The MoEDAL experiment at the LHC: In search of magnetic monopoles

1 Classical magnetic monopoles

James Clerk Maxwell developed his theory of electromagnetism based on the experimental observation of electric and magnetic interactions and on the Faraday’s concept of field. Maxwell’s theory of the electromagnetic field was a fundamental breakthrough because it not only unified magnetism and electricity in one simple theory but it also explained the properties of light, which was shown to be an electromagnetic wave. Furthermore, the theory derived numerically the value of the speed of light, demonstrating that it is constant, and therefore paved the way for the theory of relativity. Although Maxwell’s equations do not explicitly consider magnetic charges, their structure allows to include them easily (see Box 1 in PDF). In contrast, magnetic monopoles seem incompatible with quantum mechanics. Here the fields $\vec{E}$ and $\vec{B}$ are described in terms of a scalar potential, ϕ, and a vector potential, $\vec{A}$. In classical physics the description in terms of potentials is, in a certain sense, optional because observable quantities do not depend on ϕ and $\vec{A}$. By contrast, in quantum physics the potentials couple directly to the quantum wave function, with real physical consequences, as in the famous case of the Aharonov-Bohm effect. The use of ϕ and $\vec{A}$ cannot be avoided, see Box 2 in PDF.

The compatibility of magnetic monopoles with quantum mechanics was shown in 1931 by P. A. M. Dirac, who introduced the so-called classical magnetic monopole. Quantum theory allows the Dirac monopole under the condition of a quantized value of the magnetic charge that must assume a minimum value, $g_{D}$. The interesting aspect of the Dirac theory is that the existence of a free magnetic charge $g_{D}$ would explain the quantization of the electric charge, $e$. Dirac established the basic relation between $e$ and $g$ as

(1) $ \frac{eg}{c} = \frac{n\hbar}{2} \rightarrow g = n \cdot g_{D} = n \cdot \frac{1}{2} \frac{\hbar c}{e} \sim n \cdot \frac{137}{2} e $ ,

where n is an integer. This condition is derived in Box 2 in PDF.

If a magnetic charge $g_{D}$ exists, the Dirac relation (1) automatically implies the quantization of the electric charge, i.e. the electric charge of any particle is an integer multiple of the elementary charge, e. This is a remarkable prediction because electric charges are indeed quantized and integer multiples of the electron charge e (or of e/3, if one includes quarks that, however, have not been observed as free particles).

Even though magnetic monopoles can be consistently described in quantum theory, they do not automatically appear in Nature (unlike the famous Dirac prediction of the existence of the positron). In addition, in the Dirac model $\vec{B}$, $\vec{E}$ duality is not perfect since the unit magnetic charge is much larger than the electric unit charge. According to eq. (1), numerically one has

(2) $ g_{D} = 68.5 e = 3.3 \cdot 10^{-8} $ esu.

Gaussian-cgs units are used throughout the text.

2 Magnetic monopoles in extensions of the Standard Model

The guiding principle of the Standard Model of particle physics is the concept of gauge symmetry (Box 2 in PDF).

Although the gauge transformations involved in weak and strong interactions are more complex than in quantum electrodynamics, the structure of these theories is very similar to QED.

The Standard Model has two sectors: one is for the electroweak interactions, known in group theory as SU(2)×U(1). The U(1) group has the same structure as the gauge symmetry of Maxwell’s equations; the SU(2) symmetry for the weak interactions is somewhat more complicated. The second sector is the quantum chromo-dynamics (QCD), describing the interactions among coloured quarks. These interactions, mediated by gluons, are also called strong interactions and denoted in group theory as SU(3). Some conservation rules separate the two sectors: the lepton and baryon numbers conservation, for instance. As an effect, decay processes as

(14) $ p = \pi^{0} e^{+} $

are forbidden.

