Newphysics in%light%of% muon%g2%anomaly · 2015. 5. 20. · MAMI APEX test BaBar BaBar NA48 E774...

Motoi Endo (Tokyo)

New physics in light of

muon g-‐2 anomaly

Seminar at Maskawa institute for science and culture, 2015.5.21

Physics beyond SM

Where is new physics?

Evidences✓ neutrino oscillations: right-handed neutrinos✓ density fluctuations: inflation✓ dark matter✓ baryon asymmetry of universe✓ dark energy

> 3σ deviation

cf. Electroweak:

(possibly) a signal of new physics

[HLMNT]

[DHMZ]

Muon g-‐2

Outline

• overview of muon g-2: types of new physics

• model-I: heavy photon model

• model-II: supersymmetry

• conclusions

Muon g-‐2spin-magnetic field interaction

magnetic moment:

Dirac equation:

Radiative corrections

: tree level

: QED,

: hadronichad

: electroweak

: uncertainty (hadronic LO)

total SM [aμ] 116 591 828 (50) [10 ]

QED (α , Rb) 116 584 718.951 (0.080)

EW (W/Z/H, NLO) 153.6 (1.0)

Hadronic(leading)

[HLMNT] 6 949.1 (43)*!

6 923 (42)[DHMZ]

Hadronic (α higher) -98.4 (0.7)

Hadronic (LbL)

[RdRV] 105 (26)*!

116 (39)[NJN]

�

had

had

Standard Model

definition:

-11

5

Experiment• Lamor (spin) precession • electron emission towards

muon spin direction

• Brookhaven E821

Number of eventsat detector

> 3σ deviation

cf. Electroweak:

(possibly) a signal of new physics

[HLMNT]

[DHMZ]

Muon g-‐2

Future prospect• E821: 0.46 ppm(stat) + 0.28 ppm(syst) = 0.54 ppm

• Fermilab E989 → 0.1 ppm- (expected) data taking starts from 2016-2017

• J-PARC E34 → 0.1 ppm

• Hadronic contributions- vacuum polarization: experimental data, ~50%- light-by-light: lattice, 10% level- 8σ level, if central value is unchanged

*ppm = 0.0001%

total SM [aμ] 116 591 828 (50) [10 ]

QED (α , Rb) 116 584 718.951 (0.080)

EW (W/Z/H, NLO) 153.6 (1.0)

Hadronic(leading)

[HLMNT] 6 949.1 (43)*!

6 923 (42)[DHMZ]

Hadronic (α higher) -98.4 (0.7)

Hadronic (LbL)

[RdRV] 105 (26)*!

116 (39)[NJN]

�

had

had

Status-11

5

> 3σ deviation

newparticle

• definition!

!

• chirality flip (L↔R) by Yukawa

BSM contribution

No such particles have been discovered

BSM contribution

BSM contribution

• weak interaction, small mass‣ heavy photon model

• strong interaction, large mass‣ supersymmetry

Outline




• conclusions

kinetic mixing with SM U(1)

�

g-2 = +SM Heavy Photon

Heavy photon model(broken) extra U(1) symmetry [SM fields are singlet]

Contribution to muon g-‐2

similar to QED, but with mass

μ

excluded(muon g-2 > 5σ)

μ

APEX

test

BaBar

E774

E141

E137

electron

g-2

KLOE

Status before 2013

[Endo,Hamaguchi,Mishima w/ updates]

Beam-dump

electrong-2

Muon g-2

Fixedtarget

Flavorfactories

APEXtest

BaBar

E774

E141

E137

electrong-2

HADESWASA

KLOE

2013 updates:WASA-at-COSYHADES

Status in 2013


Beam-dump

electrong-2

Muon g-2

Fixedtarget

Flavorfactories

MAMI

APEXtest

BaBar

BaBar

E774

E141

E137

electrong-2

PHENIXHADESWASA

KLOEKLOE

Beam-dump

electrong-2

Muon g-2

Fixedtarget


Flavorfactories

Status in 2014

2014 updates:MAMI Phenix, BaBar

MAMI

APEXtest

BaBar

BaBarNA48

E774

E141

E137

electrong-2

PHENIXHADESWASA

KLOEKLOE

Beam-dump

electrong-2

Muon g-2

Fixedtarget


Flavorfactories

Status in 2015

2015 update:NA48→ exclude g-2

Electron g-‐2

μ,e

• muon- solve muon g-2 anomaly

• electron- much lighter than muon

Status of Electron g-‐2exp (Harvard) 1 159 652 180.73 (0.28) [10

total SM 1 159 652 181.78 (0.78)

