updates on muon g-2 - u-toyama.ac.jp

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Updates on Muon g − 2

Daisuke Nomura (Tohoku U.)

talk at Toyama winter workshop

February 21, 2012

Based on J. Phys. G38 (2011) 085003by K. Hagiwara, R. Liao, A. D. Martin, DN & T. Teubner

(HLMNT)+ updates (not necessarily from HLMNT)

D. Nomura (Tohoku U) Updates on Muon g − 2 Feb. 21, 2012 1 / 29

Muon g − 2: introduction


Introduction: Standard Model prediction for muon g − 2

QED contribution 11 658 471.808 (0.015) ×10−10 Kinoshita & Nio, Aoyama et al

EW contribution 15.4 (0.2) ×10−10 Czarnecki et al

Hadronic contribution

LO hadronic 694.9 (4.3) ×10−10 HLMNT11

NLO hadronic −9.8 (0.1) ×10−10 HLMNT11

light-by-light 10.5 (2.6) ×10−10 Prades, de Rafael & Vainshtein

Theory TOTAL 11 659 182.8 (4.9) ×10−10

Experiment 11 659 208.9 (6.3) ×10−10 world avg

Exp − Theory 26.1 (8.0) ×10−10 3.3 σ discrepancy

(Numbers taken from HLMNT11, arXiv:1105.3149)

n.b.: hadronic contributions:. .

. .

had.

LO

µ

had.

NLO

µγ

had.

l-by-l

µ


Introduction for ahad,LOµ

The diagram to be evaluated:

.

.

.

.

had.

µ

pQCD not useful. Use the dispersionrelation and the optical theorem.

.

.

.

.

had.

=∫

ds

π(s−q2)Im

had.

2 Im

had.

=∑

dΦ

∫ 2

had.

ahad,LOµ =

m2µ

12π3

∫ ∞

sth

ds1sK̂(s)σhad(s)

0

250

500

750

1000

1250

1500

1750

2000

2250

2500

1 10

J/ψ ψ(2S) ϒ

√s (GeV)

(2 α

2/

3 π

2)

K(s

) R

(s)

× 10

10

0.2 –0.2 1 10√s (GeV)

• Weight function K̂(s)/s = O(1)/s=⇒ Lower energies more important=⇒ π+π− channel: 73% of total ahad,LO

µ


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Recently added data

T. Teubner, talk at Tau2010D. Nomura (Tohoku U) Updates on Muon g − 2 Feb. 21, 2012 6 / 29

π+π− channel: Low Energy Tail

0

50

100

150

200

0.3 0.32 0.34 0.36 0.38 0.4 0.42 0.44

σ0 (e+e- →

π+π- )

[nb]

√s [GeV]

New FitBaBar (09)KLOE (10)

CMD-2 (06)SND (06)

OLYA-VEPP2TOF-VEPP 2M

NA7CMD-VEPP 2M

ChPT


π+π− channel: New Radiative Return Data

0

200

400

600

800

1000

1200

1400

0.6 0.65 0.7 0.75 0.8 0.85 0.9 0.95

σ0 (e+e- →

π+π- )

[nb]

√s [GeV]

BaBar (09)New Fit

KLOE (10)KLOE (08)


π+π− channel: Zoom-In at ρ-ω Region

600

700

800

900

1000

1100

1200

1300

1400

0.74 0.75 0.76 0.77 0.78 0.79 0.8 0.81 0.82

σ0 (e+e- →

π+π- )

[nb]

√s [GeV]

BaBar (09)New Fit

KLOE (10)KLOE (08)

CMD-2 (07)SND (06)

CMD-2 (04)


Rad. Rtn. Data (for π+π−) and Our Combined Result

-0.06

-0.04

-0.02

0

0.02

0.04

0.06

0.08

0.6 0.65 0.7 0.75 0.8 0.85 0.9 0.95

(σ0 R

adR

et S

ets

- σ0 F

it)/σ

0 Fit

√s [GeV]

New FitBaBar (09)

New Fit (local χ2 inf)KLOE (08)KLOE (10)


Impacts from New BaBar Data in subleading channels: (1)

