Measurement of the Hadronic Cross Section with KLOE Graziano Venanzoni INFN – LNF Frascati Seminar at BNL, 7 July 2004

Outline Motivation of s(e+e- hadrons) at low energy Status of amhad and comparison of e+e-hadrons vs t decays The KLOE experiment at the DAFNE f-factory Results on s(e+e-  p+p-) Conclusions & outlook G. Venanzoni Seminar @BNL – 7 July 2004

Motivation I will concentrate on these two items A precise measurement of low energy hadronic cross sections enters in many important tests of the Standard Model: Anomalous magnetic moment of the muon am= (gm-2)/2 Running fine structure constant at Z0 mass aQED(MZ) Test of CVC (hadronic t decays vs e+e-hadrons) I will concentrate on these two items G. Venanzoni Seminar @BNL – 7 July 2004

Hadronic contribution to am am is one of the most precise measurement in high energy physics (5 •10-7 relative accuracy!) Contribution to am amexp = (11 659 208  6)10-10 G.W. Bennett at. Al. 2004 EXP amth = amQED + amEW + amhad + amNO SM (?) EW amhad = amhad,LO+NLO + amhad,LBL LBL Had (LO+NLO) QED 10-10 G. Venanzoni Seminar @BNL – 7 July 2004

Contribution to the uncertainty on am The largest contribution comes from amhad Contribution to dam EXP EW LBL had (LO+NLO) K(S) 1/s; it emphasizes the role of low energies; particular important is the reaction e+e-  p+p- (below 1 GeV) QED 10-10 G. Venanzoni Seminar @BNL – 7 July 2004

Hadronic contributions to amhad 12 -  5 - 12 (+) 3.7 - 5 (+J/, ) 1.8 - 3.7 4 3 (+,) 2 > 4 (+KK) < 1.8 GeV Calculations based on Davier, Eidelman, Höcker, Zhang ahad 2p contrib. ahad 8% [2mp - 0.5 GeV] 54% [0.6 - 1.0 GeV] 10% [Rest<1.8 GeV] r <1.8 GeV 2[ahad] 2p contrib. dahad 8% [2mp - 0.5 GeV] 34% [0.6 - 1.0 GeV] 31% [Rest< 1.8 GeV] > 1GeV r <1.8 GeV 1% e+e- data only! G. Venanzoni Seminar @BNL – 7 July 2004

Estimate of amhad 1-1.5% 0.6% 1-5% L= 317.3 nb-1 So far, estimates of amhad from: Hadronic electron positron collider data (mostly from CMD2, SND) Measurement of s(e+e-  p+p-) with CMD-2 :0.6% syst. error 1-1.5% 0.6% 1-5% |Fp|2 L= 317.3 nb-1 114000  events in  meson region CMD2 Energy scan! 1 GeV G. Venanzoni Seminar @BNL – 7 July 2004

Estimate of amhad (II) 2) hadronic t- decays, which can be used with the help of the CVC-theorem and an isospin rotation (plus isospin breaking corrections) hadrons   W  e+ e– CVC: I =1 & V W: I =1 & V,A : I =0,1 & V However, amth(e+e-) – amth(t)  (15±8)10-10 G. Venanzoni Seminar @BNL – 7 July 2004

am SM prediction vs experiment 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 THEORY ’20/‘03 Reanalysis of e+e- e+ e- - Data: 2.7 s - Deviation t – Data: 1.4 s - Deviation Experiment BNL-E821 Values for m+(2002) and m-(2004) in agreement with each other. Precision: 0.5ppm Experiment ’20/‘04 G. Venanzoni Seminar @BNL – 7 July 2004

Comparison of e+e- vs. t for 2p channel Deviation btw. CMD-2 and t-Data in a limited Energy Range above the r-Peak! p p channel t-Data are systematically higher  10% ! Possible Explanation Fred Jegerlehner: m(r0)  m(r) ???  correct t-Data (but how much?) G. Venanzoni Seminar @BNL – 7 July 2004

Conclusions on am and e+e- vs t data: Many reasons to have a new measurement of s(e+e-  p+p-)! KLOE has already finished the analysis on this channel (using the radiative return), which I’m going to present you with today G. Venanzoni Seminar @BNL – 7 July 2004

