1. Muon g-2, Rare Decay p0 → e+e- and DarkMatter
A.E. Dorokhov (JINR, Dubna)
In collaboration with M. Ivanov, S. Kovalenko,
E. Kuraev, Yu. Bystritsky, W. Broniowski
Introduction
Muon g-2 (status)
Hadronic contributions within Instanton Model
Rare p0→e+e– Decay (status)
p0→e+e– Decay and Dark Matter
Conclusions

2. Introduction
Abnormal people are looking for traces of Extraterrestrial Guests
Abnormal Educated people are looking for hints of New Physics
Cosmology tell us that 95% of matter is not described in text-books yet
New excitements after Fermi LAT, PAMELA, ATIC, HESS and WMAP data
Interpreted as Dark Matter and/or Pulsar signals
Two search strategies:
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)m is very famous example,
0→e+e- is in the list of SM test after new exp. and theor. results
That’s intriguing

3. a3 a2 Anomalous magnetic moment of muon
From BNL E821 experiment ( )
New proposals for
BNL, FNAL, JPARC
Standard Model
predicts the result which is 3.4s below the experiment (since 2006)
LbL to g-2 a3 a2     e h h    
am(HVP)=
Integral over e+e- to Hadrons cross section

4. 1.9 s
3.4 s
M. Davier etal., 2009

5. Z*gg* effective couplinga2
The hadronic contributions to the muon AMM
(theory)   h
Hadronic Vacuum
Polarization contributes 99% and half of error   a3 h        e h h h      
Light-by-light
process
contributes 1%
and half of error
Z*gg* effective coupling

6. Instanton model f(p) is related to the quark zero
The dressed quark propagator is defined as I
f(p) is related to the quark zero
mode in the instanton field
Incorporates soft momentum physics
and smoothly transits to high-momentum
regime
Mconst.
Mcurr.

7. Leading Order Contribution to Muon Anomalous Magnetic Moment
Adler function is defined as

8. NcQM Adler function and ALEPH data
(AD, PRD, 2004)
M(p) AF
MasslessQuarks
Quark loop
ALEPH
ILM
r,w
Quark loop
pQCD
(NNNLO)
Mesons
(Nc enhanced)
NJL
Meson loop
(chiral enhanced)
cQCD
Massive Quarks
Very sensitive to quark mass: Mq= MeV

9. Leading Order Hadronic Contribution
LO is expressed via Adler function as
Phenomenological
approach  h  
From phenomenology one gets
1) Data from low energy s<1Gev are dominant
(CMD, KLOE, BaBar)
2) Until CVC puzzle is not solved t data
are not used

10. V*AV correlator and muon AMM
For specific kinematics: q2=q is arbitrary, q10
only 2 structures exists in the triangle amplitude
The amplitude is transversal with respect to vector current
but longitudinal with respect to axial-vector current
This is famous Adler-Bell-Jackiw anomaly

11. V*AV amplitude In local theory for quarks with constant mass one gets
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

12. Anomalous wL structure (NonSinglet)X X
+ rest +
Diagram with NonLocal Axial vertices
Diagram with Local vertices
In accordance with Anomaly
and ‘t Hooft duality principle
(massless Pion states in triplet)

13. Anomalous wL structure (Singlet)X X
+ rest
Diagram with NonLocal Axial vertices
Diagram with Local vertices
In accordance with Anomaly
and ‘t Hooft duality principle
(no massless states in singlet
channel due to UA(1) anomaly)

14. Instanton model (exponential)
wLT in the Instanton Model (NonSinglet)
In local theory for quarks with constant mass one gets
Vector Meson Dominance (powerlike)
In perturbative QCD
(Analog V-A)
(Czarnecki, Marciano,
Vainshtein, 2003)
Instanton model (exponential)
Absence of Power corrections at large q in chiral limit in Instanton model

15. Z*gg* contribution to am
Perturbative QCD
(Anomaly cancelation)
VMD + OPE
(Czarnecki, Marciano, Vainshtein, 2003)
Instanton model:
(Dorokhov, 2005)

16. Pion pole contribution within
Instanton model
(A.D., W. Broniowski PRD 2008)
Full kinematic dependence
Correct QCD asymptotics
Complete calculations are in progress

17. Rare Pion Decay p0→e+e-- from KTeV
PRD (2007)
One of the simplest
process for THEORY
From KTeV E799-II EXPERIMENT at Fermilab experiment ( )
99-00’ set,
The result is based on observation of 794 candidate p0  e+e- events using
KL  3p0 as a source of tagged p0s.
The older data used 275 events with the result:
97’ set

