1. Jan 17, 2007 Measuring Mass Difference using soft τ P T Slope 1 Measuring Mass Difference at LHC using soft τ P T Slope Alfredo Gurrola in collaboration with Richard Arnowitt, Bhaskar Dutta, Teruki Kamon, David Toback, Abram Krislock, Nikolay Kolev (Regina, Canada)

2. Jan 17, 2007 Measuring Mass Difference using soft τ P T Slope 2 Outline  SUSY Signature at the LHC  Analysis Methods in 2  & 3  Papers  Gaugino Universality  Measuring  M in a Non-Universal SUGRA model  Simultaneous measurement of model parameters to test Universality

3. Jan 17, 2007 Measuring Mass Difference using soft τ P T Slope 3 SUSY at LHC 1., Production is dominant SUSY process at LHC ( ) 2. Interested in events with or pairs 3. & Branching Ratios are ~ 97% 4. In Coannihilation Region of SUSY Parameter Space: GeV Soft  pppp Hard 

4. Jan 17, 2007 Measuring Mass Difference using soft τ P T Slope 4 Looking Back at 2  & 3  Papers 1. Use Hadronically Decaying  ’s 2. Sort τ’s by E T (E T1 > E T2 > …) & use OS-LS method to extract  pairs from the decays on a statistical basis 3. Use Counting Method (N OS-LS ) & Ditau Invariant Mass (M  ) to measure mass difference 4. 5. hep-ph/0603128 hep-ph/0608193

5. Jan 17, 2007 Measuring Mass Difference using soft τ P T Slope 5 Non-Universal SUGRA  Methods used in 2  & 3  papers depend on Gaugino Unification  Those methods can’t be used in a Non-Universal SUGRA model without using another observable!  How can we measure  M? SUSY Mass Hierarchy  M ~ 5 – 15 GeV

6. Jan 17, 2007 Measuring Mass Difference using soft τ P T Slope 6 P T STUDY Slope of the soft  P T distribution has a  M dependence hep-ph/0603128 Slope of P T distribution contains ΔM Information.

7. Jan 17, 2007 Measuring Mass Difference using soft τ P T Slope 7 EVENTS WITH CORRECT FINAL STATE (2  OR 3  ) - 2  + 2j + E T miss APPLY CUTS TO REDUCE SM BACKGROUND (W+jets, …) E T miss > 180 GeV, E T j1 > 100 GeV, E T j2 > 100 GeV, E T miss + E T j1 + E T j2 > 600 GeV ORDER TAUS BY P T & APPLY CUTS ON TAUS: WE EXPECT A SOFT  AND A HARD  P T all > 20 GeV, P T  1 > 40 GeV LOOK AT  PAIRS AND CATEGORIZE THEM AS OPPOSITE SIGN (OS) OR LIKE SIGN (LS) OS: FILL LOW OS P T HISTOGRAM WITH P T OF SOFTER  FILL HIGH OS P T HISTOGRAM WITH P T OF HARDER  LS: FILL LOW LS P T HISTOGRAM WITH P T OF SOFTER  FILL HIGH LS P T HISTOGRAM WITH P T OF HARDER  LOW OS HIGH OS LOW LS HIGH LS LOW OS-LS HIGH OS-LS Extracting  Pairs from Decays

8. Jan 17, 2007 Measuring Mass Difference using soft τ P T Slope 8 P T STUDY  ISAJET 7.64 to simulate our model of SUSY production  TAUOLA to re-decay the  ’s  Run generated particles through detector simulator, PGS4 (author: John Conway) using CMS parameter file  Used reconstructed jets  Used generator level  ’s after being re-decayed by TAUOLA - “visible” values of momentum and energy were used  Separate Monte Carlo routine in ROOT to simulate the effects of  identification efficiency and jet to  fake rate

9. Jan 17, 2007 Measuring Mass Difference using soft τ P T Slope 9 OS OS-LS LS E T miss + 2j + 2  Analysis: P T soft [1] E T miss, at least 2 jets, at least 2  ’s with P T vis > 20, 40 GeV [2]   = 50%, fake rate 1% [3] Cuts: E T jet1 > 100 GeV, E T jet2 > 100 GeV, E T miss > 180 GeV E T jet1 + E T jet2 + E T miss > 600 GeV

10. Jan 17, 2007 Measuring Mass Difference using soft τ P T Slope 10 Can we still see the dependence of the P T slope on  M using OS-LS Method? P T STUDY

11. Jan 17, 2007 Measuring Mass Difference using soft τ P T Slope 11 P T STUDY: E T miss + 2j + 2  What is the dependence of P T slope on mass & mass?  Luminosity = 40 fb -1 P T Slope is insensitive to mass & mass!! What is the dependence on  M?

