Neutrinos do not interact strongly with matter and they are not detected by the DØ 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:

- W
_{T} is the combined transverse mass of the system

- ∑ E
_{T} is the sum of transverse mass
energies, E_{T} =
'.m.c², of
particles in the system

- ∑
__p___{T} is the sum of
transverse momenta, __p___{T} = (p_{x}²+p_{y}²)^{½},
of particles in the system

- '= (1-((v
_{x}²+v_{y}²)/c²))^{-½}

- c is the speed of light

- v
_{x} and v_{y} are the components of the velocity __v__
in the x and y directions

Note:

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 v_{x} and v_{y} are measured in the detector's
*rest frame*.