Muon g-2, Rare Decay 0 → e+e- and DarkMatter

Introduction

Muon g-2 (status)

Hadronic contributions within Instanton Model

Rare 0→e+e– Decay (status)

0→e+e– Decay and Dark Matter

Conclusions

A.E. Dorokhov (JINR, Dubna)

In collaboration with M. Ivanov, S. Kovalenko,E. Kuraev, Yu. Bystritsky, W. Broniowski

Introduction

Cosmology tell us that 95% of matter is not described in text-books yet

Two search strategies:1) High energy physics to excite heavy degrees of freedom. No any evidence till now. LHC era has started.

2) Low energy physics to produce Rare processes in view of huge statistics.

There are some rough edges of SM.

(g-2)is very famous example,

0→e+e- is in the list of SM test after new exp. and theor. results

That’s intriguing

New excitements after Fermi LAT, PAMELA, ATIC, HESS and WMAP dataInterpreted as Dark Matter and/or Pulsar signals

Abnormal people are looking for traces of Extraterrestrial GuestsAbnormal Educated people are looking for hints of New Physics

Anomalous magnetic moment of muon

From BNL E821 experiment (1999-2006)

Standard Model

predicts the result which is 3.4 below the experiment (since 2006)

h

he

New proposals forBNL, FNAL, JPARC

LbL to g-2

a(HVP)=

Integral over e+e- to Hadrons cross section

1010)3.6(0.208 659 11 BNLa10HadrEWQEDSM 10)0.5(3.177 659 11 aaaa

M. Davier etal., 2009

1.9

3.4

h

he

hh

h

Hadronic Vacuum Polarization contributes 99% and half of error

Light-by-light processcontributes 1%and half of error

Z*effective coupling

The hadronic contributions to the muon AMM (theory)

S had,LO had,NLO had,LbLa a a a

The dressed quark propagator is defined as

1 ˆS p p M p

2qM p M f p f(p) is related to the quark zero

mode in the instanton field

22

2

at exp pp

pM

0.35

7.14 106

M p2

30 p

qq

qGq 2Mconst.

Mcurr.

Incorporates soft momentum physicsand smoothly transits to high-momentumregime

Instanton model

2

22

222

02V V

Vd QQ

d

Qdt t

tQ

QD

Q

Adler function is defined as

Leading Order Contribution to Muon Anomalous Magnetic Moment

21

(2)hvp 2

0 0

221

1

/ 28 1

3 V V

x x K ta

xdx D m

xxdt

tt

NQM Adler function and ALEPH data

NJL

ALEPHILM

Quark loop

Quark loop

Mesons(Nc enhanced)

Meson loop(chiral enhanced)

M(p)

pQCD(NNNLO)

QCDMassive Quarks

AFMasslessQuarks

eea ,103.41.689 10(2)hvp

10(2)hvpInst, 1050633 a

Very sensitive to quark mass: Mq=200-240 MeV

(AD, PRD, 2004)

LO is expressed via Adler function asLeading Order Hadronic Contribution

2

2(2)hvp

2

4

(0) ( (

) 3

)

m

R sK s

sa ds

Phenomenologicalapproach

h

is known kinematical factor

emphasizing the low energ

( )

y

1/

reg o

i n

K s s

8

(2)hvp

8

6,94 0.08 10 , ,

7,11 0.09 10 , , ,

e e ea

e e e

From phenomenology one gets

hadrons

R se e

e e

1) Data from low energy s<1Gev are dominant (CMD, KLOE, BaBar)2) Until CVC puzzle is not solved data are not used 0 aCVC nd : e e X X

V*AV correlator and muon AMM

For specific kinematics: q2=q is arbitrary, q10 only 2 structures exists in the triangle amplitude

21 2 2 1 2 1 2 2 1 2 2 1 2, ,T LT wq q q q q q qw q q q q q q

The amplitude is transversal with respect to vector current

021

TqTq

but longitudinal with respect to axial-vector current

22 2 1 2Lq T qw q q

This is famous Adler-Bell-Jackiw anomaly

V*AV amplitude

Perturbative nonrenormalization of wL (Adler-Bardeen theorem, 1969)Nonperturbative nonrenormalization of wL (‘t Hooft duality condition, 1980)Perturbative nonrenormalization of wT (Vainshtein theorem, 2003)Nonperturbative corrections to wT at large q are O(1/q6) (De Rafael et.al., 2002)Absence of Power corrections to wT at large q in chiral limit in Instanton model (Dorokhov,2005)Massive corrections (Teryaev, Pasechnik; Jegerliner, Tarasov, 2005; Melnikov,2006)

NnLO QCD =0 for all n>0

In local theory for quarks with constant mass one gets

1

2 2 200

12

33 1

22

1L

CC

mT

x xNdx

x xw

N

qq mw

Anomalous wL structure (NonSinglet)

