Status of the Higgs to tau tau Carlos Solans 26th March 2010

Status of the Higgs to tau tau - 26th March 2010 Introduction The aim of this analysis is to set the exclusion limit and expected significance of a signal for the neutral MSSM Higgs in the ditau decay channel (and finally to lepton hadron) using a bayesian technique We will use visible mass instead of invariant mass to be able to analyze first data Similar analysis have been already presented in ATLAS for the CSC notes and in the Statistics forum We will innovate by incorporating template morphing Similar tools are available: RooStats, BAT We will use our own minimization package based on the very well known Minuit implementation in ROOT. Carlos Solans Status of the Higgs to tau tau - 26th March 2010

Status of the Higgs to tau tau - 26th March 2010 Bayesian analysis Starting from Bayes’ theorem for conditional probability, where the whole information for the event is contained in the posterior… The posterior probability for a set of parameters given the data is proportional to the likelihood of those parameters to the data times the prior for the parameters. If we assume that the prior for the parameters is uncorrelated, we can split it in a product of priors for each parameter We will incorporate systematic uncertainties via nuisance parameters (as priors). Another possibility will be to incorporate our knowledge about the constraints on the nuisance parameters into the likelihood, leaving the priors as non-informative. Anyways is accepted by the ATLAS Statistics forum Parameter of interest Nuisance parameters Data Carlos Solans Status of the Higgs to tau tau - 26th March 2010

Status of the Higgs to tau tau - 26th March 2010 Profiling In order to eliminate the dependence of the posterior on the nuisance parameters, we maximize the likelihood times the prior with respect to the nuisance parameters. The alternative is to marginalize the prior We obtain the maximum likelihood estimator of the nuisance parameters through and iterative procedure (maximization) called profiling In fact what we do is maximize the likelihood times the prior for the nuisance parameters. Where we consider the prior for the parameter of interest to be non-informative (flat) in the range As we will see, there is no need to include the prior for the data in the maximization. In both cases considered here it won’t affect the result. Maximum likelihood estimator x f(x) Carlos Solans Status of the Higgs to tau tau - 26th March 2010

Status of the Higgs to tau tau - 26th March 2010 Setting limits Given the posterior probability for the parameters given the data normalized to a given value, we can do a scan in the parameter of interest (cross-section) and compute the cross-section value at which 95% of the probability lies. We use the bayesian credibility limit (p-value) definition to define the upper exclusion limit to the Higgs cross section (θL) with p=0.05 For each cross section value we compute the posterior independent of the nuisance parameters which is proportional to value of the likelihood times the prior. Note the proportionality constant is the same for all values of the cross section. We obtain the upper limit cross section by numerically integrating the posterior normalized to zero cross-section. Avoid computing the proportionality constant We repeat this operation for many pseudo-experiments under the null signal hypothesis and compute the upper exclusion limit as the median of the distribution. θL for this pseudo-experiment Carlos Solans Status of the Higgs to tau tau - 26th March 2010

Setting limits summary For each pseudo-experiment we compute the value of the cross-section under which 95% of the integral lies The upper exclusion limit at 95% CL will be the median of the distribution for many pseudo-experiments Carlos Solans Status of the Higgs to tau tau - 26th March 2010

Estimating significance Given the definition of the Bayes factor as the ratio of posterior to prior odds of full signal strength hypothesis (θ1) to null signal hypothesis (θ0). Which is independent of the prior for the parameter of interest (and the prior for the data). This test statistic is commonly used in bayesian analysis in ATLAS To estimate the significance of a discovery, we generate many pseudo-experimental data under the background only (B) assumption and the signal plus background (S+B) assumption. We compute the p-value of the S+B data being a fluctuation of B data And convert the p-value into number of sigmas of a double sided gaussian distribution by means of the inverse normal cumulative distribution (Φ-1) Carlos Solans Status of the Higgs to tau tau - 26th March 2010

Estimating significance summary For a given cross section, we compute the B10 statistic for many pseudo-experimental data with signal and without signal. We compute the probability of S+B data being a fluctuation of B as the percentage of B10B that is over the median of the B10S+B distribution. Carlos Solans Status of the Higgs to tau tau - 26th March 2010

Status of the Higgs to tau tau - 26th March 2010 PHYSICS Carlos Solans Status of the Higgs to tau tau - 26th March 2010

Status of the Higgs to tau tau - 26th March 2010 Signal production Direct production Associated production Carlos Solans Status of the Higgs to tau tau - 26th March 2010

Status of the Higgs to tau tau - 26th March 2010 Background processes Z  tau tau t tbar QCD Carlos Solans Status of the Higgs to tau tau - 26th March 2010

Status of the Higgs to tau tau - 26th March 2010 MSSM Higgs Carlos Solans Status of the Higgs to tau tau - 26th March 2010

Status of the Higgs to tau tau - 26th March 2010 MSSM Higgs Carlos Solans Status of the Higgs to tau tau - 26th March 2010

Status of the Higgs to tau tau - 26th March 2010 Hands on profiling To start working on our analysis we need a set of efficiency distributions (templates) for our observable (Mvis). It is commonly accepted that the likelihood function is a poisson distribution where the mean value is the expected number of counts. In our case, the likelihood function is a binned likelihood function where the expected number of counts in each bin is a function of the parameter of interest and the nuisance parameters Our parameter of interest is the signal cross section: σA Nuisance parameters can be: Those that modify the number of counts in each bin: L Those that modify the shape of the template (In our case by taking into account two other templates): fj In both cases the prior for the nuisance parameters is a Gaussian p.d.f. Carlos Solans Status of the Higgs to tau tau - 26th March 2010

