To achieve the desired sensitivity to sin2θ13 of 0.01 or better, beside the highly sensitive equipment to detect neutrinos, it is necessary to discriminate the cosmic muon backgrounds from signal events. For Daya Bay experiment, it is highly desir-able that these cosmic muon induced backgrounds be measured in an underground laboratory that has similar overburdens and rock types as those in the Daya Bay experiment.
The Aberdeen Tunnel laboratory in Hong Kong turns out to be a good location
for this purpose. It has an overhurden of approximately 250 m of rocks with similar composition to those in Daya Bay experiment. The laboratory is located at the cross junction of the tunnel tubes at the middle of the Aberdeen Tunnel in Hong Kong. It is 22 m above see level at 22.23◦N and 114.6◦E. Most of the rocks in Hong Kong Island is granite with an average density about 2.5 to 2.8 g/cm−3.
The detector in Aberdeen Tunnel laboratory, it consists of a muon tracker and a neutron detector. The muon tracker is made up of three layers of proportional tubes and three hodoscopes of plastic scintillators for triggering on the cosmic-ray muons, and for determining the position of the incident muon in the offline analysis. The neutron detector contains two zones. The outer part is mineral oil to reduce the background such as γ-ray from radioactivity and cosmic moun-induced neutrons. The inner part is the liquid scintillator, which gives the signal when a neutron is captured. Fig. 2.4 shows the configuration of the Aberdeen Tunnel Lab.
Figure 2.4: The detector configuration for studying the cosmic background at the Aberdeen Tunnel Laboratory.
Chapter 3
Estimation of the muon-induced neutrons
For the low energy neutrino experiments, fast neutrons from cosmic-ray muons known to be an important background. This is because the muon-induced neu-trons often contaminate the neutrino detection signals . When an anti-neutrino is captured by inverse beta decay and a positron and a neutron are produced. The signals of anti-neutrino are detected by the detections of positions and neutrons.
The muon-induced neutron often mimicked the signals, when it interacted with the detector. Unlike charged hadrons, which can be tagged by the veto system, neutrons can not be identified until they are finally captured.
In this chapter, we discuss the yield of muon-induced neutron, the neutron energy spectrum, and the neutron angular distribution by the Monte Carlo sim-ulation package, FLUKA 2006.3, and we compare our result with that obtained by earler versions of FLUKA[12, 13, 16] and that by another simulation package, Geant41[14, 15, 16].
1This part of simulation has done by a colleague.
3.1 Background to Reactor Antineutrino Exper-iments
In reactor antineutrino experiments, the signal events (inverse beta decay reactions) have a distinct signature of two time-ordered events: a prompt signal resulting from position annihilation and a delayed neutron-captured signal. There are mainly two sources of neutron background in reactor antinetrino experiments.
One is local radioactivity which forms the uncorrected background, and the other is cosmic-ray muon which forms the correlated one. The correlated background is defined in such a way that when a background event is triggered by the prompt signal and delayed signal, both signals come from the same source. For example, the the muon-induced neutron gives a delayed signal, and the recoiled proton gives prompt signal. On the contrary, the uncorrelated background is defined when two signals come from different sources but satisfy the trigger requirements by chance. For example, local radioactivity and the single neutron events induced by cosmic muons may occur within a time coincidence window accidentally to form an uncorrelated background. We can measure the neutron background from local radioactivity by changing the time coincidence window. The neutron yield from cosmic-ray muons strongly depends on the depth due to the energy loss of muon when penetrating into the underground site. The muon-induced neutron background is more important for such reactor antineutrino experiments. There are several reasons for this:
1. The muon-induced neutrons can mimic the neutrino event detected via the inverse beta decay interaction by a detector. When a fast neutron propagate in the detector, it interacts with the surrounding material and the proton in the nucleus recoils. the recoiled proton behave like a prompt signal of e+. The fast neutron is then slowed down and finally captured that gives a delayed signal.
2. A detector can be protected against neutrons from the rock activity by
hydrogen-rich material, However such material will be a target for cosmic-ray muons and then produce more muon-induced neutrons surrounding the detector.
3. Cosmic-ray muons often have enough energy to penetrate through the de-tector and produce secondary particles, including secondary neutrons. But the primary particles will also interact with surrounding material and have the possibility to produce neutrons. These neutrons given by muon cascade make the background more complex and produce more fake signal events.
It is very difficult to measure these backgrounds, since they fulfill the whole requirements as an antineutrino event. In the ideal case, the background can be measured if the antineutrino sources, i.e. the nuclear reactors, are turned off.
Obviously this is almost impossible. The simulation of muon-induced neutron is needed to give a rough estimation of the background. Before detailing the simulation, it is necessary to understand the origins of fast neutrons.
3.1.1 Origins of the fast neutrons
The primary cosmic ray particle interact with molecules of our atmospere producing hadronic showers. At sea level, about 75% of the particles are muons and others are pions, protons, neutrons, electrons, and gamma rays. Excpet muon, all of the above particles can not penetrate through rock top underground. This is why most of neutrino experiments are performed underground to protect their detectors against the contamination of cosmic ray.
