 471.9 ± 0.1) 10–10

e+e  BNL

.0

Knecht-Nyffeler (2002), Melnikov-Vainhstein (2003)

Davier-Marciano(2004)

Kinoshita-Nio (2006)

Observed Difference with BNL using e+e:

Estimate using  data consistent with E-821

HEP 2010


Isr cross sections in e e and implications on muon g 2

Revisited Analysis using  Data: Belle + new IB

Relative comparison of  and ee spectral functions

( green band)

arXiv:0906.5443 M.Davier et al.

slope…

KLOE

CMD-2, SND

Global test of spectral functions:

prediction of  BR using ee data

 larger disagreement with KLOE

HEP 2010


Isr cross sections in e e and implications on muon g 2

Revisited Analysis using  Data: including Belle

HEP 2010


Isr cross sections in e e and implications on muon g 2

Revisited Analysis  Data: new IB corrections

HEP 2010


Isr cross sections in e e and implications on muon g 2

Data/MC Tracking Correction to ppg,mmg cross sections

  • single track efficiency

  • correlated loss probability f0

  • probability to produce more than 2 tracks f3

and similarly for pp

mmm

mpp

HEP 2010


Isr cross sections in e e and implications on muon g 2

Particle Identification

* isolated muons Mmm > 2.5 GeV

 efficiency maps (p,v1,v2)

impurity (1.10.1) 10-3

* correlated efficiencies/close tracks

 maps (dv1,dv2)

  • Particle identification required

    to separate XX final processes

  • Define 5 ID classes using cuts and

    PID selectors (complete and

    orthogonal set)

  • Electrons rejected at track definition

    level (Ecal, dE/dx)

  • All ID efficiencies measured

    xI

Barrel

ZIFR

fIFR

XIFR

  • a tighter  ID (h) is used for tagging

    in efficiency measurements and to

    further reject background in low cross

    section regions.

YIFR

Forward Endcap

Backward Endcap

HEP 2010


Isr cross sections in e e and implications on muon g 2

Data/MC PID corrections to mm and pp cross sections

mmg

Two running

periods with

different IFR

performance

ppg

HEP 2010


Isr cross sections in e e and implications on muon g 2

PID separation and Global Test

All ‘xx’  solve for all xx(0) and compare

with no-ID spectrum and estimated syst. error

BaBar

BaBar

  • N(o)ii

hist: predicted from PID

dots: measured (no ID)

mpp(GeV)

HEP 2010


Isr cross sections in e e and implications on muon g 2

Backgrounds

  • background larger with loose 2 cut used in 0.5-1.0 GeV mass range

  • q q and multi-hadronic ISR background from MC samples + normalization

    from data using signals from 0ISR (qq), and  and  (0)

  • global test in background-rich region near cut boundary

BG fractions in 10-2 at mpp values

Fitted BG/predicted = 0.9680.037

BaBar

pp

multi-hadrons

mpp (GeV)

HEP 2010


Isr cross sections in e e and implications on muon g 2

2 cut Efficiency Correction

loose c2

  • depends on simulation

    of ISR (FSR), resolution

    effects (mostly ISR 

    direction) for mm and pp

  • c2 cut efficiency can be

    well measured in mm data

    because of low background

  • main correction from lack of angular distribution for

    additional ISR in AfkQed

  • common correction: 1% for loose c2, 7% for tight c2

  • additional loss for pp because of interactions

    studied with sample of interacting events

    much better study now, 2 independent methods

mmgg

secondary interactions

data/MC 1.51  0.03

syst error 0.3 - 0.9 10-3

HEP 2010


Isr cross sections in e e and implications on muon g 2

Additional ISR

mmgg

Angular distribution

of add. ISR /beams!

Energy cut-off for

add. ISR in AfkQed

ppgg

HEP 2010


Isr cross sections in e e and implications on muon g 2

Additional FSR

FSR

Angle between add 

and closest track

mmgg

ISR

Large-angle add.ISR

in data  AfkQed

Evidence for FSR

data  AfkQed

ppgg

data/MC

 0.960.06

 1.210.05

HEP 2010


Isr cross sections in e e and implications on muon g 2

Checking Known Distributions

Cosq* in XX CM /g

mm

flat at threshold

1+cos2q* bm1

pp

sin2q*  

P>1 GeV track requirement  loss at cos*1

HEP 2010


Isr cross sections in e e and implications on muon g 2

Unfolding  Mass Spectrum

  • measured mass spectrum distorted by resolution effects and FSR (mpp vs. s’)

  • iterative unfolding method (B. M. arXiv:0907-3791) : one step is sufficient

  • mass-transfer matrix from simulation with corrections from data

  • 2 MeV bins in 0.5-1.0 GeV mass range, 10 MeV bins outside

  • most salient effect in - interference region (little effect on ampp)

