New Results on the Hadronic Vacuum Polarization Contribution to the - - PowerPoint PPT Presentation

M.Davier HVP/g-2 Phi2Psi Beijing 13-16/10/2009 1

New Results on the Hadronic Vacuum Polarization Contribution to the Muon g-2

Michel Davier (LAL – Orsay)

• the muon magnetic anomaly
• revisited τ spectral functions: Belle + updated

corrections

• ee spectral functions after KLOE and BaBar
• combination of all ee data
• discussion and perspectives

M.Davier HVP/g-2 Phi2Psi Beijing 13-16/10/2009 2

Most recent data and analyses

τ → π π0 ντ data from Belle PRD 78 (2008) 072006

e+ e− → π+ π− data

• KLOE PLB 670 (2009) 285
• BaBar

arXiv:0908.3589v1 updated τ-based analysis arXiv:0906.5443v2

MD, A. Hoecker, G. Lopez Castro, B. Malaescu, X.H.Mo, G. Toledo Sanchez,

• P. Wang, C.Z. Yuan, Z. Zhang

updated ee-based analysis arXiv:0908.4300v1

MD, A. Hoecker, B. Malaescu, C.Z. Yuan, Z. Zhang

M.Davier HVP/g-2 Phi2Psi Beijing 13-16/10/2009 3

Hadronic Vacuum Polarization and Muon (g –2)μ

2

2 had 2 4

( ) ( ) 3

m

a R s K s s d s

π

μ

α π

∞

=

∫

Dispersion relation

μ γ

γ

had

γ

( )

2 (0)

Born: ( ) ( ) / ( ) s s s σ σ α α =

Im[ ] ∝ | hadrons |2

) ( ] ) ( hadrons [ ) ( Im 12 s R e e s

pt

≡ → = Π

− +

σ γ σ π

γ

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

M.Davier HVP/g-2 Phi2Psi Beijing 13-16/10/2009 4

The E-821 aμ Measurement at BNL Updated

⇒ change in aμ (+0.92 10−10) (see next review in RPP2009 (Hoecker-Marciano) aμ

exp = (11 659 208.9 ± 5.4 ± 3.3) 10−10 updated

(± 6.3) (0.54 ppm) aμ measured from a ratio of frequencies ωa = ωprecession − ωcyclotron ωprecession = ωL + ωT λ= ωL /ωp = μμ /μp from muonium hyperfine splitting value used by E-821 3.18334539(10) new value 3.183345137(85) Mohr et al., RMP 80 (2008) 633

M.Davier HVP/g-2 Phi2Psi Beijing 13-16/10/2009 5

The Role of τ Data through CVC – SU(2)

hadrons

τ ντ

W hadrons

γ

e+ e –

CVC: I=1 & V W: I=1 & V,A γ: I=0,1 & V

Hadronic physics factorizes (spectral Functions)

2 ( 1)

4

I

e e s

τ

υ τ π π ν πα σ π π

= + − + − − −

⎡ ⎤ → = → ⎣ ⎦ ⎡ ⎤ ⎣ ⎦

( ) ( )

2 2 2 2

BR 1 / 1 1 / BR

e

dN N d m m s m e s s

ππ ππ τ τ τ τ τ τ

υ τ π τ π π ν ν ν π ν τ

− − − − − −

⎡ ⎤ → ⎣ ⎦ ⎡ ⎤ → ⎡ ⎤ → ∝ + ⎣ ⎦ − ⎣ ⎦

branching fractions mass spectrum kinematic factor (PS)