As said, even other particles are blocked, there is still background coming from cosmic-ray muons. Fast neutrons from cosmic-ray muons are produced in the following processes.
1. Muon interactions with nuclei via a virtual photon producing a nuclear dis-integrations, resulting in the original muon and a neutron coming out. This process is usually referred to as ”muon spallation”.
producing a nuclear disintegration. This process is usually referred to as ‘‘muon spallation’’ and is the main source of theoretical uncertainty.
!b" Muon elastic scattering with neutrons bound in nuclei.
!c" Photonuclear reactions associated with electromag-netic showers generated by muons.
!d" Secondary neutron production following any of the above processes.
Processes !b" and !c" are reasonably well understood while !a" and !d" are the root of the difficulties described in previous calculations. Neutrons can be also produced from muons which stop and are captured, resulting in highly ex-cited isotopes emitting one or more neutrons. This process is reasonably well understood and its contribution to total neu-tron yield can be calculated. All the experimental results re-ferred to in this paper do not include these neutrons since they can be easily identified and eliminated. Neutron produc-tion from neutrinos is negligibly small at the depths consid-ered and thus is not discussed in this paper.
The muon spallation process is schematically illustrated in Fig. 1. The desired #-N cross section is then calculated as
$
#!N" !
N%!&
"$ &
%-Nvirt!&
"d&!1"
where &"E!E ! , E and E ! are energies of initial and final muons, and N
%(&) the virtual photon energy spectrum. The-oretical calculations often treat the virtual photons according to the Weizsa¨cker-Williams approximation '18(, in which the passage of a charged particle in a slab of material pro-duces the same effects as a beam of quasireal photons. A general expression of the Weizsa¨cker-Williams formula is given in Ref. '10(:
N%!
&
"" ) initial and final muons.
Since in the above approximation it is assumed that the
%-N cross section is the same for real and virtual photons, the measured %-N cross section can be used to calculate the
#-N cross section in Eq. !1". At low muon energy the situ-ation is more complicated. Here, the virtuality of the photon becomes comparable to its energy and cannot be neglected.
It follows that the Weizsa¨cker-Williams approximation can
no longer be used. In addition, the interaction of the virtual photon with the nucleus is a collective excitation of the nucleus 'giant dipole resonance !GDR"( rather than a single photon-nucleon interaction. This implies that the GDR model would have to be applied to virtual photons, introduc-ing further theoretical and technical complications. However, it might be reasonable to assume that neutron production by low-energy muon interactions is small as compared to neu-tron photoproduction by low-energy bremsstrahlung photons and adds therefore only a minor contribution to the total neutron yield.
In addition to these assumptions, there are a number of problems associated with analytical calculations: first, they cannot reliably calculate all daughter products for every nucleus if the %-N interaction is very violent so that the nucleus becomes highly excited; second, they cannot prop-erly take into account secondary neutron production. Hence, while these calculations provide useful guidance and, at shal-low depths, where hadronic shower effects are small, they may even give quantitatively sound predictions '10(, in gen-eral they cannot be considered particularly reliable.
Monte Carlo approaches are commonly used to properly model hadronic cascades. Currently the most complete code to describe both hadronic and electromagnetic interactions up to 20 TeV is
FLUKA'17(. In this program, different physi-cal models, or event generators, are responsible for the vari-ous aspects of particle production at different energies '19(.
High-energy hadronic interactions are described based on the dual parton model followed by a preequilibrium-cascade model. In addition, models for nuclear evaporation, breakup of excited fragments, and % deexcitation treat the disintegra-tion of excited nuclei. Hadronic interacdisintegra-tions of photons are simulated in detail from threshold !GDR interactions" up to TeV energies !vector meson dominance model". For nuclei up to copper, measured photonuclear cross sections in the low-energy region are used '21(. Hadronic interactions of muons are based on the Weizsa¨cker-Williams approximation as formulated by Bezrukov and Bugaev '20(. A spectrum of virtual photons is generated which interact with nuclei simi-lar to real photons. As a result of the above theoretical and technical complications in the description of hadronic inter-actions of virtual photons at very low energies, the simula-tion is restricted to photon energies above the delta reso-nance threshold. The implementation of hadronic interactions of muons has been shown to give reliable pre-dictions for the MACRO experiment '22(.
In the following
FLUKAis used to obtain a consistent and complete estimate of neutron production from cosmic muons. We model a simple cubic detector filled with liquid scintillator C
nH2n#2, where n is taken to be 10. Muons with monochromatic energy are tracked in the detector, and sec-ondary neutrons and other hadrons are analyzed.
III. NEUTRON YIELD
The total neutron yield is probably the most measured quantity in our problem. There are many experimental results from different depths which can be compared with the model.
FIG. 1. The Feynman diagram of a muon spallation process.
Y.-F. WANG et al. PHYSICAL REVIEW D 64 013012
Figure 3.1: The Feynman diagram for a muon spallation process.
2. Muon elastic scattering with neutrons bound in nuclei.
3. Photonuclear reactions associated with eletromagnetic showers generated by muons.
4. There are secondary neutrons produced following any of the above processes.