Magnetic Monopole Search at high altitude with the SLIM experiment

The SLIM experiment was a large array of nuclear track detectors located at the Chacaltaya high altitude Laboratory (5230 m a.s.l.). The detector was in particular sensitive to Intermediate Mass Magnetic Monopoles, with masses 10^5<M<10^{12} GeV. From the analysis of the full detector exposed for more than 4 years a flux upper limit of 1.3 x 10^{-15} cm^{-2} s^{-1} sr^{-1} for downgoing fast Intermediate Mass Monopoles was established at the 90% C.L.


Introduction
In 1931 Dirac introduced Magnetic Monopoles (MMs) in order to explain the quantization of the electric charge, obtaining the formula eg = n c/2, from which g = ng D = n c/2e = n 68.5e = n 3.29 · 10 −8 in the c.g.s. symmetric system of units [1]; n is an integer, n = 1, 2, 3, ... MMs possessing an electric charge and bound systems of a magnetic monopole with an atomic nucleus are called dyons. An extensive bibliography on MMs is given in ref. [2]. Relatively low mass classical Dirac monopoles have been searched for at high energy accelerators [3,4].
Magnetic Monopoles are present in a variety of unified gauge models with a wide range of masses. Grand Unified Theories (GUT) of the strong and electroweak interactions at the mass scale M G ∼ 10 14 ÷ 10 15 GeV predict the existence of magnetic monopoles, produced in the early Universe at the end of the GUT epoch, with very large masses, M M ≥ 10 16 GeV. Such monopoles cannot be produced with existing accelerators, nor with any foreseen for the future. In the past, GUT poles were searched for in the cosmic radiation. These poles are characterized by low velocities and relatively large energy losses [5]. The MACRO experiment set the best limits on GUT MMs with g = g D , 2g D , 3g D and dyons at the level of ∼ 1.4 · 10 −16 cm −2 s −1 sr −1 for 4 · 10 −5 < β = v/c < 0.7 [6].
Some GUT models and some supersymmetric models predict Intermediate Mass Monopoles (IMMs) with masses 10 5 < M M < 10 12 GeV and with magnetic charges of multiples of g D ; these MMs may have been produced in later phase transitions in the early Universe and could be present in the cosmic radiation [7,8].
IMMs may be relativistic since they could be accelerated to high velocities in one coherent domain of the galactic magnetic field. In this case one would have to look for downgoing, fast (β > 0.03), heavily ionizing MMs 1 .
The main purpose of the SLIM (Search for LIght Monopoles) experiment at the Chacaltaya laboratory in Bolivia at 5230 m a.s.l., was the search for IMMs [9]. An exposure at a high altitude laboratory allows to search for MMs of lower masses, higher magnetic charges and lower velocities, see Fig. 1.
The searches for IMMs by Earth based detectors are essentially limited to downgoing particles [10]. Water Cherenkov detectors are limited to fast downgoing IMMs (with β > 0.5), and a search can be done if the detectors are able to discriminate against the large background of cosmic ray muons [11]. The SLIM detector was also sensitive to Strange Quark Matter nuggets [12,13] and Q-balls [14]. The results on these Dark Matter candidates are discussed in ref. [15].
In the following, we present a short description of the SLIM apparatus, the calibrations of the Nuclear Track Detectors (NTDs), the etching and analysis procedures, and the limits obtained by the experiment on IMMs and GUT Magnetic Monopoles.

Experimental procedure
The SLIM experiment was an array of NTDs 2 with a total surface area slightly greater than 400 m 2 [9]. The array was organized into 7410 modules, each of area 24 × 24 cm 2 . All modules were made up of: three layers of CR39 R 3 , each 1.4 mm thick; 3 layers of Makrofol DE R 4 , each 0.48 mm thick; 2 layers of Lexan each 0.25 mm thick and one layer of aluminum absorber 1 mm thick (see Fig. 2 right). The CR39 used in about 90% of the modules (377 m 2 ) was of the same type used in the MACRO experiment [6]. The remaining modules, 50 m 2 , utilized CR39 containing 0.1% of DOP additive, CR39(DOP).
Each module (stack) was sealed in an aluminized plastic bag (125 µm thick) filled with dry air at a pressure of 1 bar. The modules were transported to La Paz, Bolivia, from Italy in wooden boxes and their position with respect to the other modules in the shipping crate was recorded. The stacks were deployed under the roof of the Chacaltaya Laboratory, roughly 4 m above ground (see Fig. 2  The atmospheric pressure at Chacaltaya is about 0.5 bar; before shipping to Chacaltaya, in Bologna we checked the air tightness of the envelopes sealed with air at a pressure of 1 bar by placing a sample of them in an airtight tank at a pressure of 0.3 atm for a few months; no significant leakage was detected.
From the experience gained with the MACRO Nuclear Track Subdetector [6], we know that the used CR39 does not suffer from "aging" or "fading" effects for exposure times as long as 10 years [16].

