1. Measurement of the Hadronic Cross Section at DA F NE with KLOE Achim G. Denig for the KLOE Collaboration 1. 4. 2004 La Thuile, Vallée d’Aoste XXXIX th Rencontres de Moriond - QCD

2. Achim G. Denig Radiative Return @ DA F NE Moriond -QCD 2004 Outline:  Motivation & Radiative Return  Analysis s hadr  Results & Outlook

3. Achim G. Denig Radiative Return @ DA F NE Moriond -QCD 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 G. Denig Radiative Return @ DA F NE Moriond -QCD 2004 Hadronic contribution to a m can be estimated by means of a dispersion integral: - K(s) = analytic kernel-function - above sufficiently high energy value, typically 2…5 GeV, use pQCD Hadronic Cross Section Input: a) hadronic electron-positron cross section data b) hadronic t - decays, which can be used with the help of the CVC -theorem and an isospin rotation (plus isospin breaking corrections) H 1 / s 2 makes low energy contributions especially important: in the range < 1 GeV contributes to 70% !

5. Achim G. Denig Radiative Return @ DA F NE Moriond -QCD 2004 Muon-Anomaly: Theory vs. Experiment Comparison Experimental Value with Theory - Prediction a m - 11 659 000 ∙ 10 -10 THEORY ’20/‘03 e + e - - Data: 2.7 s - Deviation t – Data: 1.4 s - Deviation Experiment ’20/‘04 Experiment BNL-E821 Values for m + (2002) and m - (2004) in agreement with each other. Precision: 0.5ppm New cross section data have recently lowered theory error: a) CMD-2 (Novosibirsk/VEPP-2M) p + p - channel with 0.6% precision < 1 GeV b) t -Data from ALEPH /OPAL/CLEO Theoretical values taken from M. Davier, S. Eidelman, A. Höcker, Z. Zhang hep-ex/0308213

6. Achim G. Denig Radiative Return @ DA F NE Moriond -QCD 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 ’= M pp 2 “Radiative Return” to r -resonance: e + e -  r + g  p + p - + g ds ( e + e -  p + p - g  ) dM pp r0r0 MC - Generator PHOKHARA = NLO J. Kühn, H. Czyż, G. Rodrigo Radiator-Function H(s) ISR H(s) s’s’

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

9. Achim G. Denig Radiative Return @ DA F NE Moriond -QCD 2004 Background p + p - g       e  e   signal region M TRK (MeV) mm      tail Rad. Bhabhas e + e -  e + e - g Pion-Electron-Separation by means of a Particle-ID algorithm using EmC-cluster- signature of tracks and TOF f  p + p - p 0 e + e -  m + m - g Kinematic Separation: „Trackmass“ M pp – dependent M TRK -Cut Residual background after cuts Fit MC-Spectrum for signal und background with free normalization parameters mm mm

10. Achim G. Denig Radiative Return @ DA F NE Moriond -QCD 2004 Luminosity Polar Angle [°]Acoll. [°]Momentum [MeV] Cut 55°< Q <125° p>400MeV Acoll.<9° MC Data Bhabhas L = N Bhabhas / s eff MC Experimental precision:Theory precision (radiative corrections): Large Angle Bhabha Events > 55º Excellent agreement Data – MC Background-”free” ( 0.5% p + p - ) Experimental uncertainty 0.3% BABAYAGA event generator (Pavia group) systematic comparison among other generators (Berends, KKMC, VEPP-2M), max. D =0.7% Theoretical uncertainty 0.5% (BABAYAGA)

11. Achim G. Denig Radiative Return @ DA F NE Moriond -QCD 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, Statistics: 141pb -1 of 2001-Data 1.5 Million Events 1.0% 0.5% 0.3% exp 0.5% theo r-w Interference High Statistics ! High Resolution ! Errors:

12. Achim G. Denig Radiative Return @ DA F NE Moriond -QCD 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 s ( e + e -  p + p - ) Vacuum Polarization Cross Section

13. Achim G. Denig Radiative Return @ DA F NE Moriond -QCD 2004 FSR Corrections 2 approaches for FSR corrections: Approach 1: “exclusive NLO-FSR“ - Correcting measured s ppg for FSR - Use MC with pure ISR in analysis - Add FSR-contrib. to s pp (ca. 0.8%) by hand Approach 2: “inclusive NLO-FSR“ - Correct for „unshifting“, i.e. s‘  M pp - Use MC with ISR + FSR in analysis Both methods in excellent agreement! For the error on the model dependence of FSR (scalar QED) we take 0.5% line = approach 1 + = approach 2 ratio = approach 1 / approach 2 Pion Formfactor after FSR corrections Suppressed by Acceptance cuts To be included !

14. Achim G. Denig Radiative Return @ DA F NE Moriond -QCD 2004 Muon Anomaly a   = ( 389.2  0.8 stat  4.7 syst  3.7 theo ) 10 -10  We have evaluated the dispersions integrals for the 2-Pion-Channel in the energy range 0.35 < M pp 2 <0.95 GeV 2  Comparison with CMD-2 in energy range 0.37 < M pp 2 <0.93 GeV 2 (376.5  0.8 stat  5.4 syst+theo ) 10 -10 (378.6  2.7 stat  2.3 syst+theo ) 10 -10 KLOE* CMD2 * Error on model dependence FSR and VP not included!  Discrepancy of ca. 10% between e + e - - Data und t – Data (ALEPH) for M pp 2 > 0.6 GeV 2 KLOE – data confirms discrepancy with respect to t – data ! Explanation: m(r 0 )  m(r  ) ???

15. Achim G. Denig Radiative Return @ DA F NE Moriond -QCD 2004 |F  | 2  CMD2 — KLOE 0.50.70.9 0 20 40 10 30 0

16. Achim G. Denig Radiative Return @ DA F NE Moriond -QCD 2004 Summary  We have proven the feasibility to use the Radiative Return to perform a high-precision measurement of the hadronic cross section at the f -factory DA F NE  Statistical Error is negligible  In the energy range M pp 2 > 0.6 GeV 2 we do reproduce the large deviation seen by t -data with respect to e + e -  Our evaluation of the hadronic contribution of the muon anomaly confirms the deviation btw. Theory and Experiment of about 3 sigma A draft for a paper is under collaboration-wide review! and in this sense data has still to be considered as PRELIMINARY

17. Achim G. Denig Radiative Return @ DA F NE Moriond -QCD 2004 Outlook  Study events at large photon angles to access lower M  2 region Photon tagging will be possible in this case  Use mmg events for normalization advantages from experimental and theoretical point of view  Check FSR parametrization (scalar QED) by testing the Charge Asymmetry 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

18. Achim G. Denig Radiative Return @ DA F NE Moriond -QCD 2004 Work supported by: Emmy – Noether – Programm