Precision Measurement of the e+e+()
Cross Section with the ISR Method
Michel Davier
(LAL – Orsay)
(on behalf of the BaBar Collaboration)
• physics goals
• analysis steps
• e+e+()
• e+e+()
 discussion
M.Davier BaBar pi pi
Tau08 22-25/9/2008
1
Hadronic Vacuum Polarization and Muon (g –2)
Contributions to the Standard
Model (SM) Prediction:
g 2
a  
 
2


aQED
Born:  (0) (s )   (s ) ( /  (s) )
 0 [e+ehadrons ()]
12 Im (s) 
 R(s)
 pt
]  |
Im[
ahad 

3 2
2


ds
4 m2
K (s )
s
hadrons |2
+
ahad
+
aweak
2
Dominant uncertainty from
lowest order hadronic piece.
Cannot be calculated from
QCD (“first principles”) – but:
we can use experiment
h
a
d
R (s )


”Dispersion relation“
had

...
M.Davier BaBar pi pi
Tau08 22-25/9/2008

2
Goals of the Analysis







Measure R =   pt (also RKK) with high accuracy for vacuum
polarization calculations, using the ISR method
 channel contributes 73% of ahad
Dominant uncertainty also from 
Also important to increase precision on (MZ2) (EW tests, ILC)
Present systematic precision of e+e experiments
CMD-2 0.8%
SND 1.5%
in agreement
KLOE (ISR from 1.02 GeV) 1.3% some deviation in shape
Big advantage of ISR: all mass spectrum covered at once, from
threshold to 4-5 GeV, with same detector and analysis
Interesting to compare to spectral functions from  decays
discrepancy /e+e evaluations (3.0  1.1)%
 aim for a measurement with <1% accuracy
M.Davier BaBar pi pi
Tau08 22-25/9/2008
3
Situation at ICHEP-Tau06
ahad [ee] = (690.9 ± 4.4)  10 –10
a [ee] = (11 659 180.5 ± 4.4had ± 3.5LBL ± 0.2QED+EW)  10 –10
including:
Hadronic HO
– ( 9.8 ± 0.1)  10 –10
Hadronic LBL
+ (12.0 ± 3.5)  10 –10
Electroweak
QED
.0
(15.4 ± 0.2)  10 –10
(11 658 471.9 ± 0.1)  10 –10
Knecht-Nyffeler, Phys.Rev.Lett. 88 (2002) 071802
Melnikov-Vainshtein, hep-ph/0312226
Davier-Marciano, Ann. Rev. Nucl. Part. Sc. (2004)
Kinoshita-Nio (2006)
BNL E821 (2004):
aexp = (11 659 208.0  6.3) 10 10
Observed Difference with BNL using e+e:
a [exp] – a [SM] =
(27.5 ± 8.4)  10 –10
 3.3 „standard deviations“
M.Davier BaBar pi pi
Tau08 22-25/9/2008
4
The Relevant Processes
ISR
FSR
ISR + add. ISR
M.Davier BaBar pi pi
Tau08 22-25/9/2008
ISR + add. FSR
5
The Measurement
 ISR photon at large angle in EMC
 1 (for efficiency) or 2 (for physics) tracks of good quality
 identification of the charged particles
 separate /KK/ event samples
 kinematic fit (not using ISR photon energy) including 1 additional photon
 obtain all efficiencies (trigger, filter, tracking, ID, fit) from same data
 measure ratio of () to () cross sections to cancel
ee luminosity
additional ISR
otherwise 3-4% syst error
vacuum polarization
ISR photon efficiency
 still need to correct for |FSR|2 contribution in () and additional FSR,
both calculated in QED, but also checked in data
(ISR-FSR interference, additional detected photons)
0

[()](s)

[()](s)
R(s)
R exp (s) 





 [()](s) (1+ FSR
) 0 [()](s) (1+ FSR
) (1+addFSR
)
M.Davier BaBar pi pi
Tau08 22-25/9/2008
6
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
M.Davier BaBar pi pi
Tau08 22-25/9/2008
7
Analysis Steps
230.8 fb-1 ((4S) on-peak & off peak)





Geometrical acceptance
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
Results on  cross section and calculation of dispersion integral
M.Davier BaBar pi pi
Tau08 22-25/9/2008
8
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 QED with additional radiation:
ISR with structure function method,  assumed collinear to the beams and
with limited energy
FSR using PHOTOS
Phokhara 4.0: exact second-order QED matrix element, no more radiation

Studies comparing Phokhara and AfkQed at 4-vector level with fast simulation

M.Davier BaBar pi pi
Tau08 22-25/9/2008
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Particle-related Efficiency Measurements
tag particle (track, ID)
γISR
candidate (p, , φ)
 benefit from pair production for 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 /K/ samples, tracking, study of secondary
interactions…
 assumes that efficiencies of the 2 particles are uncorrelated
 in practice not true  this is where 95% of the work goes!
study of 2-particle overlap in the detector (trigger,tracking, EMC, IFR) required
a large effort to reach per mil accuracies (hence the duration of the analysis)
M.Davier BaBar pi pi
Tau08 22-25/9/2008
10
Data/MC Tracking Correction to , cross sections
 single track efficiency
 correlated loss probability f0
 probability to produce more than 2 tracks f3

