standard model prediction for muon g 2 - riken
TRANSCRIPT
Standard Model predictionfor muon g − 2
Daisuke Nomura (YITP, Kyoto U.)
talk at the workshop
‘Storage Rings and Tests of Fundamental Symmetries’
at RIKEN, Wako
March 2, 2016
D. Nomura (YITP, Kyoto U.) Standard Model prediction for muon g − 2 March 2, 2016 1 / 35
Muon g − 2: introduction
D. Nomura (YITP, Kyoto U.) Standard Model prediction for muon g − 2 March 2, 2016 2 / 35
Introduction: Standard Model prediction for muon g − 2
QED contribution 11 658 471.808 (0.015) Kinoshita & Nio, Aoyama et al
EW contribution 15.4 (0.2) Czarnecki et al
Hadronic contributions
LO hadronic 694.9 (4.3) HLMNT11
NLO hadronic −9.8 (0.1) HLMNT11
light-by-light 10.5 (2.6) Prades, de Rafael & Vainshtein
Theory TOTAL 11 659 182.8 (4.9)
Experiment 11 659 208.9 (6.3) world avg
Exp − Theory 26.1 (8.0) 3.3 σ discrepancy
(in units of 10−10. Numbers taken from HLMNT11, arXiv:1105.3149)
n.b.: hadronic contributions:. .
. .
had.
LO
µ
had.
NLO
µγ
had.
l-by-l
µ
D. Nomura (YITP, Kyoto U.) Standard Model prediction for muon g − 2 March 2, 2016 3 / 35
Improvements in the past few years (1)
QED contribution5-loop calculation completed:
now aµ(QED) = 11 658 471.895(8) × 10−10
(number from Aoyama et al (2012))
See Nio-san’s talk
EW contributionHiggs-boson mass just fixed:
now aµ(EW) = 15.4(1) × 10−10 Gnendiger et al ’13
was aµ(EW) = 15.4(2) × 10−10 Czarnecki et al ’02
cf: aexpµ − aSM
µ =
{(26.1 ± 8.0) × 10−10 HLMNT11
(28.7 ± 8.0) × 10−10 Davier et al ’10
D. Nomura (YITP, Kyoto U.) Standard Model prediction for muon g − 2 March 2, 2016 4 / 35
Improvements in the past few years (2)
NNLO hadronic contributionaµ(had, NNLO) = (1.24 ± 0.01) × 10−10
Numbers and Figs. fromA. Kurz et al, arXiv:1403.6400
3a: +0.80 × 10−10
3b: −0.41 × 10−10
3b,lbl: +0.91 × 10−10
3c: −0.06 × 10−10
3d: +0.0005 × 10−10
cf: aexpµ − aSM
µ =
{(26.1 ± 8.0) × 10−10 HLMNT11
(28.7 ± 8.0) × 10−10 Davier et al ’10
aµ(had, NLO) = (−9.8 ± 0.1) × 10−10 HLMNT11
D. Nomura (YITP, Kyoto U.) Standard Model prediction for muon g − 2 March 2, 2016 5 / 35
Improvements in the past few years (3)
lbyl-NLO hadronic contribution
aµ(had, lbyl-NLO) = (0.3 ± 0.2) × 10−10
had
Number and Fig. from Colangelo et al,arXiv:1403.7512
=⇒ Negligible. But it is always goodto confirm that higher order termsare really negligible.
