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Without cuts

This is a summary of what I have done related to f(t)  replacing e  t/  with biased cuts, and the resolution vs VPDL. Dec. 3, 2004 B physics Workshop (Indiana) Kin Yip. Only MC “Truth” information. VPDL ~ Lxy(B)*M(B)/p T (D s  ). Without cuts. x–axes in cm. With cuts.

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Without cuts

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  1. This is a summary of what I have done related to f(t)  replacing et/ with biased cuts, and the resolution vs VPDL. Dec. 3, 2004 B physics Workshop (Indiana) Kin Yip

  2. Only MC “Truth” information VPDL ~ Lxy(B)*M(B)/pT(Ds) Without cuts x–axes in cm With cuts

  3. Consider the ratios of VPDL with and without certain cuts. x–axes in cm

  4. f(t) • f(t) ~ ( p2 - p0ep1t ) et/ • With no biased cuts, reconstructed lifetime distribution in data ~  EG dt where E ~ et/ when t0; otherwise E=0; • With biased cuts, the distribution is ~  E( p2 - p0ep1t) G dt

  5. Fitting  EG dt against the reconstructed VPDL when there is no cut applied. Fitting  E( p2 - p0ep1 t ) G dtagainst the reconstructed VPDL when all the cuts are applied. VPDL ( cm ) VPDL ( cm )

  6. Taking away the two cuts cos(D,B) and cos(D+µ, B), we get back the lifetime () and Gaussian . VPDL (cm)

  7. Unfortunately, without these 2 cuts, the lifetime in DATA looks like : VPDL (cm)

  8. Now, we look at the VPDL resolutions. We need to use two Gaussians to fit the resolution curve.

  9. All cuts Unbiased cuts VPDL (cm)

  10. With a cut (Lxyb) < 0.008, in this case, resolution is reduced from ~62 µmto ~46 µm though statistics is reduced by ~35%. unbiased cuts only Resolutions (cm) VPDL (cm)

  11. Plan as I understand it … • We don’t need the f(t) stuff in the binned likelihood fit. • For the unbinned likelihood fit in the future, we use f(t) like what I have shown, but with different resolutions at different VPDL’s. • Just that the resolutions need to be the ones in the Data (somewhat larger than those in Monte Carlo).

  12. Backup Slides VPDL resolution One Gaussian fit Two Gaussian fit x–axes in cm

  13. With a cut (Lxyb) < 0.008 unbiased cuts only Resolutions (cm) VPDL (cm)

  14. Without biases, lifetime distribution ~ et/ • convoluted with a Gaussian in real life (RECO) due to finite detector resolution • With lifetime-dependent/biased cuts, it is no longer et/, but (say) f(t)  which is what I am after. • Goal is to find f(t) from the Monte Carlo using the “Truth” information which does not suffer from detector resolution. • Reco-ed tracks are matched with the MC: • |pT| < 0.5, ||< 0.02, ||< 0.02

  15. Biased cuts: • Imp()/ > 9 || Imp()/ > 9 || Imp(K)/ > 9 ; • Imp()/ alone > 2 • If ( Lxy(D) < Lxy(B) ) |Imp(BD)/| < 3 • cos(D,B) > 0.85; cos(D+µ, B) > 0. Unbiased cuts: • pT() > 1.5 ; pT() > 0.7; pT(K) > 0.7 • Ptot(B) > 8 ; Ptot() > 3 ; Prel() > 1 • 1.006 < M() < 1.032 GeV • Helicity (K,D) > 0.5

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