Ctrack

 

data
track
MC
track
2
 (1  f 0  f 3 ) data

MC
(
1

f

f
)
0
3


1  Ctrack

1  Ctrack
m
M.Davier BaBar pi pi
and similarly for 
m
Tau08 22-25/9/2008
11
Particle Identification




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
 a tighter  ID (h) is used for tagging
in efficiency measurements and to
further reject background in low cross
section regions.
* isolated muons M > 2.5 GeV
 efficiency maps (p,v1,v2)
impurity (1.10.1) 103
* correlated efficiencies/close tracks
 maps (dv1,dv2)
Barrel
ZIFR
XIFR
Forward Endcap
M.Davier BaBar pi pi
Tau08 22-25/9/2008
fIFR
YIFR
Backward Endcap
12
Data/MC PID corrections to  and  cross sections

Two running
periods with
different IFR
performance

M.Davier BaBar pi pi
Tau08 22-25/9/2008
13
PID separation and Global Test
All ‘xx’  solve for all xx(0) and compare
with no-ID spectrum and estimated syst. error
 N(o)ii
hist: predicted from PID
dots: measured (no ID)
M.Davier BaBar pi pi
m (GeV)
Tau08 22-25/9/2008
14
Kinematic Fitting
()
 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
 Each event recorded on 2D plot
 Typical regions defined
 Loose 2 cut (outside BG region in plot)
for  and  in central  region
 Tight 2 cut (ln(2+1)<3)
for  in  tail region
M.Davier BaBar pi pi
Tau08 22-25/9/2008
15
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 f (0)
 global test in background-rich region near cut boundary
BG fractions in 10-3 at m values
Fitted BG/predicted = 0.9680.037

multi-hadrons
m (GeV)
M.Davier BaBar pi pi
Tau08 22-25/9/2008
16
Additional ISR

Angular distribution
of add. ISR /beams!
Energy cut-off for
add. ISR in AfkQed
M.Davier BaBar pi pi

Tau08 22-25/9/2008
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Additional FSR

FSR
Angle between add 
and closest track
ISR
Large-angle add.ISR
in data  AfkQed
Evidence for FSR
data  AfkQed
M.Davier BaBar pi pi

Tau08 22-25/9/2008
18
2 cut Efficiency Correction
loose 2
 depends on simulation
of ISR (FSR), resolution
effects (mostly ISR 
direction) for  and 
 2 cut efficiency can be
well measured in  data
because of low background

 main correction from lack of angular distribution for
additional ISR in AfkQed
 common correction: 1% for loose 2, 7% for tight 2
 additional loss for  because of interactions
studied with sample of interacting events
agreement data/MC
M.Davier BaBar pi pi
Tau08 22-25/9/2008
1.00  0.16 loose 2
1.07  0.11 tight 2
syst error 0.5-1.5 10-3
19
Checking Known Distributions
Cos* in XX CM /

flat at threshold
1+cos2* b1

sin2*
 b
P>1 GeV track requirement  loss at cos*1
M.Davier BaBar pi pi
Tau08 22-25/9/2008
20
QED Test with  sample
 absolute comparison of  mass spectra
in data and in simulation
J/y excluded
 simulation corrected for data/MC
efficiencies
 AfkQed corrected for incorrect NLO
using Phokhara
 results for different running periods
consistent:
(7.9 7.5) 10-3
 full statistics
(0.2 – 5.0 GeV)
ISR  efficiency 5.2 syst.
trig/track/PID 4.0
M.Davier BaBar pi pi
Tau08 22-25/9/2008
BaBar ee luminosity
21
Unfolding Mass Spectrum
 measured mass spectrum distorted by resolution effects and FSR (m vs. s’)
 unfolding uses mass-transfer matrix from simulation
 2 MeV bins in 0.5-1.0 GeV mass range, 10 MeV bins outside
 most salient effect in - interference region (little effect on a)
M.Davier BaBar pi pi
Tau08 22-25/9/2008
22
Systematic Uncertainties
 ISR lumi
fitted w.r.t.
LO formula