cf: aexpµ − aSM
µ =
{(26.1 ± 8.0) × 10−10 HLMNT11
(28.7 ± 8.0) × 10−10 Davier et al ’10
ahad,lbylµ =
{(10.5 ± 2.6) × 10−10 Prades et al, ’09
(11.6 ± 3.9) × 10−10 Jegerlehner+Nyffeler, ’09D. Nomura (YITP, Kyoto U.) Standard Model prediction for muon g − 2 March 2, 2016 6 / 35
Updated Standard Model prediction for muon g − 2
Aoyama et al ’12Gnendiger et al ’13
HLMNT11
Davier et al ’10
HLMNT11Kurz et al ’14Prades et al ’09Colangelo et al ’14
BNL
Table from TDR for g − 2/EDM experiment at J-PARC (J-PARC E34)
D. Nomura (YITP, Kyoto U.) Standard Model prediction for muon g − 2 March 2, 2016 7 / 35
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 =m2
µ
12π3
∫ ∞
sth
ds1
sK̂(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)
× 1
010
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,LOµ
D. Nomura (YITP, Kyoto U.) Standard Model prediction for muon g − 2 March 2, 2016 8 / 35
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D. Nomura (YITP, Kyoto U.) Standard Model prediction for muon g − 2 March 2, 2016 9 / 35
Important Channels
Contributions from various channels to aµ(LO,had) for√s < 1.8GeV:
channel HLMNT11 Davier et al ’10 diffπ+π− 505.65 ± 3.09 507.80 ± 2.84 −2.15π+π−π0 47.38 ± 0.99 46.00 ± 1.48 1.38K+K− 22.09 ± 0.46 21.63 ± 0.73 0.46π+π−2π0 18.62 ± 1.15 18.01 ± 1.24 0.612π+2π− 13.50 ± 0.44 13.35 ± 0.53 0.15K0
SK0L 13.32 ± 0.16 12.96 ± 0.39 0.36
π0γ 4.54 ± 0.14 4.42 ± 0.19 0.12...
......
...Sum 634.28 ± 3.53 633.93 ± 3.61 0.35
table taken from HLMNT11D. Nomura (YITP, Kyoto U.) Standard Model prediction for muon g − 2 March 2, 2016 10 / 35
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 (YITP, Kyoto U.) Standard Model prediction for muon g − 2 March 2, 2016 11 / 35
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 (YITP, Kyoto U.) Standard Model prediction for muon g − 2 March 2, 2016 12 / 35
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 (YITP, Kyoto U.) Standard Model prediction for muon g − 2 March 2, 2016 13 / 35
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 (YITP, Kyoto U.) Standard Model prediction for muon g − 2 March 2, 2016 14 / 35
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 (YITP, Kyoto U.) Standard Model prediction for muon g − 2 March 2, 2016 15 / 35
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)
experiment
BNL
BNL (new from shift in λ)
D. Nomura (YITP, Kyoto U.) Standard Model prediction for muon g − 2 March 2, 2016 16 / 35
SUSY Contributions to Muon g − 2
Suppose that the 3.3 σ deviation is due to SUSY...Leading SUSY contributions in the mZ/mSUSY
expansion:. .
W̃ − H̃−
µL µRν̃µ
(a)
B̃
µL µ̃L
m2LR
µ̃R µR
(b)
B̃ H̃0
µL µRµ̃L
(c)
W̃ 0 H̃0
µL µRµ̃L
(d)
H̃0 B̃
µL µRµ̃R
(e)
In most cases, the χ̃±-ν̃ diagram (a) and/or the
B̃-µ̃L/R diagram (b) dominate. (Lopez-Nanopoulos-Wang,
Chattopadhyay-Nath, Moroi, · · · )D. Nomura (YITP, Kyoto U.) Standard Model prediction for muon g − 2 March 2, 2016 17 / 35
MSSM Contributions to Muon g − 2
x-axis: M2
(gaugino mass)
y-axis: ml̃
(slepton mass)
Figs from Cho,Hagiwara, Matsumoto,
and DN
D. Nomura (YITP, Kyoto U.) Standard Model prediction for muon g − 2 March 2, 2016 18 / 35
Very recent updates
