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Pion form factors and decays .

Pion form factors and decays. A. E. Dorokhov in collaboration with W . Broniowski and E . Ruiz Arriola. Introduction g-2 Transversity pion form factor: c models vs Lattice Conclusions. Cosmology tell us that 95% of matter is not described in text-books yet. Two search strategies:

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Pion form factors and decays .

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  1. Pion form factors and decays. A.E. Dorokhov in collaboration with W. Broniowskiand E. Ruiz Arriola Introduction g-2 Transversity pion form factor: c models vs Lattice Conclusions

  2. Cosmology tell us that 95% of matter is not described in text-books yet • Two search strategies: • High energy physics to excite heavy degrees of freedom. • No any evidence till now. We live in LHC era! • 2) Low energy physics to produce Rare processes in view of huge • statistics. • There are some rough edges of SM. Muon anomaly(g-2)m is the most famous example That’s intriguing

  3. Some Definitions A charged particle with spin S has a magnetic moment m PDG Gyromagnetic ratio mμ=105.6583692(94) MeV, mτ = 1776.99 (29) MeV mμ/me= 206.768 2838(54) Anomaly

  4. The general form of theffgvertex is • F1 is the electric charge distribution el=eF1(0) • F2 corresponds to Anomalous Magnetic Moment (AMM) al=(gl-2)/2=F2(0) • F3 corresponds to Anomalous Electric Dipole Moment dl=-el/(2ml )F3(0) dl=0 due to T- and P symmetries However, in SM alis not zero due to Radiative Corrections

  5. Magnetic Anomaly QED Hadronic Weak SUSY... ... or other new physics ? Basic of Standard Model

  6. Lepton Anomalies • Electron anomaly is measured extremely accurately. QED test. • It is the best for determining a • For a lepton L, Mass Scale Lcontributes to aLas • Tau anomaly is difficult to measure since its fast decay • Muon anomaly is measured to 0.5 parts in a million (ppm) SM test. • Thus muon AMM leads to a (mm/me)2~ 40 000 enhancement of the sensitivity to New Physicsversus the electron AMM.

  7. Electron AMM To measurable level ae arises entirely from virtual electrons and photons The theoretical error isdominated by the uncertainty in the input value of the QED coupling α ≡ e2/(4π) Dasistfantastisch! QED is at the level of the best theory ever built to describe nature

  8. Tau anomaly • Tau due to its highest mass is the best for searching for New Physics, • But Tau is short living particle, so the precession method is not perspective • The best existing limits • -0.052<atExp<0.013 • are obtained at OPAL, L3 and DELPHI (LEP, CERN) from the high energy process • e+e- e+e- t+t- , • While the SM estimate is • atSM=1.17721(5) 10-3

  9. SM Contributions to Muon AMM from BNL FromBNL E821 g-2 experiment (1999-2006) New Prop. E989 at Fermilab 0.14 ppm From Standard Model A. Hoecker Tau2010 Update

  10. Kinoshita&Nio 2004, 2006 plus Czarnetski&Marciano&Vainshtein 2003 plus the Hadronic Contribution estimated as M. Davier, A. Hoecker, B. Malaescu, Z. Zhang 2010; F. Jegerlehner, Robert Szafron 2011 The main question how to get such accuracy from theory.

  11. Strong contributions to Muon AMMM LbL to g-2 a3 a2     e h h     Hadronic Light-by-Light Scattering (Dubnicka, Bartos, Kuraev AED, Radzhabov, Zhevlakov) Hadronic Vacuum polarization (Davier, Hoecker, Zhang)

  12. (0) W: I=1 &V,A CVC: I=1 &V : I=0,1 &V  e+   hadrons W e– hadrons

  13. Structure of hadronic LbL contribution Phenomenological and QCD Constraints are used to reduce Model Dependence

  14. Interpretations SUSY mSUSY ≈100-500 GeV Multi-Higgs Models Extra Dimensions<2TeV Dark Photons ∼10-150MeV, α’=10-8 Light Higgs <10MeV? g-2 is the most important constraint (for SUSY), even more important than dark matter Davier etal 2010

  15. Sincethe pion has spin zero, its longitudinal spin structure in terms of quark and gluon degrees of freedom is trivial. An instructive quantitydescribing the transverse spinstructure of hadrons is the probability densityr (x,ktr,str) In terms of moments one has the Generalized Form Factors (GFFs) Connection with Generalized Parton Distributions (GPDs)

  16. The Generalized Form Factors of the Pion Introduce auxiliary vectors

  17. Matrix Elements in the Chiral Models The Quark Propagator And the Quark-Pion vertex In the local (NJL) model one has

  18. Transversity pion form factor (momentum space)

  19. Transversity pion form factor (impact parameter space)

  20. Forward: distribution function

  21. Transverse size distribution function

  22. Normalized density dT2(x)=bT2(x)/f(x)

  23. One can interpret it as an evolution of the probability density for a stochastic motion of a particle in the transverse plane h=log(1/x)

  24. QCD evolution GFFs BT evolve multiplicatively For Local Model one has for the Normalizations

  25. The results: Lattice vs Local Model

  26. The results: Lattice vs Nonlocal Models The transversity form factors in thechiral model (solid line) and in the instanton-motivated model(dashed line) for Mq = 300 MeV.

