Magnetic Monopole Searches with AMANDA and Other Detectors

Magnetic Monopole Searches with AMANDA and other detectors

Matilda Åberg Lindell

May 2010

Abstract

Magnetic monopoles are hypothetical particles carrying isolated magnetic charges, analogous to electrically charged particles. They have never been observed in experiments, but there are theoretical indications that they might exist. Several experiments have been carried out over the years in order to detect monopoles, or to set upper limits on their abundance in the Universe. In this work, underlying theory of the properties of magnetic monopoles is presented, together with some of the experiments performed in the past, the present and the future. Emphasis is put on AMANDA and other Cherenkov neutrino telescopes. Results of the described experimental searches are summarized.

Contents

1 Introduction 1

2 Theory and properties of magnetic monopoles 2 2.1 Classical electrodynamics ...... 2 2.2 The Dirac monopole ...... 2 2.3 GUT monopoles ...... 3 2.4 Creation in the early Universe ...... 4 2.5 Acceleration ...... 4 2.6 Interaction with matter ...... 5 2.6.1 Ionization and excitation ...... 5 2.6.2 Radiative losses ...... 5 2.6.3 Cherenkov radiation ...... 5 2.6.4 Catalysis of nucleon decay ...... 5 2.6.5 Induction ...... 6

3 Detector types and searches 7 3.1 Water and ice Cherenkov detectors ...... 7 3.1.1 AMANDA ...... 7 3.1.2 ANTARES ...... 8 3.1.3 Baikal ...... 10 3.1.4 IceCube ...... 10 3.1.5 IMB ...... 11 3.1.6 Kamiokande ...... 12 3.1.7 RICE ...... 12 3.2 Superconducting induction devices ...... 13 3.2.1 Cabrera experiment ...... 13 3.3 Scintillators ...... 14 3.3.1 MACRO ...... 14 3.4 Gaseous detectors ...... 15 3.4.1 KGF ...... 15 3.4.2 MACRO ...... 15 3.4.3 Soudan 2 ...... 16 3.5 Nuclear track detectors ...... 16 3.5.1 MACRO ...... 16 3.5.2 Ohya ...... 16 3.5.3 Price ...... 16 3.5.4 SLIM ...... 17 3.6 Accelerators ...... 18 3.6.1 CDF ...... 18 3.6.2 H1 ...... 19 3.6.3 Oklahoma experiment ...... 19

4 Experimental bounds 20 4.1 GUT monopoles and IMMs ...... 20 4.2 Classical monopoles ...... 24

5 Conclusions and outlook 25

References 26 1 Introduction

Electricity and magnetism are two manifestations of the same phenomenon - electromagnetism. Positive and negative electric monopoles, e.g. protons and electrons, have for a long time been known to exist. Magnetic charges, known as north and south poles, are also well established in physics. However, whereas the electric charges can be isolated, the magnetic charges have always shown up in pairs. When a magnet is cut in two halves, the result is thus not two pieces carrying net magnetic charges, but instead two new magnetic north-south dipoles.

Based on quantum mechanical arguments, Paul Dirac introduced the notion of magnetic monopoles in 1931, as a means of explaining the quantization of electric charge. This would restore the beautiful symmetry between electricity and magnetism that is lacking in Maxwell's classical view on electromagnetism. The possibility that monopoles might occur has since then intrigued theorists as well as experimentalists, and large eort has been made to show that magnetically charged particles do exist. Theories predict a wide range of monopole masses and velocities, with several dierent detector approaches as a result.

This thesis aims at presenting some important experimental searches for magnetic monopoles performed since the concept of monopoles was introduced, as well as describing some of the underlying theories for monopoles from dierent contexts. To achieve this, literature covering both theoretical and experimental aspects of monopoles has been studied. Section 2 comprises some basic properties of monopoles, needed for the understanding of the detection methods. In section 3, a selection of dierent signicant searches is presented. Results sprung from these experiments are found in section 4. Finally, in section 5 the outlook of future searches is briey discussed.

1 2 Theory and properties of magnetic monopoles

Discussed in this section are theories that permit, or even demand, the existence of magnetic monopoles. Theories on the creation and acceleration of monopoles in the Universe are described, as well as dierent interactions of monopoles with matter.

2.1 Classical electrodynamics In classical electrodynamics, electric and magnetic elds are described by the well-known Maxwell equations below:

∇ · E = 4πρe (1) ∇ · B = 0 (2) 1 ∂E 4π ∇ × B − = j (3) c ∂t c e 1 ∂B −∇ × E − = 0, (4) c ∂t where E and B represent the electric and magnetic elds respectively, and ρe and j stand for electric charge and current densities. As opposed of electric e charges, magnetic charges have never been found experimentally, and asymmety in equations 1-4 is at hand. If one introduces magnetic monopoles to Maxwell's equations, the symmetry is restored and equations 2 and 4 above will instead look like

∇ · B = 4πρm (5) 1 ∂B 4π −∇ × E − = j . (6) c ∂t c m Here, and j denote the hypothetical magnetic charge and current densi- ρm m ties [1]. This substitution is not theoretically forbidden. As Paul Dirac describes it: The theoretical reciprocity between electricity and magnetism is perfect [2].

