1 TTU report “Dijet Resonances” Kazim Gumus and Nural Akchurin Texas Tech University Selda Esen and Robert M. Harris Fermilab Jan. 26, 2006

2 Outline Narrow resonances Data Analysis method Binned Maximum likelihood 95% CL exclusion & 5 sigma discovery limits Interpolation of other masses Linear interpolation method Update of 5 sigma discovery plot Conclusions and future plans

3 Narrow Resonances Resonance Z’, etc s - channel

4 Data sample and software Z’ Data 700 GeV Z’: 5600 Z’ decaying to dijet events 2 TeV Z’: 6400 Z’ decaying to dijet events 5 TeV Z’: 6500 Z’ decaying to dijet events Software PYTHIA, OSCAR 3_7_9 for simulation., ORCA 8_7_1 for digitization. Jet Reconstruction: ORCA_8_7_1. All samples produced with pileup at lum = 2 x cm -2 s -1. RecJetRoot trees were used to write jets on cmsuaf at Fermilab. QCD data DC04 data samples at Fermilab.

5 Analysis Iterative cone jet algorithm with R=0.5. Correct jets with jetCalibV1. –Correction back to particles in jet cone before pileup. Find the two jets in the event with highest P T : leading jets. –Require each leading jet have |  | < 1. –Dijet mass: M = sqrt( (E 1 +E 2 ) 2 - (p x1 +p x2 ) 2 – (p y1 +p y2 ) 2 – (p z1 +p z2 ) 2 ). Plot dijet mass in bins equal to mass resolution: bin size increases with mass. Divide rate by the luminosity and bin width: differential cross section

6 Narrow resonance shape in CMS Model narrow resonance line shape at CMS with Z’ Simulation. Corrected dijet mass peaks around generated value –Gaussian core with resolution  /m = / sqrt(m) –Long tail to low mass caused by QCD radiation. Data here is in bins equal to the measured mass resolution above.

7 Cross section for QCD and Z’ signals

8 Z’ sensitivity Z’ is hard to find due to low cross section

9 QCD cross section and fit We fit the QCD background to a smooth parameterization –Removes fluctuations that would distort our likelihood. –We are smoothing the background

10 Binned Maximum Likelihood Likelihood for seeing the observation given the prediction –L = P 1 * P 2 *.....P n Probability P i of observing n i events when m i are predicted –P i = m i * exp( - m i ) / factorial( n i ) (Poisson function) n i : Observed events –Case I: observed events are QCD only –Case II: observed events are QCD plus a mass resonance. m i : the predicted number of events m i = alpha * Nsignal i + Nqcd i where; Nsignal i : Predicted signal events in mass bin i Nqcd i : Predicted qcd background events in mass bin i.

11 Likelihood distributions (no signal) The 95% area point gives us the limit.

12 5 sigma discovery cross section Method: To produce 5 sigma discovery cross section, we formed a new distribution of "signal + background“. We found the likelihood for this distribution. We increased the signal cross section until we had a gaussian likelihood that was above zero cross section by 5 sigma (conservative approach). The result was very close to a 5 sigma exclusion from the likelihood distribution without signal, as it should be for large statistics."

13 Likelihood distributions (signal) The likelihoods are gaussian and the most likely cross section is 5 sigma above 0

14 95%C.L. and 5σ Sensitivities With 1 fb -1 we can exclude at 95% CL all models above the dotted line. With 1 fb -1 we can discover at 5 sigma significance all models above the solid line We need to do estimates for more resonance points, and make the line into a realistic curve. We also need systematics.

15 INTERPOLATION OF OTHER MASSES

16 Linear Interpolation Method Assume 2 probability distribution functions (p.d.f.s), f 1 (x) and f 2 (x) (for x > -inf ), Corresponding cumulative distribution functions (c.d.f.s) (1) (2) The goal is to obtain a new p.d.f. with its corresponding c.d.f. (3) The first step of the interpolation procedure is to find x 1 and x 2 where the cumulative distributions F 1 and F 2 are equal for a given cumulative probability y, (4)

17 Linear interpolation Method (cont’d) The cumulative probability for the new distribution is set to same value y at a linearly interpolated position x, The constants a and b express the interpolation distance between the extreme values of the relevant parameter for the two existing distributions (a+b=1). This could be the relative position of the mass hypothesis between two masses for which simulation is available. The p.d.f. is obtained by inverting the c.d.f. in Eqs.(4) and (5), substituting these results in Eq. (6), (7) Deriving this with respect to y and solving for the interpolated p.d.f. A.L, Read, “Linear interpolation of histograms”,Nuc. Inst. And Meth. In Phys. Res.”, A 425 (1999) (8) (5) (6)

18 Simulated 700 & Interpolated 800GeV

19 Interp. 1900, Sim. 2000, Intep. 2100GeV

20 Interpolated 4900 & Simulated 5000GeV

21 95C.L. and 5σ Sensitivities with Interpolated points The change in the limit in the region between 1.1 and 1.3 TeV is almost exactly what we expect from the prescale change at 1130 GeV. In the region below 1.1 TeV almost all of the resonance is in the prescaled trigger (high threshold) and in the region of 1.3 TeV and greater almost all the resonance is in the unprescaled trigger (ultra).

22 Expected mass limits and discovery range Object 95% CL Exclusion Range ( 1 fb -1, stat err only) 5  Discovery Range (1 fb -1, stat err only) Excited Quarkup to ~ 4.5 TeVup to ~3.5 TeV Axigluonup to ~4.5 TeVup to ~3.5 TeV E6 diquark up to ~ 5 TeVup to ~4 TeV Color octet technirho up to ~ 3.0 TeVup to ~ 2.4 TeV Randall Sundrum Graviton up to ~ 1.1 TeVup to ~0.7 TeV W’up to ~ 0.9 TeVNone Z’None

23 Conclusions and future plans Made a first estimate of CMS ability with 1 fb -1 to exclude (at 95% CL) or discover (at 5  ) resonances in the dijet mass distribution. Plan to do 100pb -1 and 10fb -1 luminosities. Plan to do the first estimates of systematic uncertainties for 100 pb -1, 1 fb -1, 10 fb -1. Prepare the analysis for PTDR 2.

24 New trigger table (L=10 33 cm -2 s -1 ) Path L1HLT E T (GeV) Pre- scale E T (GeV) Rate (Hz) Low Med High Ultra