Hoi,
I took the PDG2002 lifetime averages and calculate the BF for B0 and
B+ from them. I get
bfch := 0.10424
bfnu := 0.11316
You can check that they have the correct ratio (1.086) and
average (0.1087). It's described below how I calculate it.
On the BRECO Nsl sample (11582 B0 and 20583 B+), I find an effective
BF = 10.75 (this is a 1.1% change)
Weighting the lifetime according to the Nsl numbers, I get
tau = 1.5895
Weighting the lifetime according to the Nu numbers, I get
tau = 1.6021
Using these number for BF(B->Xu l nu) and |Vub| I find
BF(Brecoil ->X l nu) tau BF(Brecoil -> Xu lnu) |Vub|
----------------------------------------------------------------------
10.87 1.608 2.14 4.52
10.75 1.608 2.12 4.50
10.75 1.5895 2.12 4.52
10.75 1.6021 2.12 4.50
The BF changes by 1%, |Vub| correspondingly by 0.5%. It could be
useful if someone would check this.
Cheers,
--U.
#----------------------------------------------------------------------
# Lifetimes of B+ and B0
> tch := 1.542:
> tnu := 1.674:
>
# B(B->Xlnu)
> bf := 0.1087:
>
# Assume f+-/f00 = 1, i.e. sl BF is equally from B+ and B0
> f:= 0.5:
>
# Assume further b+/b0 = tch/tnu (with equal s.l. widths)
# and then solve b = f*b+ + (1-f)*b0 for either b+ or b0
> bfch := bf / (f + (1-f)*tnu/tch);
bfch := 0.1042384329
> bfnu := bf / (f*tch/tnu + (1-f));
bfnu := 0.1131615671
# Calculate the visible BF on the BRECO sample
> nch := 20583:
> nnu := 11582:
> bfeff := (nch*bfch + nnu*bfnu) / (nch + nnu);
bfeff := 0.1074514825
# Calculate weighted lifetime
> teff := (nch*tch + nnu*tnu) / (nch +nnu);
teff := 1.589530670
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