QED (α , Rb) 1 159 652 180.07 (0.77)

EW (W/Z/H, NLO) 0.0297(0.0005)

Hadronicvac. pol.

leading 1.866 (0.011)

higher -0.2234(0.0014)

Hadronic (LbL) 0.035 (0.010)

�

had

had

5

Constraint by electron g-‐2

[Endo,Hamaguchi,Mishima]

excluded

MAMI

APEXtest

BaBar

BaBarNA48

E774

E141

E137

electrong-2

PHENIXHADESWASA

KLOEKLOE

Beam-dump

electrong-2

Muon g-2

Fixedtarget


Flavorfactories

Status in 2015

2015 updates:NA48→ exclude

beam

target/shield

detector

Beam-‐dump experimentsE774, E141,…: electron beam dump

Fixed-target experiments:kinematics instead of shield

MAMI

APEXtest

BaBar

BaBarNA48

E774

E141

E137

electrong-2

PHENIXHADESWASA

KLOEKLOE

Beam-dump

electrong-2

Muon g-2

Fixedtarget


Flavorfactories

Status in 2015

2015 updates:NA48→ exclude

BaBar (2014)heavy photon predicts narrow dilepton resonance↔ smooth background except meson resonances

(GeV)-e+em0 2 4 6 8 10

Entr

ies

/ 0.1

GeV

510

610

710

(GeV)-e+em0 2 4 6 8 10

Entr

ies

/ 0.1

GeV

510

610

710 Data- e+ eγ → -e+MC e

ψ J/γ → -e+MC e(2S)ψ γ → -e+MC e(1S)Υ γ → -e+MC e(2S)Υ γ → -e+MC e

b.g. fit by polynomials

NA48 (2015)

)2 (MeV/ceem0 20 40 60 80 100 120

)2Ev

ents

/ (1

MeV

/c

1

10

210

310

410

510

610 selection:D/2KData

D0/±/A±K

i±µD0/A±K

background: MC+data

signal background

heavy photon predicts narrow e+e- resonance

MAMI

APEXtest

BaBar

BaBarNA48

E774

E141

E137

electrong-2

PHENIXHADESWASA

KLOEKLOE

Beam-dump

electrong-2

Muon g-2

Fixedtarget


Flavorfactories

Status in 2015

Constraints rely oncoupling to electron

Lμ-‐Lτ Gauge Symmetry

�

g-2 = +SM Lμ-Lτ gauge boson

• (broken) U(1) symmetry: anomaly-free• interact only with 2nd & 3rd generation leptons

Viable in low-‐mass region

[Altmannshofer,Gori,Pospelov,Yavin]

severely constrained by neutrino-trident production:

8

where KF is a loop function that can be found e.g. in [43].Out of the three SM neutrinos only the muon-neutrinoand tau-neutrino are a↵ected by Z 0 loops. Therefore, thecorrection to the Z coupling to neutrinos is e↵ectivelygiven by

gV ⌫

gSMV ⌫

=gA⌫

gSMA⌫

=

��1 +2

3

(g0)2

(4⇡)2KF (mZ0)

�� . (33)

In order to obtain constraints on the mass and couplingof the Z 0, we combine the experimental results from LEPand SLC [44] on the Z couplings to all leptons and neu-trinos, taking into account the error correlations. Wefind the 95% C.L. constraints depicted in gray in Fig. 3.We note also that the constraint on the parameter spacewould be stronger, if we had a sizable kinetic mixing [45].

• Z ! 4` searches at the LHC. Both ATLAS andCMS collaborations have reported the measurement ofthe branching ratio of Z decaying into four charged lep-tons [46, 47]3. In particular, the ATLAS analysis [47] hasbeen performed with the full 7+8 TeV LHC data set andit gives BR(Z ! 4`) = (4.2 ± 0.4)10�6, to be comparedto the SM prediction BR(Z ! 4`) = (4.37 ± 0.03)10�6.Our model gives a positive NP contribution to the pro-cess. The most important e↵ect comes from the Feynmandiagram shown in Fig. 5, with an intermediate on-shellZ 0 boson dominating the rate for mZ0 < mZ (see also [19]for a recent analysis).

We have recast the ATLAS analysis in [47], gener-ating events using MadGraph 5 [49], interfaced withPythia6.4 [50] for parton showering. Events should haveexactly four isolated leptons with the leading three withpT > 20, 15, 8 GeV, and if the third lepton is an electronit must have pT > 10 GeV. Lepton identification e�cien-cies have been taken from [51]. The invariant mass of theopposite sign same flavor (OSSF) lepton pair closest tothe Z mass should be m1 > 20 GeV. The second OSSFlepton invariant mass should be m2 > 5 GeV. Finally,the invariant mass of the four lepton system should beclose to the Z mass: 80 GeV < m4` < 100 GeV.

