The Hadronic Cross Section Measurement at KLOE Marco Incagli - INFN Pisa on behalf of the KLOE collaboration EPS (July 17th-23rd 2003) in Aachen, Germany

Still measuring hadronic cross section: why? The hadronic cross section is a fundamental tool to evaluate the hadronic contributions to a  and to  (M Z ) These quantities are not evaluable in pQCD, but one can use DATA by means of optical theorem + analyticity: For example a  can be evaluated with the dispersion integral: Im[ ]  | hadrons | 2 a  had = K(s) ~ 1/s (kernel function)

The factors 1/s and  (e  e   hadr) in the integrand of the dispersion relation make the low energy region and the large resonances particularly relevant The e  e      channel accounts for ~70% of the contribution both to a  had and to   (a  had ) Contributions, as of today, to the error   (a  had )  (  s<0.5GeV)  (except  )  (  region)   rest (<1.8GeV) rest (1.8-5 GeV) pQCD (>5GeV)   (a  had ) (from Davier, Eidelman, Hoecker, Zhang)

The role of the  a  HAD can also be evaluated starting from  data and using the (approximate) isospin invariance The recent very precise BNL determination of a  and some discrepancies between the value of a  HAD as evaluatated with ee energy scan and  data, make a new measurement relevant eeee    

 (had) through the radiative return at KLOE the Radiative Return A way to get the hadronic cross section  (e + e      ) vs Q 2 at a fixed energy machine: the Radiative Return (Binner, Kuehn, Melnikov, Phys.Lett. B 459 (1999) 279) EEEE Q2Q2Q2Q2 Radiation function H ( Q 2,   )

Radiative ReturN: PROs and CONs luminosity and energy scale is estabilished at  s=M  and applies to all values of M  2 =Q 2 do not need to run the collider at different energies  requires precise understanding of radiative processes MC used by KLOE : PHOKHARA ver.2.0 (on Tuesday 10, Jul 2003 we have received ver.3.0 which includes FSR!)

DA  NE e + e - machine at Frascati (Rome) e + e   s ~ m  = MeV beams cross at an angle of 12.5 mrad LAB momentum p  ~ 13 MeV/c BR’s for selected  decays K+K-K+K- 49.1% KSKLKSKL 34.1%  +       15.5% ee e+e+ KLOE detector Cross sections:  3.3  b ee  b ee  b  e  o   b   b

KLOE detector and Fiducial Volume Definition of fiducial volume: 50 o <   <130 o   165 o where  is the two-pion system This cut enhances the signal wrt ee  events in which the photon is radiated from the pion (final state radiation: FSR)    6 m 7 m The price is that the kinematic region below Q 2 =0.3GeV 2 cannot be probed by these small photon angle events

Getting the  cross section L=140.7pb -1 of data collected in  10 6 evts  ~11000 evts/pb <Q 2 <0.97 GeV 2 ( MeV) Bin width = 0.01 GeV 2 (~7 MeV) To get the cross section must evaluate: background ; efficiencies ; luminosity Background Selection efficiencyLuminosity  events M  2 (GeV 2 )       number of events (x10 3 )

Background rejection I - e/  separation  e/  separation using a likelihood method: electron and pion likelihood definition based on TOF and cluster shape the log of the ratio of the two likelihoods is the discriminating variable eff(  ) ~ 98% eff(e) ~ 3% log(L pion /L electron )  signal + bkgd events       events e + e   events

Kinematic separation between signal and background in the (M  2,M TRK ) plane where M TRK is defined as: (p  -p  -p  ) 2 =p  2 =0 with: p  =(  p  2 +M TRK 2,p) this cut effects multiphoton processes (ee  ) efficiency evaluated using MC Background rejection II - closing the kinematics       e  e   signal region M   (GeV 2 ) M TRK (MeV)       tail 

Efficiency of kinematic separation and FSR The efficiency of the (M  2,M TRK ) cut has been evaluated by MC This efficiency evaluation does not include  events with a FSR photon M TRK efficiency M  2 (GeV 2 )  A preliminary run with the new PHOKHARA shows that the FSR contribution is at most 2-3% As of now, we do not apply any correction for FSR and add a contribution of 2% to the systematic error M  2 (GeV 2 ) 1 - )()&( 22 dQ ISRd dQ FSRISRd    without TrackMass cut with TrackMass cut A.Denig, H.Czyz  peak

Luminosity with Large Angle Bhabhas Luminosity measured with Large Angle Bhabhas: 55 o <  e <135 o 2 independent generators used for radiative corrections: BABAYAGA (Pavia group):  eff = (428.8  0.3 stat ) nb BHAGENF (Berends modified):  eff = (428.5  0.3 stat ) nb Systematics from generator claimed to be 0.5% Experimental systematic error determined by comparing data and MC angular and momentum distributions Systematics on Luminosity Theory0.5 % Acceptance0.3 % Background (  ) 0.1 % Trigger+Track+Clustering0.2 % Knowledge of  s run-by-run 0.1 % TOTAL 0.5 % theory  0.4% exp = 0.6 %

Summary of systematics  Experimental Acceptance0.3% Trigger0.2% Tracking0.3% Vertex1.0% Likelihood0.1% Track Mass0.2% BKG subtr.0.5% Unfolding0.6%  TOTAL1.4% (  1%)  Theory Luminosity0.6% Vacum Pol.0.1%  TOTAL0.7%  FSR (NNLO processes) 2.0% (  <1%) Systematic error can be reduced to in a short time scale

Observed cross section Absolute e  e       cross section after bkg subtraction To get  ( e  e      ) we need the H(Q 2 ) function e  e       ISR (  Radiation function H(Q 2 ) H(Q 2 ) is obtained from PHOKHARA MC setting F  (Q 2 )=1 and swithcing off vacuum polarization  ( e  e      ) ~ d  /dQ 2 (nb/GeV 2 ) M  2 (GeV 2 ) ee ee     F  (Q 2 ) ee ee      V.P.  

Hadronic cross section Hadronic cross section after dividing by the function H(Q 2 ) The cross section to be inserted in the dispersion integral is the bare cross section e  e       d  /dQ 2 (nb/GeV 2 ) M  2 (GeV 2 ) Must correct for running of   (s) (correction to  s   had (s) from F. Jegerlehner

Preliminary value for a  had In order to see how our result compares with existing data, we have integrated the bare cross section in the same region covered by CMD2 (0.37<Q 2 <0.95):  a  had (0.37:0.95) =  1.1 stat  5.2 syst  2.6 theo (  0. FSR) The published CMD-2 result is :  a  had (0.37:0.95) =  2.6 stat  2.2 syst+theo The two numbers are compatible, given the systematic error, but FSR corrections must be included before performing a detailed point to point comparison

Comparison e + e  vs  data Q 2 KLOE  a  had CMD2*  a  had 0.37:  4.1 ( FSR)249.7  :  2.1 ( FSR)119.8  % relative difference  The difference with CMD2 value is mostly below the  peak  It is very difficult, with our data, to explain the discrepancy between e + e  and  data in the region above the  resonance * our evaluation based on CMD2 published table Q 2 (GeV 2 )  peak

Summary and outlook  KLOE has shown the feasibility of using initial state radiation to obtain the hadronic cross section at low energies  Measurement using small angle photon events      is almost finalized  we have a new MC for a more precise evaluation of FSR  Preliminary result on  a  had slightly higher, but compatible with, CMD2 value  Next steps: Finalize current analysis Study events at large photon angles      which allow us to cover the region (2m  ) 2 <M  2 <0.35 GeV 2 Use  events as normalization sample to reduce the systematic error