Rare decay 0 → e+ e- and its implication to muon (g-2)μ

A.E. Dorokhov (JINR, Dubna)

Introduction

Model Independent Approach to 0→e+e– Decayand KTeV Data

Model dependent approaches

Other P →l+ l– decays

Conclusions

Introduction

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

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

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

Anomalous magnetic moment of muon

BNL 10a 11 659 208.0(5.4)(3.3) 10

From BNL E821 experiment (1999-2006)

Standard Model SM QED EW Hadr 10a =a +a +a +... 11 659 178.5(6.3) 10

predicts the result which is 3.4 below the experiment

h

he

q

3q 2q 1q

X

Rare Pion Decay 0→e+e-- from KTeV

KTeV 87.49 0.29 0.25 10 e e

B

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

KTeV 8old 7.04 0.46 0.28 10 e e

B

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

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

From condition one has the unitary limit

KTeV99-00

Progress in Experiment

>7 from UL

Still no intrigue

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

The Real Part is knownup to Constant

The Constant is the Amplitudein Soft Limit q2 0

In general it is determined inModel Dependent way

PT approach (D’Ambrosio,Espriu(86),Savage,Luke,Wise(92))

is unknown LE constant

I. The Decay Amplitude in Soft limit q20

The accuracy is of order O(mem2. Thus the amplitude is fully reconstructed!

2 2 2 2em m m

A.D., M.A.Ivanov PRD 07’

The unknown constant is expressed as inverse moment of Pion Transition FF!!!

2

2(2)hvp

24

(0) ( (

) 3

)

m

R sK s

sa ds

2Re 0 3ln eP

mA q

2

22

0 0

15 3 5 3ln

4 2 4

, ,

2

,P

tdt dt dt

t t

F t t F t t F t t

t

22

22 242

2 2 2 22 2

2,

e

q k qki d kA q

q k iF k k

k q i k p m iq

Still no intrigue

II. CLEO data and Lower Bound on Branching

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

and CLEO data (98’)

KTeV 87.58 0.40 10R

CLEOCLEO0

1,0

1 /F t

t s

Intrigue appears

III. F(t,t) general arguments

Let then

1. Fromone has

2. From OPE QCD 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

KTeV 87.49 0.39 10B 3.3 below data!! 0 8theory 6.2 0.1 10B e e

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!

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!

B. F(t,t) VMD parametrization (M.Knecht, A.Nyffeler, EPJC 01’)

Nicely confirms general arguments!Parameters for LbL

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

D. F(t,t) Nonlocal Quark Models

ILM

I

2

e

-1

L 0 8M

5 3 3Re 0 3ln ,

m 4 2 2

300 50 MeV, 1.7 GeV

6.2 10

qE q

q

MA q I M

M

B e e

Nicely confirms general arguments!

(A.Dorokhov 06’)

Instanton Model and Pion Transition FF

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 08’ confirmed Numerics. 2) Mass corrections (tiny)A.D., M.Ivanov 08’

3) New physicsKahn, Schmidt, Tait 07’ Low mass dark matter particles

4) Experiment wrongWaiting for new results from KLOE, NA48, BESII,…

Possible explanations of the effect

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

=-3.4%

Other P →l+l– decays

5 Ce2.7 10 lsius/Wasa 2008B e e

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, BES II) might help to remove the dust.

Conclusions

Summary of speed of light measurements

It is interesting that the series of four measurements from1930-1940 displays a 17km/sec systematic shift from the true value

Klein,Roodman Ann.Rev.Nucl.Part.Sci.55:141-163,2005

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

We found 3 difference between theory and 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.

Theory vs KTeV experiment

0 8theory 6.2 0.1 10B e e

KTeV 87.49 0.29 0.25 10 B e e

0Unitary Lim 84.69 10B e e

CLEO lim 85.85 0.03 10 B e e

3.3 effect!!!

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 t data are not used 0 aCVC nd : e e X X