updates on muon g-2 - u-toyama.ac.jp
TRANSCRIPT
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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
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
D. Nomura (Tohoku U) Updates on Muon g − 2 Feb. 21, 2012 3 / 29
Introduction for ahad,LOµ
The diagram to be evaluated:
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.
.
.
had.
µ
pQCD not useful. Use the dispersionrelation and the optical theorem.
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.
.
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
D. Nomura (Tohoku U) Updates on Muon g − 2 Feb. 21, 2012 4 / 29
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D. Nomura (Tohoku U) Updates on Muon g − 2 Feb. 21, 2012 5 / 29
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
D. Nomura (Tohoku U) Updates on Muon g − 2 Feb. 21, 2012 7 / 29
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)
D. Nomura (Tohoku U) Updates on Muon g − 2 Feb. 21, 2012 8 / 29
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)
D. Nomura (Tohoku U) Updates on Muon g − 2 Feb. 21, 2012 9 / 29
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)
D. Nomura (Tohoku U) Updates on Muon g − 2 Feb. 21, 2012 10 / 29
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.
D. Nomura (Tohoku U) Updates on Muon g − 2 Feb. 21, 2012 11 / 29
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...)
D. Nomura (Tohoku U) Updates on Muon g − 2 Feb. 21, 2012 12 / 29
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)
D. Nomura (Tohoku U) Updates on Muon g − 2 Feb. 21, 2012 13 / 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.
D. Nomura (Tohoku U) Updates on Muon g − 2 Feb. 21, 2012 15 / 29
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
D. Nomura (Tohoku U) Updates on Muon g − 2 Feb. 21, 2012 18 / 29
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)
D. Nomura (Tohoku U) Updates on Muon g − 2 Feb. 21, 2012 19 / 29
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.
D. Nomura (Tohoku U) Updates on Muon g − 2 Feb. 21, 2012 20 / 29
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))
D. Nomura (Tohoku U) Updates on Muon g − 2 Feb. 21, 2012 22 / 29
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)
D. Nomura (Tohoku U) Updates on Muon g − 2 Feb. 21, 2012 23 / 29
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
D. Nomura (Tohoku U) Updates on Muon g − 2 Feb. 21, 2012 24 / 29
(Some of) Recent/Ongoing Activities(not ours but by others)
New (preliminary) analysis from KLOE (“KLOE11”)
Update in QED contribution
D. Nomura (Tohoku U) Updates on Muon g − 2 Feb. 21, 2012 25 / 29
P. A. Lukin (KLOE, Budker), talk at Phipsi11D. Nomura (Tohoku U) Updates on Muon g − 2 Feb. 21, 2012 26 / 29
P. A. Lukin (KLOE, Budker), talk at Phipsi11D. Nomura (Tohoku U) Updates on Muon g − 2 Feb. 21, 2012 27 / 29
P. A. Lukin (KLOE, Budker), talk at Phipsi11D. Nomura (Tohoku U) Updates on Muon g − 2 Feb. 21, 2012 28 / 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
D. Nomura (Tohoku U) Updates on Muon g − 2 Feb. 21, 2012 29 / 29