Radiative Return e+ e-  g + Hadrons, 4mp2£ sp = ( mf2 –2mf·Eg) £ mf2 The standard method of measuring (e+e-hadrons) is an energy scan by varying the beam energy within the desired range. Since at DANE the collision energy is fixed, one uses the radiative return which exploits the process e+ e-  g + Hadrons, where the photon is emitted in the initial state (ISR). [Binner, Kühn, Melnikov] sp , the invariant mass of the hadronic system, varies continuously between: 4mp2£ sp = ( mf2 –2mf·Eg) £ mf2 In this approach the overall normalisation enters only once! However careful evaluation of radiative corrections: PHOKHARA Generator (J. Kühn, H. Czyż, G. Rodrigo) G. Venanzoni Seminar @BNL – 7 July 2004

DAFNE: a f-factory at INFN-National Laboratories in Frascati (near Rome) Main Rings Linac Damping ring Beam test facility KLOE hall Synchrotron light G. Venanzoni Seminar @BNL – 7 July 2004

DAFNE : e+ e - high luminosity collider (Ldesign= 5x1032cm-2s-1) set at the F peak: s = MF = 1.02 GeV s(F)  3.3 mb a f-factory is mostly a kaon factory kaons are produced back to back in the CoM with |p|~110 MeV e+e- in two separate rings with crossing angle 25mrad at IP (small F momentum pF13MeV) DEAR Decay BR(%) f  K+ K- 49.1 f  KS KL 33.8 f  r p / p+p-p0 15.6 f  h g 1.26 G. Venanzoni Seminar @BNL – 7 July 2004

DAFNE performances DAFNE Parameters  L(pb-1) 450 pb-1 from 2001-2002 Design 2002 (KLOE) N bunches 120+120 51+51 Lifetime (mins) 120 40 Bunch current(mA) 20 Lbunch (cm-2s-1) 4.4 · 1030 1.5 · 1030 Lpeak (cm-2s-1) 5.3 · 1032 0.8 · 1032 Standard analysis sample: 450 pb-1 from 2001-2002 Beam trajectory length ~ 98 m Beam crossing frequency 368.25 MHz Bunch spacing : 2.7 ns Bunch sizes @ I.P.: sx sy sz 2mm 20 mm 3 cm Lpeak = 2 · 1032 cm-2s-1 L int / day = 10 pb-1 L int / year = 2 fb-1 (2109KSKL) 2004 goal G. Venanzoni Seminar @BNL – 7 July 2004

Physics reach vs Integrated luminosity 1999 2000 Today 2001 5 pb-1 50 pb-1 500 pb-1 5 fb-1 KS physics BR(KS  p+p-)/BR(KS  p0p0) BR(KS pen) f radiative decays f  f0g, a0g f  hg, hg KS semileptonic asymmetry, KS  3p0, KL  2p, KL gg, K  mn,pp,ppp,pen,ppen, s(e+e-  hadrons) to 1% Interferometry e/e to O(10-4) via double ratio rare KS,L decays, CPT tests G. Venanzoni Seminar @BNL – 7 July 2004

The KLOE detector Electromagnetic Calorimeter (EMC) Fine sampling Pb (0.5 mm thick) / Scifi (1 mm ø) Hermetical coverage High efficiency for low energy photons E/E = 5%/E(GeV) t = 50ps/E(GeV) Central drift chamber (DCH) Large detection volume Uniform tracking and vertexing in all volume Helium based gas mixture v = 1 mm pt /pt= 0.5% r, =200 m z = 2 mm Quadrupoles’ calorimeter (QCAL) Pb/Sci tile calorimeter covering quads inside KLOE G. Venanzoni Seminar @BNL – 7 July 2004

The KLOE detector DC Lead Scifi ECAL Quadrupoles End-cap ECAL SC coil B=6kG Lead Scifi ECAL DC Spherical Beam Pipe e- e+ Quadrupoles End-cap ECAL Spherical Beam Pipe G. Venanzoni Seminar @BNL – 7 July 2004

Kaon physics at KLOE: current status of the analyses KS  p0p0p0 Preliminary results KS  p+p-(g) KS  p0p0 Phys. Lett. B538 21 (2002) Update with ’01-’02 data KS pen Phys. Lett. B535 37 (2002) Preliminary update with ’01-’02 data K0 mass KLOE Note 181 (http://www.lnf.infn.it/kloe) KL  gg/KL  3p0 Phys. Lett. B566 61 (2003) KL  pen KL  pmn KL  p+ p- p0 In progress Vus CP violation & interference K+  p+p0p0 Preliminary results (hep-ex/0307054) G. Venanzoni Seminar @BNL – 7 July 2004