Environmental measurements
During the first phases of the detector deployment we evaluated possible effects of climatic conditions on the detector response and possible backgrounds. Previous tests had shown that the CR39 response does not depend on the time elapsed from its production and the passage of the particle if the ambient temperature ranges between -20 • C and +30 • C. The minimum and maximum values of the air temperature in each detector hall in Chacaltaya was recorded 3 times a day over the lifetime of the experiment. The temperature values usually ranged from 0 • C to 30 • C with an average value of 12 • C for the whole year and from one year to the other; however in the summer months in very few cases temperatures down to -5 • C were measured in the early morning. Therefore, no significant variations were expected in the detector response over the exposure period.
We performed measurements of the radon concentration in different locations of the experimental rooms where the SLIM detectors were placed. We used for this purpose E-PERM R radon dosimeters. The measured radon activity was about 40 ÷ 50 Bq/m 3 of air. According to our previous experience with the MACRO NTDs, we concluded that this level of radon induced radioactivity did not present a problem for the experiment, even in case of radon diffusion into the module bags.
Two different types of neutron detectors (BTI bubble counters and a BF3 counter detectors) were used to measure the neutron flux at Chacaltaya, during the first installation shift of 2001 over the energy range of a few hundred keV to about 20 MeV [18]. Neutrons of these energies interacting inside the detectors could induce background tracks, and their density could affect the scanning speed and efficiency. Both types of neutron detectors measured the accumulated dose. Consistent results were obtained by both types of detectors. The accumulated dose measured in open air and near the detectors was very similar. The absolute neutron flux was computed using the BTI bubble counters for which the efficiency is known. A value of (1.7 ± 0.8) · 10 −2 cm −2 s −1 was obtained, which is in agreement with other reported neutron flux data at the altitude of Chacaltaya and with more recent measurements at the same location [19]. The necessity to reduce the neutron induced background in CR39 required us to study special etching procedures, mainly based on the addition of ethyl alcohol to the etching solutions. As discussed in the next section, the addition of alcohol reduces the background tracks on the detector sheets and improves the surface quality (i.e. greater transparency), at the expense of a higher threshold [17].

Etching procedures
The passage of a magnetic monopole in NTDs, such as CR39, is expected to cause structural line damage in the polymer (forming the so called "latent track"). Since IMMs have a constant energy loss through the stacks, the subsequent chemical etching should result in collinear etch-pit cones of equal size on both faces of each detector sheet. In order to increase the detector "signal to noise" ratio different etching conditions [16,17] were defined. The so-called "strong etching" technique allows better surface quality and larger post-etched cones to be obtained. This makes etch pits easier to detect under visual scanning. Strong etching was used to analyze the top-most CR39 sheet in each module. "Soft etching" was applied to the other CR39 layers in a module if a candidate track was found after the first scan. This process allows to proceed in several etching steps and study the formation of the post-etched cones.

NTD calibrations
The CR39 and Makrofol nuclear track detectors were calibrated with 158 A GeV In 49+ and Pb 82+ beams at the CERN SPS and 1 A GeV Fe 26+ at the Brookhaven National Laboratory (BNL) Alternating Gradient Synchrotron (AGS). The calibration layout was a standard one with a fragmentation target and CR39 (plus Makrofol) NTDs in front of and behind the target [20]. The detector sheets behind the target detected both primary ions and nuclear fragments of decreasing charge.
We recall that the formation of etch-pit cones ("tracks") in NTDs is regulated by the bulk etching rate, v B , and the track etching rate, v T , i.e. the velocities at which the undamaged and damaged materials (along the particle trajectory), are etched out. Etch-pit cones are formed if v T > v B . The response of the CR39 detector is measured by the etching rate ratio p = v T /v B .
After etching the standard calibration procedure was the following: (i) measure the base area of each track in NTDs with an automatic image analyzer system [21]. The projectile fragments carry the same β and approximately the same direction of the incident ion; the Z of each resolved peak is identified via the base area spectrum. The average base area distributions of the In (1 pixel 2 = 0.3 µm 2 ).
(ii) For each calibration peak the Z/β is obtained and the reduced etch rate (p − 1) is computed. The Restricted Energy Loss (REL) due to ionization and nuclear scattering is evaluated, thus arriving to the calibration data of (p − 1) vs REL shown in Fig. 4 for both strong and soft etching conditions for CR39 and CR39(DOP). For soft etching the threshold in CR39 is at Z/β ∼ 7 corresponding to REL ∼ 50 MeV cm 2 g −1 . For strong etching the threshold is at Z/β ∼ 14, corresponding to REL ∼ 200 MeV cm 2 g −1 .
The extrapolation of the calibration curves to p = 1 gives REL < ∼ 40 MeV cm 2 g −1 for soft etching and REL < ∼ 160 MeV cm 2 g −1 for strong etching. For CR39(DOP) the threshold in soft etching conditions is at Z/β ∼ 13 corresponding to REL ∼ 170 MeV cm 2 g −1 ; the threshold in strong etching conditions is at Z/β ∼ 21 corresponding to REL ∼ 460 MeV cm 2 g −1 . The extrapolation of the calibration curves to p = 1 gives REL < ∼ 240 MeV cm 2 g −1 for strong etching. For magnetic monopoles with g = g D , 2g D , 3g D we computed the REL as a function of β taking into account electronic and nuclear energy losses, see Fig. 5 [22].
For the Makrofol polycarbonate the detection threshold is at Z/β ∼ 50 and REL ∼ 2.5 GeV cm 2 g −1 [17]; for this reason the use of Makrofol is restricted to the search for fast MMs.

