The Hadronic Contribution to μ (observations of an amateur) · B. Lee Roberts, INT Seattle – 27...
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B. Lee Roberts, INT Seattle – 27 October 2008 - p. 1/44
The Hadronic Contribution to aμ(observations of an amateur)
Lee RobertsDepartment of Physics
Boston Universityroberts @bu.edu
http://physics.bu.edu/people/show/roberts
B. Lee Roberts, INT Seattle – 27 October 2008 - p. 2/44
The Hadronic Contribution to aμ(observations of an amateur)
Lee RobertsDepartment of Physics
Boston Universityroberts @bu.edu
http://physics.bu.edu/people/show/roberts
La Gazza Ladra of talks
B. Lee Roberts, INT Seattle – 27 October 2008 - p. 4/44
Outline
• Introduction to aμ (Had)• Paths to the lowest order hadronic contribution• Status of the measurements (Post Tau-2008)• Status of hadronic light-by-light scattering• Summary and lack of conclusions.
Many thanks to Michel Davier, Ivan Logashenko and Graziano Venanzoni for answering many questions about the R measurements. Also thanks to Eduardo de Rafael, Arkady Vainshteinand Bill Marciano.
B. Lee Roberts, INT Seattle – 27 October 2008 - p. 5/44
The SM Value for electron and muon anomalies
e vrs. μ : relative contribution of heavier things
e,
e*,
e,
e,
e,
e, e,
e,
e,
e,e,
B. Lee Roberts, INT Seattle – 27 October 2008 - p. 6/44
The SM Value for electron and muon anomalies
e vrs. μ : relative contribution of heavier things
B. Lee Roberts, INT Seattle – 27 October 2008 - p. 7/44
a(Had) and e+e- → Hadronsspectral representation, (using analiticityand the optical theorem)
so the hadronic contribution can be obtained from data
Bouchiat-Michel ’61, Brodsky-de Rafael ’68
(see Miller, de Rafael, BLR, Rep Prog. Phy. 70(2007) 795
hadronic spectral function
analyticity and the optical theorem
B. Lee Roberts, INT Seattle – 27 October 2008 - p. 8/44
R(s) measurements at low s
VEPP-2M
Babar/Belle (ISR)
KLOE (ISR)
VEPP-2000
At low s the cross-section is measured independently for each final state
from Davier/Höcker
B. Lee Roberts, INT Seattle – 27 October 2008 - p. 9/44
Data from CMD2, SND and KLOE. The vector meson ρprovides the dominant feature of the cross section. BaBarhas a large data set that was presented at Tau2008.
96
95,98
97
CMD-2 SND
ρ−ω meson interference
KLOE hep-ex 0809.3950
from I. Logashenko - φ to ψ 2006
B. Lee Roberts, INT Seattle – 27 October 2008 - p. 10/44
An Intermezzo: tau for two (π)?
Can we use hadronic τdecay to get aμ(Had)?
B. Lee Roberts, INT Seattle – 27 October 2008 - p. 11/44
a(Had) from the vector current in hadronic τ decay?
