Monte Carlo generators and radiative corrections used and needed in the KLOE ISR analyses. S. Müller

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1 Monte Carlo generators and radiative corrections used and needed in the KLOE ISR analyses S. Müller (for the KLOE -group) Radio MONTE CARlow WG Meeting in Beijing, October 008

2 Abs. Norm. vs ratio /µµ Measure the (ISR) - radiative cross section d ( ) /dm : using as normalization the integrated luminosity Ldt obtained from Bhabha events: obs d" ## +$ ($ ) dm ## = %N Obs & %N Bkg %M ## ' 1 ( Sel ' ) 1 Ldt Then extract from d ( ) /dm via theoretical radiator function H(s, M ): ( ) $ s d" M ##% (% ) ( ## ) " ## M ## & dm ## 1 H(s,M ## ) OR Obtain from the ratio of d ( ) / d µµ ( : " Born ## (M ## ) $ d" obs ##% /dm ## d" obs µµ% /dm ## " Born µµ (M ## )

3 3 Small angle event selection pion tracks at large angles 50 o < θ π <130 o Photons at small angles θ γ < 15 o or θ γ > 165 o high statistics for ISR events low relative FSR contribution suppression of φ + 0 background Region below 0.35 GeV kinematically suppressed photon momentum from kinematics: r p " = p r miss = #( p r + + p r # ) statistics: 40pb -1 3 Million Events

4 4 Large angle event selection pion tracks at large angles 50 o < θ π <130 o At least 1 photon with 50 o < θ γ <130 o and E > 50 MeV photon detected independent complementary analysis threshold region (m π ) accessible γ ISR photon detected (4-momentum constraints) lower signal statistics larger contribution from FSR events large φ π + π π 0 background contamination irreducible background from φ decays (φ f 0 γ ππ γ) Nr. of events / 0.01 GeV Preliminary 00 data events L = 40 pb -1 s [GeV ]

5 5 KLOE analyses symmary Small angle photon, absolute normalization with Bhabha events using 140pb -1 of 001 data Phys. Lett. B 606 (005) 1 Small angle photon, absolute normalization with Bhabha events using 40pb -1 of 00 data arxiv: hep-ex/ subm. to Phys. Lett. B Large angle photon, absolute normalization with Bhabha events using 40pb -1 of 00 data Large angle photon, absolute normalization with Bhabha events using 00pb -1 of 006 data (outside -resonance) Small angle photon, normalization with µµ events from data using 40pb -1 of 00 data Large angle photon, normalization with µµ events from data using 40pb -1 of 006 data (outside -resonance) Future In progress F π from π/µ using coll. events for 4 points around M φ

6 Acceptance corr. Observed Spectrum for ( ) events (Level3 Trigger) FILFO corr. Background Subtr. M Trk + E Miss corr. Unfolding (M Rec M True ) Corr. for border eff. in Acc. /e likelihood +TCA corr. Tracking corr. Trigger corr. Unshifting (M M ) Acceptance corr. KLOE small angle analysis flow MC+Detector simulation enter Strong dependence on MC and/or rad. corrections Observed Spectrum for µµ ( ) events (Level3 Trigger) FILFO corr. Background Subtr. Corr. for border eff. in Acc. M Trk + E Miss corr. Unfolding (M Rec M True ) /e likelihood +TCA corr. Tracking corr. Trigger corr. Acceptance corr. FSR ISR corr. Luminosity corr. Luminosity corr. d /dm ππ measurement Acceptance corr. Division by Radiator H (for large angle, add f 0 +ρπγ correction) Acceptance corr. ( µµ,isr /,IFSR ) Corr. for FSR F measurement Corr. for Vac. Pol. measurement F from ratio

7 % Small angle cuts: MC: FSR /(ISR + FSR) Phokhara M ππ [GeV ] % Large angle cuts: MC: FSR /(ISR + FSR) Phokhara M ππ [GeV ]

8 Unshifting : M ππ M γ Photon emissions from the pions changes the measured value of M ππ from the invariant mass squared of the virtual photon produced in the e + e - collision, M γ M ππ M γ Use special version of PHOKHARA which allows to determine whether photon comes from initial or final state build matrix which relates M ππ to M γ. ISR only: (M 0 ππ ) M γ = M ππ FSR photon present: M γ = M ππγ(fsr) e+e- + - FSR events ( lo FSR )are unshifted to M γ = 1.04 GeV M ππ Would be nice to have also for µµγ channel!

9 Unshifting : M ππ M γ Relative increase of events with 1 γ ISR and 1 γ FSR over pure ISR events at low values of M ππ increases the effect in this region for small angle analysis. M [GeV ] Effect is higher for large angle analysis due to the greater presence of FSR, especially at very high and very low M ππ

10 θ Σ correction (Acceptance) θ Σ is the angle of the photon (system) obtained from r the momenta of the two charged tracks in the small angle analysis: p " = p r miss = #( p r + + p r # ) π + γ r p " π This acceptance depends on FSR (as does the acceptance for θ γ in the large angle analysis) strong dependence on the implementation of FSR in PHOKHARA5/6/ Effect of second hard photon from FSR???

