BackgroundsPhysIntro
Introduction
The Mu2e Experiment is hunting for an extremely rare process, even if we are fortunate enough to have a "strong" signal. It is therefore critical for us to keep our backgrounds low and for these backgrounds to be well-understood. Our backgrounds include anything that can be mistakenly selected as an electron from a muon conversion. This includes electrons from other sources that have either had their momenta mis-measured, or that happen to have the same momentum as our signal electrons. But the backgrounds can also come from particles that are mis-identified as electrons. We have sources of backgrounds both from the running of the experiment (beam-related backgrounds, cascades of particles in the detector due to other interactions) and also from nature (in the form of cosmic rays, or other natural sources of radiation.) Our ability to control and understand these backgrounds is directly tied to the sensitivity of our measurement. The primary sources of background are described below.
Decay In Orbit
When a "free" muon---one that is not in the field of a nucleus---decays, there is a limit to the energy that the outgoing electron can achieve. If we consider a muon at rest, the maximum energy is achieved when the two neutrinos from the decay are produced in the opposite direction of the electron. (The total kinetic energy of the outgoing particles is determined by the difference between the muon rest mass and the masses of the outgoing particles, in order to conserve energy. To maximize the kinetic energy of the outgoing electron and satisfy conservation of momentum, we need to have the electron produced back-to-back with the two neutrinos. Any other arrangement would reduce the kinetic energy of the outgoing electron.) If we consider that we must conserve energy and momentum, this upper limit can be found by subtracting the rest mass of the electron from the rest mass of the muon, and dividing the result by two, giving an upper limit of approximately 53 MeV, or half the mass of the muon. This is safely below our signal value of 105 MeV.
If the muon decays while it is in the orbit of a nucleus, however, it can exchange momentum with the nucleus. In the extreme (and rare) case where the outgoing neutrinos carry very little momentum, this can look like the two-body decay that we expect from the muon conversion signal, where the outgoing electron recoils off the nucleus. Precisely measuring the energy spectrum of these decays, which approach the signal energy, is an important part of the Mu2e analysis plan, and will allow us to predict this small, but challenging, background.
Radiative Pion Capture
The muon beam that is transported to the stopping target will have some pion contamination. The pions can also be captured by the nuclei in the stoping target, and a few percent of the time this capture process will result in the emission of a photon. The energy of the photons peaks at nearly the same energy as our signal electron. If the photon pair produces (forming an electron-positron pair in the field of a nucleus), and if the energy is shared asymmetrically between the electron and positron with the bulk of the energy carried by the electron, the electron energy can be similar to that of our signal electrons. The primary technique for reducing this background is ensuring a long enough waiting period between the delivery of the proton pulse and the live window of Mu2e data-taking, since radiative pion capture is a process that will occur quite soon after the beam pulse, whereas the muon to electron conversion can occur much later. The beam structure (ratios and placements of on-off beam time) coupled with the choice of aluminum as the stopping target and the design of the beam extinction system are all part of the strategy to control this background.
Electrons or Muons from Cosmic Rays
On the surface of the earth we are being bathed with cosmic rays, in spite of the protections of our atmosphere. Many particle physics experiments that are looking for low-rate processes build their detectors under mountains or at the bottom of mine shafts in order to benefit from a large amount of additional material to shield them from cosmic rays and reduce the impact of these plentiful particles from nature on the processes that they hope to study. Mu2e, however, needed to be located near Fermilab's intense beam of protons in order to create an intense enough beam of muons to be able to improve our sensitivity to our signal. We need a huge number of muons in our denominator in order to reach very low rates of muon decays where the signal could be hiding. This dictated that the detector be built on the surface, which means that we need to deal with an extremely high rate of particles pouring through our detector from cosmic rays.
There are a number of ways that we deal with this background. We do have passive shielding around the detector that blocks some of the particles from cosmic rays and reduces the flux of related particles through the detector. We also have active scintillating detectors that surround the experiment and let us know when a cosmic ray is passing through the detector so that we can veto the related detector activity as coming from cosmic rays and not a potential muon to electron conversion signal. We rely on this cosmic ray veto detector to catch over 99% of the cosmic rays that interact with Mu2e in order for us to be sensitive to the low rates of muon to electron conversion that we want to probe. Dedicated particle identification algorithms have been developed to tag muons from cosmic rays that get trapped in the solenoid field of the tracker to help reduce this contamination. Additionally, when we look to reconstruct our signal electrons, we assume in our algorithms that they originate from the stopping target. This geometric requirement means that we are only sensitive to those particles from cosmic rays that happen to pass through our detector in this particular way, which is a rare occurrence.
Radiative Muon Capture
We can consider muon capture in two categories: ordinary and radiative. In ordinary muon capture in Al, a neutrino and Magnesium nucleus are the products: an up quark in the proton converts to a down quark, which produces a neutron, through the exchange of a W boson with the muon. In radiative muon capture, there is also a photon produced. The photon can pair-produce in material, giving an electron and positron, which can then go on to interact with the Mu2e detector. This background can be controlled because the energy of the produced photon is capped at several MeV below the conversion electron signal energy---limited by the mass difference between the initial and final nuclei. This background can be controlled through the excellent performance of the tracking chamber in accurately measuring a particle's momentum.
Delayed particles from the beamline
Most of the beam background is eliminated by the waiting period between when the proton pulse is delivered and when the Mu2e trigger will begin looking for interesting interactions, but there are cases where the beam backgrounds are delayed. Slowly moving particles, and the resulting sprays of particles produced from their interactions with matter, can interact in the detector in our "live" window. The energies and rates of these particles are being studied with simulation.
Misreconstruction
In many of these background categories, we rely on the separation between the energy of the Mu2e conversion electron signal and the energy of the electrons produced by the backgrounds to allow us to discriminate between signal and background. The better the resolution of the Mu2e tracking detector to reconstruct this energy precisely, the better job we can do measuring and constraining these backgrounds. The tracker measures particle energy/momentum by reconstructing the helix formed by charged particles as they traverse the magnetic field. The helix radius is related to the particle's momentum. But there are a number of ways that this reconstruction can be tampered with. If the particle interacts with material in the tracker in a way that changes its trajectory, kinks in the helix can result in a mis-measurement of the particle momentum. In addition, if there are other particles simultaneously traversing the tracking detector, interactions from these particles can interfere with the correct reconstruction of the helix by causing the algorithm to confuse the path of one particle with the paths of others, resulting in the wrong momentum being reconstructed. It is therefore necessary for us to think not only of physics processes that can mimic our signal electron, but also detector and software effects that can produce backgrounds.