M.Davier HVP/g-2 Phi2Psi Beijing 13-16/10/2009 6

SU(2) Breaking

Corrections for SU(2) breaking applied to τ data for dominant π –π + contrib.: Electroweak radiative corrections: dominant contribution from short distance correction SEW subleading corrections (small) long distance radiative correction GEM(s) Charged/neutral mass splitting: mπ – ≠ mπ0 leads to phase space (cross sec.) and width (FF) corrections ρ -ω mixing (EM ω → π –π + decay) corrected using FF model mρ – ≠ mρ0 *** and Γρ – ≠ Γρ0 *** Electromagnetic decays: ρ → π π γ ***, ρ → π γ, ρ → η γ, ρ → l+l – Quark mass difference mu ≠ md (negligible)

Cirigliano-Ecker-Neufeld’ 02 Lopez Castro et al.’ 06 Marciano-Sirlin’ 88 Braaten-Li’ 90 Alemany-Davier-Höcker’ 97, Czyż-Kühn’ 01 Flores-Baez-Lopez Castro’ 08 Davier et al.’09

M.Davier HVP/g-2 Phi2Psi Beijing 13-16/10/2009 7

Situation at ICHEP’06 / 08

aμ

had [ee]

= (690.9 ± 4.4) × 10–10 aμ [ee] = (11 659 180.5 ± 4.4had ± 3.5LBL ± 0.2QED+EW) × 10–10

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

3.3 „standard deviations“ = (27.5 ± 8.4) × 10–10 aμ [exp] – aμ [SM]

Observed Difference with BNL using e+e−:

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

.0

Davier-Marciano (2004) Kinoshita-Nio (2006)

e+e− τ BNL But estimate using τ data consistent with E-821 !

M.Davier HVP/g-2 Phi2Psi Beijing 13-16/10/2009 8

Revisited Analysis using τ Data: including Belle

Test of the spectral function shapes from different experiments: WA BR used

M.Davier HVP/g-2 Phi2Psi Beijing 13-16/10/2009 9

Revisited Analysis τ Data: new IB corrections

talk by G. Lopez Castro disagreement with Maltman-Wolfe arXiv:0908.2391

M.Davier HVP/g-2 Phi2Psi Beijing 13-16/10/2009 10

Consistency of τ Data: Dispersion Integrals

• using BR from each experiment makes

results independent from each other

• consistent results
• using WA BR checks consistency

for the spectral function shapes

• WA BR + combined spectral

function ⇒ aμ

2π,LO=(515.2±2.0exp±0.9Be±2.1Bππ±1.6IB) 10−10

• 0.7% precision

M.Davier HVP/g-2 Phi2Psi Beijing 13-16/10/2009 11

Comparison of ee and τ Data Revisited (1)

CMD-2, SND KLOE Relative comparison of IB-corrected τ and ee spectral functions (τ green band) ⇒ better agreement than before with CMD2-SND ⇒ strong disagreement with KLOE : slope…

M.Davier HVP/g-2 Phi2Psi Beijing 13-16/10/2009 12

Comparison of ee and τ Data Revisited (2)

Global test of spectral functions: prediction of τ BR using ee data ⇒ apply to ππ0 channel IB corrections applied to ee data this time

• data from CMD2-SND
• verconsistent ?
• fair agreement CMD2-SND with τ
• larger disagreement with KLOE

M.Davier HVP/g-2 Phi2Psi Beijing 13-16/10/2009 13

Data on e+e− → hadrons (1)

Mass [GeV]

0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Cross section [nb]

200 400 600 800 1000 1200 1400

CMD2-2004

Mass [GeV]

0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Cross section [nb]

200 400 600 800 1000 1200 1400

Mass [GeV]

0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Cross section [nb]

200 400 600 800 1000 1200 1400

CMD2-2006

Mass [GeV]

0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Cross section [nb]

200 400 600 800 1000 1200 1400

Mass [GeV]

0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Cross section [nb]

200 400 600 800 1000 1200 1400

KLOE-2008

Mass [GeV]

0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Cross section [nb]

200 400 600 800 1000 1200 1400

Mass [GeV]

0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Cross section [nb]

200 400 600 800 1000 1200 1400

SND

Mass [GeV]

0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Cross section [nb]

