Simulations of neutrino and muon interaction in matter for geological structures radiography
© The Society of Geomagnetism and Earth, Planetary and Space Sciences (SGEPSS); The Seismological Society of Japan; The Volcanological Society of Japan; The Geodetic Society of Japan; The Japanese Society for Planetary Sciences; TERRAPUB 2010
Received: 1 December 2008
Accepted: 17 June 2009
Published: 22 February 2010
Neutrino and muon radiography seems to provide a method complementary to the more conventional seismic studies for getting information on the very deep geological structures. Here we describe the status of the simulations of neutrino and muon interaction in matter.
The internal density profile and shape of Earth is commonly studied by indirect physical methods, starting from the 1793 deduction by Cavendish that the Earth must have a dense core, based on a gravitational calculation, to the current methods which use sismic wave propagation, studies of the vibrational modes of the Earth as an elastic body, or temperature constraints. However, these studies are still subject to intrinsic ambiguities (Aki and Richards, 1980; Lay and Wallace, 1995). For these reasons, independent measurements of the density profile would be of considerable value and in the last years complementary methods for Earth radiography were pursued, by using cosmic beams of neutrinos and muons. The principle of tomography by energetic beams is essentially the same as X-ray tomography, except for substituting penetrating particles in place of X-rays. By measuring their absorption along different paths through a solid body, one can deduce the nucleon density in the interior of the object.
The Earth’s tomography with ultra-high energy cosmic neutrinos seems to provide a viable independent determination of the Earth’s internal structure (Jain et al., 1999; Reynoso and Sampayo, 2004), giving some information on its internal density distribution. On the other side, cosmic ray muon radiography can be applied to km-size objects located at elevations above where the detector is placed (Ambrosio et al., 1995; Nagamine et al., 1995; Tanaka et al., 2003, 2005, 2007a–c, 2008; Tanaka and Yokoyama, 2008).
The idea of neutrino tomography is based on the fact that Earth becomes opaque to neutrinos of energy exceeding ∼10 TeV, since at this energy the diameter of Earth corresponds to about one absorption length. Such neutrinos are produced by collisions of cosmic rays with the Earth atmosphere, and interact during their travel in such a way that the charged leptons produced, essentially muons, could emerge from the surface and be detected by a km3 Neutrino Telescope (NT). In this concern, after the first generation of telescopes which has proved the feasibility of the Cerenkov detection technics under deep water (Balkanov et al., 1999) and ice (Ahrens et al., 2002) by detecting atmospheric neutrinos, we are likely approaching the first detections of astrophysical neutrinos at the IceCube (Ahrens et al., 2004) telescope, being completed at the South Pole, and possibly at the smaller ANTARES (Spurio, 2006) telescope under construction in the Mediterranean. Moreover, ANTARES as well as NESTOR (Aggouras et al., 2006) and NEMO (Migneco et al., 2008) are involved in R&D projects aimed at the construction of a km3 NT in the deep water of the Mediterranean sea, coordinated in the European network KM3NeT (Katz, 2006).
On the other side, cosmic ray muons are also generated from cosmic rays in the atmosphere and arrive at angles ranging from vertical to horizontal (Thompson and Whalley, 1975) with a smaller number of neutrino-induced muons directed upward. These particles are highly penetrating and a typical horizontally-arriving cosmic-ray muon with an energy of 1 TeV penetrates 2.6 km of water. Thus, cosmic ray muon radiography can be applied to Earth structures with size of the order of a km, placing a detector with a smaller area than a NT (∼m2) near a volume that is higher in elevation adjacent to the detector.
In both of these technics, full Monte Carlo simulations are needed for the extraction of physical parameters from the detected numbers of events. In the following we will report on the status of studies, aiming to simulate the interaction of neutrinos inside the Earth and the propagation of their parents leptons inside matter.
2. Earth’s Tomography with Neutrinos and Muons
In order to understand how the number of charged lepton events at a km3 NT depends on the density of matter crossed by HE neutrinos, let us remind the formalism developed in Cuoco et al. (2007). In the following we will refer our calculation to a km3 NT placed at NEMO site.
- 4)Finally, the μ lepton emerging from the Earth rock propagates in water and enters the NT fiducial volume through the lateral surface Σ a at the point r⃗ a with energy E μ . The corresponding survival probability is
3. Simulation of Neutrino and Lepton Propagation Inside Matter
Our work aims to the development of Monte Carlo methods for simulating neutrino and muon interaction in matter. A possible line towards this purpose is based on the combination of two existing Monte Carlo, the HERWIG hadron generator (Corcella et al., 2001) to simulate neutrino interactions inside the Earth, and GEANT4 (Geometry ANd Tracking) (Agostinelli et al., 2003; Allison et al., 2006, http://www.geant4.org) to simulate the propagation of the produced muons in matter.
HERWIG (Corcella et al., 2001) is an event generator for high-energy processes particularly suited for detailed simulation of QCD parton showers. It provides simulation of hard lepton-lepton, lepton-hadron and hadron-hadron scattering and soft hadron-hadron collisions within a single package. In particular, HERWIG can simulate the neutrino interaction and, in a previous work (Ambrosio et al., 2003), it was already combined with the Monte Carlo CORSIKA (Heck et al., 1998), by some of the present authors, to develop a new version of CORSIKA capable of simulating atmospheric showers induced by neutrinos.
Geant4 is a toolkit for the simulation of the passage of particles through matter. Its areas of application include high energy, nuclear and accelerator physics, as well as studies in medical and space science.
In the simulations here described, we have generated a large number of tracks crossing the NEMO site by means of a detailed Digital Elevation Map of the under-water Earth surface, which is available from the Global Relief Data survey (ETOPO2): a grid of altimetry measurements with a vertical resolution of 1 m averaged over cells of 2 minutes of latitude and longitude. The Earth is described by a simplified version of the Preliminary Reference Earth Model (PREM) (Dziewonski, 1971), with three density regions: crust, mantle, and core.
In order to test the results coming from the link of HERWIG and GEANT4, we developed also a simplified Monte Carlo, which simulates neutrino interaction in Earth, and propagates the outgoing muon, taking into account the phenomenon of neutrino regeneration by NC interaction and muon energy loss in matter. The number of neutrinos injected at each angular bin was scaled according to the known flux of atmospheric neutrinos, depending on energy and angle. An energy threshold was applied to the muons detected in the fiducial volume.
To simulate the radiography of Earth structures by cosmic ray muons, a beam of muons is tracked while crossing the rock of the considered geological structure. Since the dimensions of the detector are orders of magnitude smaller than the dimensions of the structure that we want to investigate, in first approximation we can consider the detector as pointlike and, by using a Digital Elevation Map, for each direction crossing the detector we can evaluate the amount of rock crossed by the muon. In such a way, as in the case of neutrino Earth radiography, we can define the dimensions of the passive material where GEANT4 performs the tracking. To study the presence of holes or of zones with a different density in the passive material structure, one or more substructure can be added. The output gives information about the outgoing muon energy and direction.
4. Results and Conclusions
By summarizing, the results we have presented confirm that neutrino or muon radiography of geological structures is a very promising research field, and with the help of the simulations we are developing one can achieve the final goal of recognizing a non trivial density profile with a good level of statistical confidence.
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