NP e↵ects arise only in the four muon bin. In this bin,ATLAS observes 77 events, to be compared to the 78events expected. To set the bound, we assume a Poissondistribution for the observed events, and we exclude atthe 95% C.L. the benchmarks that predict more than 94events in the four muon bin. The region on the left ofthe dashed black line in Fig. 3 is excluded by the ATLASanalysis. As we can note from the figure, the region fa-vored by (g � 2)µ has been almost fully probed by LHCmeasurements of Z to four leptons.

3 Note that LEP performed the measurement of the cross sectionof the four-fermion final state arising from the process e+e� !`+`�ff where ` is a charged or neutral lepton and f any chargedfermion [48]. However, as also shown in [15], the constraints onthe g0�mZ0 parameter space coming from this measurement areslightly less stringent than the LHC constraints discussed in thefollowing.

q

q

Z

µ

µ

Z 0µ

µ

FIG. 5. The main NP contribution to the Z ! 4` process atthe LHC.

�

N N

⌫

⌫

µ�

µ+

Z 0

FIG. 6. The leading order contribution of the Z0 to neutrinotrident production. This diagram interferes constructively(destructively) with the corresponding SM diagram involvinga W -boson (Z-boson).

• Neutrino trident production. In the last partof this section, we present a powerful new constraint onthe Lµ � L⌧ current coming from measurements of neu-trino trident production, i.e. the production of a muonanti-muon pair in the scattering of muon neutrinos inthe Coulomb field of a target nucleus. The leading con-tribution of the Z 0 to such a process is shown in Fig. 6.This diagram interferes with the SM contribution involv-ing similar diagrams, but with the W and Z bosons in-stead of the Z 0. In the SM, the contribution from theZ-boson is smaller than the one of the W -boson andcomes with an opposite sign that leads to destructiveinterference [52]. The Z 0 coupling to both muons andmuon-neutrinos has the same sign and the Z 0 contribu-tion interferes constructively (destructively) with the W -boson (Z-boson), leading therefore to an enhancement ofthe trident production. Working in the approximationof a heavy Z 0, where the leptonic 4-fermion operator is(g0)2 (µ�↵µ) (⌫�↵PL⌫) /m2

Z04, the ratio of the total tri-

4 We estimate that the description of the Z0 contribution by an

CCFR Z→4lLHC

g-2 [±2σ]

Outline

その前に




• conclusions

BSM contribution

• weak interaction, small mass‣ heavy photon model

• strong interaction, large mass‣ supersymmetry

Two-‐Higgs doublet model• Higgs bosons: h (=SM), H, A, H±

!

!

• type-X: enhance H/A-lepton couplings

�1 �2 uR dR `R QL, LL

Type-I + � � � � +

Type-II + � � + + +

Type-X + � � � + +

Type-Y + � � + � +

Table 1: Charge assignments of the Z2 symmetry in the four types of 2HDM.

⇠uh ⇠dh ⇠`h ⇠uH ⇠dH ⇠`H ⇠uA ⇠dA ⇠`A

Type-I c↵/s� +c↵/s� +c↵/s� s↵/s� s↵/s� s↵/s� � cot � +cot � +cot �

Type-II c↵/s� �s↵/c� �s↵/c� s↵/s� c↵/c� c↵/c� � cot � � tan � � tan �

Type-X c↵/s� +c↵/s� �s↵/c� s↵/s� s↵/s� c↵/c� � cot � +cot � � tan �

Type-Y c↵/s� �s↵/c� +c↵/s� s↵/s� c↵/c� s↵/s� � cot � � tan � +cot �

Table 2: Yukawa couplings in the four types of 2HDM.

In the interaction basis, the Yukawa interactions of these Higgs bosons can be written as

�LY = QL(Yd1 �1 + Y d

2 �2)dR + QL(Yu1 �1 + Y u

2 �2)uR + LL(Y`1�1 + Y `

2�2)eR +H.c., (2.4)

where �i = i�2�⇤i with �2 the Pauli matrix, QL and LL denote the left-handed quark and

lepton doublets, and uR, dR and eR are the right-handed up-type quark, down-type quark and

lepton singlet, respectively. The Yukawa coupling matrices Y fi (f = u, d, `) are 3⇥ 3 complex

matrices in flavour space.