0

1

2

3

4

5

6

7

1.4 1.5 1.6 1.7 1.8 1.9 2

σ0 (e+e- →

K0 sK

π) [n

b]

√s [GeV]

Fit (w/o BaBar)Fit (all sets)BaBar (08)

DM1 (82)DM2 (91)

0

5

10

15

20

25

30

35

40

45

1.4 1.5 1.6 1.7 1.8 1.9 2

σ0 (e+e- →

π+π- π+

π- ) [n

b]

√s [GeV]

Fit w/o BaBarFit all sets

BaBar (05)DM2 (90)DM1 (82)M3N (79)

e+e− → K0SKπ (left) and e+e− → 2π+2π− (right)

In these cases, the new BaBar data agree well with theold data, and improve them in a peaceful way.


Impacts from New BaBar Data in subleading channels: (2)

0

2

4

6

8

10

12

14

16

1.4 1.5 1.6 1.7 1.8 1.9 2

σ0 (e+e- →

π+π- π+

π- π0 ) [n

b]

√s [GeV]

2003 fitNew fit (w BaBar)

BaBar (08)MEA (81)M3N (79)gg2 (81)

DM1 (81)

0

2

4

6

8

10

12

14

16

1.4 1.5 1.6 1.7 1.8 1.9 2

σ0 (e+e- →

π+π- π+

π- π0 π0 ) [n

b]

√s [GeV]

2003 fitNew fit (w BaBar)

BaBar (06)M3N (79)DM2 (86)gg2 (81)

MEA (81)

e+e− → 2π+2π−π0 (left) and 2π+2π−2π0 (right)In these cases, the new BaBar data do not agree verywell with the old data, and improve them ‘radically’.Note that the old data are really old (those from the ’80sor older...)


Region between 1.4 – 2.0 GeV

1

1.5

2

2.5

3

3.5

1.4 1.5 1.6 1.7 1.8 1.9 2

Rha

d(s)

√s [GeV]

ExclusiveInclusive

Exclusive (2003)


T. Teubner, talk at Tau2010D. Nomura (Tohoku U) Updates on Muon g − 2 Feb. 21, 2012 14 / 29

Sum Rules: choice of weight functions

0

0.5

1

1.5

2

2.5

3

0 0.5 1 1.5 2 2.5 3

2√s

f(s)

(ke

rnel

val

ue w

ith J

acob

ian)

√s [GeV]

Sum rule kernel functions (with Jacobian factor included)

√s0 = 2.6 GeV, (mn) = (10)(mn) = (11)(mn) = (20)

√s0 = 2.0 GeV, (mn) = (10)(mn) = (11)(mn) = (20)(mn) = (00)

We choose the weight functions in such a way that theyemphasize the region in question, 1.4–2.0 GeV.


Sum Rules for 1.4 – 2.0 GeV: Results

0.1 0.12 0.14αS(M 2Z)

inclusive

inclusive

inclusive

inclusive

inclusive

exclusive

exclusive

exclusive

exclusive

exclusive

(mn, √s–

0) data (fraction (%))

(00, 2.6) (26.6)

(10, 2.6) (30.2)

(11, 2.6) (39.6)

(00, 2.0) (47.3)

(11, 2.0) (48.3)

(00, 2.6) (32.3)

(10, 2.6) (37.8)

(11, 2.6) (45.1)

(00, 2.0) (55.8)

(11, 2.0) (55.5)

Sum of exclusive data: now more consistent with pQCD.D. Nomura (Tohoku U) Updates on Muon g − 2 Feb. 21, 2012 16 / 29

T. Teubner, talk at Tau2010

At 2.6–3.73 GeV we use pQCD (with the BESII (09) uncertainty)D. Nomura (Tohoku U) Updates on Muon g − 2 Feb. 21, 2012 17 / 29

Results: ahad,LOµ , ahad,NLO

µ and ∆α(5)had(M

2Z)

aµhad,LO VP

∆α(5)had (M 2

Z)

value (error)2

mπ

0.6

0.9

1.42

∞rad.

mπ0.6

0.91.4

2∞

mπ 0.60.9

1.42

4

11

∞rad.

