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Mixing Limits of the Strange B 0 Meson

Mixing Limits of the Strange B 0 Meson. Jamie E. Hegarty Advised by Phil Gutierrez Capstone 2005. Background & Motivation Standard Model Quarks B s Production & Detection B s Decay & Mixing The B s Mixing Process Simulating Mixing Events Raw Decays and Detector Resolution

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Mixing Limits of the Strange B 0 Meson

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  1. Mixing Limits of the Strange B0 Meson Jamie E. Hegarty Advised by Phil Gutierrez Capstone 2005

  2. Background & Motivation Standard Model Quarks Bs Production & Detection Bs Decay & Mixing The Bs Mixing Process Simulating Mixing Events Raw Decays and Detector Resolution Neutrino Smearing Tagging Mistagging Analysis & Calculations Fitting to Simulated Data Dilution Comparison Sensitivity Calculation Results & Conclusions Sensitivity Results To-Do & Preliminary Conclusions Ref’s & Ack’s. Mixing Limits: Outline Jamie E. Hegarty - Mixing Limits of the Strange B0 Meson

  3. Background & Motivation

  4. Standard Model Quarks • Quarks come in 6 flavors, and 3 “flavor doublets”, as do their antiquarks: • Hadrons are composites of 2 or 3 quarks • Mesons are hadrons which contain quark-antiquark (q,qbar) pairs. • The B0 meson contains (bbar,d). • The strange B0 (Bs) contains (bbar,s). CHARGE CONJUGATION Jamie E. Hegarty - Mixing Limits of the Strange B0 Meson

  5. Bs Production & Detection • Our Bs currently produced at the Tevatron (Fermilab), detected at DØ. • DØ only detects stablelong-lived, charged particles (e, m, p, etc.) • Bs not detected directly - must be reconstructed from tracks of other particles • TeV is a hadron collider (not designed for B physics), so reconstruction is messy Images: http://www.fnal.gov Jamie E. Hegarty - Mixing Limits of the Strange B0 Meson

  6. Bs Mass Eigenstates Bs Decay & Mixing Bs Decay at DØ • Lifetime of Bs must be Reconstructed • inherent error in lifetime measurement (vertex not always well-defined) http://www.fnal.gov • Bs and Bsbar are Uncharged • Exist in superposition of 2 mass/CP eigenstates (differ by Dms) • Dmssmall (~10 meV … mB~100 MeV) • Bs may transition to Bsbar or v.v.[mixing] • “mixing” may occur before decay Jamie E. Hegarty - Mixing Limits of the Strange B0 Meson

  7. time b s (u,c,t) Bsbar Bs W+ W- (ubar,cbar,tbar) bbar sbar The Bs Mixing Process • Bs transforms into Bsbar via exchange of virtual W’s between quarks • Weak, flavor-changing interaction • Dominated by top quark • Statistical Frequency of Mixing determined by difference in mass. • Measurement of mixing frequency allows measurement of Dm Ultimate Goal: Set a Limit on Measurement of Dm Jamie E. Hegarty - Mixing Limits of the Strange B0 Meson

  8. Simulating Mixing Events “Toy” Monte Carlo Production

  9. Simulating Mixing Events • Lifetime tpRandomly Selected from Raw Exp. Decay Dist. e-t/t t is the mean Bs lifetime: t =1.5 * 10-12 s • tp is “smeared” to Account for Time-Resolution of the Detector  Random “smearing” Value Selected from Gaussian (centered at 0, width st )… added to tp Smeared Lifetime Jamie E. Hegarty - Mixing Limits of the Strange B0 Meson

  10. Simulating Mixing Events • Lifetime tp smeared again to account for (unmeasured) neutrinos in primary decay Bs Ds- + m+ + nm • Higher momentum (longer tp) Bs decay to higher momentum nm • This smearing is lifetime-dependent (s = tpsn) • Random Value Selected from Gaussian (cent. at 0, width tpsn) … added to tp Jamie E. Hegarty - Mixing Limits of the Strange B0 Meson

