1. 1 Introduction to Dijet Resonance Search Exercise John Paul Chou, Eva Halkiadakis, Robert Harris, Kalanand Mishra and Jason St. John CMS Data Analysis School January 27, 2011

2. Outline l Exercise Goals l Dijet Production l Dijet Resonances l Search with Dijet Mass Distribution Search with Dijet  Ratio l Final Words

3. Goals l Our goal is to teach you a simple analysis searching for dijet resonances è You will learn some tools and techniques while looking at data l Concentrate on the actual dijet data where you will learn to make 1. Basic kinematic distributions of jets in a dijet sample 2. Dijet mass distribution in the data 3. Dijet  ratio, a simple measure of dijet angular distributions l You will fit the dijet mass and dijet centrality ratio to a parameterization è A smoothness test that is the simplest search for dijet resonances l You will learn to analyze MC data of dijet resonance signals  Producing MC mass bumps in both rate and dijet  ratio l You will learn some simple statistics, but you will not learn how to set limits. Robert Harris, Fermilab3

4. Background Material Phys.Rev.Lett.105:211801,2010AN-2010/108-v14 Robert Harris, Fermilab4 The exercise will follow the first analysis steps of the published CMS dijet resonance search with 3 pb -1. You will make similar plots as in the analysis note using a similar dataset.

5. Dijet Production Robert Harris, Fermilab5

6. 6 Jets at LHC in Standard Model Proton q, q, g Proton q, q, g The LHC collides protons containing colored partons: quarks, antiquarks & gluons. q, q, g The dominant hard collision process is simple 2  2 scattering of partons off partons via the strong color force (QCD). Jet Each final state parton becomes a jet of observable particles. The process is called dijet production.

7. Robert Harris, Fermilab7 Experimental Observation of Dijets Calorimeter Simulation   ETET 0 1 Jet 1 Jet 2 Dijet Mass l Dijets are easy to find è Two jets with highest P T in the event. è No significant physics backgrounds: photons and leptons are < 1% of jet rate at high mass. CMS Barrel & Endcap Calorimeters proton  =-1 proton Jet 1 Jet 2  =1  Transverse  =0  You will make this display

8. Dijet Mass Spectrum from QCD l Steeply falling spectrum. l Always use a log scale on the vertical axis. l We use variable mass bins on horizontal axis è Here roughly the dijet mass resolution è So that a delta function resonance would produce a peak in at least ~3-4 mass bins centered on the resonance. Robert Harris, Fermilab8

9. Events and Differential Cross Section l Spectrums are frequently presented as a differential cross section è Events = Differential Cross Section x Integrated Luminosity x Bin Width è To get differential cross section you need to divide by luminosity & bin width Robert Harris, Fermilab9 divide by luminosity & bin width

10. Dijet Angular Cuts l We will introduce two cuts on dijet angular quantities in the mass analysis  |  | < 1.3: to reduce the large QCD rate at high values |  |  |  | < 2.5: to have a well defined region of  inside barrel and endcap Robert Harris, Fermilab10 You will make these plots for data

11. Dijet Resonances Robert Harris, Fermilab11

12. Robert Harris, Fermilab12 Dijet Resonance Production l New particles that decay to dijets è Produced in “s-channel” è Parton - Parton Resonances à Observed as dijet resonances.  Many models have small width  à Produce narrow dijet resonances X q, q, g Time Space Mass Rate Breit- Wigner  M 11 11 22  11 1+1+ ½+½+ 0+0+ J P qq0.01SingletZ ‘Heavy Z q1q2q1q2 0.01SingletW ‘Heavy W qq,gg0.01SingletGR S Graviton qg …0.04MixedS String qq0.05OctetCColoron qq0.05OctetAAxigluon qg0.02Tripletq*Excited Quark ud0.004TripletDE 6 Diquark Chan  / (2M) ColorXModel Name Intrinsic Width

13. Dijet Resonance Shapes l Narrow dijet resonances after reconstruction. l Significantly larger width than intrinsic Breit-Wigner from two main sources 1. Detector resolution producing Gaussian Core 2. Final state radiation producing long tail to low mass. More from gluons than from quarks. Robert Harris, Fermilab13 You will make this plot for q*  qg

14. Search using Dijet Mass Robert Harris, Fermilab14

15. Fitting Data for Background l We see if data is consistent with a smooth background l Fit data with a parameterization l Check that fit is good   2 /DF close to 1 è Probability > ~10 % è If there was a big signal, we wouldn’t get good fit ! l No evidence for signal Robert Harris, Fermilab15 You will make this plot

16. Looking Closer at Fit: Pulls l Pulls show if fit is reasonable l Pulls = (Data – Fit) / Error è Deviation between data and fit in units of the error on each data point: “sigma”. l For a good fit the pulls should “scatter” like the error è Oscillating about a pull of 0 è ~1/3 of the points should be have | pull | > 1 è ~5% of the points should have | pull | > 2 è | pull | > 3 should be rare. l Fit looks good Robert Harris, Fermilab16 You will make this plot

17. Size of Deviations: Residuals l Residuals, or fractional difference, shows the difference between data and fit in units of the fit l Residuals = (Data – Fit) / Fit = (Data / Fit ) - 1 l You can show the shape and magnitude of a resonance on the same plot l Shows what we would expect to see if there was a signal l No evidence for signal Robert Harris, Fermilab17 You will make this plot

18. Search using Dijet  Ratio Robert Harris, Fermilab18

19. Robert Harris, Fermilab19 Dijet  Ratio Dijet  Ratio is a simple variable to measure angular distribution Dijet  Ratio = N(|  |<0.7) / N(0.7<|  |<1.3)  Number of events in which the two leading jet have |  |<0.7, divided by the number with 0.7<|  |<1.3 l Ratio >1 for signal and < 1 for QCD background. Jet 1 Jet 2 Numerator |  | < 0.7 Signal rich Denominator 0.7<|  | < 1.3 QCD rich Jet 1 Jet 2 z z Center of Momentum Frame

20. Angular Distributions & Dijet  Ratio l Resonance signal is s-channel  Practically flat in cos  * è Depends in detail on the spin of the resonance and the spin of the decay products è Flat for Excited Quark signal l QCD is mainly t-channel  Peaks at cos  * = 1, large  Cos  * ≈ tanh (  / 2 )  Outer cut at |  | = 1.3 corresponds to cos  * = 0.57  Inner cut at |  | = 0.7 which corresponds to cos  * = 0.34. Dijet  Ratio increases with amount of signal Robert Harris, Fermilab20 ** Center of Momentum Frame Parton Jet outer  cut Inner  cut

21. Dijet  Ratio l Ratio is plotted versus dijet mass to scan for resonances l Ratio in data is flat and < 1 è Consistent with QCD l Resonance signal creates a bump in dijet ratio è At the same dijet mass bins as it creates a bump in event rate è Critical confirmation of dijet resonance signal in the angular distribution ! è Sensitive to spin of signal. Robert Harris, Fermilab21 You will make this plot

22. Final Words l Doing this exercise will teach you the basics of a doing a simple search for dijet resonances l You will learn analysis by doing analysis l There are many things we do not teach and some things you need to ask questions to learn l Please do not hesitate to ask any questions è No questions are too simple or too advanced l Good luck with your search for dijet resonances ! Robert Harris, Fermilab22