Analysis
After exposure at Chacaltaya the modules were brought back by air flights to Italy in order to be etched and analyzed in the Bologna laboratory. Three "reference" holes of 2 mm diameter were drilled in each module with a precision machine (the hole locations were defined to within 100 µm). This allowed us to follow the passage of a "candidate" through the stack. The bags (envelopes) were opened, the detectors were labeled and their thicknesses were measured, using a micrometer, in 9 uniformly distributed points on the foil surface.
The analysis of a SLIM module started by etching the uppermost CR39 sheet using strong conditions in order to reduce the CR39 thickness from 1.4 mm to ∼ 0.9 mm. After the strong etching, the CR39 sheet was scanned twice, with a stereo microscope, by different operators, with a 3× magnification optical lens, looking for any possible correspondence of etch pits on the two opposite surfaces. The measured single scan efficiency was about 99%; thus the double scan guarantees an efficiency of ∼ 100% for finding a possible signal. Further observation of a "suspicious correspondence" was made with an optical 20 ÷ 40× stereo microscope and classified either as a defect or a candidate track. This latter was then examined by an optical microscope with 6.3 ob × 25 oc magnification and the axes of the base-cone ellipses in the front and back sides were measured.
A track was defined as a "candidate" if the computed p and incident angle θ on the front and back sides were equal to within 20%. For each candidate the azimuth angle ϕ and its position P referred to the fiducial marks were also determined. The uncertainties ∆θ, ∆ϕ and ∆P defined a "coincidence" area (< 0.5 cm 2 ) around the candidate expected position in the other layers, as shown in Fig. 6.
In this case the lowermost CR39 layer was etched in soft etching conditions, and an accurate scan under an optical microscope with high magnification (500× or 1000×) was performed in a square region around the candidate expected position, which included the "coincidence" area. If a two-fold coincidence was detected, the CR39 middle layer was also analyzed.
The bottom CR39 sheet was etched in about 50 cases; the third CR39 sheet was etched only in few cases, when there was still a possible uncertainty, and for checks (∼ 16 times). Some Makrofol foils were etched for reasons similar to the previous point and for other checks concerning the Makrofol itself (∼ 12 times).  Figure 6: Illustration of the procedure used to define the "confidence" area where the possible continuation of a candidate track inside two (or more) sheets of the same module was searched for (see text for details).

Results
From the detector calibration we computed the SLIM acceptance for downgoing IMMs with g = g D , 2g D , 3g D and for dyons. For the i th module of area S i the acceptance was computed as The total acceptance is the sum of all the individual contributions. Since no candidates were found, the 90% C.L. upper limit for a downgoing flux of IMMs and for dyons was computed as where ∆t is the mean exposure time (4.22 y), SΩ is the total acceptance, ǫ is the scanning efficiency estimated to be ∼ 1.
Two "strange events" were observed and were finally classified as manufacturing defects in a small subset of CR39 NTDs. These "strange events" are discussed in detail elsewhere [23].  Superheavy GUT magnetic monopoles in the cosmic radiation can traverse the Earth. Therefore the SLIM limit on their flux is one half of the IMM flux: φ GUT < 6.5 · 10 −16 cm −2 s −1 sr −1 for β > 0.03 for g = g D [6]. Fig. 8 shows the flux upper limits for MMs of charge g = g D and β > 0.05 vs monopole mass. Note that the SLIM limit is 1.3 · 10 −15 cm −2 sr −1 s −1 for MM masses smaller than ∼ 5 · 10 13 GeV and 0.65 · 10 −15 cm −2 sr −1 s −1 for masses larger than ∼ 5 · 10 13 GeV. In Fig. 8 are also shown the limits obtained by the MACRO [6] and OHYA [24] experiments for g = g D magnetic monopoles with β > 0.05.

Conclusions
SLIM is the first experiment to extend the cosmic radiation search for Magnetic Monopoles to masses lower than the GUT scale with a high sensitivity.
The addition of SLIM data to the MACRO data would improve the MACRO limits by only 18%. Large scale underwater and under ice neutrino telescopes (Amanda, IceCube, ANTARES, NEMO) have the possibility to search for fast IMMs with β > 0.5 to a level lower than the Parker bound [11,25].  [6] and OHYA [24] experiments. MMs with masses smaller than ∼ 5 · 10 13 GeV are detected only if coming from above; MMs with masses larger than ∼ 5 · 10 13 GeV can traverse the Earth, so an isotropic flux is expected. The Parker bound [26], obtained from the survival of the galactic magnetic field, and the limit obtained from the mass density for a uniform density of monopoles in the Universe [27] are also plotted.