Update on: An iterative method to correct a factorizable efficiency

1. Update on:An iterative method to correct a factorizable efficiency Fabian Jansen Nicola Serra Niels Tuning Studies to correct acceptance effects in the Forward-Backward-Asymmetry in Bd→K*μμ

2. Outline • Reminder of the iterative method • Previous results with the iterative method • RDWG meeting 30 September 2009 • Retrieved the factorizable efficiencies of μ-μ+ K+/-π-/+ in variables p and η. • Improvement of previous result • Bin-size and low statistics effects • Overview of current results Previous presentations : • Rare Decay Working Group meeting 30 September 2009 • Rare Decay Working Group meeting 18 February 2009 • Angular Acceptance meeting 28 April 2009 Rare Decays Working Group

3. The iterative method • Goal : Forward-Backward Asymmetry (AFB) in Bd→(K*→K+/-π--/+)μ-μ+ • Unknown acceptance/efficiency effects in Bd→(K*→K+/-π--/+)μ-μ+ • Determine efficiency from control channel Bd→(K*→K+/-π--/+)(J/Ψ →μ-μ+) • Use efficiency from control channel Bd→K*J/Ψ to reweight Bd→K*μ-μ+ events • Create AFB with reweighted Bd→K*μ-μ+ events However • Many variables to determine efficiency in, with relatively little events • 4 particles K+/-π--/+μ-μ+ with variables p and η = 8 variables • 10 bins per variable = 108 bins • needs >108Bd→K*J/Ψ events to fill • Bd→K*J/Ψ does not cover full phase space as Bd→K*μ-μ+ • In Bd→K*J/Ψ √s = mass(μ-μ+) is limited to J/Ψ-mass. This correlates μ-μ+ variables A way out • If factorizable into single-particle efficiencies : ε(K+/-π--/+μ-μ+) =ε(K+/-) ε(π--/+) ε(μ-) ε(μ+ ) • 4 x 102 = 400 bins in stead of 108 • efficiencies uncorrelated by definition Rare Decays Working Group

4. The iterative method • With • P(K,π,μ-,μ+) is the physics probability of producing an event • ε(K,π,μ-,μ+) is the efficiency of detecting an event then find 4 single-particle efficiencies e(K), e(π), e(μ-) and e(μ+) , such that • e(K) ∫dπdμ-dμ+ P(K,π,μ-,μ+) e(π)e(μ-)e(μ+) = ∫dπdμ-dμ+ P(K,π,μ-,μ+) ε(K,π,μ-,μ+) • e(π) ∫dKdμ-dμ+ P(K,π,μ-,μ+) e(K)e(μ-)e(μ+) = ∫dKdμ-dμ+ P(K,π,μ-,μ+) ε(K,π,μ-,μ+) • e(μ-) ∫dKdπdμ+ P(K,π,μ-,μ+) e(K)e(π)e(μ+) = ∫dKdπdμ+ P(K,π,μ-,μ+) ε(K,π,μ-,μ+) • e(μ+) ∫dKdπdμ- P(K,π,μ-,μ+) e(K)e(π)e(μ-) = ∫dKdπdμ- P(K,π,μ-,μ+) ε(K,π,μ-,μ+) In wordsε(K,π,μ-,μ+) and e(K)e(π)e(μ-)e(μ+) give equal effective efficiencies In other words e(K)e(π)e(μ-)e(μ+) is the projection of ε(K,π,μ-,μ+) onto factorizable efficiency • If ε = ε(K+/-)ε(π--/+)ε(μ-)ε(μ+ ) factorizable, then e(particle)= ε(particle) • Calculate e(particle) (for example e(K)) iteratively via or rather, to ensure convergence, with suitable y and α via • I choose to do this binned, i.e. K, π, μ- and μ+ are divided into bins. Rare Decays Working Group

5. Previous toy results • Shown in Rare Decay Working Group meeting of 30 September 2009 • With toy, retrieved efficiencies in 2 variables of all 4 particles. • Confusion at the RDWG meeting of 30 September 2009 • Two effects in any p-η bin of a particle • Bin-size: events may not be spread out evenly throughout a p- η bin • Low statistics in some corners of phase space Rare Decays Working Group

6. Improved previous toy result • Mitesh proposed to use an “infinite” event sample, so that bin-sizes can be chosen small and statistics is large. • We do not have an infinite event sample, but can do the following: • Rather thancuttingevents, weight the events with the toy input efficiency. Then there are no fluctuations due to statistically cutting. Small statistics plays no role! • Weight always with the toy input efficiency calculated in the center of a bin, independent of where in the bin the event falls. The bin size plays no role! • The next slide shows the result of the above • Sample of 100.000 Gauss generated Bd→(K*→K+/-π-/+)μ+μ- events (not same Gauss as slide 5!) • K+/-, π--/+ , μ- and μ+ in variables p (absolute momentum) and η (pseudo rapidity) • Every p in 10 bins , every η in 4 bins • Toy efficiencies • This 10 times for 10 different samples give 10 iteration results giving an average result and error Rare Decays Working Group