However, the new set of equations does not predict the magnitudes of ρm and j , and quantization of charges cannot be derived from the equations [3]. m 2.2 The Dirac monopole Paul Dirac showed in his famous paper from 1931 that magnetic monopoles are consistent with quantum electrodynamics, and may explain the quantization of charges [2]. The relationship between electric and magnetic monopole charges is n c eg = ~ , (7) 2 where e and g represent electric and magnetic charge, and n is an integer. This leads to an expression for the elementary magnetic charge, the Dirac charge [1]: c e g = ~ = ≈ 68.5 e, (8) D 2e 2α where α = e2/(~c) ≈ 1/137 is the ne-structure constant. If the basic electric charge is in fact that of a quark, q = 1/3, the magnetic charge would conse- quently be three times larger [4].

2 Dirac also notes that the attractive force between two monopoles of opposite charges is (137/2)2 ≈ 4700 times larger than that of two electric charges, such as an electron and a proton. This could possibly explain why no monopole pairs have been found separated in nature [2].

Still there is no prediction of the Dirac monopole mass, but a rough estimate can be made assuming that the monopole radius equals e.g. the radius of a classical electron:

2 2 2 g e g me (9) rM = 2 = re = 2 ⇒ mM = 2 . mM c mec e For the elementary magnetic charge, this expression gives the relatively large mass of 2.4 GeV [4].

2.3 GUT monopoles Grand Unied Theories (GUTs) are physical models based on the unication of electromagnetic, weak and strong interactions that occurs at suciently large energies [1]. As stated by 't Hooft and Polyakov in 1974, the properties of magnetic monopoles are predictable and calculable, and even necessary in these theories [5, 6]. Depending on the GUT model used, the predicted monopole mass varies between 4·104 GeV and an astounding 1017 GeV [3]. The extremely large masses are described by Preskill as comparable to the mass of a bacterium, or the kinetic energy of a charging rhinoceros, and could never be produced in any man-made accelerator, existing or conceivable [7].

As well as the Dirac monopole, GUT monopoles have charges quantized according to eq. 7, but are far more complicated objects. Within a core of radius of 10−29 cm (denoted X in g. 1), the GUT symmetry is preserved. Surrounding it are pairs of virtual elementary particles and gauge bosons. The interaction of a particle with the monopole core might violate the baryon number conservation, which would give rise to nucleon decay (see section 2.6.4) [1].

Figure 1: Possible structure of a GUT monopole [8] .

3 2.4 Creation in the early Universe It is assumed that currently no process in the Universe is energetic enough to produce supermassive monopoles. They must have been formed earlier, shortly after the Big Bang, when the energy distribution of the Universe was much more dense [7]. The monopoles allegedly formed as topological defects arising when the Universe expanded and cooled, causing the GUT symmetry to spon- taneously break [1, 9]. A phase transition allowed for production of monopole- antimonopole pairs in the intersections of so-called domains (similar to the domains in a ferromagnet), which are not causally connected [7, 10].

The critical mass density of the Universe, ρc, is the density for which the grav- itational attraction and the expansion of the Universe balance each other. For some time, the mass density of monopoles was estimated to be many orders −18 3 of magnitude larger than the critical mass density; ρM ∼ 5 · 10 g/cm ver- −29 3 sus ρc ∼ 8 · 10 g/cm [4]. Such a scenario implies that the Universe would stop expanding and nally collapse in a Big Crunch, while observations on the contrary tell us that the expansion rate of the Universe is accelerating. This dis- crepancy is of course unacceptable, and is referred to as the monopole problem. Since monopoles are stable, annihilation of monopole-antimonopole pairs is the only process that could reduce their abundance [7]. The expansion of the Uni- verse however makes the annihilation rate small, and thus annihilation is shown to have no signicant eect on the number of monopoles [11]. A proposed so- lution to the problem, provided by Guth and Linde, involves the commonly accepted exponential expansion of space during the inationary phase [12, 13]. Ination might in fact reduce the monopole density enough to outrule the possibility of ever detecting one. Still though, there is no denite limit on how much the monopole ux falls below current experimental limits, and experimental physicists should not be discouraged from searching [7].

2.5 Acceleration Long-range cosmic magnetic eld lines accelerate monopoles in the same manner as electric elds accelerate electric charges. For example our Galaxy has a magnetic eld strength B ∼ 3 · 10−6 G and coherence length ξ ∼ 300 pc. According to equation 10, a monopole carrying one Dirac charge, gD, in our Galaxy acquires a kinetic energy of up to 6 · 1010 GeV [1, 4]. Z Ekin = g B · dl ∼ gBξ (10)

Typically, various cosmic accelerators provide the monopoles with enough energy to make them relativistic if the mass falls below ∼ 1015 GeV [14]. The kinetic energy gained by the monopoles depletes the magnetic eld strength. However, magnetic elds are continuously generated due to turbulence and nonuniform rotation of the Galaxy disk [15]. In order for the galactic elds to survive, the dissipation of magnetic elds must not exceed the regeneration. This requirement implies that an upper ux limit, known as the Parker bound, −15 −2 −1 −1 can be set to Φ . 10 cm s sr [16]. An extended Parker bound takes into account the survival of a small galactic seed eld, and lowers the ux limit −16 17 −2 −1 −1 to Φ ≤ 10 (mM /10 GeV ) cm s sr [17].

4 Acceleration of monopoles can also be caused by gravitation, which typically causes a galactic infall velocity of 10−3 c for monopoles of arbitrary mass [7].

2.6 Interaction with matter The detection of magnetic monopoles is made possible by their interaction with matter. Some dierent types of interaction processes will be briey presented here.