  11. Simulating Mixing Events • Tagging: Separating Bs from Bsbar U(tp) = “Unmixed” (Bs or Bsbar remained intact) M(tp) = “Mixed” (Bs became Bsbar, or v.v.) • U, M related by: • Random Number Selected from a flat dist. -1 ≤ n ≤ 1 n < cos (Dm tp)  Unmixed n > cos (Dm tp)  Mixed Jamie E. Hegarty - Mixing Limits of the Strange B0 Meson

  12. Simulating Mixing Events • Mistagging: Tagging Bs as Bsbar or v.v. • With mistag rate a : • Mistagging affects only the amplitude of the cosine. (1-2a) is called “Dilution” Jamie E. Hegarty - Mixing Limits of the Strange B0 Meson

  13. Analysis & Calculations Determining Sensitivity of a Dilution Measurement to Changes in Other Parameters

  14. Fitting to the Simulated Data • A long, complicated function f(t) was used • 5 parameters (!): tag, st-fit, Dmfit, tfit, afit • Unbinned Likelihood Amplitude Fitting: • [unbinned] MC lifetime data compared event-by-event (rather than being histogrammed first) • [likelihood] Each value of tp in the MC compared to distribution f(tp) to determine likelihood that tp was selected from f(t) • [amplitude] All parameters exceptafit held fixed during the fit only fit for Dilution (D=1-2a) Jamie E. Hegarty - Mixing Limits of the Strange B0 Meson

  15. W A R N I N G !  If error in Dfit 1, true Dm cannot be determined! ! Analysis: Dilution Comparison • Each fit done ~20 times, varying Dmfit each time. • Resulting Values of Dfit=(1-2afit) divided by DMC (dilution in the MC), then plotted against Dmfit • Dfit/DMC peaks to 1 when Dmfit = DmMC • Errors in Dfit greater for larger Dmfit Jamie E. Hegarty - Mixing Limits of the Strange B0 Meson

  16. Sensitivity Calculation • Goal: Find Dmfit for which error in Dfit is  1 … regardless of true Dm • DmMC set very high (>1eV, or 1000 ps-1) so no peak occurs • Error in Dfit/DMC plot vs. Dmfit • Dmfit where error = 1: Sensitivity of D to these MC/fit conditions • Correct D (and Dm)would only be measurable below the Sensitivity value. Dmfit Error in Dfit/DMC Dmfit (ps -1) Jamie E. Hegarty - Mixing Limits of the Strange B0 Meson

  17. (Preliminary)Results & Conclusions

  18. Sensitivity Results • Sensitivity Calculated for: •  20% variation in st (detector time resolution) •  20% variation in D (dilution) • No neutrino smearing used here (sn = 0) • Fit values for D are “initial” values Jamie E. Hegarty - Mixing Limits of the Strange B0 Meson

  19. To-Do & Preliminary Conclusions • Up Next: • Sensitivity for  20% variation in sn • Add background noise • Repeat all this with Full DØ-MC • Potential Problems: • Fit function becomes extremely difficult (non-analytical?) with sn included! • Signal-to-Noise ratio unknown. • We might be entirely forgetting something. • Conclusions: • This method works great … up to a point • Either sn will need to be “ignored” in fitting, or another method must be used. Jamie E. Hegarty - Mixing Limits of the Strange B0 Meson

  20. References & Acknowledgements • References • Anikeev et. Al, “B Physics at the Tevatron: Run II and Beyond”, FERMILAB-Pub-01/197, December 2001 • Perkins, Donald H., Introduction to High Energy Physics, 4th ed., Cambridge UP, 2000 • “CP Violation in B Meson Decay: FAQ”, http://www.physics.uc.edu/~kayk/cpviol/CP_A0.html, 09/30/04 • Griffiths, David, Introduction to Elementary Particles • Acknowledgements • Phil Gutierrez (advisor) • Peter Williams (theory guru) • Images: • B-event: http://quarknet.fnal.gov/run2/b_lifetime2.shtml • DØ cutaway: http://www-d0.fnal.gov/public/detector/picures.html Jamie E. Hegarty - Mixing Limits of the Strange B0 Meson

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