• Assume: CVC, • no 2nd-class currents
– then an even number of pions in the final state implies that the decay goes through the vector current
• isospin breaking corrections. – e+e- goes through neutral ρ – while τ-decay goes through charged ρ
• n.b. τ decay has no isoscalar piece, e+e- does– no ρ − ω interference
12A. Höcker – The Muon g–2 Challenge
hadrons
τντ
W hadronsγ
e+
e–
CVC: I =1 & VW: I =1 & V,A γ: I =0,1 & V
Hadronic physics factorizes in Spectral Functions :
Isospin symmetry connects I =1 e+e– cross section to vectorτ spectral functions:
2( 1) 04I e e
s τυ τ π π νπασ π π= + − + − − −⎡ ⎤→ = →⎣ ⎦ ⎡ ⎤⎣ ⎦
( ) ( )0
0
2
22
0
2
0 BR
1 / 1 1
/
BR e
dNN d
m
ms me s sππ
ππ
τττ
τ τ τ
υ τ πτ π π
νν ν
πν
τ−
−
−−
−
−
⎡ ⎤→⎣ ⎦⎡ ⎤→
⎡ ⎤→ ∝+
⎣⎦ −⎣
⎦
branching fractions mass spectrum kinematic factor (PS)
fundamental ingredient relating long distance (resonances) to short distance description (QCD)
Using also Tau Data through CVC – SU(2)
from Andreas Höcker
B. Lee Roberts, INT Seattle – 27 October 2008 - p. 13/44
Testing CVC with one number (circa 2004)
Infer τ branching fractions (more robust than spectral functions) from e+e– data:
Difference: BR[τ ] – BR[e+e – (CVC)]:
4.5+ 0.92 ± 0.21τ – → π – π 0 ντ
0.7– 0.08 ± 0.11τ – → π – 3π 0 ντ
3.6+ 0.91 ± 0.25τ – → 2π – π + π 0 ντ
Δ(τ – e+e –) `Sigma‘Mode
ee data on π – π + π 0π 0 not satisfactory
from Michel Davier
B. Lee Roberts, INT Seattle – 27 October 2008 - p. 14/44
τ -decay data from ALEPH, CLEO and OPAL
the vector spectral function– note the absence of the ρ – ω interference
Davier-Eidleman-Höcker-Zhang, EPJ: C27-497(03), C31, 503 (03)
15
τ
ππ
τπ
ππ
πππ τ
⎡ ⎤⎛ ⎞ ⎛ ⎞⎢ ⎥− +⎜ ⎟ ⎜ ⎟
π=
⎢ ⎥⎝ ⎠ ⎝ ⎠⎦×
⎣
00
0
2
2
2ud E2 2
W e s 2s1 1dN1
N ds m m6 V S
(s)m Β
Β v
πππ β
=π
23(s F(s)12
)) (s0
v
Result (2): Mass spectrum
Mass spectra
= Phase space
× Form Factor
10
10 2
10 3
10 4
10 5
10 6
0 0.5 1 1.5 2 2.5 3(Mππ
0)2(GeV/c2)2
Belle
Num
ber
of e
ntri
es
/0.0
5(G
eV/c
2 )2
Data
G&S Fit(ρ(770) + ρ(1450) + ρ(1700))
Νum
ber
of e
ntri
es /0
.05
(GeV
/c2 )
2
± 0 2(Mπ π ) 2 2( / )GeV c
Unfolded Results
Belle data
from Hisaki Hayashii
Tau - 2008
ρ
ρ′ρ′′
16
10-3
10-2
10-1
1
10
0 0.5 1 1.5 2 2.5 3(Mππ
0)2 (GeV/c2)2
|Fπ|
2
Belle
G&S Fit(ρ(770) + ρ(1450) + ρ(1700))
Result (3) Pion Form Factor |Fπ|2
From 64M τ+τ− pairs, Belle selects 5.5M τ− π−π0ντ events!
