Heiko Lacker wrote:
> Hi Jeff,
> 
> I learned from Frank Tackmann, collaborator of Zoltan Ligeti, that there 
> is an important connection between B->Xulnu and B->Xsll:
> In the B->Xsll you are applying a cut in MX and q^2. The MX cut applied 
> is around 1.8 GeV and the q^2 region between 1 and 6 GeV^2 if I'm not 
> mistaken. This is in the shape function region and hence is an important 
> theoretical error in the interpretation of B->Xsll wrt NP.
> 
> Now, as you already know from Zoltan this error could be significantly 
> reduced if one used the measured rates B->Xulnu by applying the same 
> MX-q^2 cuts. In the main analysis we are cutting on MX<1.7 GeV and
> q^2>8 GeV^2. However, there is no reason to not quote in addition partial 
> BF's for other cuts if they can be useful for B->Xsll. 
> 
> The VubRecoil group aims for a publication of the MX-q^2 analysis in the 
> forthcoming months. I think it might be useful if we already take into 
> account that the B->Xsll analysis would profit from quoting partial BF's 
> for certain sets of MX-q^2 cuts. These would be partial BF's unfolded for 
> detector effects, that is, the quoted MX-q^2 cut values are the true ones.
> 
> To use our results you have to do of course the same in B->Xsll. Maybe 
> you could profit from the one-bin unfolding method used in the VubRecoil-
> MX-q^2 analysis. What do you think?
> 
> Cheers,
> Heiko
> 
> 

Hello Heiko--

Thanks for thinking of us; here are our (the b -> sll analysis group's) 
needs along those lines.

For the purpose of extracting a b -> sll signal, q^2 is not a serious 
consideration:  signal efficiency and background levels do not vary
dramatically as a function of q^2 (nor with lepton momentum, for that 
matter).  The only q^2 cuts employed are to veto the large non-penguin
background from J/psi X and psi(2S) X.   The PBF in q^2 range 1-6 Gev^2 
is favored by *theorists* as a higher-precision observable in the sense
of more controlled perturbative calculations (the low q^2 cut avoids the
"photon penguin pole" at q^2 = 0 and the upper cut is right below ccbar
threshold and thus avoids large NLO corrections from charm quark loops).
Experimentally we can measure any q^2 range except for small slices of
q^2 around the J/psi and Psi(2s).

Mx, on the other hand, is a serious consideration especially for mX > mD
where larger combinatoric backgrounds start creeping in.  The original
analysis chose mX < 1.8 (Belle has mx< 2.0) to reduce these, without
regard for any shape function effects (which have only been considered
recently).  For this summer we will attempt to raise this cut, possibly
to the 2.2 recommended by Zoltan et al.; this would largely eliminate 
the shape function error but is expected to be suboptimal for extracting 
a cleaner signal.

Unfolding is also not a serious consideration because we are analyzing
fully-reconstructed signal candidates and thus Mx and q^2 resolution for 
correctly reconstructed candidates is quite good and cross-feed much 
reduced by mES and DeltaE constraints.

Given these considerations, the main use of the B -> Xulnu results would 
be for interpreting the b -> sll low-q^2 PBF (1-6 GeV^2), where for Mx 
cuts below 2.2 the shape function error is non-negligible.  The relevant
(unfolded) PBFs would be

q^2 = 1-6 GeV^2
MX = 0-Mcut

where Mcut is 1.8,1.9,2.0,2.1,2.2 (or at minimum 2.0 and 2.2) so that,
depending on the statistically optimal choice of Mcut, we can obtain
a precision test of the standard model in the ratio of PBFs.

It may also be useful to do a similar ratio for the high q^2 region
above the psi(2s), where the b -> sll PBF is predicted using
different methods.  This would be in the q^2 range
q^2 > 3.8^2 = 14.44 GeV^2 with the same Mx cuts as above.


It may additionally be useful to compute similar ratios for
B -> Kll/K*ll with B ->pilnu/rholnu.  Modulo SU(3) breaking in
the form factors this would constrain |Vts/Vub|.


To what precision can you expect to compute these PBF's in B ->xulnu?

--Jeff