2.6.1 Ionization and excitation Electromagnetic interaction causes particles with electric charges to lose energy to atoms in target matter by ionization or excitation. The mean energy loss per path length, dE/dx, is proportional to (ze)2, where z and e represent atomic number and electric unit charge respectively.

Fast particles with magnetic charges also lose energy in ionization processes. dE/dx can be described for monopoles similarly as for electric charges, only ze has to be replaced with gβ. Thus, a monopole with Dirac charge gD and velocity β ≈ 1 loses as much energy to ionization as a nucleus with z ≈ 69, or (g/e)2 ≈ 4700 times more than a proton [1]. For magnetic monopoles with 10−4 < β < 10−3, kinetic energy is mainly transferred to recoiling atoms or nuclei [4].

2.6.2 Radiative losses The energy loss caused by radiative processes such as pair production, bremsstrahlung and photo-nuclear interactions predominates for highly relativistic monopoles [1]. For massive monopoles, bremsstrahlung can be considered neg- ligible since it is inversely proportional to the mass [14].

2.6.3 Cherenkov radiation When traversing a medium such as water or ice, relativistic monopoles will lose some of their energy to Cherenkov radiation, which can be described as the optical equivalent to a sonic boom. When the monopole velocity exceeds the speed of light in that particular medium, photons are emitted from excited atoms in the medium. Electrically charged particles also give rise to Cherenkov radiation, but the number of photons emitted is then much smaller. In water and ice, having refractive index n ≈ 1.33, a monopole with one Dirac charge 2 generates (gDn/e) ≈ 8300 more photons than a particle with one electric unit charge traveling with the same speed [1]. The radiation can only be produced by particles with speeds above a threshold of β = 1/n ≈ 0.75 [3].

2.6.4 Catalysis of nucleon decay It has been suggested that the boson in the core of a GUT monopole (denoted X in g. 1) can cause nucleons to decay by performing transitions between quarks and leptons, the Rubakov-Callan eect [3, 18]. Thus, the conservation of baryon number might be violated. Examples of such processes can be seen in g. 2.

5 Figure 2: Possible reactions of monopole catalyzed nucleon decay [19]

The branching ratios of the decay channels shown in the gure exceed 90% for proton and neutron decay respectively [9]. The catalysis cross section, σcat, is roughly of the same order as strong interaction cross sections, 10−26 cm−2 [3]. It depends however on the relative velocity between monopole and nucleon, β, as seen in equations 11 and 12 [9]. σ β > β : σ = 0 (11) 0 cat β α σ0 β β < β0 : σcat = (12) β β0

Here, β0 and α have dierent values for dierent nuclei. The value of σ0 is far from certain. Some suggestions range between 10−28 and below 10−30 cm−2. Possibly, at suciently low velocities, the relation is better described by the 2 equation σcat = σ0/β [9].

The decay products are much lighter than the parents, which would make them highly relativistic. Therefore, along the trajectory of a catalysing monopole in a medium, there are outbursts of Cherenkov radiation. Nucleon decay catalysis thereby permits detection of extremely massive subrelativistic monopoles [9]. However, not all unied gauge theories include this phenomenon [1].

2.6.5 Induction A monopole passing through a closed loop of superconducting wire will give rise to an electric current signal, regardless of the monopole's speed [7]. The induced current, ∆i, in a coil with N turns is:

∆i = 4πNngD/L, (13) where L is the inductance of the loop and n is an integer [4].

6 3 Detector types and searches

Described in this section are some of the experimental monopole searches carried out in the past and the present, and some planned for operation in the near future. The main focus lies on AMANDA and other neutrino telescopes.

3.1 Water and ice Cherenkov detectors Highly energetic neutrinos carry information on cosmic processes such as gamma- ray bursts, supernovae and quasars. The probability of neutrinos interacting with matter is extremely small. Due to the small cross sections, very large detector volumes are needed for detection.

Neutrino telescopes consist of large arrays of photomultipliers deployed under water or ice, and can detect Cherenkov light from charged particles moving at relativistic speeds. Charged current interactions of muon neutrinos, νµ, with nucleons, N, produce muons, µ, in the reaction νµ + N ⇒ µ + X, where X is a hadronic cascade. The Cherenkov radiation generated by the muons can then be detected, and paths and energies of the incident neutrinos can be deduced [1, 20].

The ability of detecting Cherenkov light make the neutrino telescopes well suited also for the search of magnetic monopoles of varying velocities (see sections 2.6.3 and 2.6.4). Light, relativistic monopoles are featured by vast Cherenkov emission, whereas the heavy subrelativistic monopoles are distinguished by their slow velocities [1].

Several neutrino telescope projects are currently operating. Some of them, along with some completed and coming experiments, are described in sections 3.1.1- 3.1.7.

3.1.1 AMANDA The participants in the AMANDA (Antarctic Muon And Neutrino Detector Ar- ray) collaboration are scientists from 19 universities and institutes in the United States, Europe, and Venezuela.

AMANDA is a neutrino telescope situated under the Antarctic ice at the ge- ographic South Pole [1].Cable strings with optical modules (OMs) attached to them are vertically deployed deep down in the Antarctic ice, in order to register Cherenkov light emanating from particles interacting with the surrounding ice.

