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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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slide1
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

slide2

Only MC “Truth” information

VPDL ~

Lxy(B)*M(B)/pT(Ds)

Without cuts

x–axes in cm

With cuts

slide4
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

slide5

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 )

slide6

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

VPDL (cm)

slide8
Now, we look at the VPDL resolutions. We need to use two Gaussians to fit the resolution curve.
slide9

All cuts

Unbiased cuts

VPDL (cm)

slide10

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)

slide11
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).
slide12

Backup Slides

VPDL resolution

One Gaussian fit

Two Gaussian fit

x–axes in cm

slide13

With a cut (Lxyb) < 0.008

unbiased cuts only

Resolutions (cm)

VPDL (cm)

slide14
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
slide15
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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