The unification of the two sectors of the Standard Model is the ambitious goal of Grand Unified Theories (GUTs). In GUT s the unification of electromagnetic, weak and strong interactions occur at energies of about 10¹⁵ GeV. One of the characteristics of GUT theories is that baryon and lepton numbers are not separately conserved: processes as the one in (14) are allowed.

Different symmetry groups have been proposed as GUT s. The prediction of a finite proton lifetime by the process in (14) or by other more complex ones, provides an experimental possibility to verify GUTs. So far no proton decay has ever been observed. Experimental results thus rule out the simplest symmetry groups, as the first SU(5) GUT proposed by Georgi and Glashow. In addition to proton decay, SU(5) GUT predicts also magnetic monopoles with high masses, ~ 10¹⁶ GeV/c². The requirement of magnetic monopole solutions is not specific to SU(5): it was shown that practically any group theory unifying strong and electroweak interactions would have monopole solutions.

It is practically impossible to perform experimental tests at accelerators at GUT energies. The predicted magnetic monopoles, if they exist, would be stable particles. Their stability implies that if they were produced at any time in the thermal history of the Universe, they would still be present today as relic particles. The search for relic magnetic monopoles is another possibility for experimentalists to test GUTs.

The Dirac magnetic monopole is assumed as a structure-less, point-like particle whose mass is not predicted. On the contrary, GUT magnetic monopoles are very massive, composite objects, as shown in fig. 3. Their mass depends on the particular model, but it is always in the range of the GUT energy scale, $\ge $10¹⁶ GeV/c². Inside their virtual core, bosons allowing baryon number violation are present. In addition, the monopole structure could contain condensate fourfermion bags that would enhance the proton decay process through the so-called Rubakov-Callan mechanism.

Magnetic monopoles with Intermediate Mass (IMM), ~ 10⁵–10¹³ GeV/c², are predicted by theories with an intermediate energy scale between the GUT and the electroweak energies. The structure of an IMM would be similar to that of a GUT monopole, but without any term violating baryon number conservation. Monopoles with intermediate mass might have been produced in the early Universe and survived as relics; they would be stable and do not catalyze proton decay.

In addition to GUT monopoles, some modifications of the Standard Model foresee magnetic monopoles of smaller masses. Predictions introduced by earlier papers, yielding finite-mass monopole solutions, were recently generalized in a way compatible with accelerator data. According to these authors, there is the possibility, consistent with present constraints on the Standard Model, that there may exist an electroweak magnetic monopole with mass $< 5.5$ TeV/c². Such magnetic monopoles could be pair-produced at the LHC.

Finally, some superstring models predict monopoles or dyons (particles with both a magnetic and an electric charge) with a mass low enough (~ 1 TeV/c²) to be produced at the LHC.

3 Searches for magnetic monopoles

Magnetic monopoles ($\mathcal{M}$s, as also used hereinafter) belong to the family of well-known undiscovered objects. Searches for classical Dirac monopoles at accelerators and in the cosmic radiation were and still are performed.

3.1 Monopole energy losses

A $\mathcal{M}$ with velocity $v = \beta c$ creates an electric field that in matter can ionize/excite atoms or molecules.

Monopoles with $\beta > 10^{-2}$ and charge $g = n g_{D}$, where n is an integer, behave as having an equivalent electric charge $e_{\mathrm{eq}} = g \beta$. Energy losses are proportional to $g^{2} \beta^{2}$. A $\beta \sim 1$ magnetic monopole with charge $g = g_{D} $ would ionise ~ 4700 times more than a minimum ionizing particle (about 8 GeV g^–1 cm^–2), thus it should be easily identifiable. Monopoles with $10^{-4}< \beta < 10^{-2}$ lose energy in ionization or excitation of the atoms or molecules. The energy loss, computed in the interval $10^{-3}< \beta < 10^{-2}$ by approximating the medium as a degenerate electron gas, is proportional to $\beta$. Finally, monopoles with $\beta > 10^{-4}$ lose energy in elastic collisions with atoms or with nuclei. The energy loss is almost constant, independent of $\beta$.