The construction of the detector begun in the austral summer season of 1994- 1995, when four strings were deployed at a depth of 810 and 1000 meters (AMANDA-A) [3]. The strings were lowered into holes drilled with hot water, and then frozen into place [1]. In this rst conguration however, small air bubbles caused light to scatter heavily in the ice, and particle tracks could therefore not be reconstructed. At higher pressures though, these bubbles collapse [21]. The subsequent conguration, AMANDA-B, was therefore deployed deeper in the ice, mainly between 1500 and 2000 meters below the surface. The deployment went on during summer seasons for several years and in 1998, 13

7 strings had been arranged, completing the AMANDA-B conguration. After another six strings had been deployed in the ice in 2000, the nal AMANDA-II was complete [9]. The horizontal and vertical placements of the 19 strings are shown in gures 3 and 4 respectively. The detector center is placed 1730 meters

Figure 3: Arrangement of the 19 strings of AMANDA-II. The numbers correspond to the order in which the strings were deployed [1]. below the surface, with most of the 677 OMs contained within a 500 m high cylindrical volume. (However, one of the strings got stuck in the drilled hole, and accidentaly ended up at a depth 500 m too shallow [1].)

Each optical module consists of a glass pressure sphere, holding a photomultiplier tube (PMT). For a simplied drawing of an OM, see g. 5. A large PMT amplication factor of 109 ensures that pulses can travel through the 2 km long cables. Transparent silicon gel with adapted refraction index connects the glass sphere with the photocathode of the PMT. The OMs are sensitive to wave- lengths between 300 and 650 nm, with a sensitivity peak at 420 nm (see g. 6). This nearly coincides with the wavlength region where the transparency of the ice is maximized, ∼400 nm [3, 1].

The AMANDA telescope has been used for searches for both relativistic and subrelativistic monopoles. To enable separation of monopole signals from background events (everything except monopoles), Monte Carlo simulation of events in AMANDA is performed [9, 3]. Typically, three steps are required for event simulation:

• Generation Particles with randomized trajectories are generated. • Propagation Interaction with matter along the trajectory.

• Detector simulation The detector's response to particles is simulated. Commonly, background as well as signal events are simulated in order to nd separating criteria [9].

3.1.2 ANTARES ANTARES (Astronomy with a Neutrino Telescope and Abyss environmental RESearch) is a collaboration between institutes from six European countries. After its completion in 2008, ANTARES is the largest neutrino telescope in the

8 Figure 4: The 19 strings and 677 OMs of AMANDA-II are deployed deep down in the Antarctic ice [1]. northern hemisphere [22]. It complements and partially overlaps the sky cover- age of the AMANDA detector [23]. The detector is located in the Mediterranean sea, 40 km o the coast of France. 12 strings, kept vertical by buoys, are placed on the sea bed. They cover an area of approximately 180×180 m2 and together hold 900 OMs, detecting Cherenkov radiation [20].

A light backgrund is produced in the Mediterranean sea by bioluminescence (emission of light by living organisms) and decay of the radioactive potas- sium isotope 40K. Whereas hits from Cherenkov light emission are correlated, the light background hits are usually random and can thus be eectively re- moved [20]. Strategies for monopole searches via Cherenkov radiation have been developed [1].

ANTARES is together with the similar projects NEMO and NESTOR a pilot project preparing for a km3-scale neutrino telescope, KM3NeT, in the Mediter- ranean sea [24].

9 Figure 5: An optical module consists of a PMT inside a glass sphere [3].

Figure 6: The photocathode eciency of AMANDA's PMTs as a func- tion of wavelength [3].

3.1.3 Baikal The Baikal NT200 experiment is a Russian-German collaboration that started operating in 1998, with predecessors running since 1993. The conguration consists of 8 strings with a total of 192 pair-wise arranged optical modules deployed 1100 meters below the surface of Lake Baikal in Siberia. The detector has a height of 72 m and a diameter of 42 m [25]. Each OM contains a fast, high- gain scintillator and a photomultiplier tube, housed by a pressure tight glass sphere. Photoelectrons from a photocathode covering almost half the sphere are accelerated toward the scintillator and thereby detected [26]. An OM pair forms a so-called channel.

Data collected between 1998 and 2003 have been used for the search of relativistic monopoles with β > 0.8. Since these are expected to be very bright, a large number of red channels are required for triggering an event. To reduce background the downgoing events are discarded, since they usually arise from cosmic showers [25].

3.1.4 IceCube Although AMANDA has been a successful project, there are limitations set e.g. by its relativley small size. IceCube is a new neutrino telescope that was designed to overcome some of AMANDA's problems [21]. With its one hundred times larger volume and some technical improvements, IceCube acts as a natural

10 extension of AMANDA's research and development work. It will be a 1 km3- scale neutrino telescope based on the same principles as its predecessor, but with superior performance [27]. The construction is currently ongoing since the season 04/05, and the detector is scheduled to be completed in 2011 [21]. 80 strings with a total of 4800 digital optical modules (DOMs) will be deployed in a hexagonal grid, at depths of 1.4 to 2.4 km below the surface, see g. 7.

Figure 7: The IceCube array in the Antarctic ice. The dark cylinder represents the AMANDA detector [28].

IceCube will continue the search for magnetic monopoles after the shutdown of AMANDA-II in 2009, possibly with potential to lower the upper ux limits set by AMANDA by two orders of magnitude [27].