In order to avoid tree-level FCNC, it is natural to introduce a discrete Z2 symmetry [31].

All the possible nontrivial Z2 charge assignments are listed in table 1, which define the four

well-known types of 2HDM, i.e. type-I, type-II, type-X and type-Y. The Yukawa interactions

in the four models are di↵erent. In the mass-eigenstate basis, they can be unified in the form

�LY =+X

f=u,d,`

hmf ff +

⇣mf

v⇠fh ffh+

mf

v⇠fH ffH � i

mf

v⇠fAf�5fA

⌘i

+

p2

vu�muV ⇠uAPL + V md⇠

dAPR

�dH+ +

p2m`⇠

`A

v⌫L`RH

+ +H.c., (2.5)

where PL,R = (1± �5)/2 and V denotes the Cabibbo-Kobayashi-Maskawa (CKM) matrix. The

couplings ⇠fh,H,A in the four types of 2HDM are listed in table 2.

4

cf:

Status in type-‐X• muon g-2 solved by A0 exch.• Higgs partial widths

- h→AA: constrained- deviation in h→ττ and γγ

tanβ

mA [GeV]

mH0 = mH+ = 250 GeV

20

30

40

50

60

70

10 20 30 40 50 60

Exc

lude

d by

e+ e

- →ττ

A

Excluded by Z →ττ

Excluded by τ decay

Exc

luded b

y B

s →

µµ

tanβ

mA [GeV]

mH0 = mH+ = 350 GeV

20

30

40

50

60

70

10 20 30 40 50 60E

xclu

ded

by e

+ e- →

ττA

Excluded by Z →ττ

Excluded by τ decay

[Abe,Sato,Yagyu]

large Yukawa coupling for extra lepton & Higgs

[Bar-Shalom,Nandi,Soni]

Extra lepton in 2HDM

LHC signals in Higgs decay, extra matters?

[recently by Dermisek,Raval;Okada,Yagyu]

muon g-2

Exotic muon Yukawa

→ LHC?

radiative Yukawa/large mixing with extra leptons

Outline




• conclusions

symmetry between fermion and boson

Supersymmetry

chargino-muon sneutrino neutralino-smuon

→ (chirality-flip) enhanced by tanβ

SUSY solution to muon g-‐2

SM SUSY

tanβ enhancementmuon Yukawa of SUSY is enhanced by tanβ (cosβ≪1)

Note: too large tanβ is disfavored by Yukawa perturbativity



• SUSY particles in the contributions are predicted to be light (~100GeV)

• “SUSY solution” can be tested by discovering these SUSY particles

Chargino Contribution• light: LH smuon, Wino, Higgsino + Bino (LSP)• large tanβ (=40)• other SUSY particles are decoupled*

*consistent w/. multi-jet search at LHC, Higgs boson mass

Bino 200

300

400

500

600

700

800

100 200 300 400 500 600 700

Wino mass [GeV]

slep

ton

mas

s [G

eV]

LHC

g-21σ

2σ

Multi-lepton

[Endo,Hamaguchi,Iwamoto,Yoshinaga]

LHC status

mslepton < mWino

multi-lepton + missing ET

200

300

400

500

600

700

800

100 200 300 400 500 600 700

Wino mass [GeV]

slep

ton

mas

s [G

eV]

LHC

g-21σ

2σSM-bosons

Bino

→ chargino contribution is consistent with LHC

mslepton > mWino

SM bosons + missing ET


LHC status

200

300

400

500

600

700

800

100 200 300 400 500 600 700

Wino mass [GeV]

slep

ton

mas

s [G

eV]

LHC

g-21σ

2σ


SM-bosons

Multi-lepton

Prospectchargino contribution will be probed at LHC

• multi-lepton!- improve ~2 for mWino!

[Kowalska et.al,1503.08219]!

• SM bosons!- WH + MET!

~250-400GeV for 300fb-1!

[Berggren et.al,1309.7342]!

- WZ + MET!~0.8-1TeV for 300-3000fb-1!