Hadronic physics at KLOE: current status of the analyses f meson parameters Preliminary results f  p+p-p0 Phys. Lett. B561 55 (2003) h  p+p-p0 h  3g hep-ex/0402011, submitted to Phys. Lett. f  hg Phys. Lett. B541 45 (2002) Update with ’01-’02 data in progress f  f0g, a0g Phys. Lett. B536 209 (2002), B537 21 (2002) s(e+e-  p+p-g) This talk ! G. Venanzoni Seminar @BNL – 7 July 2004

sp is the invariant mass Measurement of s(e+e-+) from e+e-+-g events Selection of +-g events Measurement of ds(e+e-+-g)/dsp Extraction of s(e+e-+) p+ e+ sp is the invariant mass squared of the 2 pion system ~Fp(s) e- p- G. Venanzoni Seminar @BNL – 7 July 2004

Selection of e+e-p+p-g: 1) acceptance cuts Side view e+ e- Front view p+ p- g Pion tracks at large angles 50o < qp < 130o NO PHOTON TAGGING Photons at small angles qg < 15o and qg > 165o are shadowed by quadrupoles near the I.P. • High statistics for ISR events Reduced background contamination Low relative contribution of FSR G. Venanzoni Seminar @BNL – 7 July 2004

Selection of e+e-p+p-g: 2) identification of pion tracks (PID method) To reduce Bhabha contamination, a -e separation is performed using a particle ID estimator based on: mTRK    e e  before cutting on particle ID estimator after cutting on m+ m- g p+ p-p0 mp TOF of charged clusters in EMC Shape and energy deposition of the cluster The event is selected if at least one of the charged tracks is identified to be a pion. mTRK is the mass of the charged particle, under the hypothesis that the final state consists of two particles with the same mass and one photon. G. Venanzoni Seminar @BNL – 7 July 2004

Selection of e+e-p+p-g: 3) rejection of m+m-g, p+p-p0 events rp preselection already applied mTRK (MeV) p+ p- p0 p+p-p0 Kinematical selection in the plane (sp,mTRK) p+p-gg tail p+p-g events Mtrk~mp correponds to ppg events Mtrk>mp corresponds to the multi-photon emission (ppgg): most of these events are retained by this cut p+ p- g m+m-g m+ m- g sp (GeV2) G. Venanzoni Seminar @BNL – 7 July 2004

+-g observed spectrum Ni/0.01GeV2 141.4 pb-1 of 2001 data were selected by the mentioned cuts After selection: 1 550 000 events (11000 evts/pb-1) statistical error/bin < 1% Our cuts select events with sp >550 MeV We will measure the cross section near threshold looking at the photon at large angle (analysis is in progress, see later) sp(GeV2) G. Venanzoni Seminar @BNL – 7 July 2004 Acceptance: qpp<15o (qpp >165o), 50o<qp<130o, ES>10 MeV

Measurement of ds(e+e-+g)/dsp An absolute measurement! Residual Background Signal Acceptance Luminosity Selection efficiency Unfolding of the experimental resolution is omitted G. Venanzoni Seminar @BNL – 7 July 2004

Estimate of residual background N. of events / 0.5 MeV data  mmg Residual contamination from +-0, , and Bhabha‘s is evaluated by fitting the shape of signal and background in the trackmass distribution for different slices of sp The estimated number of background events is then subtracted from the spectrum. Mpp2  [0.32,0.37] GeV2 c2 = 87.0/88 data sum of  and mmg G. Venanzoni Seminar @BNL – 7 July 2004

Estimates of the residual background (II) N. of events / MeV data  p+p-p0 Observed spectrum Total background estimate Mpp2  [0.38,0.42] GeV2 c2 = 104.4/88 data sum of  and p+p-p0 The systematic error on the background subtraction is <0.3% above 0.55 GeV2 G. Venanzoni Seminar @BNL – 7 July 2004 Federico Nguyen