3.1.5 IMB The IMB detector was an Irvine-Michigan-Brookhaven collaboration designed to observe nucleon decay. It started collecting data in 1982 and was shut down in 1991 due to a water leak. IMB was the world's rst very large water Cherenkov detector, situated east of Cleveland, Ohio in the Fairport salt mine 600 m below ground (1570 m water equivalent). The benets of putting the detector in a salt mine include shielding from high-energy muons and low radioactivity in the surrounding rock [18, 29]. A rectangular cavity was lled with 8000 tons of water, that was continuously ltered to remove biological and ionic contamination. Over the six cavity walls, 2048 PMTs were uniformly distributed as shown in g. 8. From 1986, data from IMB was used to search for monopole catalyzed nucleon decay among other phenomena [29].

11 Figure 8: PMT grid arrangement of the IMB detector [29]

3.1.6 Kamiokande The Kamiokande (KAMIOKA Nucleon Decay Experiment) experiment was a water Cherenkov detector located 1000 m under ground in Kamioka mine in Gifu, Japan. It started operating in 1983, and was three years later upgraded to Kamiokande-II [19, 30]. Today, they are replaced by the higher-performance detector Super-Kamiokande.

Kamiokande was originally designed to search for energy liberated from proton decay, but has also served as a neutrino detector [30]. It contained 3000 tons of water and 1000 PMTs. By observing multiple nucleon decay signals, slow monopoles could have been detected [31].

3.1.7 RICE The Radio Ice Cherenkov Experiment (RICE) consists of 16 antennas of band- width 200-1000 MHz, buried in ice near the geographical south pole. The antennas are contained within a cube with sides of length 200 m, having its center 150 m below the surface. It primarily searches for radio Cherenkov signals arising when ultra-high energy neutrinos collide with nuclei in the ice.

RICE is also sensitive to Intermediate Mass Monopoles (IMMs), which due to their relatively low masses, ranging between 105 and 1012 GeV, reach ultra- relativistic velocities (β ≈ 1). When traversing the ice, they lose a large amount of energy, giving rise to showers detectable in RICE. Data collected between 2001 and 2005 have been analyzed in order to set an upper limit on the ux of relativistic monopoles [32, 33].

12 3.2 Superconducting induction devices As mentioned in section 2.6.5, a monopole passing through a closed loop of superconducting wire will induce a current. A superconducting induction detector, composed of a detection coil coupled to a SQUID (Superconducting QUantum Interferometer Device), should be sensitive to monopoles of any velocity [4]. It is therefore in one sense the ideal detection method. Limitations on the supercon- duction method are however set by signal-to-noise ratios and the requirement of shielding from magnetic uctuations [7]. For example, a 1 m loop with 250 µm wire has an inductance, L, of about 10 µH. According to equation 13, the current induced by a Dirac charge is 0.4 nA. This is not an extremely small current to measure, but the measurement of the current is obstructed by the fact that it decreases rapidly. In addition, very small variations in the Earth's eld (perhaps caused by a distant bicycle) can produce similar currents [34].

3.2.1 Cabrera experiment In the early 80's, Blas Cabrera of Stanford University performed a mass- and velocity-independent search for monopoles. A superconducting four-turn loop with an area of 20 cm2 was monitored during a total of 151 days. For shielding, the loop together with a SQUID magnetometer were placed inside a cylinder of MuMetal [35], a ferromagnetic material that does not retain a macroscopic internal eld after the removal of an external magnetizing eld [36]. Apart from the many small disturbances caused by service of the detector, one large event was recorded, on Valentine's day 1982. Fig. 9 shows the monopole candidate event together with typical data. Within an uncertainty of ± 5 %, the event

Figure 9: The three data records in (a) show the detector's typical stability, whereas (b) represents the monopole candidate event [35]. is consistent with the passage of a Dirac unit charged monopole. Cabrera does

13 not claim to have detected a monopole, but lists instead a number of statements about spurious detector response [35].

Several groups have made eorts to explain the result of Cabrera's experiment, but none of them have succeeded [34].

3.3 Scintillators Since magnetic monopoles act to ionize the matter they traverse, scintillators can be used for monopole detection. Above the threshold β ∼ 10−4, the monopole light yield is large compared to that of a minimum ionizing particle. Between β ∼ 10−3 and β ∼ 10−1 there is a saturation eect, but for even faster monopoles the production of delta rays (secondary ionization) causes the light yield to increase [4].

3.3.1 MACRO MACRO (Monopole, Astrophysics and Cosmic Ray Observatory) was an experiment running between 1988 and 2000 deep underground in the Gran Sasso National Laboratory in Italy. The collaborating institutions were mainly from Italy and the U.S. The principal goal of MACRO was to observe magnetic monopoles or set experimental ux limits signicantly lower than any previously existing, in the velocity range 10−4 < β < 1 [37].

In the MACRO experiment, three dierent detector principles were used in order to complement each other - liquid scintillator counters, limited streamer tubes (see section 3.4.2) and nuclear track detectors (see section 3.5.1). The full detector lled a volume of 76.5×12×9.3 m3, divided into six sections called supermodules. A cross-sectional view of the detector can be seen in g. 10. The

Figure 10: Cross-sectional view of the MACRO detector [37]. cosmic radiation muon ux was suppressed by the shielding rock by a factor of almost 106. Apart from cosmic radiation, natural radioactivity was the largest source of background [38].

