Muon g2, Rare Decay p0 e e and DarkMatter

1
Muon g-2, Rare Decay p0 ? ee- 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?ee Decay (status) p0?ee 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?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)
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
?
?
?
?
h
e
h
?
?
?
?
am(HVP)
Integral over ee- to Hadrons cross section
4
1.9 s
3.4 s
M. Davier etal., 2009
5
a2
The hadronic contributions to the muon AMM
(theory)
?
?
Hadronic Vacuum Polarization contributes 99 and
half of error
h
?
?
a3
h
?
?
?
?
?
?
?
h
e
h
h
?
?
?
?
?
?
Light-by-light process contributes 1 and half
of error
Zgg effective coupling
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Instanton model
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.
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Leading Order Contribution to Muon Anomalous
Magnetic Moment
Adler function is defined as
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NcQM Adler function and ALEPH data
(AD, PRD, 2004)
M(p)
AF MasslessQuarks
Quark loop
ALEPH
ILM
r,w
Quark loop
Mesons (Nc enhanced)
pQCD (NNNLO)
NJL
Meson loop (chiral enhanced)
cQCD Massive Quarks
Very sensitive to quark mass Mq200-240 MeV
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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
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VAV correlator and muon AMM
For specific kinematics q2q 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
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VAV 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 ngt0
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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)
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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)
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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

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Zgg contribution to am
Perturbative QCD (Anomaly cancelation)
VMD OPE (Czarnecki, Marciano, Vainshtein, 2003)
Instanton model (Dorokhov, 2005)
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Pion pole contribution within Instanton model
(A.D., W. Broniowski PRD 2008)
Full kinematic dependence Correct QCD
asymptotics Complete calculations are in progress
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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 Unitary
limit
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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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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
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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
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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 (Brodsky, Lepage)
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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C. Fp(t,t) Quark Models (Bergstrom 82)
Constituent constant Quark mass
MQ135MeV
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BABAR, arXiv0905.4778
A.E. Dorokhov, arXiv0905.4577
MQ135MeV
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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 (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, WASA_at_COSY, BESIII,
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Radiative Corrections (Bergstrom
83, A.D.,Kuraev, Bystritsky, Secansky 08)
-3.4
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Power corrections
A.D., M. Ivanov, S. Kovalenko 08-09
Zh(Mh/Mr)20.5,
Zp(Mp/Mr)20.03, Zh1(Mh1/Mr)21.5 Xe(M
e/Mr)2 ln(Xe)--15, ln(Xm)--4
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Enhancement in Rare Pion Decays from a Model of
MeV Dark Matter (BoehmFayet) 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
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Rare decay p0 ? ee- 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 ? ee- point to a very light A01 with
mA01 ? 135 MeV and Xd 0.10 -0.08
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Other P ?ll decays A.D., M. Ivanov, S.
Kovalenko (Hep-ph/09)
p-gtee will be available from WASAatCOSY
Mass power corrections are visible for h(h1)
decays
BESIII for one year will get for h ,h -gtll the
limit 0.710-7
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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.
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Summary

• The processes P ? ll- 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?ee-
• KLOE, WASA_at_COSY, BESS III are interested in new
  measurements
• If effect found persists it might be evidence for
  the SM extensions with low mass (10-100 MeV)
  particles (Dark Matter, NSSM)

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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 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.
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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, WASA_at_COSY, 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.
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X
p
m
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