D. Nomura (YITP, Kyoto U.) Standard Model prediction for muon g − 2 March 2, 2016 19 / 35
BESIII new pion form factor data (1)
[GeV]s'0.6 0.65 0.7 0.75 0.8 0.85 0.9
2 | π|F
10
15
20
25
30
35
40
45 BESIII fit
BESIII
Fig. from M. Ablikim et al (BESIII Collaboration), arXiv:1507.08188v3
Data taken by using the
ISR technique
D. Nomura (YITP, Kyoto U.) Standard Model prediction for muon g − 2 March 2, 2016 20 / 35
BESIII new pion form factor data (2)
[GeV]s'0.6 0.65 0.7 0.75 0.8 0.85 0.9
/ B
ES
III fi
t - 1
2 | π|F
-0.15
-0.1
-0.05
0
0.05
0.1
0.15
BESIII fit
BaBar
BESIII
Fig. from M. Ablikim et al (BESIII Collaboration), arXiv:1507.08188v3
[GeV]s'0.6 0.65 0.7 0.75 0.8 0.85 0.9
/ B
ES
III fi
t - 1
2 | π|F
-0.15
-0.1
-0.05
0
0.05
0.1
0.15
BESIII fit
KLOE 08
KLOE 10
KLOE 12
D. Nomura (YITP, Kyoto U.) Standard Model prediction for muon g − 2 March 2, 2016 21 / 35
BESIII new pion form factor data (3)
]-10(600 - 900 MeV) [10,LOππµa
360 365 370 375 380 385 390 395
BaBar 09
KLOE 12
KLOE 10
KLOE 08
BESIII
1.9± 2.0 ±376.7
0.8± 2.4 ± 1.2 ±366.7
2.2± 2.3 ± 0.9 ±365.3
2.2± 2.3 ± 0.4 ±368.1
3.3± 2.5 ±368.2
Prediction for aππµ from BESIII data is more consistent
with those from KLOE data sets than that from BaBar data
Fig. from M. Ablikim et al (BESIII Collaboration), arXiv:1507.08188v3D. Nomura (YITP, Kyoto U.) Standard Model prediction for muon g − 2 March 2, 2016 22 / 35
Slide by T. Teubner (Liverpool), talk at ‘High-precision QCD at low energy,’ Aug. ’15
D. Nomura (YITP, Kyoto U.) Standard Model prediction for muon g − 2 March 2, 2016 23 / 35
Near future (5-7yrs) prospects
D. Nomura (YITP, Kyoto U.) Standard Model prediction for muon g − 2 March 2, 2016 24 / 35
Slide by V. B. Golubev (BINP), talk at “Tau 2014”, Sept. 2014D. Nomura (YITP, Kyoto U.) Standard Model prediction for muon g − 2 March 2, 2016 25 / 35
Near Future Prospects (Blum et al, arXiv:1311.2198)
Current status and near-future(∼ 5-7 yrs) improvementsin δaµ (in units of 10−11)
[20]: DHMZ[21]: HLMNT
Near-future improvements in δaHLOµ
mainly from VEPP-2000 and BES-III.
Table and Fig. from T. Blum et al, arXiv:1311.2198
D. Nomura (YITP, Kyoto U.) Standard Model prediction for muon g − 2 March 2, 2016 26 / 35
Near Future Prospects, Lattice (Blum et al)
As for the hadronic vacuum polarization (HVP),
“...the lattice-QCD uncertainty on aµ(HVP), currently at the5%-level, can be reduced to 1 or 2% within the next few years.”
“With increasing experience and computer power, it should bepossible to compete with the e+e− determination of aµ(HVP) bythe end of the decade, perhaps sooner with additional technicaladvances.”
As for l-by-l,
“... a lattice calculation with even a solid 30% error would alreadybe very interesting. Such a result, ..., is not out of the questionduring the next 3-5 years.”
From T. Blum et al, arXiv:1311.2198D. Nomura (YITP, Kyoto U.) Standard Model prediction for muon g − 2 March 2, 2016 27 / 35
Byproducts
D. Nomura (YITP, Kyoto U.) Standard Model prediction for muon g − 2 March 2, 2016 28 / 35
Byproducts: QED coupling at the Z-boson mass
⋆ α(M2Z): the least well known among {Gµ,MZ, α(M2
Z)},which are used as input to precision electroweak fits.⋆ 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).
