Rare decay p0 ? e e-

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Rare decay p0 ? e e- and its implication to
muon (g-2)µ
A.E. Dorokhov (JINR, Dubna)
Introduction Model Independent Approach to
p0?ee Decay and KTeV Data Model dependent
approaches Other P ?l l decays Conclusions
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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 was not
described in text-books yet

• Two search strategies
• 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)m is very famous example,
• 0?ee- is in the list of SM test after new exp.
  and theor. results
• Thats intriguing

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Anomalous magnetic moment of muon
From BNL E821 experiment (1999-2006)
Standard Model
predicts the result which is 3.4s below the
experiment
a3
a2
X
?
?
p
?
?
h
e
h
?
?
?
?
m
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Rare Pion Decay p0?ee-- from KTeV
PRD (2007)
One of the simplest process for THEORY
From KTeV E799-II EXPERIMENT at Fermilab
experiment (1997-2007)
99-00 set,
The result is based on observation of 794
candidate p0 ? ee- events using KL ? 3p0 as a
source of tagged p0s. The older data used 275
events with the result
97 set
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Classical theory of p0?ee 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
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one has the unitary limit
From condition
Progress in Experiment
gt7s from UL
KTeV 99-00
Still no intrigue
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Dispersion approach (Bergstrom et.al.(82))
The Real Part is known up to Constant The
Constant is the Amplitude in Soft Limit q2 ?0 In
general it is determined in Model Dependent way
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cPT approach (DAmbrosio,Espriu(86),Savage,Luke,Wi
se(92))
is unknown LE constant
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I. The Decay Amplitude in Soft limit q2?0
A.D., M.A.Ivanov PRD 07
The unknown constant is expressed as inverse
moment of Pion Transition FF!!!
The accuracy is of order O(me/mr)2. Thus the
amplitude is fully reconstructed!
Still no intrigue
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II. CLEO data and Lower Bound on Branching
Use inequality
and CLEO data (98)
Intrigue appears
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III. Fp(t,t) general arguments
Let
then
1. From
one has
one has
2. From OPE QCD
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 its intriguing!
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A. Fp(t,t) QCD sum rules (V.Nesterenko,
A.Radyushkin, YaF 83)
From
one has
and
Nicely confirms general arguments!
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B. Fp(t,t) VMD parametrization (M.Knecht,
A.Nyffeler, EPJC 01)
Nicely confirms general arguments! Parameters for
LbL
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C. Fp(t,t) Quark Models (Bergstrom 82)
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D. Fp(t,t) Nonlocal Quark Models
(A.Dorokhov 06)
Nicely confirms general arguments!
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Instanton Model and Pion Transition FF
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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.
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Possible explanations of the effect
1) Radiative corrections KTeV 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 physics Kahn, Schmidt, Tait
07 Low mass dark matter particles 4) Experiment
wrong Waiting for new results from KLOE, NA48,
BESII,
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Radiative Corrections (Bergstrom
83 A.D.,Kuraev, Bystritsky, Secansky 08)
-3.4
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Other P ?ll decays
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Conclusions
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 II) 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.
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Summary of speed of light measurements
Klein,Roodman Ann.Rev.Nucl.Part.Sci.55141-163,200
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It is interesting that the series of four
measurements from1930-1940 displays a 17km/sec
systematic shift from the true value
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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 3s
difference between theory and 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.
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Theory vs KTeV experiment
3.3s effect!!!
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Leading Order Hadronic Contribution
a2
?
LO is expressed via Adler function as
Phenomenological approach
?
h
?
?
From phenomenology one gets
1) Data from low energy slt1Gev are dominant
(CMD, KLOE, BaBar) 2) Until CVC puzzle is not
solved t data are not used