1. Achim Denig Radiative Return @ DA F NE MENU 2004 Measurement of the Hadronic Cross Section via Radiative Return at DA  NE Achim Denig for the KLOE Collaboration MENU 2004 September 3 rd Beijing, IHEP Universität Karlsruhe Institut für Experimentelle Kernphysik

2. Achim Denig Radiative Return @ DA F NE MENU 2004 hep-ex/0407048, sent to Phys. Lett. B Outline:  Muon Anomaly  Radiative Return at KLOE  Results & Outlook Further KLOE-Results: St. Müller (Session B2)

3. Achim Denig Radiative Return @ DA F NE MENU 2004 Motivation: Determination of Hadronic Vacuum Polarization = High Precision Test of the Standard Model Anomalous magnetic moment of the muon a m = (g- 2) m Running fine structure constant at Z 0 -mass a QED (M Z ) Dirac-Theory: (g - 2 ) = 0 Quantum corrections: (g - 2 )  0 due to corrections of: - electromagnetic interaction - weak interaction - strong interaction (and maybe NEW PHYSICS ???) Hadronic Vacuum Polarization 2nd largest contrib., cannot be calculated in pQCD Error of hadronic contribution is dominating total error ! Muon - Anomaly

4. Achim Denig Radiative Return @ DA F NE MENU 2004 Hadronic contribution to a m can be estimated by means of a dispersion integral: - K(s) = analytic kernel-function, almost flat in s - above 2…5 GeV, use pQCD Hadronic Cross Section Input Dispersion Integral: a) hadronic electron-positron cross section data, e.g. e + e -  p + p - b) hadronic t - decays ( CVC -theorem, taking into account isospin breaking corrections), e.g. t -  p 0 p - n t H 1 / s 2 makes low energy contributions especially important: in the range < 1 GeV contributes to 70% !

5. Achim Denig Radiative Return @ DA F NE MENU 2004 Muon-Anomaly: Theory vs. Experiment a m - 11 659 000 ∙ 10 -10 THEORY ’20/‘03 Experiment ’20/‘04 Experiment BNL-E821 Values for m + (2002) and m - (2004) in agreement with each other. Precision: 0.5ppm Dispersion integral for hadronic contribution to a m evaluated for: a) e + e - -Data ONLY CMD-2 (VEPP-2M) measured p + p - channel with 0.6% precision < 1 GeV 2.7 s – Deviation b) t -Data ONLY (if available) ALEPH /OPAL/CLEO 1.4 s – Deviation Theoretical values taken from Davier, Eidelman, Höcker, Zhang: hep-ex/0308213 a m - 11 659 000 ∙ 10 -10 e + e - data and t data differ for p + p - channel in a specific energy window above 0.6 GeV 2 (above the r -peak)! Status up to July ‘04

6. Achim Denig Radiative Return @ DA F NE MENU 2004 Radiative Return Standard method for cross section measurement is the energy scan, i.e. the systematic variation of the c.m.s.-energy of the accelerator DA  NE is a f - factory and therefore designed for a fixed c.m.s.-energy:  s = m f = 1 019 MeV; a variation of the energy is not foreseen in near future Complementary approach: Take events with Initial State Radiation ( ISR ) Cross section as a function of the 2-Pion invariant mass s p = M pp 2 “Radiative Return” to r(w) -resonance: e + e -  r(w) + g  p + p - + g ds ( e + e -  p + p - g  ) dM pp r0r0 ISR MC - Generator PHOKHARA = NLO J. Kühn, H. Czyż, G. Rodrigo Radiator-Function H(s) H(s) spsp g

7. Achim Denig Radiative Return @ DA F NE MENU 2004 Background Signal Selections-Efficiency Luminosity Acceptance Analysis p + p - g Final state e + e -  p + p - g  relatively easy signature, however cross section measurement on percent level is a challenging task (normali- zation, efficiencies, background) KLOE Detector designed for CP – violation, we are having a high resolution tracking chamber ideal for the measurement of M pp ! Analysis- Items:

8. Achim Denig Radiative Return @ DA F NE MENU 2004 Selection p + p - g 50 0 <  < 130 0  < 15 0  > 165 0   Pion tracks at large angles 50° < q p < 130° High statistics for ISR events Reduced background contamination Low relative contribution of FSR Photons at small angles q g 165° are shadowed by quadrupoles near the I.P. Drift Chamber EM Calorimeter NO PHOTON TAGGING

9. Achim Denig Radiative Return @ DA F NE MENU 2004 Background p + p - g       e  e   signal region M TRK (MeV) mm      tail 1) Pion-Electron-Separation Rad. Bhabhas e + e -  e + e - g are separated by means of a Likelihood- Method (Signature of EmC-Clusters and TOF of particle tracks ) mm mm 2) Kinematic Separation f  p + p - p 0 e + e -  m + m - g using „Trackmass“-variable M pp – dependent M TRK -Cut 3) Residual Background Fit Trackmass-Spectra for signal and background with free normalization parameters (shape from MC)

