1. Study of pair-produced doubly charged Higgs bosons with a four muon final state at the CMS detector (CMS NOTE 2006/081, Authors : T.Rommerskirchen and T.Hebbeker) Feb. 11,2009 Jongseok Lee (Sungkyunkwan University) 1

2. Statistical interpretation 2 The CL s Method P(μ;n) reflects the probability to obtain the result n in a counting experiment if μ is expected. The discrimination variable used in the CL s method can be calculated for each bin as: where s i () is the number of signal events in bin i and b i is the number of background events in bin i. Both number are normalized to an integrated luminosity of 10 fb -1. where n i is the number of background events in bin i or the number of signal plusbackground events in bin i.

3. Statistical interpretation 3 The CL s Method If the hypothesis of having measured background only is true, the integral is investigated, where X 0 is the value of -2lnQ from an experiment (real data) or the mean value of the signal plus background -2lnQ distribution (simulated data). In the same way one can test the significance of an excess of signal above the background, If no signal will be discovered an exclusion limit can be calculated by convention with 95% confidence. Thus, the probability for excluding the presence of signal is less than 5%, which can be mathematically described by

4. Statistical interpretation 4 Background Event Statistic To calculate the signal significance for doubly charged Higgs boson masses greater than 500 GeV, the empty bins had to be filled by an estimated background distribution. Two possible solutions are: 1.The empty bins are filled, using Poisson statistics: If a backgrounds has no entries in a certain bin, the mean of the corresponding Poisson distribution has, at 95% confidence level, to be<=3 events. Distribution of the invariant reconstructed H ±± mass for all background events, before and after the empty bins have been filled with upper limits to the Poisson statistics

5. Statistical interpretation 5 Background Event Statistic 2. An exponential decreasing curve is fitted to the reconstructed invariant mass spectrum of the background: The fitted curve and the errors on the fit are: exp[4.5(±1)-1.5*10 -2 (±4*10 -3 )*m inv ], where m inv is the reconstructed invariant mass in GeV. Distribution of the invariant reconstructed H ±± mass for all background events and the estimated distribution of the invariant mass following an exponential decreasing curve

6. Statistical interpretation 6 Discovery Limit 1-CL b as a function of the reconstructed invariant doubly charged Higgs boson mass, the discovery limit is 650 GeV The discovery limit as a function of the integrated luminosity, calculated with the CL s method Exclusion Limit

7. Statistical interpretation 7 Exclusion Limit If no signal can be detected for an integrated luminosity of 10fb-1 the existence of a doubly charged Higgs boson in the four muon decay channel can be excluded at 95% confidence level up to a mass of 760 GeV. CL s as a function of the reconstructed invariant doubly charged Higgs boson mass, the exclusion limit is 760 GeV

8. Experimental uncertainties 8 Background The uncertainties on the discovery and exclusion limit resulting from systematical errors have yet to be studied in detail. Uncertainties associated with the background production rates can arise from: Parton Density Function and QCD scale at NLO (1% to 6%) LHC luminosity (~5%) Uncertainty due to lack of simulated background Uncertaintes associated with the CMS detector performance (hardware/software) and analysis- specific cuts can be due to: trigger efficiencies muon reconstruction efficiency (~0.2%) efficiency of the Impact Point cut resolution of the reconstructed doubly charged Higgs boson mass

9. Experimental uncertainties 9 Signal The uncertainties related to the NLO corrections to the signal production and to the parton density function were calculated by Spira and Muhlleitner to be in total 10~15%. Approximated total uncertainties Assuming a total systematic error on the background cross section, σ background, to be 6% using an uncertainty of 5% on the luminosity, ￡, and an uncertainty on the signal cross section σ signal of 10%, the systematic errors on exclusion and discovery limits can be approximated as:

10. Search for the doubly charged Higgs Feb. 11,2009 Jongseok Lee (Sungkyunkwan University) 10

11. 10k events of fast simulation data (generated by Chawon Park) 11

12. isolP T 12 black : MC muon from Higgs red : global muon green : track purple : MC charged particle

13. # of muons per event 13 pt>10, |η|<2.4 black : MC muon red : global muon green : track pt>10, |η|<2.4 isolPt<10, cone=0.3 black : MC muon red : global muon green : track isolated isolPt<3

14. P T & η 14 pt>10, |η|<2.4 black : MC muon red : global muon green : track pt>10, |η|<2.4 black : MC muon red : global muon green : track pt>10, |η|<2.4 isolPt<10, cone=0.3 black : MC muon red : global muon green : track pt>10, |η|<2.4 isolPt<10, cone=0.3 black : MC muon red : global muon green : track isolated isolPt<3

15. Muon efficiency 15 global muon efficiency VS pt black : pt>10, |η|<2.4 red : pt>10, |η|<2.4, isolPt<10 global muon efficiency VS η black : pt>10, |η|<2.4 red : pt>10, |η|<2.4, isolPt<10 MC muon efficiency VS pt black : pt>10, |η|<2.4 red : pt>10, |η|<2.4, isolPt<10 MC muon efficiency VS η black : pt>10, |η|<2.4 red : pt>10, |η|<2.4, isolPt<10

16. Mass of two highest pt muons ( black : global muon, red : matched global muon with MC muon from Higgs) 16 pt>10, |η|<2.4 isolPt<10 pt>10, |η|<2.4 isolPt<10 isolated

17. Matching ratio 17 black : pt>10, |η|<2.4 red : pt>10, |η|<2.4, isolPt<10 black : pt>10, |η|<2.4 red : pt>10, |η|<2.4, isolPt<10

18. Isolated track 18 black : pt>10, |η|<2.4 red : pt>10, |η|<2.4, isolPt<10 black : pt>10, |η|<2.4 red : pt>10, |η|<2.4, isolPt<10

19. Mass of matched two highest P T muons with MC muon (1k events of full simulation data : generated by Chawon Park) 19 pt>10, |η|<2.4 pt>10, |η|<2.4, isolPt<10 pt>10, |η|<2.4 pt>10, |η|<2.4, isolPt<10