14 The scintillator system of MACRO consisted of 476 scintillators organized in layers of horizontal and vertical counters. A hydrocarbon dissolved in mineral oil acted as liquid scintillator. Each counter was viewed by one or two PMTs. The overall timing and position measurements in a counter had resolutions of about 0.5 ns and 10 cm respectively [37].

3.4 Gaseous detectors Various types of gaseous detectors have been used in the search for magnetic monopoles [4]. They are obtained at a low cost compared to scintillators, and are well suited for large arrays [34]. Free electrons and positive ions are produced in the gas along the track of an ionizing particle. By applying an electric eld between a cell's walls and an anode wire, the charges can be collected. The signals produced can indicate the passage of a magnetic monopole.

3.4.1 KGF The Kolar Gold Field (KGF) detector is a Japanese-Indian collaboration that started operating in 1980 as a nucleon decay experiment. It consisted of 34 layers of proportional wire chambers, lled with argon (90%) and methane (10%), and was located at a depth of 2300 m (7600 mwe) [34, 39, 40]. Data collected over a 2.5 year period were analyzed in terms of monopole interactions. The features searched for were heavily ionizing particles, very slow massive particles and monopole catalysis of nucleon decay [39].

3.4.2 MACRO The MACRO detector (see section 3.3.1) had a system of streamer tubes designed to search for magnetic monopoles with velocities in the range 10−4 < β < 1 [38]. Eight cells of dimension 2.9×2.7 cm2 constituted a basic unit of the system. In the center of each cell, a silvered Be-Cu anode wire was placed, and the cell sides were coated with graphite. The system held 6192 basic unit chambers, which means that almost 50000 wires were in operation. Streamer tubes were placed horizontally and vertically. The horizontal tubes were equipped with readout strips, enabling a three dimensional track reconstruction of events.

The 465 m3 of ll gas used was a mixture of helium (73%) and n-pentane (27%) [37]. These particular gases were chosen to in order to exploit the Drell- Penning eect. A monopole with velocity 1.1·10−4 < β < 10−3 passing through a helium atom will leave it in a metastable state. When the excited helium atom then collides with n-pentane, the n-pentane ionizes. The cross sections for both processes are high, and this gas mixture gives a 100% eciency in detecting monopoles.

For higher velocities (β > 10−3) the standard monopole ionization mechanism ensures a very high energy release. The charge collected on a wire depends logarithmically on the released energy, which makes it possible to distinguish between monopoles and muons [38].

15 3.4.3 Soudan 2 The British-American Soudan 2 detector in Minnesota, U.S. , was used to search for monopoles between 1989 and 1992. It was located 713 m below ground, at 2100 mwe. Stacks of 1 m long, 16 mm diameter plastic tubes were enclosed in gas-tight containers lled with argon (85%) and CO2 (15%). Inside the tubes copper wires were placed, and uniform electric elds parallel to the tube axes were applied. When an ionizing particle traversed a tube, charges were collected and a plane of crossed horizontal cathode strips worked together with vertical anode wires to determine which of the many tubes was traversed. To nd monopoles, one searched for tracks having signicantly higher ionization than the average muon [41].

3.5 Nuclear track detectors Nuclear track detectors (NTD) are used in many dierent branches of science and technology. When a heavily ionizing particle such as a magnetic monopole passes a thin NTD sheet, a damage trail arises due to energy loss [42]. The damaged region is more chemically reactive than the surrounding material. By chemical etching of the material, tracks can thus be enhanced and made visible under an optical microscope [34].

The polymer known as CR39 is the most sensitive of the NTDs. It has a threshold for detection at Z/β ≈ 5, which makes it suitable for searching monopoles over a wide range of velocities. Polycarbonates by the names Makrofol and Lexan are also widely used, but their ten times larger threshold restrict them to searches for relativistic monopoles [4].

3.5.1 MACRO The MACRO detector in Italy (see section 3.3.1) had a nuclear track subdetector covering 126 m3. Stacks consisting of three layers of CR39, three layers of Lexan and an aluminum absorber were placed in bags of Mylar, an aluminized polyester lm [43], and placed deep underground for an average of 9.5 years. After etching, the CR39 foils were scanned twice for inhomogeneities caused by traversing particles. No candidates were found, and the Lexan sheets, having a much higher threshold, were therefore not analyzed [38].

3.5.2 Ohya A Japanese NTD experiment was carried out between 1986 and 1990. Modules of CR39 sheets, with a total area of 2000 m2, were placed underground at the Ohya stone quarry, 100 km north of Tokyo. Each module had four foils enclosed in an aluminum bag with 1 atm pressured air. The average exposure time of the NTDs was 2.1 years. The monopoles searched for are GUT monopoles heavier than about 1012 GeV [44].

3.5.3 Price In 1973, Buford Price together with a small group of American scientists performed an experiment to study ultraheavy cosmic rays (Z≥60). A balloon was

16 equipped with a stack of Cherenkov lm, emulsion and 33 Lexan sheets, and sent for 2.6 days of exposure. The detector stack was composed as seen in g. 11.

Figure 11: Stack of detector sheets from Price's balloon experiment [45].

Analysis of the sheets revealed an interesting event, diering from any event seen previously in balloon ight experiments. In all of the Lexan sheets, a series of produced tracks corresponded to either a nucleus with 125 Z 137 or a 2 . . gD charged monopole. The emulsion sheet on the other hand, showed a track indi- cating either a nucleus with Z≈80 or, again, a monopole charged with 2 gD/q. The authors concluded that the only interpretation consistent with the experimental data was that a monopole with β ≈ 0.5 had traversed the detectors [45].

