Hello folks,
I have been trying to understand things a bit better myself, please
apologize if I make mistakes.
First, I am confused about the issue of the orders at which things are
computed. It would be useful, also for posterity, that somebody, most
likely Urs, writes down which are the formulas he points at that support
our calculation.
I will just start from Sven's posting
http://babarhn.slac.stanford.edu:5090/HyperNews/get/ISLDecays/222.html
and assume
lambda_bar = 0.48+/0.09 (with error mutuated from PDG and the rescaling
from Sven)
lambda_1 =0.30+/0.14
I will also assume the correlation to be 0.8 ( Eckhard, where does the +
come from? the correlation in all plots is always negative!!)
I then assume that the relationships between mb,a and lambda_bar,lambda1
are
lamda_bar = mBmb+(3*lambda_2(mBmb)^2/(1+a))/2*mb
lambda_1=3 lambda_bar^2/(1+a)
where I have neglected lambda_2/mb^2 terms in the third addendum of the
first equation (actually I have also tried removing the third addendum
overall with no real change).
I then built the chi^2
chi^2=[(lambda_bar0.48)/0.09]^2+[(lambda_1+0.3)/0.14]^2
and plotted it :
a) in the case where no correlation is assumed
http://www.slac.stanford.edu/~rfaccini/phys/vub/theo/mba_nocorr.eps
b) with a correlation of 80%
http://www.slac.stanford.edu/~rfaccini/phys/vub/theo/mba_90.eps
c) blowing up the error to 150 MeV
http://www.slac.stanford.edu/~rfaccini/phys/vub/theo/mba_150.eps
My shapes are different from Eckhard's ones maybe because of the sign of
the correlation or maybe because we are typing different formulas (I get a
bit lost in maple code...), but the conclusions are similar: surprisingly
the correlations increase the range in which each of the axes vary. On the
contrary correlations should be taken into account, so I think we should
make the systematics extracting lambdabar and lambda1 and then recomputing
a and mb. The only problem is that we need to be sure of the equations and
the values of the lamdas that should be used
In summary I think that the next steps are:
 write cleanly the relationships we use to convert cleo's or PDG
results into our measurement (they might already be somewhere, but I could
not find them)
 implement the systematics in terms of lambda_1,lambda_bar and
their correlation
[this with the time scale of the conference, not of today...)
let me know what you think of this
ciao
ric
P.S. where is the 'code from Sven'?
On Mon, 17 Feb 2003, Eckhard Elsen wrote:
> I reevaluated the correlations of Friday. (They were in error since the
> mean values of the parameters had not entered the MAPLE equations).
>
> The new version
> http://www.slac.stanford.edu/~elsen/amb_new.pdf
>
> investigates the case of zero and 0.8 correlation between lambda_1 and
> Lambda_bar. Consequently the assumed uncertainty of 0.09 (value of
> draft) translates into a 0.09 GeV (0.15 GeV) uncertainty on m_b for
> correlation=0 (or 0.8).
>
> The actual contour shape in the parameter a varies with the assumed
> correlation. However, since the resulting uncertainty from a is smaller
> it is probably not worth the effort to go into detailed simulations.
>
> The proposal is hence to increase the theoretical of m_b to 0.15 GeV,
> such that it is by far the dominant error with ~20%...
>
> Eckhard
>
>
