Problem with vector pseudoscalar Decays

1
Problem with vector - pseudoscalar Decays

• Matrix Elements evaluated in rest frame of parent
• This change introduced a subtle bug in the PVP
  M.E.
• Many thanks to Ko, Amir, and Harry for spotting
  the problem
• Help me Understand This
• http//web.hep.uiuc.edu/e831/mcfocus/boosts/
• Talk Outline
• Topology and Symptoms
• Some Mechanics of MCFOCUS Event Generation
• Fundamental Problem and Possible Explanation
• Expedient Fix

2
Topology and Symptoms

• This matrix element applies to awide variety of
  decays
• Intensity function is cos(q)2 q is the angle
  between thevector mesons son and its unclein
  the vectors R.F.
• Intensity function does not reach zero at its
  minimum!

3
MCFOCUS Mechanics

• First, MCFOCUS decays D into f, p in Ds RF
• Both these are boosted into lab frame, saved in
  GB
• p is boosted into fs RF, saved in parameter
  array
• Second, f is decayed into K,K- in fs RF
• Intensity function calculates cos2 with 3-vectors
• Rejection loop is used to sculpt the PDF
• Once accepted, K,K- are boosted into lab frame,
  written into GB

4
The Underlying Problem

• Fact file
• Angle measured in intensity function (f RF) is
  different from angle measured from GB 4-momentum
  (using invariants)
• If we boost uncle p from f RF into lab, result is
  different
• Angle measured between this p and K (using lab
  frame quantities) is equal to that in the
  intensity function.
• Could this be
• Start with p in f RF. Boost into Ds RF, then
  the lab, then back into the fs RF again. Same
  p, different direction!
• This effect is the Wigner rotation
• Usually important when dealing with helicity,
  ignored otherwise
• But were using parallel-axis boosts. Doesnt
  that help?
• It shouldnt matter how you get into a reference
  frame! Are directions absolute or relative?

5
Easy Solution

• Dont correct for this rotation when boosting the
  two kaons
• Account for it by boosting pion into lab, then
  backwards into the f RF (not directly as before)

Much better!
6
Questions

• Did we just loose the benefit of evaluating
  matrix elements in the parents rest frame?
• We decided to use parents RF for numerical
  reasons
• Probably loosing a little bit, but only for this
  M.E.
• Were at least able to use double precision
• Is this explanation really true, or have I just
  bungled the boosts?
• Could this affect anything else?
• Probably not.

7
Equations

• Cos q
• Boost