11 Final State Radiation (FSR) σ ππ needs to be inclusive with respect to final state radiation when used in the dispersive integral. Therefore the analysis has been designed to provide a final spectrum which is inclusive in FSR@(M γ ). Concerning the F π, we undress the spectrum from FSR by dividing for (1+η FSR ), which is calculated assuming radiation from pointlike pions (sqed) Net effect of FSR is ca. 0.8%

12 Radiator function - ISR-Process calculated at NLO-level PHOKHARA generator (Czyż, Kühn et.al) Theoretical Precision: 0.5% Biggest theor. uncertainty in SA analysis H(s,M ππ) s" d# $$% = # $$ (s) & H(s,M ππ dm ) $$ M ππ s is the collider energy. We obtain the radiator function technically by setting F π =1 in the PHOKHARA Monte Carlo generator, and generate ISR events inclusive in θ π and θ Σ : ) H(s,M "" ) = s # 3M "" "$ % # d& ""' (M "" 3 " dm "" MC F" (M "" ) =1 How well does the factorization of H work in the presence of FSR?

13 Luminosity: KLOE measures L with Bhabha scattering at large angles F. Ambrosino et al. (KLOE Coll.) Eur.Phys.J.C47: , < θ < 15 acollinearity < 9 p 400 MeV New: generator used for σ eff BABAYAGA (Pavia group): C. M.C. Calame et al., NPB584 (000) 459 C. M.C. Calame et al., NPB758 (006) e + new version (BABAYAGA@NLO) gives 0.7% decrease in cross section, and better accuracy: 0.1% e γ Systematics on Luminosity Theory Experiment TOTAL 0.1 % th 0.3% exp = 0.3% 0.1 % 0.3 %

14 Vacuum Polarisation For use in the dispersive integral for a µ, one needs to subtract effects from vacuum polarization (VP) to obtain a bare cross section σ 0 ππ : 0 (s) = " dressed % ## (s) $(0) ( ' * & $(s) ) " ## = " ## (s) /+(s) Points obtained from F. Jegerlehner s webpage (the only points which are publically available!) Correction is applied only to the cross section σ 0 ππ (not on σ ππγ and F π ). NOT APPLIED when comparing with F π from CMD/SND! Error on VP points introduces an relative error on the value of a µ of 0.1%.

15 Vacuum Polarisation Confronting the VP points from F. Jegerlehner s webpage with the one in MCGPJ shows some disagreement between 0.6 and 1 GeV : $ 1 ' & ) % 1" # Time ( s) ( % 1 ( ' & 1" #e$ Space ( s * )) MCGPJ $ 1 ' & % 1" # Space ( s ) )( % 1 ( ' & 1" #e$ Space ( s * )) Jegerlehner Fred is currently updating his function, as it does not yet include the recent results from BaBar in that region.

16 f 0 +ρπ correction φ (f 0 +σ)γ ππγ: φ πρ π(πγ): Checked with PHOKHARA 6.1 generator, latest Achasov model with parameters from KLOE f 0 π 0 π 0 analysis Contribution negligible in small angle analysis: (ISR+sQED+f 0 +ρπγ) / (ISR+sQED)

17 f 0 +ρπ correction φ (f 0 +σ)γ ππγ: φ πρ π(πγ): Checked with PHOKHARA 6.1 generator, latest Achasov model with parameters from KLOE f 0 π 0 π 0 analysis Contribution relevant in large angle analysis: (ISR+sQED+f 0 +ρπγ) / (ISR+sQED) Trkms cut w/o Trkms cut M ππ (GeV )

18 f 0 +ρπ correction As the interference between ISR and (FSR+f 0 ) leads to a non-vanishing forward-backward asymmetry, one can use this asymmetry to further optimize/scrutinize the model parameters Binner, Kühn, Melnikov, Phys. Lett. B 459, 1999 Czyz, Grzelinska, Kühn, hep-ph/04139 A = N("+ > 90 o ) # N(" + < 90 o ) N(" + > 90 o ) + N(" + < 90 o ) F.-b. Asymmetry M ππ (MeV) For this a (semi)analytical parametrization of the asymmetry as a function of the model parameters would be very welcome!!

19 Conclusions After the large improvement in the precision of the luminosity reference cross section with the biggest theoretical uncertainties for the small angle analyses come from the radiator function and the knowledge of FSR. Radiator function contributes 0.5% uncertainty Box graphs? Factorization? FSR enters in many places in the analysis (Unshifting, θ Σ,...) Second hard photon? FSR for muons (PHOKHARA Omega)? The same holds for the large angle analysis, where in addition one needs to control the contribution from scalar mesons. (Semi)analytic description of asymmetry? Both large angle analyses using the absolute normalization with 00 data ( on-peak ) and 006 data ( off-peak ) are in a very advanced state. Manpower?

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