It did not take long though, until the alleged evidence for detection of a monopole was dismissed. Price et al. had overlooked the possibility of a fragmenting Plat- inum nucleus being the process responsible for the tracks. A Platinum nucleus (Z=78) losing an alpha particle becomes Osmium (Z=76), which then frag- ments once more into Tantalum (Z=73). This gives an excellent t, by far more probable than the detection of a magnetic monopole [46].

3.5.4 SLIM The SLIM experiment (Search for LIght Monopoles) was a large array of NTDs, located 5230 m above sea level at Chacaltaya high altitude Laboratory in Bo- livia. Its main purpose was searching for intermediate mass monopoles.

17 The array covered a surface area larger than 400 m2, divided into 7410 24×24 cm2 modules. Each module consisted of three layers of CR39, three layers of Makro- fol, two layers of Lexan foil, and a layer of aluminum absorber. The modules were sealed in air-tight bags lled with dry air at 1 bar pressure. The installa- tion of the modules took place between the years 2000 and 2002.

After four years of exposure time, the NTD sheets were etched and analyzed. Most of the possible background eects were estimated to be small. However, neutrons could give rise to background tracks. A certain etching procedure re- duced the neutron background, but at the same time resulted in higher threshold.

No monopole candidates passed the search criteria. Two strange events were observed, but classied as manufacturing defects of a small set of the CR39 foils [47].

3.6 Accelerators The classical Dirac monopoles, which have relativley low masses (see section 2.2), could possibly be produced at accelerators. If so, they would be relativistic and heavily ionizing, and thereby easy to distinguish [4].

There are two types of accelerator searches - direct and indirect. Direct searches involve free monopoles and include searches for previously produced monopoles trapped in material, as well as searches for ionization and radiation produced by monopoles. In indirect searches on the other hand, one looks for eects caused by the virtual existence of monopoles [48]. A majority of the searches is sensitive to monopoles with magnetic charges g = ngD/q with 0.5 < n < 5 [49].

3.6.1 CDF The Collider Detector at Fermilab (CDF) experiment has many collaborators from all over the world, however most of them from the United States. It consists of a magnetic spectrometer, a scintillator time-of-ight system, electromagnetic and hadronic calorimeters and muon detectors. A superconducting solenoid produces a 1.4 T magnetic eld parallel to the beam direction.

During 2003, the Fermilab Tevatron accelerator produced collisions at CM en- √ pp ergy s = 1.96 TeV, with the possibility of detecting pair-produced monopoles and antimonopoles. The events were collected by the CDF detector using a special trigger which required large light pulses. The magnetic eld accelerates the monopoles produced, and causes light monopoles to be swept out of the detector, whereas massive monopoles arrive at the TOF detector too late to cause a trigger. Masses below 200 GeV and above 700 GeV are excluded. A production cross section limit was achieved [50].

18 3.6.2 H1 The H1 collaboration has a large number of member institutions, mainly Euro- pean. The HERA accelerator in Hamburg, Germany, produced + collisions √ e p at s = 300 GeV. The particles produced in the collision were collected in the H1 detector.

Monopoles may have been created in the process e+p → e+MMp, and then stopped and permanently trapped in the aluminum beam pipe surrounding the H1 interaction point. The beam pipe used in 1995-1997 was cut into 75 strips and passed in steps through a magnetometer at the Southampton Oceanography Centre, UK (see g. 12). The magnetometer consisted of three superconducting coils of diameter 8.1 cm, and was sensitive down to 0.1 gD. After each step of typically 5 cm, the current in the superconducting loop was measured. Any monopole trapped in the pipe strips would give rise to a current step (see section 2.6.5). The experiment set upper limits on the monopole pair production cross section for monopoles of magnetic charges 1 gD to 6 gD and masses up to 140 GeV [51].

Figure 12: Samples from the HERA accererator beam pipe, possibly containing trapped monopoles, were passed through a superconducting coil and the current was measured [51].

3.6.3 Oklahoma experiment The Oklahoma experiment (or Fermilab experiment E882) was performed at the University of Oklahoma over a 7 year period. It searched for Dirac monopoles created by the Tevatron accelerator and then trapped in matter surrounding the D0 collision region. Al and Be samples were pulled through two superconducting loops connected to SQUIDs. Background runs were made between every two samples, since the nylon string pulling the samples could be magnetically contaminated. For calibration, a pseudopole was used, i.e. a long thin magnetic solenoid carrying a small charge was passed through the detector in a way similar to the samples [52]. 8 samples out of 660 signals caused signal events. They were remeasured, leaving no monopole candidates. Mass limits were then obtained [48].

19 4 Experimental bounds 4.1 GUT monopoles and IMMs So far, no plausible monopole candidates have been observed. Upper limits on the ux of magnetic monopoles must therefore be established solely based on the non-observation of monopoles in experiments. Table 1 contain results from GUT monopole searches.