[ATLAS-PHYS-PUB-2013-007!,CMS-NOT-13-002]



• SUSY particles in the contributions are predicted to be light (~100GeV)

• “SUSY solution” can be tested by discovering these SUSY particles

Neutralino contribution• left- and right-handed smuons, Bino are light• other SUSY particles are decoupled• large smuon LR mixing (∝ μ tanβ)

- too large LR mixing spoils stability of EW vac

Vacuum instability

V

stau-Higgs

stauL-stauR-Higgs trilinear coupling is correlatedwith smuon left-right mixing

EW

too large trilinear coupling spoils vacuum stability

Yτ μ tanβ

Constraint on SUSY mass

w/o vacuum condition w/ vacuum condition

1σ 2σ

excluded

[Endo,Hamaguchi,Kitahara,Yoshinaga]

lightest smuon mass [GeV] lightest smuon mass [GeV]

Current status

LHC2σ1σ

lightest smuon mass [GeV]

neut

ralin

o m

ass

[GeV

]


stau lightest

slepton is lighterthan 460GeV

Future prospect

2σ1σ


neut

ralin

o m

ass

[GeV

]


Whole parameter region can be tested at LHC and ILC

LHC 14TeV, 100fb-1

[Eckel,Ramsey-Musolf,Shepherd,Su]

[1TeV ILC]

LHC

Relaxing stability bound

excluded


potential is stabilised by large quadratic term


Slepton non-‐universalitylepton mass term:

soft mass matrix in superCKM basis [same for RH sleptons]

LFV, CPV

non-universality:

Lepton flavor violationmuon τ → μγ

MEGMEG*Mu3e

COMET/Mu2e

PRISM/PRIME

1 10

0.1

0.2

0.3

0.4

0.5

0

Belle!BaBar

superKEKB

LFVs are generated by stau-smuon non-universality

1 10

CP violationelectron EDM muon EDM

ACMEFr, ThO

YbF, WN

J-PARC: 10-21 ecm

10-24 ecm

slepton non-universality generates EDM as well as LFV

Status and Prospects

Status:

Prospect:

• LHC/ILC may discover SUSY particles [universal]• LFV/CPV is sensitive to slepton non-universality

SUSY solution to muon g-2 anomaly is consistent with constraints, e.g., LHC

BonusWhen g-2 anomaly is indeed due to Bino contribution

Neutralino contribution parameters

Reconstruction

Reconstruct neutralino contribution:

* Winos and Higgsinos are decoupled

Neutralino contribution parameters

Reconstruction

Table 1: Parameters and mass spectrum and at our sample point. The masses are in unitsof GeV, and ℓ denotes selectrons and smuons.

Parameters mℓ1 mℓ2 mτ1 mτ2 mχ01

sin θµ sin θτ a(ILC)µ

Values 126 200 108 210 90 0.027 0.36 2.6× 10−9

where Msoft is a mass scale of colored superparticles and heavy Higgses, MH is the Higgsinomass, MW is the Wino mass, and Q (∼ mℓ) is an energy scale. The differences among gY ,gY,L and gY,R can be O(1–10)% if Msoft, MH and MW are larger than ∼ 1TeV. Note thatthe leading contribution of (6) is proportional to the product gY,LgY,R (cf. Eq. (4)). Sincethe corrections to the gaugino couplings can be sizable, both of the couplings should bedetermined directly at ILC. It is also noted that gY,L, gY,R and g2 are universal for (at least)light generations.

In the following discussion, we choose a specific sample point to make our discussionconcrete and quantitative. The mass spectrum at the sample point is summarized in Table 1.All the sleptons and the lightest neutralino are within the reach of ILC with

√s = 500GeV.

Their masses are set to be close to those of the SPS1a′ benchmark point [13], so thatresults of the previous ILC studies can be applied. The lighter sleptons are chosen to bealmost left-handed in order to avoid LHC limits (see below). The lightest neutralino massis 90GeV, which is the lightest superparticle among the MSSM ones including sneutrinos.Other superparticles such as colored ones as well as Winos and Higgsinos are assumed to beso heavy that they are not observed at LHC nor ILC (so that their masses are different fromthose for SPS1a′).#1 Trilinear couplings of sleptons, Aℓ, are set to be zero. The left-right

mixing parameter, m2µLR, (or equivalently µ tan β) is chosen to realize that a(ILC)

µ definedin Eq. (17) becomes equal to 2.6 × 10−9, which is close to the central value of the currentdiscrepancies (3); µ tan β = 6.1× 103 GeV.

The mass spectrum is consistent with present collider limits. Light sleptons decaying tothe lightest neutralino are searched for by studying the di-lepton signatures at LHC [14,15].Our sample point is not excluded because masses of the left-handed selectron and smuon areclose to that of the neutralino. Also, constraints on the right-handed ones are weak, sincethe production cross sections are small. On the other hand, collider limits on the stau massis weaker as mτ1 > 81.9GeV at 95% CL by LEP [16]. Exclusions from the three-leptonsearches at LHC [15,17] are also negligible, since Winos and Higgsinos are heavy.