BaBar

Absolute difference

unfolded(1)  raw data

unfolded(2)  unfolded(1)

Statistical errors (band)

Mass (GeV)

BaBar

Relative difference

HEP 2010


Isr cross sections in e e and implications on muon g 2

Obtaining the () cross section

Acceptance from MC + data/MC corrections

Unfolded spectrum

Effective ISR luminosity from () analysis (similar equation + QED)

Additional ISR almost cancels in the procedure (() / () ratio)

Correction (2.5 1.0) 103   cross section does not rely on accurate

description of NLO in the MC generator

ratio mm ISR lumi / LO formula

should behave smoothly

(HVP effects on resonances cancel)

Use measured lumi in 50-MeV bins

averaged in sliding 250-MeV bins

for smoothing

HEP 2010


Isr cross sections in e e and implications on muon g 2

Changes since preliminary results at Tau08

  • preliminary results Sept. 2008: only 0.5-3 GeV (excess/expect. near threshold)

  • problem explored (Oct. 2008- Feb. 2009): trigger/BGFilter, ee background

  • `’ re-investigated  direct measurement achieved using ID probabilities

    before: model for correlated loss, no precise direct check

     significant changes  efficiency for ISR lumi  +0.9%

     contamination in `’ sample 

      cross section  1.8% 0.525 GeV

    1.0% 0.775 GeV

    1.4% 0.975 GeV

  • other changes: - MC unfolding mass matrix corrected for data/MC differences

    (small) - ISR lumi now used in 50-MeV sliding bins, instead of global fit

    - cancellation of add ISR in / ratio studied/corrected

  • extensive review

HEP 2010


Isr cross sections in e e and implications on muon g 2

f2 Story

HEP 2010


Isr cross sections in e e and implications on muon g 2

BaBar vs.other ee data (r-w interference region)

  • mass calibration of BaBar checked with ISR-produced J/y mm

  • expect (0.16  0.16) MeV at  peak

  •  mass determined through VDM mass fit

    mωfit mωPDG = (0.12  0.29) MeV

  • Novosibirsk data precisely calibrated using resonant depolarization

  • comparison BaBar/CMD-2/SND in - interference region shows

    no evidence for a mass shift

SND

CMD-2

BaBar Preliminary Fit

BaBar Preliminary Fit

HEP 2010


Isr cross sections in e e and implications on muon g 2

Obtaining the average cross section

relative weights

  • local weighted average performed

  • full covariance matrices and error

  • propagation

  • local 2 used for error rescaling

  • average dominated by BaBar and

  • KLOE, BaBar covering full range

error scale factor

integrand (dispersion integral)

error

HEP 2010


Isr cross sections in e e and implications on muon g 2

Consistency of Experiments with Average

HEP 2010


Isr cross sections in e e and implications on muon g 2

g-2 Values for Various Mass Intervals

(1010)

HEP 2010


Isr cross sections in e e and implications on muon g 2

Combined Spectral Functions Comparison

HEP 2010


Isr cross sections in e e and implications on muon g 2

Discussion

  • BaBar 2 data complete and the most accurate, but expected precision

  • improvement on the average not reached because of discrepancy with KLOE

  • however, previous /ee disagreement strongly reduced

  • 2.9 (2006)  2.4 ( update)  1.5 (including BaBar)

  • a range of values for the deviation from the SM can be obtained, depending

  • on the 2 data used:

  • BaBar 2.4

  • all ee 3.2

  • all ee BaBar 3.7

  • all ee KLOE 2.9

  •  1.9

  • all approaches yield a deviation, but SM test limited by systematic effects not

  • accounted for in the experimental analyses (ee) and/or the corrections to  data

  • at the moment some evidence for a deviation (24), but not sufficient to establish

  • a contribution from new physics

HEP 2010


Isr cross sections in e e and implications on muon g 2

Perspectives

  • first priority is a clarification of the BaBar/KLOE discrepancy:

  • - origin of the ‘slope’ (was very pronounced with the 2004 KLOE results,

  • reduced now with the 2008 results)

  • - normalization difference on  peak (most direct effect on a)

  • - Novosibirsk results in-between, closer to BaBar

  • - slope also seen in KLOE/ comparison; BaBar agrees with 

  • further checks of the KLOE results are possible: as method is based on MC

  • simulation for ISR and additional ISR/FSR probabilities  test with  analysis

  • contribution from multi-hadronic channels will continue to be updated with

  • more results forthcoming from BaBar, particularly 2 20

  • more ee data expected from VEPP-2000 in Novosibirsk

  • experimental error of E-821 direct a measurement is a limitation, already now

  •  new proposal submitted to Fermilab to improve accuracy by a factor 4

  •  project at JPARC

HEP 2010


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