The Hadronic Contribution to μ (observations of an amateur) · B. Lee Roberts, INT Seattle – 27 October 2008-p 1. 4/4 The Hadronic Contribution to aμ (observations of an amateur)

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


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


Gioachino Rossini


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.


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,


The SM Value for electron and muon anomalies

e vrs. μ : relative contribution of heavier things


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


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


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


An Intermezzo: tau for two (π)?

Can we use hadronic τdecay to get aμ(Had)?


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


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


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


Back to the matter at hand: e+ e− → π+π−


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


De Rujula: theorist is farmer, experimentalist truffle pig


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


23

“Narrow” resonances

(782)ω (1020)ϕMass and width are measured to ≈0.1 MeV, Γee to ≈2-3%


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+ − + −→


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′ ′′


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


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


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


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


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)


BaBar results


BaBar results in ρ region


BaBar vs. other experiments at large mass


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.


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


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)


-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)



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)


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


The Hadronic Light-by-Light Contribution


• 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


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.


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.


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. 45/44- p. 45/68

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

qq

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

The Hadronic Contribution to μ (observations of an amateur) · B. Lee Roberts, INT Seattle – 27 October 2008-p 1. 4/4 The Hadronic Contribution to aμ (observations of an amateur)

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