3 Fun with ILC

In the rest of this letter, we discuss how and how accurately the SUSY contribution to themuon g − 2 is determined at ILC. At the sample point, only the sleptons and the lightest

#1This setup is minimal to reconstruct the SUSY contributions to the muon g − 2. If some of the heavysuperparticles such as Winos would be additionally discovered, the reconstruction could be improved.

4

Sample point

* other SUSY particles [Wino,Higgsino,colored] are decoupled.Table 2: Observables necessary for the reconstruction of a(ILC)µ , and their uncertainties with√

s = 500 GeV and L ∼ 500–1000 fb−1. Processes relevant to determine each observable arealso shown. The second and third rows are the information to determine m2

µLR. For thedetermination of mχ0

1, analyses of the productions of selectrons and smuons are combined.

The uncertainties in g(eff)1,L are those from the experiment and theory, respectively.

X δX δXa(ILC)µ Process

m2µLR 12 % 13 % e+e− → τ+τ− (cross section, endpoint)

(sin 2θτ ) (9 %) − e+e− → τ+1 τ−

1 (cross section)(mτ2) (3 %) − e+e− → τ+

2 τ−2 (endpoint)

mµ1, mµ2 200 MeV 0.3 % e+e− → µ+µ− (endpoint)mχ0

1100 MeV < 0.1 % e+e− → µ+µ−/e+e− (endpoint)

g(eff)1,L a few+1 % a few+1 % e+e− → e+

L e−R (cross section)

g(eff)1,R 1 % 0.9 % e+e− → e+

Re−R (cross section)

changing the polarization. Unfortunately, the acceptance as well as the accuracy of the crosssection measurement is not found in the literature. In this letter, we assume that σ(e+

L e−R)is measured with the accuracy of a few percents. Numerically, if it is determined at the 2 %(4 %) level, the accuracy of g(eff)

1,L is estimated to be about 1 % (2 %), where δg(eff)1,R /g(eff)

1,R = 1 %is applied.

In addition to the experimental uncertainty, the process e+e− → e+L e−R involves the t-

channel exchange diagrams of heavier neutralinos. They contribute to the cross section viathe Wino–Higgsino and Bino–Higgsino mixings. Their contamination to the measurementof g(eff)

1,L depends on their masses. Assuming that Wino and Higgsino masses are above

500 GeV, we estimate that g(eff)1,L involves a theoretical (systematic) uncertainty of 0.9 %,

while it is reduced to be 0.2 % for MW ,H > 1 TeV. On the other hand, contaminations fromcorrections to the Wino coupling with the (s)electrons are smaller than it. As a result, theaccuracy of the measurement of the gaugino coupling is estimated to be

δg(eff)1,L /g(eff)

1,L = a few % (exp) + 1 % (th), (37)

or better. Here, the first term in the right-hand side comes from the measurement of the crosssection for e+e− → e+

L e−R, and the second term is due to the contamination from the undis-covered Winos and Higgsinos. Then, the uncertainty is sub-dominant in the reconstructionof a(ILC)

µ compared to that in m2µLR.

12

Reconstruction [ ]

Neutralino contribution to muon g-2 is reconstructedby measuring all sleptons

at the sample point with[ME,Hamaguchi,Iwamoto,Kitahara,Moroi]

Reconstruction at ILC

Summary• >3σ discrepancy for muon g-2

• Heavy photon model- simple model is excluded- Lμ-Lτ model is viable in low-mass region

• Supersymmetry- SUSY solution is consistent with constraints- SUSY particles are within future LHC/ILC sensitivity- slepton non-universality may be probed by LFV/EDM

Channel global χ2min/d.o.f. globally infl. err. locally infl. err. ‘global – local’

2π 1.4 3.06 3.09 −0.033π 3.0 1.08 0.99 +0.10

4π(2π0) 1.3 1.19 1.26 −0.074π(no π0) 1.7 0.49 0.47 +0.02K+K− 1.9 0.57 0.46 +0.11

K0SK

0L 0.8 0.16 0.16 −0.003

5π(1π0) 1.2 0.09 0.09 0

6π(2π0) 4.0 0.39 0.24 +0.16

Table 1: Global χ2min/d.o.f., globally and locally inflated error of aµ and their difference for

several channels. (Range of integration from threshold to 2 GeV.) The five and six pion channelsare used as input for our updated isospin analysis (see below).

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)

Figure 1: Fit with all data in the 2π channel: light (yellow) band. Radiative return data fromBaBar [5] are shown by the darker (green) band, whereas the KLOE [3, 4] data are displayedby the markers as indicated in the plot.