increased to 20. for preliminary results, pending investigations
M.Davier BaBar pi pi
Tau08 22-25/9/2008
23
BaBar results
M.Davier BaBar pi pi
Tau08 22-25/9/2008
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BaBar results in  region
M.Davier BaBar pi pi
Tau08 22-25/9/2008
25
BaBar vs. other experiments at large mass
M.Davier BaBar pi pi
Tau08 22-25/9/2008
26
BaBar vs.other ee data (0.5-1.0 GeV)
CMD-2
direct relative comparison of cross
sections in the corresponding 2-MeV
BaBar bins (interpolation with 2 bins)
deviation from 1 of ratio w.r.t. BaBar
stat + syst errors included
SND
M.Davier BaBar pi pi
KLOE
Tau08 22-25/9/2008
27
BaBar vs.other ee data ( interference region)
 mass calibration of BaBar checked with ISR-produced J/y 
 expect (0.16  0.16) MeV at  peak
  mass can be determined through mass distribution fit (in progress)
 Novosibirsk data precisely calibrated using resonant depolarization
 comparison BaBar/CMD-2/SND in - interference region shows
no evidence for a mass shift
CMD-2
M.Davier BaBar pi pi
SND
Tau08 22-25/9/2008
28
BaBar vs. IB-corrected  data (0.5-1.0 GeV)
relative comparison w.r.t. BaBar of
isospin-breaking corrected  spectral
functions
BaBar data averaged in wider  bins
and corrected for - interference
M.Davier BaBar pi pi
Tau08 22-25/9/2008
29
Computing a
a (1010)
ALEPH-CLEO-OPAL
(DEHZ 2006)
(DEHZ 2003)
(2008)
FSR correction was missing in Belle, new value 523.5  3.0  2.5
Direct comparison 0.630-0.958 GeV
M.Davier BaBar pi pi
BaBar
369.3  0.8  2.2
CMD-2 94-95 362.1  2.4  2.2
CMD-2 98
361.5  1.7  2.9
SND
361.0  1.2  4.7
Tau08 22-25/9/2008
30
Conclusions
 BaBar analysis of  and  ISR processes completed
 Precision goal has been achieved: 0.6% in  region (0.6-0.9 GeV)
 Absolute  cross section agrees with NLO QED within 1.2%
 Preliminary results available for  in the range 0.5-3 GeV
 Structures observed in pion form factor at large masses
 Comparison with results from earlier experiments
discrepancy with CMD-2 and SND mostly below 
large disagreement with KLOE
better agreement with  results, especially Belle
 Contribution to a from BaBar agrees better with  results
 Deviation between BNL measurement and theory prediction
significantly reduced using BaBar  data
a [exp ] – a [SM ]=(27.5 ± 8.4)  10 –10  (14.0  8.4)  1010
 Wait for final results and contributions of multi-hadronic modes
M.Davier BaBar pi pi
Tau08 22-25/9/2008
31
Backup Slides
M.Davier BaBar pi pi
Tau08 22-25/9/2008
32
PID correction to  cross section
Two running
periods with
different IFR
performance
M.Davier BaBar pi pi
Tau08 22-25/9/2008
33
Measurement of -ID efficiencies
• ‘’ ID is a set of negative conditions
• use  sample from ISR-produced  with h tag:
0.6<m<0.9 GeV
impurity = (3.70.5) 103
• ID and mis-ID efficiencies stored in 2D maps
• unlike muons, efficiency sample is not from isolated tracks
• biases from tagging and correlated loss studied with MC
10-3 level
M.Davier BaBar pi pi
Tau08 22-25/9/2008
34
PID correction to  cross section
M.Davier BaBar pi pi
Tau08 22-25/9/2008
35
2 cut Efficiency Correction: Interactions

loose 2
 secondary interactions
mostly from beam pipe
(tight doca cut on tracks)
 tag events with interactions
using displaced vertex with
a ‘bad’ track in transverse
plane (Rxy)
Beam pipe
 agreement data/MC
1.00  0.16 loose 2
1.07  0.11 tight 2
syst error 0.5-1.5 10-3
tight 2
M.Davier BaBar pi pi
Tau08 22-25/9/2008
36
Mass Calibration
Effect of a 1 MeV mass scale shift
(calibration with J/y : (0.16  0.16) MeV)
m (GeV)
M.Davier BaBar pi pi
Tau08 22-25/9/2008
37
Present BaBar Measurements
only statistical errors
syst. 5-10%
to obtain R in the energy range 1-2 GeV the processes
+30, +40, K+K-, KSKL, KSKL, KSK+ 0
remain to be measured
M.Davier BaBar pi pi
Tau08 22-25/9/2008
38
BaBar Impact on Multi-Hadronic Modes
•
•
•
Using ISR method the cross sections of e+e  +0, 2+2, K+K+,
2K+2K reactions have been measured from threshold to 4.5 GeV.
These are the most precise measurements to date for c.m. energies
greater than 1.4 GeV.
Examples: contributions to ahad (1010) from 2+ 2 (0.56 – 1.8 GeV)
from all e+ e exp.
14.21  0.87exp  0.23rad
from all  data
12.35  0.96exp  0.40SU(2)
from BaBar
12.95  0.64exp  0.13rad
from +  0 (1.055  1.8 GeV)
•
from all e+ e exp.
2.45  0.26exp  0.03rad
from BaBar
3.31  0.13exp  0.03rad
Davier-EidelmanHoecker-Zhang 2003
total 696.37.2
More modes to come
M.Davier BaBar pi pi
Tau08 22-25/9/2008
39