⋆ Similar dispersion relation: (=⇒ byproduct of ahad,LOµ )
∆α(5)had(s) = −
αs
3πP
∫R(s′)ds′
s′(s′ − s)
⋆ Our results: ∆α(5)had(M
2Z) = (276.3 ± 1.4) × 10−4,
α(M2Z)
−1 = 128.944 ± 0.019.D. Nomura (YITP, Kyoto U.) Standard Model prediction for muon g − 2 March 2, 2016 29 / 35
Byproducts: 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 (YITP, Kyoto U.) Standard Model prediction for muon g − 2 March 2, 2016 30 / 35
Byproduct: Standard Model prediction for electron g − 2
QED contribution 115 965 218 00.7 (0.6)4loop(0.4)5loop(7.6)α (using α(87Rb)) Aoyama et al
EW contribution 0.2973 (0.0052)Czarnecki et al
Hadronic contributions
LO hadronic 18.66 (0.11) DN & TT (was 18.75(0.18) Davier et al ’98)
NLO hadronic −2.23 (0.01) DN & TT (was −2.25(0.05) Krause ’97)
light-by-light 0.39 (0.13) Jegerlehner+Nyffeler
Theory total 115 965 218 17.8 (0.6)4loop(0.4)5loop(0.2)had(7.6)α
Experiment 115 965 218 07.3 (2.8) Gabrielse et al
Theory − Exp 10.5 (8.1) 1.3σ discrepancy
(in units of 10−13. Numbers taken from Giudice et al, JHEP11(2012)113)
n.b.: hadronic contributions:. .
. .
had.
LO
e
had.
NLO
e
γhad.
l-by-l
e
D. Nomura (YITP, Kyoto U.) Standard Model prediction for muon g − 2 March 2, 2016 31 / 35
Hyperfine Splitting?
Fig. from WikipediaD. Nomura (YITP, Kyoto U.) Standard Model prediction for muon g − 2 March 2, 2016 32 / 35
Mu HFS: Leading Hadronic Contributions
Diagrams:
Can be written as an integral over σ(e+e− → hadrons)with weight function KMu(s):
∆ν(had-vp) =1
2π3
me
mµ
νF
∫dsσ(s)KMu(s)
= 232.7(1.4)Hz DN & TT
(cf: 231.2(2.9) Hz, Eidelman et al ’02)
Fig. from Karshenboim+Shelyuto
PLB517(2001)32
D. Nomura (YITP, Kyoto U.) Standard Model prediction for muon g − 2 March 2, 2016 33 / 35
Mu HFS: Summary Table
contribution (Hz)νHFS(QED) 4 463 302 720(253)mµ/me
(98)QED(3)ανHFS(weak) − 65νHFS(had-vp) 231(3) → 232.7(1.4) DN & TTνHFS(had-h.o.) 5(2)νHFS(theory) 4 463 302 891(272)νHFS(exp) 4 463 302 776(51) → (8)expected at MuSEUM
Black numbers are from CODATA10, arXiv:1203.5425
D. Nomura (YITP, Kyoto U.) Standard Model prediction for muon g − 2 March 2, 2016 34 / 35
Summary
Hadronic contrib. to the muon g − 2: key to improve theStandard Model prediction
≳ 3 σ discrepancy in (g− 2)µ between experiment and theory=⇒ New physics? “Light” new particles like µ̃, µKK, . . . ???=⇒ Worth studying µ-EDM, µ → eγ, µ-e conv., . . .!(⇔ No new physics seen at the LHC so far. What does thismean?)
Two new experiments to measure the muon g − 2 planned atJ-PARC and Fermilab.
To establish this discrepancy more firmly, important to resolvethe tension between the KLOE and BaBar data=⇒ new data from BES-III just appeared!=⇒ new precise data from VEPP-2000 and SuperKEKBstrongly awaited.
D. Nomura (YITP, Kyoto U.) Standard Model prediction for muon g − 2 March 2, 2016 35 / 35