Post on 13-Jan-2016
description
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
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