Evaluation of efficiencies Trigger including Cosmic-ray Veto Eff. Total Efficiency Reconstr. Filter Tracking / Vertex 60% -e separation Trackmass blue = estimated from data and/or indep. control samples p+p-p0, p+p- Kinematics simulated by MC red = estimated from MC and compared with data sp(GeV2) G. Venanzoni Seminar @BNL – 7 July 2004

Unfolding MC • data The detector matrix “almost” diagonal 80% in the central bins sp true sp obs The detector matrix “almost” diagonal We unfold the spectrum using GURU (A. Höcker et.al./ALEPH), a package based on SVD decomposition Issues: - Reliability of MC simulation  - Correct choice of the regularization parameter MC • data Systematics: Bin-by-Bin changes for different values of the regularization parameter large (up to 3%)  uncorrelated systematic error! Due to nature of the dispersion integral the effect on am is almost negligible G. Venanzoni Seminar @BNL – 7 July 2004

Luminosity measurement * Data Babayaga (MC) (Pavia theory group) Bhagenf (MC) (Berends adapted by E. Drago and G. Venanzoni) track momentum (MeV) Large angle Bhabha: 55° < q < 125° acollinearity < 9° p  400 MeV BABAYAGA: sbha = ( 428.8 ± 0.3stat ) nb BHAGENF: sbha = ( 428.5 ± 0.3stat ) nb e- e+ g of s Theoretical Systematic Error = 0.5% Total Error = 0.6% G. Venanzoni Seminar @BNL – 7 July 2004 Federico Nguyen

The cross section ds(e+e-+g)/dsp Efficiencies: - Trigger & Cosmic veto Tracking, Vertex p/e- separation Reconstruction filter Trackmass-cut Unfolding resolution Acceptance ds/dMpp2 (nb/GeV2) sp (GeV2) r-w Interference Errors: 0.9% Background: e+ e- e+ e- g e+ e-  m+ m- g f  p+ p- po 0.3% Luminosity: Bhabhas at large angles seff = 430 nb, 0.3%exp 0.5%theo G. Venanzoni Seminar @BNL – 7 July 2004

|Fp(s)|2 2) Extraction of s(e+e- p+ p- ) Neglecting FSR emission: sp is invariant mass of the 2p Neglecting FSR emission: e+ e- p+ p- ~Fp(s) ~1 H(s)= = |Fp(s)|2 dsppg(sp)= s=sp s is invariant mass of the intermediate photon s H(s) From which we obtain G. Venanzoni Seminar @BNL – 7 July 2004

Fp(s) s s= mf2 mf2 Which Kind of FSR? The cross section e+e- p+p- has to be inclusive with respect to NLO FSR events: G. Venanzoni Seminar @BNL – 7 July 2004

LO FSR Corrections p+ e+ ~Fp(mf2) e- s=mf2 p- LO FSR is a background since the Pion form factor is evaluated at the same fixed scale s=mf 2 e+ e- p+ p- ~Fp(mf2) s=mf2 Must to be subtracted as much as possible! sp(GeV2) LO - FSR % This contribution becomes < 1% due to our acceptance cuts G. Venanzoni Seminar @BNL – 7 July 2004

NLO FSR Correction: simultaneous emission of ISR and FSR 10% FSR (nlo) /ISR 8% 6% 4% Before trackmass cut 2% This contribution is as large as 5% in low M2pp bins FSR contribution + cut efficiency are evaluated by MC (PHOKHARA Generator) 0% -2% After trackmass cut -4% 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 M2pp G. Venanzoni Seminar @BNL – 7 July 2004

Extraction of s(e+e- p+ p- ) in presence of simultaneous emission of ISR and FSR In presence of NLO FSR, our procedure must be modified since ssp p+ e+ sp dsppg(s)= ~Fp(s) e- ssp p- |Fp(s)|2 = p+ e+ sp H(s)= ~1 e- s=sp p- H(s) Acceptance corrections G. Venanzoni Seminar @BNL – 7 July 2004

which is inclusive in FSR (hard, soft & virtual) In this way we get: which is inclusive in FSR (hard, soft & virtual) p+ e+ e- s p- Remember that for am calculation we need spp inclusive w.r.t. FSR and corrected for VP (bare cross section) G. Venanzoni Seminar @BNL – 7 July 2004

