Estimating B flight direction

Study originally motivated by looking for new cut to help with D*l combinatorics.  If one can transform to the B0 rest frame, the neutrino and D*l candidate should be back-to-back -> neutrino momentum is know so the D*, lepton and neutrino can be added together to give B mass similar to M_ES cut.  The following plot shows the calculated B mass using MC truth to boost into B rest frame.

MCtruth.eps

A new application is getting a per-event correction to our delta z to delta t conversion.  We would like to do something like the BReco people and use the average tau approximation to improve our resolution.  The one piece of information we really need is cos(theta*), the flight angle of the B in the CM frame.  Here are 3 possible methods for estimating cos(theta*)

1.  Use the difference in tag, reco vertices boosted into CM to give direction of Breco.  In this method, each decay is considered an event in 4-space.  If we define:

    dx = x_reco-x_tag
    dy = y_reco-y_tag
    dz = z_reco-z_tag
    dt=dz/c(gamma)beta

Then P_tag = (0,0,0,0)     and   P_reco = (dx,dy,dz,dt).

I create this four vector and boost into CM frame (tag remains unchanged) using the Y(4S) boost vector.  In the Y(4S) rest frame, the Bs decay back-to-back so the time coordinate is disregarded at this point (but is was required when boosting).  The boosted values of dx,dy,dz can be used to calculate theta, phi.

Problems:

The dt isn't exactly right
Only have Y(4S) energy and momentum average, not per-event values.
The dz values are small, a small perturbation can cause a very large change in value of cos(theta)
I haven't rotated z axis yet, but this should be a small effect.
Still looking for a possible flaw in the above logic.

VertexBoostTheta.eps
VertexBoostPhi.eps

2.  Sum all charged tracks not used in D*l candidate to estimate tag B's momentum.  Boost this 4-vector into CM frame and call .theta() member function.

Problems:

Could miss soft tracks, pick up extra tracks from various interactions
Current track lists incomplete, charged tracks not used for D*l (tag/vertex) suppressed
            from D*l track list (tagging track list)

Currently processing ntuples with extra info

TagTheta.eps

3.  Use Tag momentum calculated by VtxTagBtaSelFit and boost into CM frame

Problems:

Not currently in our ntuple
Doesn't use all charged tracks on tag side, just the ones that vertex (probably fatal flaw, but will still investigate)