5a.
http://atlas.physicsmasterclasses.org/en/zpath_messung2.htm
Identify with mass!
Hold on! You are about to dig into some important
physics concepts!
In the more complete version of Einsteins formula
[eq_inline:E_rel12.png], E is the
energy of the particle, p its momentum and m0 its mass
when at rest. It so happens that this definition of mass is
conserved in Nature and is called “Invariant Mass”.
Shuffling the formula we get:
[eq_div:E_rel14.png]
Since this quantity is conserved we can use it to infer
the Z boson mass of a decaying (“mother”) particle: You
measure the energy and momentum of the decay
products, from which the mass of the “mother” particle
is inferred, since what comes in must go out. Quite
straightforward and simple, isn't it?
In the case of a Z boson decaying to an electron (e-)
positron (e+) pair the sum of energies and momenta of
the electron and positron lead to the mass of the Z
boson in the following way:
[eq_div: E_rel15.png]
The Z boson energy and momentum, EZ = Ee- + Ee+ and
, are hence known because the ATLAS
detector can measure the energy and momentum of the
decay-products. That means you have all you need to
infer the mass of the Z boson, or that of other particles
like J/ and !
In fact this, so-called invariant mass method works for a
variety of combinations of decay products, such as , l+l(l=e,), l+l-l+l-, and more, as you will find out when
studying the Z boson, searching for the Higgs boson, or
even exploring the Unknown!
[comment: No need for the “Invariant Mass” file
anymore.]