Hi all,

 when studying momentum resolution in lepton ID I realized that
that bremsstrahlung for electrons can introduce large biases in
p* efficiency and resolution. It can also affect the mm2 resolution
and finally it produces large biases in the inclusive Mx reconstruction.

 I the past we always neglected this point.

 A couple of examples. Here is the p* resolution comparison
between e and mu:

http://www.slac.stanford.edu/~daniele/exclvub/bremstudy/resoelemu.eps

 that shows that the effect is large. And this is mm2 for pi0lnu:

http://www.slac.stanford.edu/~daniele/exclvub/bremstudy/mm2pi0elemu.eps

(for the inclusive calculation of mm2 the effect is smaller because the
brem photon is included in the X system and then recoil has it).

 I implemented a brem recovery algorithm that is very similar to the one
in Beta. Code is in VubAnalysis (in util.icc).
 It is based on two variables

 - Delta(theta): it is the difference between the theta of the brem photon
   and the electron one. They should be the same within resolutions.

 - DD = (Phi(gamma)-Phi(e production))/Phi(e EMC)-Phi(e production)): here
   I am requesting that the phi of the gamma is in between the phi of the
   electron at the EMC and the phi at the origin. I used this ratio
   (instead of a simple cut on Phi(gamma)-Phi(e production) as in Beta)
   because numerator and denominator are somehow proportional.

 Here the distributions for electrons
 Delta(theta) (for -0.3<DD<0.6)
 http://www.slac.stanford.edu/~daniele/exclvub/bremstudy/Deltatheta.eps

 DD (for -0.04<Delta(theta)<0.04)
 http://www.slac.stanford.edu/~daniele/exclvub/bremstudy/DD.eps

 I finally select brem photon with these cuts
 -0.04<Delta(theta)<0.04 && -0.3<DD<0.6
 and I redefined the electron p4 as p4+p4(brem photon). Moreover the
brem photons are removed from the good photon list (goodPhoton[i] = 0)


 The following plots are a comparison with and without the correction:

 resolution in p*:
 http://www.slac.stanford.edu/~daniele/exclvub/bremstudy/resoelecorr.eps

 mm2 for pi0lnu:
 http://www.slac.stanford.edu/~daniele/exclvub/bremstudy/mm2pi0elecorr.eps

 inclusive mm2
 http://www.slac.stanford.edu/~daniele/exclvub/bremstudy/mm2elecorr.eps
 (small effect as expected, see above, mostly due to gain in p* cut
  efficiency)

 inclusive fitted X mass (mxhadfit)
 http://www.slac.stanford.edu/~daniele/exclvub/bremstudy/mxhadfitelecorr.eps


 Conclusions:
 - brem recovery improves largely the resolution in p* and the efficiency
   of p* cut (~+5%)
 - it improves mm2 resolution in exclusive calculation of mm2. total mm2
   cut efficiency increase by 10-15% depending on the mode.
 - the removal of brem photon changes and improves significantly the
   reconstruction of the inclusive X mass (mxhadfit)

 Daniele