12. Jan 17, 2007 Measuring Mass Difference using soft τ P T Slope 12 Measuring  M from the P T Slope P T STUDY: E T miss + 2j + 2   Luminosity = 40 fb -1

13. Jan 17, 2007 Measuring Mass Difference using soft τ P T Slope 13 How accurately can  M be measured for our reference point?  Considering only the statistical uncertainty: We can measure  M to ~ 6% accuracy at 40 fb -1 & ~ 12% accuracy at 10 fb -1 for mass of 831 GeV. P T STUDY: E T miss + 2j + 2 

14. Jan 17, 2007 Measuring Mass Difference using soft τ P T Slope 14  Can parameterize the our observables as functions of  M,, &  N OS-LS, to first order, does not depend on mass. A large increase or decrease in mass is needed to obtain a point that lies outside the error bars  Cross-Section is dominated by the gluino mass Simultaneous Measurement of Model Parameters

15. Jan 17, 2007 Measuring Mass Difference using soft τ P T Slope 15 Simultaneous Measurement of Model Parameters

16. Jan 17, 2007 Measuring Mass Difference using soft τ P T Slope 16 Testing Gaugino Unification CONTOURS OF CONSTANT VALUES ( L = 40 fb -1 ) Intersection of the central contours provides the measurement of  M,, & Auxilary lines determine the 1  region 1 st order test on Universality

17. Jan 17, 2007 Measuring Mass Difference using soft τ P T Slope 17 SUMMARY  Soft  P T distribution is sensitive to  M  P T slope is independent of gluino mass and neutralino mass   M can measured to ~ 12% accuracy at 10 fb -1 for our reference point  Methods used in 2  and 3  papers can’t be used in a Non-Universal SUGRA model  We can combine counting method, ditau invariant mass measurement and P T slope to test the idea of gaugino unification to first order

18. Jan 17, 2007 Measuring Mass Difference using soft τ P T Slope 18 PROBLEM: OS-LS method does NOT give the “true” slope P T STUDY

19. Jan 17, 2007 Measuring Mass Difference using soft τ P T Slope 19 P T STUDY – Method I How accurately can we measure  M with this method?  Assuming the theoretical dependence (‘True’ Fit) of  M on Slope: We can measure  M to ~ 8-9% accuracy at 40 fb -1 for mass of 831 GeV. Slope does NOT change with ~ 10% change in gluino mass, but the uncertainty changes due to change in N OS-LS

20. Jan 17, 2007 Measuring Mass Difference using soft τ P T Slope 20 P T STUDY  BACKGROUND: SM, SUSY, soft  ’s  from the   ’s from the is the dominant background! How can the slope be corrected? What causes this difference?

21. Jan 17, 2007 Measuring Mass Difference using soft τ P T Slope 21 Correcting the Slope: Method I  Defining the measured P T slope by and the theoretical (“true” identification) P T slope by, the mean statistical uncertainty on the slope is with the mean statistical uncertainty of. The shift S due to background effects is given by the mean difference of the theoretical slope and the measured slope: The root-mean-square uncertainty is With these definitions, the CORRECTED measured Slope is

22. Jan 17, 2007 Measuring Mass Difference using soft τ P T Slope 22.003166 S.008900.002032 A plot of the distribution of the shift S between theoretical and measured values. The shift S is fairly close to being constant. A summary of the calculated uncertainties and shift in GeV. Correcting the Slope: Method I

23. Jan 17, 2007 Measuring Mass Difference using soft τ P T Slope 23 Correcting the Slope: Method II  Soft  ’s from is the dominant background  By increasing the second  P T cut, this source of background can be reduced  Other Background (SM & other SUSY Background) is reduced

24. Jan 17, 2007 Measuring Mass Difference using soft τ P T Slope 24 Correcting the Slope: Method II

25. Jan 17, 2007 Measuring Mass Difference using soft τ P T Slope 25 Optimizing  P T Cut Optimized Cut would be ~ 70 – 80 GeV for  M = 10.6 GeV

26. Jan 17, 2007 Measuring Mass Difference using soft τ P T Slope 26