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

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

a3 a2 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     e h h     am(HVP)= Integral over e+e- to Hadrons cross section

1.9 s 3.4 s M. Davier etal., 2009

Z*gg* effective coupling a2 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

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.

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

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=200-240 MeV

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

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

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

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)

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)

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

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

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

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 (1997-2007) 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

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

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

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

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

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

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!

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

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

BABAR, arXiv:0905.4778 A.E. Dorokhov, arXiv:0905.4577 MQ=135MeV

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.

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@COSY, BESIII,…

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

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)2 ln(Xe)=--15, ln(Xm)=--4

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

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| = 0.10 +-0.08

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

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.

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, WASA@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)

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.

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, WASA@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.

X p m