Hoi,
I rechecked my formulas, I think the only bug was that I had swapped
the lifetimes. Ergo once more:
# Lifetimes of B+ and B0
> tnu := 1.542:
> tch := 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 := .1131615672
> bfnu := bf / (f*tch/tnu + (1-f));
bfnu := .1042384329
# Calculate the visible BF on the BRECO sample
> nch := 20583:
> nnu := 11582:
> bfeff := (nch*bfch + nnu*bfnu) / (nch + nnu);
bfeff := .1099485176
# Calculate weighted lifetime
> teff := (nch*tch + nnu*tnu) / (nch +nnu);
teff := 1.626469330
# Calculate weighted lifetime
> nuch := 91:
> nunu := 76:
> tefff:= (nuch*tch + nunu*tnu) / (nuch +nunu);
tefff:= 1.613928144
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 (original)
10.99 1.608 2.17 4.55
10.99 1.6265 2.17 4.52
10.99 1.6139 2.17 4.54
The formulas are
BF(B -> u l nu) = BF(B -> X l nu) * BRBR
Vub = 0.4 * sqrt( BF(B -> u l nu) / tau )
The BF changes by 1.1%, |Vub| correspondingly less (if you look at
more digits than displayed up there). There is compensation: B+ have a
higher BF(B->X l nu), thus raise BF(B ->u l nu). They have a longer
lifetime and thus will lower |Vub|.
Assigning a systematic error of 1% should cover all grounds.
Again, an independent cross check might be good.
Cheers,
--U.
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