ρρ′
ρ′′
5
10
15
20
25
30
35
40
45
0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7 0.75 0.8(Mππ
0)2 (GeV/c2)2 |F
π|2
Belle
ALEPH
CLEO
G&S Fit
Error bars include both statistical and systematic
Interference between ρ’ and ρ”
Fit with BW
± 0 2(Mπ π ) 2 2( / )GeV c
2πF
2
4
6
8
10
12
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4(Mππ
0)2 (GeV/c2)2
|Fπ|
2
Belle
ALEPH
CLEO
G&S Fit
1717
Impact on aμLO,ππ (τ)
[Preliminar]
As applied to results of BELLE (arXiv: 0805.3773)[τ→π−ων removed ]
17
-13.7 -19.4
(-3.9)
π0γ
New isospin calculations
Gabriel López CastroTau - 2008
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Contributions and errors to the integral:
2π
,ω ϕ2 GeV<
2 5 GeV−5 GeV>
2π
,ω ϕ2 GeV<
2 5 GeV−
5 GeV>
thanks to Vanya Logashenko
2006, from I. Logashenko, phi-psi 2006
2008, from S. Eidelman, Tau – 2008, pre-BaBarresults
B. Lee Roberts, INT Seattle – 27 October 2008 - p. 20/44
De Rujula: theorist is farmer, experimentalist truffle pig
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De Rujula: theorist is farmer, experimentalist truffle pig
caution and care are needed in including the radiative corrections
I Logashenko Tau 2008
22
Novosibirsk Radiative corrections
ISR+FSR
ISR+FSR+VP
Radiation terms
Vacuum polarization• CMD-2 uses custom Monte-Carlo generator to calculate RC
ee, μμ, ππ final states: 1 γ at large angle, multiple γ’s along initial or final particles (≤0.2%)
• CMD-2 calculation is consistent with independent calculations (BHWIDE, KKMC)
• SND uses BHWIDE for ee final state and CMD-2 generator for μμ, ππ final states
from Ivan Logashenko
Tau - 2008
I Logashenko Tau 2008
23
“Narrow” resonances
(782)ω (1020)ϕMass and width are measured to ≈0.1 MeV, Γee to ≈2-3%
I Logashenko Tau 2008
24
Cross-section e+e- 4π
Systematic error:Systematic error ≈5-7%
Efficiency determination gives main contribution to the systematic error
SND = 8%CMD2= 15% (discrepancy 15-25%)problem with efficiency determination!CMD2-reanalysis preliminary = 8%
ee π π π π+ − + − + −→ 0 0e e π π π π+ − + −→
I Logashenko Tau 2008
25
Cross-section e+e- 3π0e e π π π+ − + −→
Systematic error:
≈6% (>1GeV)1-2% on omega2.5% on phi
Fit: , , , ,ω ρ φ ω ω′ ′′
I Logashenko Tau 2008
26
Overview of the results
1.0%~0.6-0.7% 0.6% 1.5 -- 3.5 % 1.5%1.5%~ 6 -- 1% 1--2% 2.5 -- 3.5 % 2.0%
Systematic error:Total error:
Error of R(s)
CMD/SND
B. Lee Roberts, INT Seattle – 27 October 2008 - p. 27/44
We want
• CMD2/SND poor μ − πdiscrimination– calculate and subtract μμ
from ππ numerator– calculate μμ and use it for
the denominator
CMD-2
Energy deposition MeV
πe
μ
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KLOE and BaBar use ISR (radiative return)
• KLOE– sit on φ, γ is soft and goes
down the beam pipe– in data published thus far,
use theory to calculate mm cross section.
– have μ μ data being analyzed
• BaBar– runs on the Υ 4s, the γ is
hard, and is detected– excellent particle ID with
μ – π separation– measures R (s) directly
scan e+e- beam energy use ISR to lower collision energy
BINP
Always the issue of radiative corrections
KLOE
BaBar
M. Davier - Tau 208 29
ISR photon at large angle in EMC1 (for efficiency) or 2 (for physics) tracks of good qualityidentification of the charged particlesseparate ππ/KK/μμ event sampleskinematic fit (not using ISR photon energy) including 1 additional photonobtain all efficiencies (trigger, filter, tracking, ID, fit) from same data measure ratio of ππγ(γ) to μμγ(γ) cross sections to cancel
ee luminosityadditional ISRvacuum polarizationISR photon efficiency