  27. Rare Pion Decayp0→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.

  28. AED, M. Ivanov PRD (2007) 3s diff CLEO +QCD CLEO What is next? It would be very desirable if Others will confirm KTeV result Also, h mm pair decay is very perspective

  29. 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 signalfrom Galactic Center observed by INTEGRAL/SPI (2003) is naturally explained

  30. Conclusions High statistics Low-Energy experiments are important independent way to search for effects of New Physics, They complement to possible signals from High-Energy experiments (LHC,…) allowing to get combined restrictions on the parameters of hypothetical interactions They sensitive to New particles with low masses New experiments are urgent Theory has to be in good shape

  31. Photon-pion transition form factor in nonperturbative QCD approach

  32. The theory of hard exclusive processes was formulated within the factorization approach to perturbative quantum chromodynamics (pQCD) in 1977-1981 • The photon-pion transition γ*γ*→π⁰ is of special interest • it is the simplest process for theory; • related to the axial anomaly when both photons are real; • At large photon virtualities it was studied in [6,7]

  33. Photon-pion transition form factor: In the factorization approach Factorization fp J* 1/Q2 and it settle in at ~ 1 GeV2 Asymmetric kinematics (measured by BABAR) Symmetric kinematics

  34. BABAR disaster 2009 (and CELLO-1991, CLEO-1997) data A. Data higher than BL Asymptotic limit, B. TheyGROW! Passive mode Active mode

  35. BABAR puzzles

  36. Nonperturbative Nonlocal QCD Approach to pg Form Factor And its asymptotic properties AED JETP Lett. (2003) The vertex F is equivalent of the light-cone pion WF Main properties

  37. a representation N.N.Bogolyubov, D.V. Shirkov O.I. Zavialov F decays as 1/k2 or faster The main property for asymptotic analysis D=a+b+g

  38. Photon-pion transition form factor: Symmetric Kinematics Take chiral limit p2=0 and symmetric kinematics q12= q22= q2 D=a+b+g Leading Asymptotics as q2∞ corresponds to γ0 thus Da+b, gdgm0, dg1+… Factorization – Yes!

  39. Photon-pion transition form factor: Symmetric Kinematics a representation – URA! Factorization – URA!! Brodsky-Lepage - URA!!!

  40. p Distribution Amplitude Pion DA is obtained if we perform substitution then AED JETP Lett. (2003)

  41. p Distribution Amplitude For Instanton model For chiral model At x=0 one gets

  42. p Distribution Amplitude

  43. Photon-pion transition form factor: Asymmetric Kinematics Take chiral limit p2=0 and symmetric kinematics q12= q2 , q22=0 D=a+b+g Leading Asymptotics as q2∞ corresponds to γ0 or a0thus Da+b, gFgm0, Fg1+…, but keep Exp small terms! Dg+b, Gm,0a,b0, G0,ma,bgbm , Ga,bFb Small g Small a Factorization – Not always!

  44. Photon-pion transition form factor: Asymmetric Kinematics Small g Small a Factorization – Not at all! Small a! Small g

  45. Photon-pion transition form factor: Asymmetric Kinematics in Instanton Model A) Confining Propagator B) Chiral Propagator

  46. Photon-pion transition form factor: Asymmetric Kinematics in Chiral Model Exact asymptotic expression It is nonfactorizable, no representation in terms of pion DA • Thus one finds three possible Asymptotic regimes: • 1/Q2 Pion DA strongly suppressed at endpoints • “lnQ2/Q2” Pion DA vanishes at endpoints, but almost flat otherwise • lnQ2/Q2 Pion DA does not vanishes at endpoints Two last regimes may be responsible for BABAR data! BABAR puzzle is cracked!!

  47. Mq = 300 MeV Mq = 135 MeV Mq = 300 MeV

  48. CONCLUSIONS 1. BABAR measured photon-pion form factor at large Q2 in wide kinematical region and found that the data for Q2F(Q2) exceed the asymptotic Brodsky-Lepage constant limit and, moreover, continue to growth – BABAR puzzle 2. We show that depending on the properties of the quark-pion vertex there are two possible shapes of the pion distribution amplitude: vanishing or not vanishing at the endpoints 3. These different cases provide different possibilities for the asymptotic behavior of the form factor Q2F(Q2) ~ const Or Q2F(Q2) ~ln(Q2) 4. BABAR data, if will be confirmed, point out on specific properties of quark dynamics in the pion and of the underlying QCD vacuum

  49. AntiBABAR Shock therapy 2009 A) B) C) Normalization by anomaly A “Factorization” B,C OPEB Value of Parameters Mq, s and M and their meaning ? fp is external parameter, it is not defined All are based on flat (local) pion DA f(x)=1. How to justify that?? No QCD Evolution

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