The role of the radiative return data from KLOE and BaBar in the new fit is demonstrated inFig. 1 in the ρ region from about 0.6 to 0.95 GeV. The new data from BaBar [5] are representedby the darker (green) band, whereas the data from KLOE [3, 4] are displayed by the markers

as indicated on the plot. The light (yellow) band is the result of the fit of all combined 2π data,i.e. the data as used in [6] together with the new data from KLOE and BaBar. Figure 2 shows

a zoom into the peak region with the ρ− ω interference and also displays important data fromthe experiments CMD-2 [11, 12] and SND [13]. Figure 3 displays the low energy region closeto threshold, a region previously only sparsely populated by data and where BaBar has added

very valuable information. It is clear already from these figures that the KLOE data5 are lower

5The KLOE08 data are in very good agreement with those of the independent KLOE10 analysis.

5

• experimental data with dispersion relation and optical theorem

!

!

!

!

- K(s)/s is larger in lower energy

• inconsistency with τ decay data may be resolved by ρ-γ mixing [Jegerlehner,Szafron]

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 Imhad.

="

dΦ

! 2

had.

ahad,LOµ =

m2µ

12π3

! ∞

sth

ds1sK(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 –

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

µ

D. Nomura (Tohoku U) Muon g − 2 re-evaluated July 2, 2011 3 / 26

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 Imhad.

="

dΦ

! 2

had.

ahad,LOµ =

m2µ

12π3

! ∞

sth

ds1sK(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 –

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

µ

D. Nomura (Tohoku U) Muon g − 2 re-evaluated July 2, 2011 3 / 26

σhad(s): e+e- → γ → hadrons

[Hagiwara,Liao,Martin,Nomura,Teubner;Davier,Hoecker,Malaescu,Zhang]

Hadronic vacuum polarization

aμHad: ~70% from (e+e- →) γ → π+π-

- p. 32

Hadronic light-by-light scattering in the muon g − 2: SummarySome results for the various contributions to aLbyL;had

µ × 1011:Contribution BPP HKS, HK KN MV BP, MdRR PdRV N, JN FGW

π0, η, η′ 85±13 82.7±6.4 83±12 114±10 − 114±13 99 ± 16 84±13

axial vectors 2.5±1.0 1.7±1.7 − 22±5 − 15±10 22±5 −

scalars −6.8±2.0 − − − − −7±7 −7±2 −

π, K loops −19±13 −4.5±8.1 − − − −19±19 −19±13 −

π,K loops+subl.NC

− − − 0±10 − − − −

other − − − − − − − 0±20

quark loops 21±3 9.7±11.1 − − − 2.3 21±3 107±48

Total 83±32 89.6±15.4 80±40 136±25 110±40 105 ± 26 116 ± 39 191±81

BPP = Bijnens, Pallante, Prades ’95, ’96, ’02; HKS = Hayakawa, Kinoshita, Sanda ’95, ’96; HK = Hayakawa, Kinoshita ’98, ’02; KN = Knecht, Nyffeler’02; MV = Melnikov, Vainshtein ’04; BP = Bijnens, Prades ’07; MdRR = Miller, de Rafael, Roberts ’07; PdRV = Prades, de Rafael, Vainshtein ’09; N =Nyffeler ’09, JN = Jegerlehner, Nyffeler ’09; FGW = Fischer, Goecke, Williams ’10, ’11 (used values from arXiv:1009.5297v2 [hep-ph], 4 Feb 2011)

• Pseudoscalar-exchange contribution dominates numerically (except in FGW). But othercontributions are not negligible. Note cancellation between π,K-loops and quark loops !

• PdRV: Do not consider dressed light quark loops as separate contribution ! Assume it isalready taken into account by using short-distance constraint of MV ’04 onpseudoscalar-pole contribution. Added all errors in quadrature ! Like HK(S). Too optimistic ?

• N, JN: New evaluation of pseudoscalars. Took over most values from BPP, except axialvectors from MV. Added all errors linearly. Like BPP, MV, BP, MdRR. Too pessimistic ?

• FGW: new approach with Dyson-Schwinger equations. Is there some double-counting ?Between their dressed quark loop (largely enhanced !) and the pseudoscalar exchanges.