200 400 600 800 1000 1200 1400

CMD-2 (2004) CMD-2 (2006) SND (2006) KLOE (2009)

M.Davier HVP/g-2 Phi2Psi Beijing 13-16/10/2009 14

Data on e+e− → hadrons (2)

talk by Wenfeng Wang BaBar (2009)

M.Davier HVP/g-2 Phi2Psi Beijing 13-16/10/2009 15

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

CMD-2 direct relative comparison of cross sections with BaBar fit (stat + syst errors included) (green band) SND KLOE BaBar

M.Davier HVP/g-2 Phi2Psi Beijing 13-16/10/2009 16

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

relative comparison w.r.t. BaBar of isospin-breaking corrected τ spectral functions IB corrections: radiative corr., π masses, ρ-ω interference, ρ masses/widths each τ data normalized to its own BR ALEPH CLEO Belle

M.Davier HVP/g-2 Phi2Psi Beijing 13-16/10/2009 17

Combination of all e+e− Data

arXiv: 0908.4300 MD-Hoecker-Malaescu-Yuan-Zhang Improved procedure and software (HVPTools) for combining cross section data with arbitrary point spacing/binning

M.Davier HVP/g-2 Phi2Psi Beijing 13-16/10/2009 18

Obtaining the average cross section

relative weights

integrand (dispersion integral) error

error scale factor

• local weighted average performed
• full covariance matrices
• local χ2 used for error rescaling
• average dominated by BaBar and

KLOE, BaBar covering full range

M.Davier HVP/g-2 Phi2Psi Beijing 13-16/10/2009 19

Consistency of Experiments with Average

M.Davier HVP/g-2 Phi2Psi Beijing 13-16/10/2009 20

Computing aμ

ππ [2mπ ,1.8 GeV]

Pre-BaBar combined ee 503.5 ± 3.5 BaBar 514.1 ± 3.8 Combined ee 508.4 ± 2.9 Combined τ 515.2 ± 3.0 ± 1.6 (3.4)

M.Davier HVP/g-2 Phi2Psi Beijing 13-16/10/2009 21

Modes Energy [GeV]

e+e – τ

π +π – 2π0 2mπ – 1.8 16.8 ± 1.3 ± 0.2rad 21.4 ± 1.3 ± 0.6SU(2) J/ψ, ψ (2S) 3.08 – 3.11 7.4 ± 0.4 ± 0.0rad – R [QCD] 1.8 – 3.7 33.9 ± 0.5theo – R [QCD] 5.0 – ∞ 9.9 ± 0.2theo – 2π + 2π – (+BaBar) 2mπ – 1.8 13.1 ± 0.4 ± 0.0rad 12.3 ± 1.0 ± 0.4SU(2) ω (782) 0.3 – 0.81 38.0 ± 1.0 ± 0.3rad – φ (1020) Other excl. (+BaBar) R [data] 1.0 – 1.055 35.7 ± 0.8 ± 0.2rad – 2mπ – 1.8 24.3 ± 1.3 ± 0.2rad – 3.7 – 5.0 7.2 ± 0.3 ± 0.0rad –

Other hadronic contributions

from MD-Eidelman-Hoecker-Zhang NP Proc. Suppl. 169 (2007) 288 ⇒ another large long-standing discrepancy in the π+ π− 2π0 channel !

M.Davier HVP/g-2 Phi2Psi Beijing 13-16/10/2009 22

The Problematic 2π 2π0 Contribution

ee data used now (CMD2 discarded) preliminary BaBar data:

• A. Petzold, EPS-HEP (2007)
• nly statistical errors
• ld contribution 16.8 ± 1.3

update 17.6 ± 1.7 probably still underestimated (BaBar) τ 21.4 ± 1.4

M.Davier HVP/g-2 Phi2Psi Beijing 13-16/10/2009 23

BaBar Multi-hadronic Results

• nly statistical errors
• syst. 5-10%

Still more channels under analysis: K+K−, KKππ with K0

M.Davier HVP/g-2 Phi2Psi Beijing 13-16/10/2009 24

Where are we?

