Using RooFit/RooStat in rare decay searches Serra, Storaci, Tuning Rare Decays WG

Introduction (RooFit/WorkSpace) 1. RooFit is a tool for: ◦Modelling Pdfs; ◦Generate toy data ◦Performing likelihood fit to any dataset 2. RooWorkspace: ◦New object in RooFit/Root ◦Easy to use and useful for sharing Pdf, Dataset.. ◦Can be saved in a file.root

Goals Extracting the Branching ratio with an unbinned likelihood fit ◦Automatically propagate the error to the final answer ◦Increase the statistical power (partially already presented in Bs  µµ WG see ()) Assumption: ◦We have a control channel for describing the signal Pdfs ◦The sidebands perfectly describe the background under the peak

The Bs  µµ toy example Signal: flat polynomial Background: exponential e -11.7GL to match road map prediction in the sensitive region Signal: gaussian Background: flat polynomial

Toy description For each toy we produce three statistically independent samples (E.g. 1 year, BR=3.5·10 -9 ): 1.20K signal like events (control channel Bd  ππ like) 2.70K background like events (sidebands) peak like events (S+B) In reality all numbers are poisson fluctuating We extract BR using three different methods and we compare the result.

Cut based method GL cut optimization with FOM for 3σ sensitivity (Punzi method)

Binned MFA

Binned MFA II Road-Map recipit : Calculate Δχ 2 for different BR hypotheses

Unbinned likelihood fit 1.Fit: Use the sidebands to build the background Pdf Pdf_bg = GL(RooKeysPdf) Bs(Pol) Use control channel to build the signal Pdf Pdf_sg = GL(RooKeysPdf) Bs(gauss) 2. Build the Signal+ background Pdf: Pdf_peak = Ns Pdf_bg + Nb Pdf_bg 3. Simulneous fit of side-bands and peak to extract Ns Kernel estimation in High energy Physics (K. Cranmer): (non parametric Pdf) Kernel estimation in High energy Physics (K. Cranmer): (non parametric Pdf)

Pdfs used for generating/fitting Pdf peak : Ns Pdf signal (GL, Bs mass) + Nb Pdf background (GL, Bs mass) Fitting the shape from the control channel: In the experiment B d  ππ

Pdf peak : Ns Pdf signal (GL, Bs mass) + Nb Pdf background (GL, Bs mass) Fitting the shape from the control channel: In the experiment B s  ππ flatpolynomial esponential Keys Pdf Pdfs used for generating/fitting

Comparison between the resuls For more plots and comparison look at: () All three methods give a similar sensitivity. Unbinned method ~10% better.

Some more plots 2fb -1 of nominal data taking Assuming SM BR 1fb -1 of nominal data taking Assuming NUHM BR

RooStat Roostat is brand new package in RooFit aimed at: 1.Streamline statistical interpretation of measurement; 2.Facilitate future combination of measurements (e.g. Higgs measurement at ATLAS/CMS), using the RooWorkSpace. 3.So, RooFit enables to combine the information from various Pdfs, RooStat deals with the answer; It is developed by RooFit/Root/ATLAS/CMS (next tutorial in november) () RooStat is pratically a tool for computing and plotting confidence intervals enbedded in RooFit.

Nuissance parameters Other nuissance parameters for the Background: Nb number of Bg events (Poisson distribution) P0 (Bs mass Pdf shape parameter)  (Gaussian 10% error) All the parameters you measured in the experiment (Nb, p0, Br(Bd  JpsiK*) etc…) can be extracted by a likelihood fit and RooStat gives you back the Pdf of the parameters (posterior), which you would use as a prior for the nuissance paramters.

Some comments 1.There are two kind of nuissance parameters: those you get from the Pdg (type II), those you measure somewhere else in the experiment (typeI); 2. Using the posterior you got somewhere else in the experiment, for nuissance parameters (typeI) is equivalent of doing a simultaneous fit. 3. Probably we want to give the result as: Br = Br0+ stat error + syst1+ syst2+syst3… This is easy to do fixing the value of the nuissance parameters before the scan. 4. The advantage of this approach is that it is easy to combine the results and take into account systematycs even with no gaussian errors.

Profile likelihood 68% confidence interval. Fit your model twice: once with everything floating, once with signal = 0 Wilks’s theorem: This quantity approaches asymptotically a χ 2 distribution with a degree of freedom equals to the number of parameters.

Combining results Getting LHCb workspace Getting ATLAS workspace Plotting Combining Likelihoods LHCb ATLAS Combined It is easy to combine results! If we publish the workspace we can combine in the right way results with different systematics.

Cousins-Higland method(systematics) Called Hybrid-Calculator in RooStat You can compute CLs, CLb and significance. For instance for: Ns =160 Nb=70K (year of data taking) Result: Br= 13.4 · 10 -9, ~9 sigmas of significance ~4sigmas from SM You can think L(M|b) as a part of the model and L(b) as a prior. Many more statics methods than used in this talk… Look at:

The MCMC Chain Treating systematics: -Profile likelihood maximizes over nuissance parameters; -MCMC integrates the porterior over them (that’s the way you want to treat nuissance paramters of the second kind). Posterior for s MCMC is a technique which will produce a sampling of a parameter space which is proportional to a posterior. Nice for giving posteriors in many dimensions.

Constraining Wilson coefficients Replacing with BR with its expression as a function of the Wilson coefficients we can plot contours for Cp, Cs This could be useful for combining different measurements. Lot of nuissance parameters (but easy to implement)!

Constraining a particular 2HDM Function of the charged Higgs mass You can pick-up a particular model and constraining its parameters. Easy to combine results: E.g. you can insert a prior for tgβ (or Higgs mass) coming from other measurements (e.g. ATLAS/CMS) and take into account; You can give a Posterior for tgβ which theorists could use for their predictions.

Conclusion