10. Achim Denig Radiative Return @ DA F NE MENU 2004 Analysis s ( e + e -  p + p - g) Background: - e + e -  e + e - g - e + e -  m + m - g - f  p + p - p o Efficiencies: - Trigger & Cosmic veto - Tracking, Vertex - p - e - separation - Reconstruction filter - Trackmass-cut - Unfolding resolution - Acceptance Luminosity: Bhabhas at large angles > 55°, s eff = 430 nb, 0.9% 0.3% 0.3% exp 0.5% theo Statistics: 141pb -1 of 2001-Data 1.5 Million Events r-w Interference High Statistics ! High Resolution ! Errors:

11. Achim Denig Radiative Return @ DA F NE MENU 2004 Extraction s ( e + e -  p + p - ) Radiator-Function (ISR): - ISR-Process calculated at NLO-level Generator PHOKHARA (Kühn et.al ) - Comparison with KKMC (Jadach et.al.) Precision: 0.5% Radiative Corrections: i) Bare Cross Section divide by Vacuum Polarisation ii) FSR - Corrections Cross section s pp must be incl. for FSR Vacuum Polarization Cross Section Radiative Return requires ISR photon  be inclusive for ISR-FSR-events e + e -  p + p - g ISR (g FSR ) F p =1 s ( ppg ) mit F p =1 s p (GeV 2 )

12. Achim Denig Radiative Return @ DA F NE MENU 2004 Aim: Cross Section e + e -  p + p - TOTAL ERROR 1.3% To be compared with 0.9% CMD-2 Error: exp.+syst.+stat. Cross Section s ( e + e -  p + p - ) Result published now Considerable improvement in near future

13. Achim Denig Radiative Return @ DA F NE MENU 2004 2 p Contribution to a m hadr a   = ( 388.7  0.8 stat  3.5 syst  3.5 theo ) 10 -10 Dispersions Integral for the 2-Pion-Channel in Energy Range 0.35 < M pp 2 <0.95 GeV 2 Comparison with CMD-2 in the Energy Range 0.37 < M pp 2 <0.93 GeV 2 (375.6  0.8 stat  4.9 syst+theo ) 10 -10 (378.6  2.7 stat  2.3 syst+theo ) 10 -10 KLOE CMD2 KLOE data points are not in excellent but in a fair agreement with CMD-2: KLOE higher at low s p and lower at large s p 1.3 % Error 0.9 % Error Pion Formfactor CMD-2 KLOE 0.4 0.50.6 0.70.80.9 s  [GeV] 45 40 35 30 25 20 15 10 5 45 0

14. Achim Denig Radiative Return @ DA F NE MENU 2004 Comparison with t Data At large values of s  (>m  ) KLOE & CMD-2 deviate from t -Data > 10%  unsufficient understanding of isospin breaking corrections in t -Data ?! Rel. difference of e + e - -data with respect to t -data (avg.)

15. Achim Denig Radiative Return @ DA F NE MENU 2004 Conclusions M. Davier, A. Höcker @ ICHEP04 Including: New KLOE data New 4 th order QED contribution (Kinoshita) hep-ph/0402206 New Light-by-light contribution (Melnikov, Vainshtein) hep-ph/0312226 t – data excluded!  Theory (SM) - Experiment a  exp - a  theo = ( 25.2 ± 9.2 ) ·10 -10 2.7 “standard deviations” Including KLOE Status of the anomalous magnetic moment of the muon today (August ’04): KLOE has proven feasibility of the Radiative Return for high-precision hadronic cross section measurements: New hep-ex/0407048, sent to Phys. Lett. B

16. Achim Denig Radiative Return @ DA F NE MENU 2004 Outlook: KLOE Measure  (  ) in the region close to threshold, M  < 600 MeV, responsible for  20% of a m pp - This region excluded by angular selection in small angle photon approach - Complementary analysis at large photon angles At large photon angles the amount of FSR is large!  test model of scalar QED (i.e. poinlike pions)  Measure Charge Asymmetry and compare data with MC Charge asymmetry is due to different C-Parity of ISR- and FSR-amplitudes 507090110130 -20 -10 0 20 10 Asymmetry [%] Polar Angle [°] Data MC K L O E P R E L I M I N A R Y

17. Achim Denig Radiative Return @ DA F NE MENU 2004 Outlook: Muon Anomaly Theory: BaBar fills gap between DA  NE, VEPP-2M ( 2 GeV) and will measure all relevant exclusive channels (see e.g. hep-ex/0408078) KLOE/CMD-2 threshold region < 0.4 GeV 2 Future measurements at BES, VEPP-2000, CLEO, BELLE, DA F NE-2? “Real Theory“: Rad. corrections, Light-by-light-scattering, Isospin breaking... Experiment: New beam time for BNL-E821 (still limited by statistics)!? Ambitious new project for 5 th generation (g-2) m experiment at J-PARC da  (theor.)  3…4 · 10 -10 da  (exp.) < 2…3 · 10 -10 Actual Difference: 25 ± 9 · 10 -10 Future

18. Achim Denig Radiative Return @ DA F NE MENU 2004 Work supported by: Emmy – Noether – Programm