• including BaBar 2π results in the e+e− combination + estimate of hadronic

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

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
• deviation (ee) 25.5 ± 8.0

(3.2 σ)

• updated τ analysis

+Belle +revisited IB corrections

• deviation (τ) 15.7 ± 8.2

(1.9 σ)

M.Davier HVP/g-2 Phi2Psi Beijing 13-16/10/2009 25

Discussion

• BaBar 2π data complete and the most accurate, but expected gain in precision

not fully realized because of discrepancy with KLOE

• however, previous τ/ee disagreement strongly reduced

2.9σ (2006) → 2.4σ (τ update) → 1.5σ (including BaBar)

• a range of values for the deviation from the SM can be obtained, depending
• n the 2π data used:

BaBar 2.4σ all ee 3.2σ all ee −BaBar 3.7σ all ee −KLOE 2.9σ τ 1.9σ

• 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 τ data

• at the moment some evidence for a deviation (~3σ), but not sufficient to establish

a contribution from new physics (NP)

• however if NP is found at LHC, this deviation will constraint the NP phenomenology

M.Davier HVP/g-2 Phi2Psi Beijing 13-16/10/2009 26

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 ρ peak (most direct effect on aμ)
• Novosibirsk results in-between
• slope also seen in KLOE/τ comparison; BaBar agrees with τ
• further checks of the KLOE results are possible: as method is based on MC

simulation for ISR and additional ISR/ISR probabilities ⇒ long-awaited test with μμγ analysis

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

more results forthcoming from BaBar, particularly 2π 2π0

• new precise data expected from VEPP-2000 in Novosibirsk
• experimental error of E-821 direct aμ measurement is a limitation, already now

⇒ new proposal submitted to Fermilab to improve accuracy by a factor 4 ⇒ project at JPARC

M.Davier HVP/g-2 Phi2Psi Beijing 13-16/10/2009 27

Backup Slides

M.Davier HVP/g-2 Phi2Psi Beijing 13-16/10/2009 28 γ∗ (S′) µ− µ+ e+ e− γ γ∗ (S′) π− π+ e+ e− γ γ∗ (S′) π/µ π/µ e+ e− γ γ γ∗ (S′) π/µ π/µ e+ e− γ γ γ∗ (S′) µ− µ+ e+ e− γ

ISR FSR ISR + add. ISR ISR + add. FSR

The Relevant Processes

e+ e−→ μ+ μ− γ (γ) and π+ π− γ (γ) measured simultaneously

LO FSR negligible for ππ at s∼(10.6 GeV)2

M.Davier HVP/g-2 Phi2Psi Beijing 13-16/10/2009 29

QED Test with μμγ sample

ISR γ efficiency 3.4 syst. trig/track/PID 4.0 BaBar ee luminosity absolute comparison of μμ 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 ππ) (0.2 − 3 GeV) BaBar

M.Davier HVP/g-2 Phi2Psi Beijing 13-16/10/2009 30

Obtaining the ππ(γ) cross section

Unfolded spectrum Effective ISR luminosity from μμγ(γ) analysis (similar equation + QED) Acceptance from MC + data/MC corrections ππ mass spectrum unfolded (Malaescu arXiv:0907-3791) for detector response Additional ISR almost cancels in the procedure (ππγ(γ) / μμγ(γ) ratio) Correction (2.5 ±1.0) 10−3 ⇒ ππ cross section does not rely on accurate description of NLO in the MC generator ISR luminosity from μμγγ in 50-MeV energy intervals (small compared to variation of efficiency corrections)

M.Davier HVP/g-2 Phi2Psi Beijing 13-16/10/2009 31

BaBar results (arXiv:0908.3589)

e+ e− → π+ π− (γ)