mπ 0.60.91.4

2

4

11

∞

ahad,LOµ =(694.91 ± 3.72exp ± 2.10rad) × 10−10

ahad,NLOµ =(−9.84 ± 0.06exp ± 0.04rad) × 10−10

∆α(5)had(M

2Z) =(276.26 ± 1.16exp ± 0.74rad) × 10−4


Full SM Result and Comparison with Other Groups

170 180 190 200 210

aµ × 1010 – 11659000

HMNT (06)

JN (09)

Davier et al, τ (10)

Davier et al, e+e– (10)

JS (11)

HLMNT (10)

HLMNT (11)

Benayoun et al (11)

experiment

BNL

BNL (new from shift in λ)


Byproducts (1): QED coupling at the Z-boson mass

F α(M2Z): the least well known among {Gµ, MZ, α(M2

Z)},which are used as input to precision electroweak fits.F Running of α

α(M2Z) =

α

1 − ∆αlep(M2Z) − ∆α

(5)had(M

2Z) − ∆αtop(M2

Z)

where ∆αlep(M2Z) = 0.03149769 (Steinhauser),

∆αtop(M2Z) = − 0.0000728(14) and α = 1/137.035999679(94)

(PDG10).

F Similar dispersion relation: (=⇒ byproduct of ahad,LOµ )

∆α(5)had(s) = −

αs

3πP

∫R(s′)ds′

s′(s′ − s)

F Our results: ∆α(5)had(M

2Z) = (276.3 ± 1.4) × 10−4,

α(M2Z)−1 = 128.944 ± 0.019.


Byproducts (2): running QED coupling α(q2)

The hadronic contribution ∆α(5)had(q

2) to the runningQED coupling for q2 > 0 (left) and q2 < 0 (right)

-2

-1

0

1

2

3

4

10-1

1 10√s (GeV)

∆α(5

) had (

s)/α

0

0.5

1

1.5

2

2.5

3

3.5

4

10-1

1 10√s (GeV)

∆α(5

) had (

– s)

/α

Fortran subroutine to compute the above is available from us upon

requestD. Nomura (Tohoku U) Updates on Muon g − 2 Feb. 21, 2012 21 / 29

Before discussing anotherbyproduct, do you know what themost precise way to measure themuon mass is?

(cf. mµ = 105.6583668(38) MeV (PDG11))


Before discussing anotherbyproduct, do you know what themost precise way to measure themuon mass is?

(cf. mµ = 105.6583668(38) MeV (PDG11))

Answer: Muonium ground-statehyperfine splitting (MuHFS)


Mu HFS: Summary Table (as of 2002)

correction contribution (in units of kHz)νF 4459031.920(511)mµ/me

(34)α

∆ν(ae) 5170.926(1)∆ν(QED3) − 899.557∆ν(QED4) − 0.55(22)∆ν(weak) − 0.065∆ν(had-vp) 0.231(3)∆ν(had-h.o.) 0.005(2)νHFS(theory) 4463302.909(511)(34)(220)νHFS(exp) 4463302.776(51)

Table from Czarnecki, Eidelman & Karshenboim, PRD65 (2002) 053004 with

updates from Eidelman, Karshenboim & Shelyuto, Can. J. Phys. 80 (2002) 1297


(Some of) Recent/Ongoing Activities(not ours but by others)

New (preliminary) analysis from KLOE (“KLOE11”)

Update in QED contribution


P. A. Lukin (KLOE, Budker), talk at Phipsi11D. Nomura (Tohoku U) Updates on Muon g − 2 Feb. 21, 2012 26 / 29

Summary

We (HLMNT) have updated our analysis with (lotsof) new data including those from KLOE and BaBarWe find 3.3 σ discrepancy between experiment andtheory =⇒ New Physics?Two new experiments to measure the muon g − 2planned at J-PARC and Fermilab. Both experimentsrecently got stage-1 approval from KEK & Fermilab,respectively.To establish this discrepancy more firmly, it is veryimportant to resolve the disagreement in the π+π−

channel between the KLOE and BaBar data =⇒new precise data from VEPP-2000 and SuperKEKBvery welcome


updates on muon g-2 - u-toyama.ac.jp

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