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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

Bogdan MALAESCU

( LAL – Orsay )

( Representing the BaBar Collaboration )

HEP 2010

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

Lepton Magnetic Anomaly: from Dirac to QED

Dirac (1928) ge=2 ae=0

anomaly discovered:

Kusch-Foley (1948) ae= (1.19 0.05) 103

and explained by O() QED contribution:

Schwinger (1948) ae = /2 = 1.16 103

first triumph of QED

ae sensitive to quantum fluctuations of fields

HEP 2010

+ ? 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

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

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 1010)

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

aexp = (11 659 208.9 5.4 3.3) 1010

( 6.3) (0.54 ppm)

precessionrotation

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

HEP 2010

- Measure [e+ e + (FSR)] with high accuracy for vacuum polarization calculations, using the ISR method e+ e + ISR (add.)
- channel contributes 73% of ahad
- Dominant uncertainty also from
- Present systematic precision of ee 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

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

BaBar EMC:

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

- PEP-II is an asymmetric e+ecollider 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 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

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

- 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

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

- 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 0ISR (qq),

and and (0)

ppg(g)

HEP 2010

- 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

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) 103 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

s` intervals (GeV) errors in 103

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

HEP 2010

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

e+ e + (FSR) bare (no VP) cross section diagonal errors (stat+syst)

HEP 2010

VDM fit of the pion form factor

Running (VP)

add. FSR

BaBar Preliminary Fit

BaBar Preliminary Fit

BaBar Preliminary Fit

HEP 2010

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

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

0.281.8 (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

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

from Davier-Eidelman-Hoecker-Zhang (2006)

another large long-standing discrepancy in the + 20 channel !

HEP 2010

The Problematic +-20 Contribution

preliminary ISR BaBar data:

A. Petzold, EPS-HEP (2007)

e+e- +20 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

BaBar Multi-hadronic Published Results

Statistical + systematic errors

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

HEP 2010

- including BaBar 2 results in the e+e combination + estimate of hadronic
- LBL contribution (Prades-de Rafael-Vainhstein, 2009) yields
- aSM[e+e] = (11 659 183.4 4.1 2.6 0.2) 1010
- HVP LBL EW (4.9)
- E-821 updated result* (11 659 208.9 6.3) 1010
- deviation (ee) (25.5 8.0) 1010
- (3.2 )
- updated analysis
- +Belle +revisited IB corrections
- deviation () (15.7 8.2) 1010
- (1.9 )

*new proposal submitted to Fermilab

to improve accuracy by a factor 4

HEP 2010

- 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%
- eep+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 2.23.1)1010 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 +-20
- 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

HEP 2010

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

- 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– m0leads to phase space (cross sec.) and width (FF) corrections
- - mixing (EM – + decay) corrected using FF model
- m– m0 *** 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

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

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

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

* isolated muons Mmm > 2.5 GeV

efficiency maps (p,v1,v2)

impurity (1.10.1) 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

xI

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

Data/MC PID corrections to mm and pp cross sections

mmg

Two running

periods with

different IFR

performance

ppg

HEP 2010

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

- 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 0ISR (qq), and and (0)

- global test in background-rich region near cut boundary

BG fractions in 10-2 at mpp values

Fitted BG/predicted = 0.9680.037

BaBar

pp

multi-hadrons

mpp (GeV)

HEP 2010

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

mmgg

Angular distribution

of add. ISR /beams!

Energy cut-off for

add. ISR in AfkQed

ppgg

HEP 2010

FSR

Angle between add

and closest track

mmgg

ISR

Large-angle add.ISR

in data AfkQed

Evidence for FSR

data AfkQed

ppgg

data/MC

0.960.06

1.210.05

HEP 2010

Cosq* in XX CM /g

mm

flat at threshold

1+cos2q* bm1

pp

sin2q*

P>1 GeV track requirement loss at cos*1

HEP 2010

- 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

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) 103 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

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

HEP 2010

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

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

- 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 (24), but not sufficient to establish
- a contribution from new physics

HEP 2010

- 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 20
- 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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