still need to correct for |FSR|2 contribution in μμγ(γ) and additional FSR, both calculated in QED, but also checked in data (ISR-FSR interference, additional detected photons)
)1( )1(
)( )]()([ )1(
)]()([ )]()([ )]()([ )(R 0
0
exp μμμμμμ δδγμμσδγππσ
γμμγσγππγσ
addFSRFSRFSR
sRs
ssss
++=
+==
otherwise 3-4% syst error
(BaBar) The Measurement
M. Davier - Tau 2008 30
QED Test with μμγ sample
(0.2 – 5.0 GeV)
ISR γ efficiency 5.2 syst.trig/track/PID 4.0
BaBar ee luminosity
absolute comparison of μμ mass spectrain data and in simulation
simulation corrected for data/MCefficiencies
AfkQed corrected for incorrect NLOusing Phokhara
results for different running periods consistent: (7.9 ±7.5) 10-3
full statistics
J/ψ excluded
M. Davier - Tau 2008 31
Unfolding Mass Spectrummeasured mass spectrum distorted by resolution effects and FSR (mππ vs. s’)unfolding uses mass-transfer matrix from simulation2 MeV bins in 0.5-1.0 GeV mass range, 10 MeV bins outsidemost salient effect in ρ-ω interference region (little effect on aμ
ππ)
M. Davier - Tau 2008 35
BaBar vs.other ee data (0.5-1.0 GeV)
CMD-2
SND
direct relative comparison of crosssections in the corresponding 2-MeVBaBar bins (interpolation with 2 bins)
deviation from 1 of ratio w.r.t. BaBar
stat + syst errors included
KLOE comparison in Davier’s talk has a binning problem, so should be ignored.
M. Davier - Tau 2008 36
BaBar vs.other ee data (ρ−ω interference region)
CMD-2 SND
mass calibration of BaBar checked with ISR-produced J/ψ →μμexpect −(0.16 ± 0.16) MeV at ρ peakω mass can be determined through mass distribution fit (in progress)Novosibirsk data precisely calibrated using resonant depolarizationcomparison BaBar/CMD-2/SND in ρ-ω interference region showsno evidence for a mass shift
M. Davier - Tau 2008 37
BaBar vs. IB-corrected τ data (0.5-1.0 GeV)
relative comparison w.r.t. BaBar ofisospin-breaking corrected τ spectralfunctions
BaBar data averaged in wider τ binsand corrected for ρ-ω interference-0.2
-0.1
0
0.1
0.2
0.5 0.6 0.7 0.8 0.9 1√s(GeV/c2)
Δ|F π|
2 /|Fπ|
2
BABARτ(ALEPH)
B A B A RP R E L I M I N A R Y
-0.2
-0.1
0
0.1
0.2
0.5 0.6 0.7 0.8 0.9 1√s(GeV/c2)
Δ|F π|
2 /|Fπ|
2
BABARτ(CLEO)
B A B A RP R E L I M I N A R Y
-0.2
-0.1
0
0.1
0.2
0.5 0.6 0.7 0.8 0.9 1√s(GeV/c2)
Δ|F π|
2 /|Fπ|
2
BABARτ(BELLE)
B A B A RP R E L I M I N A R Y
M. Davier - Tau 2008 38
Computing aμππ
FSR correction was missing in Belle, new value 523.5 ± 3.0 ± 2.5
ALEPH-CLEO-OPAL(DEHZ 2006) (DEHZ 2003) (2008)
Direct comparison 0.630-0.958 GeV BaBar 369.3 ± 0.8 ± 2.2CMD-2 94-95 362.1 ± 2.4 ± 2.2CMD-2 98 361.5 ± 1.7 ± 2.9SND 361.0 ± 1.2 ± 4.7
aμππ (×10−10)
M. Davier - Tau 2008 39
ConclusionsBaBar analysis of ππ and μμ ISR processes completedPrecision goal has been achieved: 0.6% in ρ region (0.6-0.9 GeV)Absolute μμ cross section agrees with NLO QED within 1.2%Preliminary results available for ππ in the range 0.5-3 GeVStructures observed in pion form factor at large masses
Comparison with results from earlier experiments discrepancy with CMD-2 and SND mostly below ρ large disagreement with KLOE better agreement with τ results, especially Belle
Contribution to aμ from BaBar agrees better with τ resultsDeviation between BNL measurement and theory predictionsignificantly reduced using BaBar ππ data
aμ [exp ] – aμ [SM ]=(27.5 ± 8.4) × 10 –10 ⇒ (14.0 ± 8.4) × 10−10
Wait for final results and contributions of multi-hadronic modes
B. Lee Roberts, INT Seattle – 27 October 2008 - p. 41/44
• Must be calculated using models– models must be a good effective theory
of QCD. e.g ENJ-L, but nevertheless these models have limitations.