Common nuisance parameters The expected number of counts in each bin that will be used in the likelihood core is given by (without morphing): A pseudo-experiment is a Poisson fluctuation of contributing templates We fluctuate each bin of each template using a poisson PDF So that the observed number of counts (xi) can be built the same way as μi The un-normalized posterior takes into account systematic uncertainties on the nuisance parameters Carlos Solans Status of the Higgs to tau tau - 26th March 2010

Energy scale uncertainties Systematic uncertainties in the energy scale can be taken into account by the usage of “template morphing”. Search for Higgs bosons predicted in two-Higgs-doublet models via decays to tau lepton pairs in 1.96 TeV proton-antiproton collisions. e-Print: arXiv:0906.1014 [hep-ex] Apart from the nominal template, two new templates are computed that take into account the positive and negative energy scale shifts. i.e. To compute the jet energy shift, all jet energies have to be shifted Carlos Solans Status of the Higgs to tau tau - 26th March 2010

Status of the Higgs to tau tau - 26th March 2010 Template morphing The efficiency distributions are now a combination of nominal plus shifted templates much alike the first term of a Taylor’s expansion series In the expected number of events in each bin, we replace the efficiency distributions by the efficiency distributions with morphing (jet and electron energy scales) The morphing parameter controls the strength of the energy scale uncertainty. The prior for the morphing parameter is a Gaussian PDF with mean zero and standard deviation one. Therefore the posterior probability shall take into account these systematic uncertainties Carlos Solans Status of the Higgs to tau tau - 26th March 2010

Status of the Higgs to tau tau - 26th March 2010 DATASETS Carlos Solans Status of the Higgs to tau tau - 26th March 2010

Status of the Higgs to tau tau - 26th March 2010 Datasets For the current analysis we use MC datasets produced for Athena 12 in the MSSM mH-max scenario Signal datasets Four different values of mA: ( 150, 300, 450, 600 ) GeV With different values of tanβ Smearing of the templates for different values of tanβ should be considered. We only play with normalization here. Background datasets Z to tau tau ttbar QCD dijets (J1-J5) used for fake rate computation Carlos Solans Status of the Higgs to tau tau - 26th March 2010

Identification efficiency Carlos Solans Status of the Higgs to tau tau - 26th March 2010

Identification efficiency Carlos Solans Status of the Higgs to tau tau - 26th March 2010

Identification efficiency Carlos Solans Status of the Higgs to tau tau - 26th March 2010

Status of the Higgs to tau tau - 26th March 2010 Fake rates With the current event selection, a real Jet that is reconstructed as a tau and passes the tau selection will be removed from the Jet container by the overlap removal. This effect “is” very small when tight tau cuts are applied We define the fake rate of taus as # tau candidates after the identification cuts # jet without overlap removal We can define the fake rate of taus for loose or tight tau cuts Carlos Solans Status of the Higgs to tau tau - 26th March 2010

Status of the Higgs to tau tau - 26th March 2010 Fake rates Carlos Solans Status of the Higgs to tau tau - 26th March 2010

Status of the Higgs to tau tau - 26th March 2010 MC event Carlos Solans Status of the Higgs to tau tau - 26th March 2010

Status of the Higgs to tau tau - 26th March 2010 RESULTS Carlos Solans Status of the Higgs to tau tau - 26th March 2010

Status of the Higgs to tau tau - 26th March 2010 Exclusion limit Setting exclusion limits for two background model for all masses Uncertainty in jet and electron energy scale shifts ΔE(electron)=1%, ΔE(jet)=5%, Carlos Solans Status of the Higgs to tau tau - 26th March 2010

Upper exclusion limit at 95% CL 150 GeV 300 GeV 450 GeV 600 GeV No morphing Morphing Carlos Solans Status of the Higgs to tau tau - 26th March 2010

Upper exclusion limit at 95% CL Carlos Solans Status of the Higgs to tau tau - 26th March 2010

Status of the Higgs to tau tau - 26th March 2010 Coverage We repeat the example but this time adding signal to each pseudo-experiment 100% of the predicted cross-section by MSSM for the given parameters (mA=150 GeV, tanβ=45, mhmax scenario, σA=24500 fb) The method to set exclusion limits is slightly conservative for the MSSM model presented For conservative limit we expect < 5% of S+B pseudo-experiments to lie below the true value of S In our case, ~3.4% (morphing) and ~3.8% (no morphing) of the pseudo-experiments lie under the signal cross-section. ~3.4% ~3.8% Carlos Solans Status of the Higgs to tau tau - 26th March 2010

Status of the Higgs to tau tau - 26th March 2010 Signal significance Signal significance for two background model for all masses and different values of the cross-section Uncertainty in jet and electron energy scale shifts ΔE(electron)=1%, ΔE(jet)=5%, Carlos Solans Status of the Higgs to tau tau - 26th March 2010

Status of the Higgs to tau tau - 26th March 2010 Signal significance Carlos Solans Status of the Higgs to tau tau - 26th March 2010

Status of the Higgs to tau tau - 26th March 2010 Signal significance Carlos Solans Status of the Higgs to tau tau - 26th March 2010