Diagram with Local vertices

5

X

Diagram with NonLocal Axial vertices

X

+ rest

5

2

3 1

3

2

q

Nw C

L

In accordance with Anomalyand ‘t Hooft duality principle(massless Pion states in triplet)

+

Anomalous wL structure (Singlet)

Diagram with Local vertices

5

X

Diagram with NonLocal Axial vertices

X

+ rest

5

0)(0

2022

qL qwq

In accordance with Anomalyand ‘t Hooft duality principle(no massless states in singletchannel due to UA(1) anomaly)

wLT in the Instanton Model (NonSinglet)

2LT L Tw w w

Absence of Power corrections at large q in chiral limit in Instanton model

pQCD 2 0LTw q In perturbative QCD(Analog V-A)

Instanton model

(exponential)

Vector Meson

Dominance (powerlike)

TLLT www 2

(Czarnecki, Marciano, Vainshtein, 2003)

In local theory for quarks with constant mass one gets

1

2 2 200

12

33 1

22

1L

CC

mT

x xNdx

x xw

N

qq mw

Z*contribution to a

VMD + OPE(Czarnecki, Marciano, Vainshtein, 2003)

11EW 1002.2 a

Instanton model:(Dorokhov, 2005)

11EW 1048.1 a

Perturbative QCD(Anomaly cancelation)

EW,pQCD 0a

42

4 2

2 2 2

2 2 2 2 2 2

12 2

22

211

3

EW

Z Z

Z ZT TL

d ka G m i

k kp

kp m m

k m m k m kw w w

* * * * * *0

0

0

44LbL, 6 31

4 4 2 22 2 2 2 21 2 3 1

2 2 2 2 23

3

1 1 321 2 3 323

; , ; ,0

1

2 2

, ; .1 P Pq P

P

d qd qa e

q q q p q M p q M

GT q q p perm

g GF q q q F q q

J q

Pion pole contribution within Instanton model (A.D., W. Broniowski PRD 2008)

Full kinematic dependence Correct QCD asymptoticsComplete calculations are in progress

11LbL, 1027.6 a

Rare Pion Decay 0→e+e-- from KTeV

From KTeV E799-II EXPERIMENT at Fermilab experiment (1997-2007)

97’ set

99-00’ set,

The result is based on observation of 794 candidate 0 e+e- events usingKL 30 as a source of tagged 0s. The older data used 275 events with the result:

PRD (2007)

One of the simplest process for THEORY

8KTeV 1025.029.048.7

eeB

8KTeV 1028.046.004.7old

eeB

Classical theory of 0→e+e– decay

F

Drell (59’), Berman,Geffen (60’), Quigg,Jackson (68’)

Bergstrom,et.al. (82’) Dispersion ApproachSavage, Luke, Wise (92’) PT

The Imaginary part is ModelIndependent;Unitary limit

From condition one has the unitary limit

KTeV99-00

Progress in Experiment

>7 from UL

Still no intrigue

1. Dispersion approach (Bergstrom et.al.(82))

The Real Part is knownup to Constant

This Constant is the Amplitudein Soft Limit q2 0

In general it is determined inModel Dependent way

I. The Decay Amplitude in Soft limit q20

Thus the amplitude is fully reconstructed!in terms of moments of Pion Transition FF

The unknown constant is expressed as inverse moment of Pion Transition FFat spacelike momenta !!!

2

2(2)hvp

24

(0) ( (

) 3

)

m

R sK s

sa ds

2 2

2 2

22 2 3lnRe O( )ln

12,ee

Pe m

A mmm

m

m

2

20

15 3

4

, ,

2P

F tdt dt

t t

t F t t

Still no intrigue

2222 mmme

II. CLEO data and Lower Bound on Branching

Use inequality at spacelik e 0,, 0 F t t F tt

and CLEO data (98’)

CLEOCLEO0

1,0

1 /F t

t s

Intrigue appears

8KTeV 1038.048.7

eeR

III. F(t,t) general arguments

Let then

1. Fromone has

2. From OPE QCD(Brodsky, Lepage)

one has

OPE 2 2

2 2OPE

1,0 8 ,

8 1,

3

t

t

F t ft

fF t t

t

It follows theor 2yRe 0 21.9 0.3A q

3.3 below data!!

It would required change of s0 scale by factor more then 10!

F(t,0) F(t,t) reduces torescaling

1

1,

1 /F t t

t s

Now it’s intriguing!

