Thanks Riccardo for all this work,
Though it is not easy to follow the unlabeled plots!
I think this work confirms my intuition that the value of Lambdabar
can be taken from b > s gamma, and can be reliably translated to shape
function parameters. The same may not be true for l1.
On the other hand, if I look at the CLEO plot and restrict the variation to reasonable errors on Lambdabar, then the error we placed in l1 of 0.105 GeV2 is not unreasonable. (we have too many significant digits for l1: 0.300 + 0.105,
0.30 + 0.11)
So, I am not sure I would change much in the paper, may be increase the errors slightly. I would not apologize for this, just state plainly what we do.
Possibly mention the shape function uncertainty explicitly.
Ciao
Vera
Original Message
From: Faccini, Riccardo
Sent: Wednesday, July 02, 2003 8:45 AM
To: vubrecoil
Subject: what can we leasrn on lambda_bar and lambda_1 from our data
Alessio and I have gone through the exercise of calculating the chi^2 of the consistency of our data with a grid of values of lambda_bar and lambda_1. This is an evolution of Urs's study in http://www.slac.stanford.edu/cgibin/lwgate/VUBRECOIL/archives/vubrecoil.200306/Author/article35.html
since it is done with the full reweighting and with a chi^2 on the background subtracted distribution of Mxhadfit. This are done with the new 1D reweighting and therefore the default is BRBR = 0.0219733 + 0.00265286(stat) + 0.000977835(MC stat)
The raw results are in http://www.slac.stanford.edu/~asarti/recoil/newchiscan/
Out of them, I produced the plot of the deltaChi^2 wrt to the minimum as a function of lambda_bar and l1 in http://www.slac.stanford.edu/~rfaccini/phys/vub/SF/ll_zcol.eps
http://www.slac.stanford.edu/~rfaccini/phys/vub/SF/ll_cont.eps
where the three contours are at deltaChi^2=1 , deltaChi^2 =2.25 (1 sigma) and deltaChi^2=5. There is a funny rectangle at the bottom, but this is just a plotting feature. The ellipse represents the assumed values in our analysis. It is to be noted that the fit prefers slightly higher values of lambda_bar and of lambda_1. The long tail from CLEO is completely excluded.
In order to show the level of consistency of our assumed values and the fit results, I show the fit projections:
deltaChi^2 vs lambda_bar http://www.slac.stanford.edu/~rfaccini/phys/vub/SF/lbproj.eps
vs lambda_1 http://www.slac.stanford.edu/~rfaccini/phys/vub/SF/l1proj.eps
and vs BrBr http://www.slac.stanford.edu/~rfaccini/phys/vub/SF/brbr.eps
In these plots the arrows indicate the 1sigma contours of our assumed values. I would say that we are consistent although the central value of our fit lies ~1sigma from our assumed value, which is possible.
I would say this is the way we should go but I would not be ready to make these plots ufficial yet: what is the impact of the detector? Is there a binning effect? Claiming that we get an error on BRBR of about 10% which is what we would claim from the last plot I show needs lots more Xchecks. It basically means that we discard this configuration http://www.slac.stanford.edu/~asarti/recoil/newchiscan/RicQ2_b5l6_var.eps
at the two sigma level wrt to
the best chi^2 which is obtained in http://www.slac.stanford.edu/~asarti/recoil/newchiscan/RicQ2_b4l10_var.eps
can we get together to discuss this sometime today? can we use these plots in the discusion with CLEO anyhow?
ciao
ric
