1

TTU report“Dijet Resonances”

Kazim Gumus and Nural AkchurinTexas Tech University

Selda Esen and Robert M. HarrisFermilab

Jan. 26, 2006

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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

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Narrow Resonances

Resonance

Z’, etc

s - channel

JetJetXpp

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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 1033 cm-2s-1. • RecJetRoot trees were used to write jets on cmsuaf at Fermilab.

QCD data

• DC04 data samples at Fermilab.

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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 PT: leading jets.

– Require each leading jet have | | < 1.

– Dijet mass: M = sqrt( (E1+E2)2 - (px1+px2)2 – (py1+py2)2 – (pz1+pz2)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

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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 = 0.05 + 1.3 / sqrt(m) – Long tail to low mass caused by QCD radiation.

• Data here is in bins equal to the measured mass resolution above.

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Cross section for QCD and Z’ signals

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Z’ sensitivity

Z’ is hard to find due to low cross section

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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

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Binned Maximum Likelihood

• Likelihood for seeing the observation given the prediction – L = P1 * P2 * .....Pn

• Probability Pi of observing ni events when mi are predicted

– Pi = mi * exp( - mi ) / factorial( ni ) (Poisson function)

• ni : Observed events

– Case I: observed events are QCD only

– Case II: observed events are QCD plus a mass resonance.

• mi : the predicted number of events

mi = alpha * Nsignali + Nqcdi where;

Nsignali : Predicted signal events in mass bin i

Nqcdi : Predicted qcd background events in mass bin i.

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Likelihood distributions (no signal)

The 95% area point gives us the limit.

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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."

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Likelihood distributions (signal)

The likelihoods are gaussian and the most likely cross section is 5 sigma above 0

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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.

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INTERPOLATION OF OTHER MASSES

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Linear Interpolation Method

• Assume 2 probability distribution functions (p.d.f.s), f1(x) and f2(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 x1 and x2 where the cumulative distributions F1 and F2 are equal for a given cumulative probability y,

(4)

x

dxxfxF ')'()( 11

x

dxxfxF ')'()(

)(xf

yxFxF )()( 2211

x

dxxfxF ')'()( 22

)(xf

x1x

yxF )( 11

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Linear interpolation Method (cont’d)

• The cumulative probability for the new distribution is set to same value y at a linearly interpolated position x, 21

)(

bxaxx

yxF

F

• 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) 357-360.

(8)

)(xf

)()()( 12

11

1 ybFyaFyF

)()(

)()()(

2211

2211

xbfxaf

xfxfxf

(5)

(6)

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Simulated 700 & Interpolated 800GeV

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

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Interpolated 4900 & Simulated 5000GeV

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95C.L. and 5σ Sensitivities with Interpolated points

The change in the limit in the region between 1.1 and 1.3 TeV is almostexactly 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).

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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 Quark up to ~ 4.5 TeV up to  ~3.5 TeV

 Axigluon up to ~4.5 TeV up to  ~3.5 TeV

 E6 diquark  up to ~ 5 TeV up to ~4 TeV

Color octet technirho

up to ~ 3.0 TeV up to ~ 2.4 TeV

Randall Sundrum

Graviton

up to ~ 1.1 TeV up to ~0.7 TeV

W’ up to ~ 0.9 TeV None

Z’ None None

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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 .

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New trigger table (L=1033cm-2s-1)

Path

L1 HLT

ET

(GeV)

Pre-

scale

ET

(GeV)

Rate

(Hz)

Low 25 20000 60 2.8

Med 60 400 120 2.4

High 140 10 250 2.8

Ultra 270 1 400 2.6