8KTeV 1038.048.7

eeB

8theory 101.02.6

eeB

A. F(t,t) QCD sum rules (V.Nesterenko, A.Radyushkin, YaF 83’)

one has

From

and

CLEO

2 02e

0

QCDsr

QCDsrQ1

CDsr

3 1Re 0 ln 21.7 0.1,

2 m 4

sA q

ss

e

Nicely confirms general arguments! theor 2yRe 0 21.9 0.3A q

C. F(t,t) Quark Models (Bergstrom 82’)

theor 2yRe 0 21.9 0.3A q

2

2quark strongly violate ln QCD 1/t

2,

q

q

t

tMt t

MF

t

Constituent constantQuark mass

MQ=135MeV

0.21)0(QM A

9.06.18)0( KTeVA

A.E. Dorokhov, arXiv:0905.4577BABAR, arXiv:0905.4778

MQ=135MeV

CLEO+QCD

CLEO

3 diff

What is next? It would be very desirable if Others will confirm KTeV resultAlso, Pion transition FF need to be more accurately measured.

1) Radiative correctionsKTeV used in their analysis the results from Bergstrom 83’. A.D.,Kuraev, Bystritsky, Secansky (EJPC 08’) confirmed Numerics.

2) Mass corrections (tiny)A.D., M. Ivanov, S. Kovalenko (ZhETPh Lett 08’ and Hep-ph/09) Dispersion approach and PT are corrected by power corrections (m/m)n

3) New physicsKahn, Schmidt, Tait 08’ Low mass dark matter particlesChang, Yang 08’ Light CP-odd Higgs in NMSSM

4) Experiment wrongWaiting for new results from KLOE, NA48, WASA@COSY, BESIII,…

Possible explanations of the effect

Radiative Corrections (Bergstrom 83’,A.D.,Kuraev, Bystritsky, Secansky 08’)

=-3.4%

Power corrections A.D., M. Ivanov, S. Kovalenko 08-09’

Z=(M/MZ=(M/M)2=0.03, Z=(M/M)2=1.5

Xe=(Me/M)2ln(Xe)=--15, ln(X)=--4

The anomalous 511 keV -ray signal from Galactic Center observed by INTEGRAL/SPI (2003) is naturally explained

* 10 MeVU

M

Enhancement in Rare Pion Decays from a Model of MeV Dark Matter (Boehm&Fayet)was considered by Kahn, Schmitt and Tait (PRD 2008)

excluded

allowed

Rare decay π0 → e+e− as a sensitive probe of light CP-odd Higgs in Next-to-Minimal SuperSymmetric Model (NMSSM)(Qin Chang, Ya-Dong Yang, 2008)

They find the combined constraints from Y→ A01, aμ and 0 → e+e−

point to a very light A01 with mA01 135≃ MeV and |Xd| = 0.10 +-0.08

Other P →l+l– decaysA.D., M. Ivanov, S. Kovalenko (Hep-ph/09)

Mass power corrections are visible for decays

BESIII for one year will get for , ’->ll the limit 0.7*10-7

->ee will be available from WASAatCOSY

Hadronic Light-by-Light Contribution to Muon g -- 2 in Chiral Perturbation Theory

Ramsey-Musolf and Wise obtained in 2002 LL contribution to a

2 23LbL,hadr LbL,hadr

,l.o.pion loop

3 0

23 112ln

16 3 6

ln ln 0

O

c e

c

PT

m N m ma a f C

F mm mA

N

23

2 O LLc

mN

LbL,hadr 10 LbL,hadr 10,l.o. ,4.46 10 3.4 2.0 10Loga a

For LbL Large Logariphm contributions are highly compensated by nonleading terms.

Summary1) The processes P l+l- are good for test of SM.

Long distance physics is fixed phenomenologically. New measurements of the transition form factors are welcome.

Radiative and mass corrections are well under control.

2) At present there is 3.3 disagreement between SM and KTeV experiment for 0e+e-

KLOE, WASA@COSY, BESS III are interested in new measurements

3) If effect found persists it might be evidence for the SM extensions with low mass (10-100 MeV) particles (Dark Matter, NSSM)

Conclusions

The low-energy constant defining the dynamics of the process is expressed as the inverse moment of pion transition FF

Data on pion transition form factor provide new bounds on decay branchings essentially improving the unitary ones.

QCD constraints further the change of scales in transition from asymmetric to symmetric kinematics of pion FF

We found 3 difference between theory and high statistical KTeV data

If these results are confirmed, then the Standard Modelis in conflict with observation in one of those reactions which we thought are best understood.

The conclusion is that the experimental situation calls for clarification. There are not many places where the Standard Model fails. Hints at such failures deserve particular attention.

Possibilities:

New Physics

Still “dirty” Strong Interaction

Or

the measurements tend to cluster nearer the prior published averages than the ‘final’ value. (weather forecast style)

Much more experimental information is required to disentangle the various possibilities.

Perhaps new generation of high precision experiments (KLOE, NA48, WASA@COSY, BES III) might help to remove the dust.

q

3q 2q 1q

X