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

M.Davier HVP/g-2 Phi2Psi Beijing 13-16/10/2009 32

BaBar results in ρ region

2-MeV energy intervals

M.Davier HVP/g-2 Phi2Psi Beijing 13-16/10/2009 33

Additional ISR

500 1000 1500 2000 2.5 5 7.5 10

ln(χ2+1)add.ISR

1 10 10 2 10 3 2 4 6

Eγ add.ISR in CM (GeV)

μμγγ

1000 2000 3000 4000 2.5 5 7.5 10

DATA MC

ππγ(γ),Mππ:0.5-1GeV

ln(χ2+1)add.ISR

1 10 10 2 10 3 10 4 2 4 6

DATA MC

ππγ(γ),Mππ:0.5-1GeV

Eγ add.ISR in CM (GeV)

ππγγ

Angular distribution

• f add. ISR /beams!

Energy cut-off for

• add. ISR in AfkQed

2.5 5 7.5 10 2.5 5 7.5 10 1 10 10 2 10 3

ln(χ2+1)add.ISR ln(χ2+1)add.FSR

no γ2 no add. rad. + add.ISR add.ISR add.’FSR’ no add.Rad. 2D-χ2 cut (BG region) t r k r e c + i n t e r a c t i

• n

s + m

• r

e a d d . r a d .

M.Davier HVP/g-2 Phi2Psi Beijing 13-16/10/2009 34

Additional FSR

100 200 300 400 2.5 5 7.5 10

ln(χ2+1)add.FSR

50 100 150 200 50 100 150

θµγ2 (degree)

μμγγ ππγγ

100 200 300 50 100 150

DATA MC

ππγ(γ),Mππ:0.5-1GeV

θπγ2 (degree)

100 200 300 400 50 100 150

DATA BG(MC)

ππγ(γ),Mππ:0.5-1GeV

θπγ2 (degree)

Angle between add γ and closest track Large-angle add.ISR in data ≠ AfkQed Evidence for FSR data ∼ AfkQed

FSR ISR

2.5 5 7.5 10 2.5 5 7.5 10 1 10 10 2 10 3

ln(χ2+1)add.ISR ln(χ2+1)add.FSR

no γ2 no add. rad. + add.ISR add.ISR add.’FSR’ no add.Rad. 2D-χ2 cut (BG region) t r k r e c + i n t e r a c t i

• n

s + m

• r

e a d d . r a d .

data/MC μμ 0.96±0.06 ππ 1.21±0.05

M.Davier HVP/g-2 Phi2Psi Beijing 13-16/10/2009 35

VDM Fit of the BaBar Pion Form Factor

• add. FSR

α Running (VP)

M.Davier HVP/g-2 Phi2Psi Beijing 13-16/10/2009 36

BaBar vs.other ee data (ρ−ω interference region)

CMD-2 SND mass calibration of BaBar checked with ISR-produced J/ψ →μμ expect −(0.16 ± 0.16) MeV at ρ peak ω mass determined through VDM mass fit mω

fit −mω PDG = −(0.12 ± 0.29) MeV

Novosibirsk data precisely calibrated using resonant depolarization comparison BaBar/CMD-2/SND in ρ-ω interference region shows no evidence for a mass shift

M.Davier HVP/g-2 Phi2Psi Beijing 13-16/10/2009 37

Combined τ vs. Combined ee

M.Davier HVP/g-2 Phi2Psi Beijing 13-16/10/2009 38

Difference BaBar/Others in Broad Mass Bins

integrals in 0.1 GeV intervals

M.Davier HVP/g-2 Phi2Psi Beijing 13-16/10/2009 39

Computing aμ

ππ

(×10−10) * * arXiv:0906-5443 MD et al. 0.28−1.8 (GeV) BABAR 514.1 ± 3.8 previous e +e− combined 503.5 ± 3.5 * τ combined 515.2 ± 3.5 * * 0.7% precision