• Cannot be easily tied to data since you would need γ*γ* → π π data– there are some limits that can be used to
constrain amplitudes in the modelAll interesting calculations ≃(11±4)x10-10
vertex function
off-shell photon scattering amplitude induced by hadrons
B. Lee Roberts, INT Seattle – 27 October 2008 - p. 42/44
see also: E de Rafael, Heidelberg June 08- for some more details (but with smaller errors than have been to agreed to now for the whitepaper)
dominant contribution
Additional work is needed, and is in progress.
B. Lee Roberts, INT Seattle – 27 October 2008 - p. 43/44
My Summary and Conclusions (driven by Tau 2008)
• At present, the lowest order hadronic contribution is a study in contradictions.
• On the other hand, the H-LBL situation has improved.– representatives of the 3 principal theory groups agree on
values and errors of all of the contributions.• The τ situation
– Belle reported 100 times the τ data sample compared with LEP, however they normalized to the PDG value of the τ− → π− π0 ντ branching fraction, rather than their own value which was lower than the PDG (and would reduce the value of aμ(Had) from the Belle τ data).
– new isospin corrections reduce the difference, but do not resolve the previous e+e- -τ differences.
B. Lee Roberts, INT Seattle – 27 October 2008 - p. 44/44
Summary ctd.• The τ – e+e- differences have become more confusing
after BaBar. – recall that while the intergral from BaBar agrees with the
old tau results, the shape does not, but rather agrees with the Belle results.
– Will Belle use their π π BR for normalization?• If we take BaBar at face value, then how do we
average them with the other e+e- data?– Do we use the PDG prescription of increasing the errors so
χ2/ν → 1?– We certainly can’t throw out the other data just because
BaBar is the newest set• What about the KLOE μ μ measurement?
– we need that check of their new result• We will have to wait for the final BaBar paper to draw
further conclusions.
B. Lee Roberts, INT Seattle – 27 October 2008 - p. 46/44- p. 46/68
Lowest-order Hadronic Vacuum PolarizationDefine: photon vacuum polarization function Πγ(q2)
Ward identities: only vacuum polarization modifies electron charge
with:
Leptonic Δαlep(s) calculable in QED. However, quark loops are modified by long-distance hadronic physics, cannot (yet) be calculated within QCD (!)
Way out: Optical Theorem (unitarity) ...
Im[ ] ∝ | hadrons |2... and the subtracted dispersion relation of Πγ(q2) (analyticity)
... and equivalently for aμ [had]from Michel Davier
47
1
10
10 2
10 3
10 4
10 5
0.5 1 1.5 2 2.5 3 3.5 4
(Mπ±π0)2
(GeV/c2)2
Num
ber
of e
ntri
es /
0.05
(GeV
/c2 )2
DATA
MC(signal)
τ- → h-(nπ0)ντ
τ- → K-π0ντ
τ- → ω0π-ντ ( ω0 → π0γ )continuum B.G.
Background non-τ B.G.
feed down B.G.
m2ππ distribution
0h2π
0K−π
0
0
h 2 6.0%K 1.6%
τ
−τ
≥ π ν
π ν
qq 2.22±0.05%Tau mass limit
2 2( / )GeV c± 0 2(Mπ π )τ− π−ωντ(ω π0γ)
The signal level is different more than 4th order of magnitude betweenρ(770) and ρ’’(1700).
BG is important at threshold and ρ’’ region.
0.5%from Hisaki Hayashii
Tau - 2008
Belle data