Hoi,
I tested the result of the PRL analysis wrt to variations of the SF
parameters. I use the numbers from CLEO's CBX
http://www.slac.stanford.edu/~ursl/talks/061603/cbs0159.ps.gz
in table 1:
-------------------------------------------------------------------
Run deltamb deltaa Result (stat error only)
-------------------------------------------------------------------
sf-e-00.dat -0.065 -0.32 0.0231331 +- 0.00280705
sf-e-01.dat -0.301 +0.67 0.0380874 +- 0.00443508
sf-e-02.dat +0.005 -2.92 0.0181131 +- 0.00222707
sf-e-03.dat +0.055 -2.23 0.0159838 +- 0.00193727
sf-e-04.dat +0.045 +1.26 0.0207438 +- 0.00254212
sf-e-05.dat -0.015 +0.14 0.0222166 +- 0.00270575
sf-e-06.dat -0.015 -2.30 0.0158894 +- 0.00192506
sf-e-07.dat -0.065 +0.39 0.0246229 +- 0.00298269
sf-e-08.dat -0.065 -1.14 0.020265 +- 0.00246847
sf-e-09.dat -0.110 +0.61 0.0269626 +- 0.00324463
sf-e-10.dat -0.110 -0.76 0.0229559 +- 0.00277994
sf-e-11.dat -0.220 +0.74 0.0334033 +- 0.00394548
sf-e-12.dat -0.220 +0.16 0.0310471 +- 0.00368471
sf-e-13.dat -0.270 +0.73 0.0364401 +- 0.00426178
sf-e-14.dat -0.270 +0.51 0.0354744 +- 0.00415781
sf-e-15.dat -0.320 +0.69 0.0393289 +- 0.00456418
sf-e-xx.dat +0.0 +0.0 0.0213044 +- 0.00259884
------------------------------------------------------------------
where the rows correspond to the rows in CLEO's CBX. I run the fit
with the non-resonant model only.
A display of this is given in
http://www.slac.stanford.edu/~ursl/talks/061603/brbr.eps.gz
http://www.slac.stanford.edu/~ursl/talks/061603/lbarl1.eps.gz
where the first plot shows the distribution of BRBR (top) and at the
bottom "default - BRBR" (where default is sf-e-xx, with nonresonant
only). The second plot shows lambda1 vs. LambdaBar, in black filled
circles the CLEO points (their central value is shown in the open
circle). In red the central values we use and the error we quote
(\Delta\chi^2=1 ellipse).
The differences to the "default" (non-resonant only) BRBR seem too
large to represent the real error (maybe this is wishful thinking).
If I took the numbers in CLEO's CBX at face value, I'd conclude that
the shape function parameters are known with much less accuracy than
the HQET parameters. I think we need to understand very clearly how
much connection there is between these two interpretations, as CLEO is
probably going to complain, whereas Zoltan and Thomas had a different
opinion.
Cheers,
--U.
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