An important goal of particle physics is to describe the elementary constituents of matter, and the forces which govern them. So far three generations of fundamental fermions - leptons and quarks - have been discovered, and from precision measurements one can deduce that there cannot be more of them. We have not yet understood why there are exactly three generations of particles, for example three charged leptons, electron e, muon μ and tau τ, with similar properties. One possible explanation is that these leptons are not fundamental pointlike particles, but rather composed of even smaller objects. How can this hypothesis be tested? If for example the muon μ were a composite particle, one can expect 'excited states' μ*, particles similar to the muon, but with higher total energy and mass. A μ* will decay into the 'ground state' μ plus a photon. This is analogous to the atom, which is also a composite particle, made up of the nucleus and electrons. An excited atom has a higher energy, and decays to the ground state through the emission of a photon. So far no excited leptons or quarks have been discovered.
An excited muon must be very heavy (the mass must exceed 200 GeV), else it would have been seen in previous experiments. A μ* can be made by colliding a quark and an antiquark; when they annihilate they can transfer their energy into an excited muon. Lepton conservation laws require that the μ* is accompanied by a normal (anti)muon, see graph below. The subsequent μ* decay yields a muon and a photon. Altogether two muons (more precisely one muon and one antimuon, but for short we speak of two muons) plus one photon are produced.
The mass of the μ* is unknown, but it can be reconstructed from the measured momenta and energies of the daughter particles muon and photon. Since we have two muons in the final state, we must know which one stems from the μ*. One can calculate that it is the more energetic of the two muons which is - with high probability - the daughter of the excited muon. So we can compute for each collision event with two muons and one photon the would-be μ* mass; we call it for the moment mμγ, since we dont know yet if our μ* hypothesis is correct. The following Figure shows for all the collision events for which the DØ detector has recorded two muons plus one photon the reconstructed mass mμγ.
The Figure above shows also the expected mass distribution for the 'signal', here a μ* with a mass of 400 GeV. One would expect mμγ = mμ*;; however, due to the limited momentum and energy resolution of the detector, there is no sharp peak in the mμγ distribution at 400 GeV, but rather a broad bump around this value. Important: At high mass values above 200 GeV there are no measured events at all. This implies that there are no μ* particles! This non-observation of excited muons in the DØ data sample, corresponding to a two-year long measurement period, can be translated into an upper limit on the cross section (and subsequent decay) for μ* production, see next Figure.
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