HZ Recoil Analysis: Selection & Fitting

1. HZ Recoil Analysis:Selection & Fitting LCD WG6 Meeting, 03/04/2012 J.S. Marshall, University of Cambridge

2. HZ Recoil Analysis - Reminder • Relevant processes for this study are the recoil reaction e+e-HZHff, commonly called Higgsstrahlung. • By detecting decay products of the Z, can search for Higgs signals without further assumption about Higgs decay modes: “model independent analysis”. • For CDR V3, will search for decays Z and Zee: “X” and “eeX” channels. • Signal is selected by identifying two well-measured leptons in final state, yielding Z mass. Can then compute recoil mass: s = 500GeV Lint = 500fb-1 mH= 120GeV No polarization

3. Requests and Production Status Status on 27/03/2012:

4. Discriminant Variables • Previously, discussed procedure for finding events with two leptons produced by Z-decay. • Events passing di-lepton selection examined with aim of background rejection in mind. • Know that selection will be rather difficult at s=500GeV and with radiative effects.

5. Discriminant Variables

6. Selection - TMVA • Use ROOT TMVA to perform selection. Allows simple cut optimization and comparison of multivariate techniques. • Begin by making a few simple selection cuts to quickly veto background whilst leaving signal largely unharmed. • Use TMVA to suggest a series of cuts, choosing to use those that approximate to 90% signal efficiency for X. Cuts for 90% signal efficiency Pass Di-Lepton ID 30 GeV < Mdl < 120 GeVMrecoil < 380 GeVPTdl > 65 GeVacopdl < 2.8DPTBal > -100 GeV

7. Selection - BDT • Events passing selection cuts given to TMVA for evaluation of different multivariate techniques. • TMVA uses 50% of input events for training and 50% for testing, performing overtraining checks. • Input variables: Mdl, PTdl, cosdl, acoldl, acopdl, DPTBal • Best performance (>20% purity): Boosted Decision Tree

8. Selection - BDT • BDT also appropriate for signal selection in more difficult eeX channel (but could move to MLP). • Can achieve small improvement with more aggressive initial cuts. However, this can lead to smaller samples for BDT training and hence overtraining. TMVA overtraining report OK: • Application of full selection procedure removes all events from 2-fermion background test samples.

9. Di-lepton Mass • Choice of BDT cut value currently a little arbitrary: simply try to maintain 30-40% signal efficiency.

10. Recoil Mass • Will try to fit these distributions to extract mH, nSig, nBkg • Knew selection would be difficult. For comparison, scale results to ILD LoI cross-sections and luminosity. • For ILD LoI analysis, reduced radiative effects also result in better Higgs mass peak. Scale to ILD LoI , L

11. Kernel Estimation • Need to model signal component of recoil mass distribution. • Take half of selected signal and fit this “reference sample” using Simplified Kernel Estimation. • Signal shape is approximated by sum of many Gaussians, one for each bin in the reference sample. • Transformation x’ = x – mH allows sensitivity to Higgs mass; scaling distribution allows sensitivity to no. of signal events.

12. Background Fit • Need to model background distribution for any given number of selected background events. • Could just use available MC samples, but ideally want to remove statistical fluctuations. • Choose to fit shape of selected background – 4th order polynomial seems to be OK. • In final fit to recoil mass distribution, won’t vary background position or shape, just normalization.

13. Predicted Distribution • Using predicted signal and background, can create a prediction for any parameters mH, nSig, nBkg: mH = 120 GeV nSig = 1000 nBkg = 200 mH = 120 GeV nSig = 200 nBkg = 1000 X mH = 50 GeV nSig = 500 nBkg = 1000 mH = 200 GeV nSig = 500 nBkg = 1000

14. Fit Distribution • To produce input/fit distributions, use remaining half of signal sample, scaled back to 500fb-1. Add background by scaling polynomial fit and introducing Poisson fluctuations. • Creates input distributions shown below. Error-bars reflect fact that both signal and background components derived from high statistics samples (L=25ab-1). • Fit procedure uses MINUIT to vary mH, nSig and nBkg, producing a negative log likelihood value for each comparison of input and predicted distributions:

15. Results • X sample best fit results: • Trust MINUIT to provide error measurements for each parameter. In the case of mH, 1 shift from best-fit increases negative log likelihood by 0.5 • Will try to further optimize selection (in particular, will try varying BDT cut), but don’t expect to be able to extract parameters with much greater precision.

16. Results • eeX sample best fit results: • Approach for eeX sample not fully optimized, as have tried to maintain consistency with treatment of X sample. Could introduce differences in selection (currently only BDT training differs).