18. Classical theory of p0→e+e– decay
Drell (59’), Berman,Geffen (60’),
Quigg,Jackson (68’) Fp
Bergstrom,et.al. (82’) Dispersion Approach
Savage, Luke, Wise (92’) cPT
The Imaginary part is Model
Independent;
Unitary limit

19. Progress in Experiment
one has the unitary limit
From condition
Progress in Experiment
>7s from UL
KTeV
99-00
Still no intrigue

20. 1. Dispersion approach (Bergstrom et.al.(82))
The Real Part is known
up to Constant
This Constant is the Amplitude
in Soft Limit q2 0
In general it is determined in
Model Dependent way

21. I. The Decay Amplitude in Soft limit q20
The unknown constant is expressed as
inverse moment of Pion Transition FF
at spacelike momenta !!!
Still no intrigue
Thus the amplitude is fully reconstructed!
in terms of moments of Pion Transition FF

22. II. CLEO data and Lower Bound on Branching
Use inequality
and CLEO data (98’)
Intrigue appears

23. III. Fp(t,t) general arguments
Let
then
1. From
one has
2. From OPE QCD
(Brodsky, Lepage)
one has
F(t,0)  F(t,t) reduces to
rescaling
It follows
3.3s below data!!
It would required change of s0 scale by factor more then 10!
Now it’s intriguing!

24. A. Fp(t,t) QCD sum rules (V.Nesterenko, A.Radyushkin, YaF 83’)
From
and
one has
Nicely confirms general arguments!

25. C. Fp(t,t) Quark Models (Bergstrom 82’)
Constituent constant
Quark mass
MQ=135MeV

26. BABAR, arXiv:
A.E. Dorokhov, arXiv:
MQ=135MeV

27. Also, Pion transition FF need to be more accurately measured.
3s diff
CLEO
+QCD
CLEO
What is next? It would be very desirable if Others will confirm KTeV result
Also, Pion transition FF need to be more accurately measured.

28. Possible explanations of the effect
1) Radiative corrections
KTeV 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 cPT are corrected by power corrections (mp/mr)n
3) New physics
Kahn, Schmidt, Tait 08’ Low mass dark matter particles
Chang, Yang 08’ Light CP-odd Higgs in NMSSM
4) Experiment wrong
Waiting for new results from
KLOE, NA48, BESIII,…

29. Radiative Corrections (Bergstrom 83’,
A.D.,Kuraev, Bystritsky, Secansky 08’)
=-3.4%

30. Power corrections Zh=(Mh/Mr)2=0.5, Zp=(Mp/Mr)2=0.03, Zh1=(Mh1/Mr)2=1.5
A.D., M. Ivanov, S. Kovalenko 08-09’
Zh=(Mh/Mr)2=0.5, Zp=(Mp/Mr)2=0.03, Zh1=(Mh1/Mr)2=1.5
Xe=(Me/Mr) ln(Xe)=--15, ln(Xm)=--4

31. 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
The anomalous 511 keV g-ray signal from Galactic Center observed
by INTEGRAL/SPI (2003) is naturally explained

34. 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→g A01, aμ and p0 → e+e−
point to a very light A01 with mA01 ≃ 135 MeV and |Xd| =

35. Other P →l+l– decays A.D., M. Ivanov, S. Kovalenko (Hep-ph/09)
p->ee will be available from WASAatCOSY
Mass power corrections are visible for h(h1) decays
BESIII for one year will get for h ,h ’->ll the limit 0.7*10-7

36. Hadronic Light-by-Light Contribution to Muon g -- 2 in
Chiral Perturbation Theory
Ramsey-Musolf and Wise obtained in 2002 LL contribution to am
For LbL Large Logariphm contributions are
highly compensated by nonleading terms.

37. Summary 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 3.3s disagreement between SM and
KTeV experiment for p0e+e-
KLOE, BESS III are interested in new measurements
If effect found persists it might be evidence for the SM extensions with low mass ( MeV) particles (Dark Matter, NSSM)

38. 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 3s difference between theory and high statistical KTeV
data
If these results are confirmed, then the Standard Model
is in conflict with observation in one of those reactions which we thought
are best understood.

39. Much more experimental information is required to disentangle the
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.
Perhaps new generation of high precision experiments
(KLOE, NA48, BES III)
might help to remove the dust.
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.

40. X p m