Search for Excited Muons in Proton-Antiproton Collisions at a Center of Mass Energy of 1.96 TeV

What are excited muons?

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.

Excited muon search at the Tevatron

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.

Since quarks (antiquarks) are the constituents of protons (antiprotons), excited muons can be produced in proton-antiproton collisions at the Tevatron accelerator. The DØ detector can identify the various known particles and measure the direction and energy of muons and photons with good precision. Since the Tevatron collider provides a very high collision energy of 1960 GeV = 1.96 TeV, this experiment has a good chance to detect excited muons - if they exist and if they are not too heavy.

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 m_μγ, 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 m_μγ.

Shown are the measured data as well as theoretical predictions. As can be seen, many events are found for small mass values - for which the existence of a μ* is already experimentally excluded. These data at small values of m_μγ can be explained by 'background' processes, which also lead to two muons plus a photon. In particular Z bosons - decaying into two muons - accompanied by a photon can fake the production of excited muons.

Search Results

The Figure above shows also the expected mass distribution for the 'signal', here a μ* with a mass of 400 GeV. One would expect m_μγ = m_μ*;; however, due to the limited momentum and energy resolution of the detector, there is no sharp peak in the m_μγ 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.

The cross section is a measure of the production rate and given in the unit pb = picobarn. The experimental cross section limit can be compared to the cross section predicted by our μ* model, as a function of a parameter Λ in the theoretical model. Λ as well as the μ* mass are unkown, but we expect Λ to be in the range 1 to 4 TeV. The Figure displays along the experimental upper limit three theoretical curves for three different assumptions on Λ. If the predicted cross section exceeds the experimental upper bound, the corresponding μ* mass is excluded. From the Figure we can read off: For Λ=1 TeV excited muons with a mass smaller than 618 GeV are excluded! This bound is more stringent than those obtained in other experiments - thus an important step forward has been made in testing the compositeness hypothesis.

If you have any questions about this analysis, please contact the principal authors