Nyffeler, INT workshop on “The Hadronic LbL Contribution to the Muon Anomaly”

Achim Denig Dark Photon Search @ MAMI/MESA

Searches using Fixed-Target Experiments

LowFenergy,%highFintensity%%accelerators%are%ideally%suited%%for%Dark%Photon%searches% %MAMI:%Eγ%<%1.6%GeV% %A1%spectrometer%setup%

Bjorken,$Essig,$Schuster,$Toro$(2009)$

me+e+$

QED%background%processes: % %%

%T.%Beranek%irreducible

Achim Denig Dark Photon Search @ MAMI/MESA

Searches using Fixed-Target Experiments

LowFenergy,%highFintensity%%accelerators%are%ideally%suited%%for%Dark%Photon%searches% %MAMI:%Eγ%<%1.6%GeV% %A1%spectrometer%setup%

Bjorken,$Essig,$Schuster,$Toro$(2009)$

me+e+$

QED%background%processes: % %%

%T.%Beranek%kinematics

HPS: A proposal to Search for Massive Photons at Jefferson Laboratory

27

identical! to! the!distribution!of! radiative! trident!events! restricted! in!an! invariant!mass!window!near! the!AY!mass.! !Moreover,! the!rate!of! the!AY!signal! is!simply!related!to! the!radiative! trident!crossIsection!within!the!spectrometer!acceptance!and!a!mass!window!of!width!δm!by![4]!

!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!" !!!→!!! !!→!ℓ!!!ℓ!

!" !!!→!!! !∗→!ℓ!!!ℓ! = ! !!!!!!!!""!

!!!!!" !!,!!!!!!!!!!!!!!!!!!!!!!(3.6)!

where!Neff!counts!the!number!of!available!decay!products.!!This!exact!analytic!formula!was!also!checked! with! a! MC! simulation! of! both! the! AY! signal! and! the! radiative! trident! background!restricted! to! a! small! mass! window! δm,! and! we! find! nearly! perfect! agreement.! ! Thus,! the!radiative! subsample! can! be! used! to! analyze! the! signal,! which! simplifies! the! analysis!considerably.!!!

It!is!instructive!to!compare!kinematic!features!of!the!radiative!and!BetheIHeitler!distributions,!as!the!most!sensitive!experiment!maximizes!acceptance!of!radiative!events!and!rejection!of!BetheIHeitler!tridents.! !Although!the!BetheIHeitler!process!has!a!much!larger!total!crossIsection!than!either!the!signal!or!the!radiative!trident!background,!it!can!be!significantly!reduced!by!exploiting!its! very! different! kinematics.! ! In! particular,! the! AY! carries! most! of! the! beam! energy! (see!discussion!in!Section!3.1),!while!the!recoiling!electron!is!very!soft!and!scatters!to!a!wide!angle.!!In!contrast,! the! BetheIHeitler! process! is! not! enhanced! at! high! pair! energies.! ! Moreover,! BetheIHeitler! processes! have! a! forward! singularity! that! strongly! favors! asymmetric! configurations!with! one! energetic,! forward! electron! or! positron! and! the! other! constituent! of! the! pair! much!softer.!

These!properties!are!discussed!further!in!the!Appendix!of![4],!and!illustrated!in!Figure!3.2.2.!!

!!!!!!!!!! !Figure 3.2.2: Left: The distribution of Bethe-Heitler background events (black) and A’ signal events (red) as a function of the sum of the electron and positron energy. Note that the signal is peaked at high energies, while the background is peaked at much lower energies. Right: The distribution of the positron versus electron energy for Bethe-Heitler background events (black dots) and A’ signal events (red dots). Note that in both plots neither the signal nor background events have been normalized to the correct number. In reality, the number of background events is much larger than the number of signal events. Also, note that

signal

background

Fixed-‐target experiments• target is not thick (shield)• signal peak in dilepton invariant mass distribution• smooth distribution by virtual photon exchange• Bethe-Heitler suppressed by kinematics

Figure 6: The total cross section of the smuon productions at LHC withps = 8TeV

(dashed) and 14TeV (solid). The parameters satisfy m˜`L

= m˜`R

= 2M1

. The left-right mixing is maximized under the vacuum stability condition with tan � = 40.

m˜` M

1

µ me1 me2 mµ1 mµ2 m⌧1 m⌧2 m�01

�aµA 300 200 756 303 304 298 309 199 380 199 16.1A0 300 200 699 303 304 299 308 209 375 199 14.6B 470 250 1680 472 472 465 479 329 581 250 10.2C 340 160 1138 343 343 336 350 199 442 160 18.0

Table 2: Model parameters and mass spectra at several model points in Fig. 5. Themasses are in units of GeV, and the muon g� 2 is scaled by 10�10. Here, m

˜` denotesm

˜`L= m

˜`R, and tan � = 40 is set.

13


A BC[neutralino type]

Mass spectrum

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