FSR Correction:How to cross-check the above procedure? We have checked our procedure with a different method: N(e+e-  p+ p- gISR gFSR) Subtract FSR (nlo) contribution to the observed ppg spectrum subtract FSR contribution Apply the analysis corrections, as in the case of pure ISR s(e+e-  p+ p- gISR) s(e+e-  p+ p- ) Schwinger term 0.8% for s<1GeV2 gFSR 0.8 .. 0.9% Schwinger ‘90 Divide for radiator H Add (pointlike) FSR correction (1+dFSR) How much do they agree? G. Venanzoni Seminar @BNL – 7 July 2004

Excellent agreement (D = 0.002  0.001) FSR corrections: comparison of the two methods 2 Excellent agreement (D = 0.002  0.001) 1.05 Pion Formfactor (KLOE) Rel. difference inclusive - 1.04 exclusive approach 1.03 1.02 1.01 1. 1 0.99 0.98 0.97 D = 0.2% ± 0.1% 0.96 0.95 0.4 0.5 0.6 0.7 0.8 0.9 FSR systematics=0.3%, two contributions: 0.2% = difference incl.-excl. correction we put an upper limit of 20% for the model of scalar QED: 20% * 1% = 0.2% G. Venanzoni Seminar @BNL – 7 July 2004

Charge asymmetry: test of FSR model At large Photon angles the amount of FSR is large! test the model of scalar QED (i.e. poinlike pions), which usually is taken for the radiation of photons from pions in MC generators  Measure Charge Asymmetry and compare data with MC  Charge asymmetry is due to different C-Parity of ISR- and FSR-amplitudes  preliminary results in a complementary ppg – analysis at large photon angles show a good agreement of data with the model of scalar QED 50 70 90 110 130 -20 -10 20 10 Asymmetry [%] Polar Angle [°] Data MC K L O E P R E L I M I N A R Y G. Venanzoni Seminar @BNL – 7 July 2004

CMD-2 error: exp.+syst.+stat. Cross Section s(e+e-  p+p-) TOTAL ERROR 1.3% To be compared the 0.9% CMD-2 error: exp.+syst.+stat. G. Venanzoni Seminar @BNL – 7 July 2004

2p contribution to amhadr At large values of sp (>mr2) we are consistent with CMD and therefore we confirm the deviation from t-data! . Pion Formfactor CMD-2 KLOE 0.4 0.5 0.6 0.7 0.8 0.9 sp [GeV2] 45 40 35 30 25 20 15 10 5 2p contribution to amhadr We have evaluated the Dispersions Integral for the 2-Pion-Channel in the Energy Range 0.35 <sp<0.95 GeV2 ampp = (388.7  0.8stat  3.5syst  3.5theo) 10-10 Comparison with CMD-2 in the Energy Range 0.37 <sp<0.93 GeV2 (375.6  0.8stat  4.9syst+theo) 10-10 (378.6  2.7stat  2.3syst+theo) 10-10 KLOE CMD2 1.3% Error 0.9% Error G. Venanzoni Seminar @BNL – 7 July 2004

Preliminary Conclusion Including KLOE result 1 KLOE has confirmed a 3s deviation btw. theory and experiment for (g-2)m! Including KLOE result Preliminary G. Venanzoni Seminar @BNL – 7 July 2004

Conclusions s(e+e- p+p-) KLOE has measured spp with 1.3% precision. The analysis is finished and we are going to publish it. KLOE confirms a 3s - deviation between the experimental and the theoretical value for the am, as well as 10% discrepancy with t-data above the r-peak We expect to reduce the systematic error well below 1%, by repeating the analysis with 2002 data. Improvements from theory are also expected in the next future (now our theoretical error on luminosity is 0.5%) Analysis with the photon at large angle (to study the region near the threshold) is in progress. See next slide G. Venanzoni Seminar @BNL – 7 July 2004

Measurement of s(e+e- p+p-) down to the threshold Measure s(pp) in the region close to threshold, Mpp < 600 MeV, responsible for 20% of ampp This region excluded by angular selection in small angle photon approach Complementary Analysis at large photon angles Mpp (MeV) 400 300 600 500 800 700 900 1000 2000 3000 4000 N(ppg) / MeV huge rp-Background large FSR-component Photon-Tagging possible investigate the possibility of an R-measurement, i.e. normalization to muons 2002 data ISR+FSR MC G. Venanzoni Seminar @BNL – 7 July 2004