This is a summary of what I have done related to f(t)  replacing
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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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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 replacing

VPDL ~

Lxy(B)*M(B)/pT(Ds)

Without cuts

x–axes in cm

With cuts



f(t) replacing

  • 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


Fitting replacing  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 )


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

VPDL (cm)



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


All cuts Gaussians to fit the resolution curve.

Unbiased cuts

VPDL (cm)


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)


Plan as I understand it … reduced from ~62

  • 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).


Backup Slides reduced from ~62

VPDL resolution

One Gaussian fit

Two Gaussian fit

x–axes in cm


With a cut (Lxyb) < 0.008 reduced from ~62

unbiased cuts only

Resolutions (cm)

VPDL (cm)


  • Without biases, lifetime distribution ~ e reduced from ~62 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


Biased cuts: reduced from ~62

  • 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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