The W Boson:
Transverse Momentum


Neutrinos do not interact strongly with matter and they are not detected by the D experiment. Because of this their momenta can not be deduced in the same way as charged particles and must be derived by conservation of momentum. The initial momentum of the system is zero (due to the proton / anti-proton beams having equal mass and velocities equal in magnitude but opposite in direction), so if we add the momenta of all the detected particles, any missing momentum in the system must belong to neutrinos.

Transverse Mass

To measure the momenta of neutrinos, we need to measure the total momentum of the products of the proton / anti-proton annihilation. However, this is not possible because we can only detect particles travelling radially outwards from the beam pipe (look at the detector to confirm this). To detect particles travelling along the beam pipe, we would need to place detectors in the pipe and obviously this is not possible. This means that the momentum of annihilation products that we can measure does not include the momentum along one axis (along the beam pipe). We can only measure the transverse momentum of the system.

To correct for this, a quantity similar to the invariant mass which only takes into account the transverse components is formed. This is the transverse mass:

For any system of particles:

  • WT is the combined transverse mass of the system
  • ET is the sum of transverse mass energies, ET = '.m.c, of particles in the system
  • pT is the sum of transverse momenta, pT = (px+py), of particles in the system
  • '= (1-((vx+vy)/c))-
  • c is the speed of light
  • vx and vy are the components of the velocity v in the x and y directions


The in the expressions for mass energy and momentum are relativistic corrections and represent the effect of special relativity. Under normal, non-relativistic, conditions is very close to 1 and is usually omitted.

In this case vx and vy are measured in the detector's rest frame.


Last modified Wed 23 January 2002 . View page history
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