Wrong Sign D Group - Harry Nelson's Plots

[Wrong Sign D Group] [CLEO] [HN Home Page]

23 November 1998

A CBX note on goodness-of-fit.

23 September 1998

The k/pi separation by dE/dx now achieved, as a function of momentum, in CLEO.

8 July 1998

A prominent background is D*+ to D0 pi+_slow, with the D0 decaying into PV, like K- rho+, then the rho+ decaying to pi+pi0, and we lose the pi0 (loosing mass), and then gain mass back by promoting a slower pi+ to a K+ and demoting a faster K- to a pi-. I did some simple kinematic studies of this background (for a D* momentum of 3 GeV):

According to this simple study, this background is flat in delta-M, and slight peaking in MD. However, David Asner's studies with CLEOG are showing different results.

A summary of our background situation, for D0>K+pi-.

15 May 1998

D-mixing is in principle sensitive to supersymmetry.

22 April 1998

Note from Alan Weinstein on the prospects for measurement of the intrinsic width of the D^*.
Some plots of my fast Monte Carlo, including only tracking resolution, that is, with setting the width of the D*+ to zero:
- M(D^*)-M(D) for CLEO 2 (no SVX) - note the non-Gaussian tails, that would be easily confused with the Lorentzian tails of the D^*.
- M(D^*)-M(D) for CLEO 2 with the SVX - note the nearly Gaussian tails.
- Spectrum of errors for the previous plot.

18 April 1998

Draft CBX on the resolution in reconstruction of M(D^*)-M(D).
Plot of measured error on delta-M v. computed error on delta-M (for D*-D) in CLEO2/SVX, from 1.5fb-1 of data (ps). (Plots made on 10/22/97; based upon the first pass2; we believe the relationship will be much better in the re-roaring now underway)

15 April 1998

Formulas pertaining to mixing.
The asymptotic form of the convolution of a gaussian with e^-t, te^-t, t²e^-t:
JPEG: (page 1), (page 2), (page 3) ; ps: (page 1), (page 2), (page 3).
Stupid TeX tricks: how do you typeset D0bar?
(ps) , (tex).

For 10 December 1997 Meeting

A memo on improved chi-squared for Poisson situations.

For 3 December 1997 Meeting

Draft of description of David Asner's Analysis.
New plot (here in ps, here in ps with caption) where the `zero' when the wrong sign amplitude is -tan^2(theta_C), x=0, and y=-0.075 is shown when the smearing is reduced. Statistics such as the mean and standard deviation of the distributions are shown.
I wanted to understand the location of the zero in some detail, and that lead to the writeup here. My conclusion that the zero in the lower left plot of Alex Smith's work for the 11/26/97 meeting (here) appears to be not quite right.
This work led me to look into whether the second-order parameterization of mixing is really actually OK. The fractional error between the second-order and all order calculations that blows up when a zero is present. Earlier, this blow-up led me to reject the second-order paramterization. However, now, I think that the blow-up is not so important, because the overall size of the time-dependent rate is so small near the zero that a large relative error does not matter. The situation is summarized in this plot (here in ps, here in ps with caption).
In the end, it has been very useful to understand the interrelationships between various mixing parameterizations, and I made a pretty concise summary here. I think we should stay with the all-orders calculation, mostly because it protects us best from future landmines.

For 26 November 1997 Meeting

Page 4 of longer memo on the status of the work of David and I.

Plots from November 1997:

Talk on delta-M resolution
Plot of resolution in delta-M (for D*-D) as a function of momentum of the D*. Here it is in postscript. Due to non-Gaussian distributions, the results of a double-Gaussian fit (ps) are a bit different.
Plot of the actual delta-M for momentum of the D* above 2.0 GeV, for data; width here is 250 KeV; this result is now out of date, as David Asner now observes 200 KeV.Here it is in postscript.

Plots from September 1997:

In this plot, the idea is that the ratio of wrong to right sign decays is really what CLEO-II found, R=0.0077, but, that the wrong sign decays were not necessarily all from DCSD (Doubly Cabibbo Suppressed Decays). So, in the middle plot, the influence on the distribution in the proper lifetime of an amount of delta-M (dispersive) mixing at the FNAL limit x=0.075, with the DCSD amplitude lowered to keep R=0.0077, is shown. The effect is to lengthen the mean lifetime of the wrong sign events (which would always here number 22 for 1.5 1/fb of data, if the D* momentum cut of 2.0 GeV is used) from the D0 lifetime of 0.415 ps, up to 1.6 times that; the actual distribution, including smearing, is shown. One can then make a simple estimate: for 2.5 times as much data, or 3.8 1/fb of data, the precision of the lifetime measurement would be crudely 1.6/sqrt(2.5*22)=0.22 ps, or sensitive at 2.8 sigma to delta-M mixing at the FNAL limit. A full fit to the distribution would probably bring the sensitivity above 3 sigma. However, background would push the sensitivity down.

The lowest plot conducts the same study for delta-Gamma (absorptive) mixing. The sensitivity is slightly greater.

The top plot simply shows the D0 flight path we currently have for right sign events, with a 2.0 GeV D* momentum cut. A pure exponential is shown, and also an exponential folded with the data is shown in blue.

Here is the same plot in postscript.
In this plot, the idea is to hold fixed that DCSD amplitude is simply tan^4(theta_c), about a factor of 3 lower than what is needed to explain the CLEO-II wrong sign result from purely DCSD. Then, mixing is blended in at the FNAL limits, to this fixed amount of DCSD: the overall number of events thus varies from case to case. The senstivity usually increases a bit over the previous scenarios, however: for example, for delta-M mixing, the FNAL limit is 2.9 sigma from no effect, because the lifetime goes up faster (to 1.9 times the D0 lifetime) than the loss of sensitivity from loss of events (from 22 to 15) goes down.

Here is the same plot in postscript.