Detector Type Upper ux limit Note (cm−2s−1sr−1) KGF Gas 2 · 10−14 β > 1 · 10−3 Kamiokande II Cherenkov ∼ 1 · 10−15 5 · 10−5 > β > 10−3 Soudan 2 Gas 8.7 · 10−15 β > 2 · 10−3 −15 12 Ohya NTD 3.2 · 10 mM > 10 GeV IMB Cherenkov 1 − 2.7 · 10−15 10−5 > β > 10−1 MACRO Gas, scintillator, NTD 1.4 · 10−16 IMM Baikal NT200 Cherenkov ∼ 1 · 10−17 0.8 > β > 1 SLIM NTD 1.3 · 10−15 IMM and lower masses AMANDA-II Cherenkov ∼ 1 · 10−17 0.8 > β > 1 ∼ 1 · 10−16 Subrelativistic RICE Cherenkov ∼ 1 · 10−18 IMM, β ≈ 1

Table 1: Results from GUT monopole searches

In the early 90's, the upper ux limits were usually rather close to the Parker bound, as shown in gure 13. The Soudan 2 limit is e.g. 8.7·10−15 cm−2s−1sr−1 for β > 2 · 10−3 [41]. The KGF limit from 1984 is 2 · 10−14 cm−2s−1sr−1 for β > 10−3 [39], whereas the IMB limits set one decade later vary between 1.0 · 10−15 cm−2s−1sr−1 and 2.7·10−15 cm−2s−1sr−1, depending on the catalysis cross section used [18]. The Kamiokande-II experiment also gave results in the vicinity of 10−15 cm−2s−1sr−1 [31].

The upper limit to the local magnetic monopole ux set by the MACRO experiment is 1.4·10−16 cm−2s−1sr−1. It is well below the Parker bound in the whole velocity range in which GUT monopoles are expected, which makes MACRO unique. Figure 14 illustrates the wide velocity range covered [38]. The Ohya limit of 3.2 · 10−15 cm−2s−1sr−1 is also shown in gure 14 [44].

From the Baikal NT200 experiment, a 90% C.L. upper ux limit for monopoles with β = 1 was found to be 4.6·10−17 cm−2s−1sr−1, and 1.83·10−16 cm−2s−1sr−1 for β = 0.8 [25]. Upper ux limits resulting from the AMANDA-II conguration range between 3.8 · 10−17 cm−2s−1sr−1 and 8.8 · 10−16 cm−2s−1sr−1 for β = 1 and β = 0.8 respectively [1]. The AMANDA and Baikal results can be seen in gure 15. For subrelativistic monopoles, AMANDA's upper limits are of the order 10−16 cm−2s−1sr−1 [9].

20 Figure 13: Graph showing monopole ux limits, presented by the Soudan 2 collaboration in 1992 [41].

Figure 14: MACRO set limits well below the Parker limit for a wide monopole velocity range [1].

21 Figure 15: Current Baikal and AMANDA limits as presented by the Baikal collaboration in 2008 [25].

SLIM extended the cosmic radiation search for monopoles to masses lower than the GUT scale with a high sensitivity, see g. 16. The upper limit for 105 to 1012 GeV monopoles is 1.3 · 10−15 cm−2s−1sr−1[47].

A graph containing the 2008 RICE limits for uxes versus monopole Lorentz boost parameters 108 ≤ γ ≤ 1012 is shown in g. 17. It mostly covers a range in M, γ that is dierent from that covered by the other experiments. Clearly, it beats the best AMANDA, Baikal and MACRO limits by about a factor 100 in the overlapping part of the mass and velocity range [33].

22 Figure 16: The SLIM experiment set limits for intermediate mass monopoles [47].

Figure 17: RICE improved the ux limit by over two orders of magnitude over most of the range studied [33].

23 4.2 Classical monopoles The accelerator searches set lower limits on mass and upper limits on the production cross sections of light monopoles, see table 2. For unit charged monopoles, the Oklahoma experiment sets the cross section limit σ < 0.70 pb and the mass limit mM > 295 GeV [52]. The CDF experiment set a 95% C.L. lower mass limit of 360 GeV and a cross section limit of σ < 0.2 pb for monopoles of mass 200 to 700 GeV [50]. The H1 mass limits are not as strong, but in some cases reach smaller cross sections for lower masses [48].

Experiment Lower mass limit Upper cross section limit

(MMs with 1 gD)(pp¯-collisions) Oklahoma 295 GeV 0.7 pb CDF 360 GeV 0.2 pb

Table 2: Limits on Dirac monopoles set by accelerator searches

24 5 Conclusions and outlook

Several Cherenkov neutrino telescopes that will be searching for monopoles are planned, with the possibility of lowering existing ux limits signicantly. Men- tioned earlier are IceCube and KM3NeT, but also the Baikal collaboration plan for a km3 volume detector (the Gigaton Volume Detector, GVD) [25]. The construction of KM3NeT is expected to begin at the earliest in 2011, which is the year when IceCube will be completed [24, 21]. For an estimated achievable upper ux limit for km3 detectors in the range 0.5 > β > 1, see g. 18.

Figure 18: Limits on the ux of relativistic monopoles achievable with KM3NeT (which is equal to the achievable ux limits of IceCube) compared to existing limits. In this gure, neither AMANDA nor Baikal limits are up to date [24].

The accelerator searches for monopoles will naturally be continued at the Large Hadron Collider (LHC) at CERN. It may lead to improvements of the cross section limits [4]. Proposed are high energy pp collisions that may produce monopole-antimonopole pairs due to γγ fusion [53].

Discovery of monopoles would give us a new deeper understanding of the funda- mentals of physics. Still there is no evidence that magnetic monopoles actually do exist, but the strong theoretical implications encourage new searches. And even though we might never be able to detect one, to cite John Preskill, our failure to observe a monopole is itself a signicant piece of information [7].

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