7. Improved previous toy result Toy input efficiency Output iterated efficiency The iterative procedure exactly reproduces the toy input efficiency! Rare Decays Working Group

8. Improved previous toy result • As an algorithm the iterative method does what it is supposed to do • Any deviation of the iterative result with the input is due to • Bin-size effects : the bin size does not represent well the physics and/or the input efficiency in that bin • Small statistics : relatively large fluctuations in the data; the data does not represent well the underlying efficiency Rare Decays Working Group

9. Iterate and reweight 1 • DaVinci generated events • Sample of 880858 DaVinci generated Bd→(K*→K+/-π-/+)μ+μ- events • Apply event selection • Retrieve efficiencies • p : 10 bins in the ranges μ+/- : 0-200GeV , K+/- : 0-150GeV , π--/+ : 0-100GeV • η : 8 bins in the ranges 1.5-5.5 • Reweight events • event contributes 1/efficiency to event distribution and 1/efficiency^2 to variance • if event is out of iteration range, or event has zero efficiency, then it gets efficiency 1 • Compare event distributions • For these results I used the same sample for reweighting as for iterating • I have used only MC truth kinematics Rare Decays Working Group

10. πion p efficiencies and distributions • Top plots : iterated efficiencies (normalized to average πion efficiency) • Bottom plots • red line : events before reconstruction/identification/selection • green line : events after reconstruction/identification/selection Rare Decays Working Group

11. πion η efficiencies and distributions • Top plots : iterated efficiencies (normalized to average πion efficiency) • Bottom plots • red line : events before reconstruction/identification/selection • green line : events after reconstruction/identification/selection Rare Decays Working Group

12. πion event distributions • red points : distributions before reconstruction/identification/selection • green points : distributions after reconstruction/identification/selection • black points : reweighted distributions eta p(MeV) 1st p bin Need finer binning in this low momentum region Big worry is large statistical uncertainty due to events with small efficiency/large weight Rare Decays Working Group

13. Decay parameters distributions s(GeV2) thetaL We think due to low momentum events thetaK phi Rare Decays Working Group

14. Iterate and reweight 2 • Variable binning : fine binning for small p, course binning for large p • p : log-type binning in all range • η : 10 bins in the ranges 1.5-5.5 Rare Decays Working Group

15. πion p efficiencies and distributions • Top plots : iterated efficiencies (normalized to average πion efficiency) • Bottom plots • red line : events before reconstruction/identification/selection • green line : events after reconstruction/identification/selection Rare Decays Working Group

16. πion η efficiencies and distributions • Top plots : iterated efficiencies (normalized to average πion efficiency) • Bottom plots • red line : events before reconstruction/identification/selection • green line : events after reconstruction/identification/selection Rare Decays Working Group

17. πion event distributions • red points : distributions before reconstruction/identification/selection • green points : distributions after reconstruction/identification/selection • black points : reweighted distributions eta p(MeV) Finer binning Better agreement in this low momentum region Rare Decays Working Group

18. Decay parameters distributions s(GeV2) thetaL Better agreement with this binning thetaK phi Rare Decays Working Group

19. Forward Backward Asymmetry Before cuts After cuts reweighted s(GeV2) Rare Decays Working Group

20. Conclusive remarks • As an algorithm the iterative method does its job. • The method iterates and converges for two variables in all four particles • In toy tests discrepancies between input and iterative output efficiencies are thought to be the result of bin-size and small statistics effects. • A first effort is made to release the iterative method on DaVinci generated events • Reweighted event distributions do not everywhere agree with input distributions • Reweighting does not improve AFB • Regions of phase space with very low efficiency give large weights = large statistical error • How to incorporate regions of phase space that you do not see? Rare Decays Working Group

21. Extra slides

22. 30 September 2009 • Shown in Rare Decay Working Group meeting of 30 September 2009 • Iteratively retrieved efficiencies in 2 variables of all 4 particles. • Sample of 100.000 Gauss generated Bd→(K*→K+/-π-/+)μ+μ- events • K+/-, π--/+ , μ- and μ+ in variables p (absolute momentum) and η (pseudo rapidity) • Every p in 10 bins , every η in 4 bins • Toy efficiencies • This 10 times for 10 different samples give 10 iteration results giving an average result and error • Results for the pion shown on the next slide Rare Decays Working Group

23. The πion input toy efficiency effective efficiency within bin iterated efficiency input fluctuations p = 4-8GeV p = 0-4GeV Sometimes deviation. Not sure why. η = 2.5-3.75 η = 3.75-5 Rare Decays Working Group