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Study of MET and Invariant Mass in GMSB Physics

This study explores the use of MET and invariant mass variables in GMSB physics analysis. De-convolution method for signal yield, background shapes, and mass estimation are discussed, along with a detailed analysis of gravitational decays and photon interactions. The application of de-convolution in experimental particle physics is emphasized.

lareina-giles
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Study of MET and Invariant Mass in GMSB Physics

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  1. Status of GMSB studies ShileiZang University of Colorado, Boulder CU CMS Meeting, 28th Apr. 2008

  2. Outline • Invariant mass of neutralino • De-convolution method

  3. MET • MET distribution is used to get signal yield, but we have two gravitinos. g jet q q jet … p p q … jet q jet g

  4. MET distribution is used to get signal yield. • Simple variable; powerful separation; largely used • 1) It’s crowded at small MET region for both signal and background. • 2) Shapes are different for signal and each bkg. • 3) Vector addition of the two gravitinos. • 4) MET resolution is difficult to estimate. • 5) Can not get mass from MET •  MET is not a much sensitive variable; bkg studies are difficult; not directly relate with mass •  Can we use the invariant mass of photon+gravitino?

  5. MET • MET • Pt2>0GeV • Peak=157 GeV • MET • Pt1>90GeV; Pt2>30GeV • Peak=160.4 GeV;

  6. Invariant mass of neutralino • Pt1>90GeV; Pt2>30GeV; MET>130GeV • Peak=223GeV; sig=61GeV • Pt2>0GeV • Peak=185GeV • Sig=77GeV • Pt1>90GeV; Pt2>30GeV; • Peak=196GeV

  7. two gravitinos. • photon and gravitino. • photon1 and gravitino2 • photon2 and gravitino1 • Cos(theta) from MC Truth

  8. Cos(theta) of and .

  9. -cos(theta) • cos(theta) • Ratio = (-cos(theta))/cos(theta) • -cos(theta) • cos(theta)

  10. mass • mass2 • mass minus • mass2 weighted • mass2 weighted • mass = CB Line; mass2weighted = CB Line + Polynomial • mass = mass2weighted for background

  11. Variables for GMSB analysis MET Rough mass of neutralino Edge of MT2 distribution Edges of some invariant masses Accurate calculation with cross-events for long decay chain Long-lived neutralinos: photon timing, cluster shapes, decay chain, .. (CDF, ATLAS, CMS) Deconvolution method accurate mass of neutralino; accurate ctau of neutralino hep-ph/9906349 CMS Note1997/079 arXiv:0802.4290v1

  12. Rough mass of neutralino • Many questions on mass: Not accurate; Bias? Shape? Backgrounds? • Signal can be fitted with CB Line? • Bkg shapes are expected to be similar (CB Line + Polynomial functions) can study all backgrounds together? • mass2weighted can be used for bkg study or as a cross check.

  13. De-convolution Method • Convolution: linear shift-invariant f(mass) (mass) system: g(mass) • Mass: rough mass Briet-Wigner (Delta) transfer Resolution (Gaussian) noise (Argus)

  14. Rough mass in Data: • Accurate mass in Data : • Rough mass in signal MC: • Accurate mass in signal MC: • Suppose we know h and f for signal MC; • We can determine the transfer function g by deconvolution using signal MC. • In Fourier space: • h, f  H, F  G g (signal MC) • h, g  H, G  F f (Data)

  15. Signal MC: GM1b~1g • h • Peak=196 • RMS=112 Gaussian f (mean=mass0 rough sigma) ? = system: g RooFit

  16. Data : • signal MC: • h0 • Peak=175 • RMS=89 • h • Peak=196 • RMS=112 • Peak=196.8GeV

  17. h • Mean=235 • Peak=196 • RMS=112 • g • Mean=1GeV • RMS=89 Signal MC: GM1e • f • Mean=196GeV • RMS=70 Gold deconvolution algorithm

  18. Convolution is largely used in: Statistics; Astronomy; Meteorology; Geophysics; Optics; Digital image; Spectroscopy; …;but not in Particle physics as I know. • Deconvolution can be used to recover the missing information. MET, resolution, … mass, width, … • A shadow is the convolution of the shape of the light source that is casting the shadow and the object whose shadow is being cast • An out-of-focus photograph is the convolution of the sharp image with the shape of the iris diaphragm. • An echo is the convolution of the original sound with a function representing the various objects that are reflecting it. • …… wikipedia

  19. Summary • We can use mass to get signal yield, CB Linefunctions. Same methods as in MET for bkg studies; or bkg studies are simple. • We can use mass-mass2weighted as a cross check of the result. • De-convolution method is introduced, which is expected to be useful in experimental particle physics. • Test the invariant mass and the de-convolution method with all GMSB points and all backgrounds. • Study the QCD control samples: • Correlation between shower shape/isolation and MET/massneed to be studied. • Can shower shape/isolation get enough control sample? Do we need photon Pt, MET, number of jets, or jets’ pt for control sample? Thank you!

  20. MT2 • hep-ph/9906349 • Left edge is known; use the right edge to get the mass. • Enough signal events close to the right edge? • Edge is not sharp; shape? Background?

  21. Edge of invariant mass Jet+photon  • CMS Note 1997/079 • Kinematics reasons 2 leptons  2 leptons+1photon 

  22. Accurate calculation with cross-events • arXiv:0802.4290v1 • 6 constraints; 8 unknowns for one event. • 6+10 constrains; 16 unknowns for two events. solve the equations • Need long decay chain. • Wrong combinations are large. • Bias? Shape? ill equations? measure uncertainties? ...

  23. Long-lived neutralino • arXiv:0804.1043v1 Search for heavy, long-lived neutralinos that decay to photons at CDF II using photon timing • arXiv:0704.0760v1 Search for heavy, long-lived particles that decay to photons at CDF II • arXiv:0710.2647v1 Search for GMSB NLSPs at LHC • PRD 69, 035003 (2004) Study of the gauge mediation signal with nonpointing photons at the CERN LHC • ……

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