3.2 Searches at colliders

The magnetic charge is conserved, as the electric charge. For this reason at colliders monopoles have been searched for in reactions as $\mathrm{e}^{+}+\mathrm{e}^{-} \rightarrow \mathcal{M} + \bar{\mathcal{M}}$, as well as in $\mathrm{e}^{+}p$, $\bar{p}p$ and pp collisions. Experimentally, detection apparata rely on scintillation counters, wire chambers, and nuclear track detectors. Searches based on induction devices are also made.

At CERN the search for magnetic monopoles began in 1961 with a counter experiment on nucleon-nucleon collisions at the Proton Synchrotron (PS). The energy available at the PS made it possible to produce $\mathcal{M}$ pairs up to a mass of ~ 2.8 GeV/c². Over the following decades, searches were made at the Interacting Storage Rings (ISR), at the Super Proton Synchrotron (SPS) and at the Large Electron-Positron (LEP) collider. At LEP monopoles were searched for in e⁺e^- collisions with the MODAL detector, an array of nuclear track detectors deployed at intersection point I6 on the LEP ring, and in the OPAL detector. In this latter experiment, pairs of $\mathcal{M}$-$\bar{\mathcal{M}}$ were searched for as back-to-back tracks with high energy release in opposite sectors of the detector.

The ATLAS Collaboration at the Large Hadron Collider (LHC) searched for $\mathcal{M}$s produced in 7 TeV and 8 TeV proton-proton collisions. Highly ionizing particles crossing the electromagnetic calorimeter were seeked for. These searches were sensitive only to $\mathcal{M}$s with charge $g = g_{D}$ since particles of higher magnetic charge would stop before reaching the calorimeter. Since no events were found, production cross section upper limits were set in the mass interval 200–2500 GeV/c² for $\mathcal{M}$s with magnetic charge in the range $0.5 g_{D} < g < 2.0 g_{D}$.

No monopole has been detected by any of the searches performed so far. The most significant current upper limits on the production cross section for monopoles as a function of their mass are shown in fig. 4.

4 The MoEDAL experiment at the LHC

The MoEDAL (Monopole and Exotic particle Detection At the LHC) experiment was approved by the CERN Research Board in 2010 as the 7th LHC experiment. Its main goal is to push the search for $\mathcal{M}$s to the highest mass scale attainable at the LHC. The experiment can search also for massive, stable or long-lived, slowly moving particles with single or multiple electric charges predicted in many scenarios beyond the Standard Model. The experiment is run by a Collaboration of about 70 physicists from 14 countries. The detector is deployed at the intersection region at Point 8 of the LHC (fig. 5 left) in the Vertex Locator cavern of the LHCb experiment, fig. 5 right. MoEDAL is made up of two main passive systems: a nuclear track detector array sensitive only to highly ionising particles, and a magnetic monopole trapping system consisting of roughly 800 kg of aluminium samples. Being passive systems, no readout electronics, high voltage, gas supply or trigger are needed. At the end of each LHC run the nuclear track detectors and the monopole trapping volumes are removed for analysis, and replaced with new ones.

4.1 The MoEDAL nuclear track detector system

The MoEDAL nuclear track detector system (NTD) is an array of 400 stacks (fig. 6). Each stack, 25 cm × 25 cm, consists of 3 layers of CR39® polymer and 3 layers of Makrofol® polycarbonate, sealed in an aluminized plastic envelope. Particles releasing energy at a rate larger than ~ 25 times minimum ionising particles are permanently recorded in the CR39® sheets. A subsequent chemical etching would lead to the formation of etch-pit cones in the front and back faces of each sheet. More details in Box 3 in PDF. A fast monopole would lead to the formation of pairs of etch-pits on each detector layer. If the monopole velocity along the NTD stack is constant, etch-pits will have the same size; if the $\mathcal{M}$ is slowing down the size of etch-pits will decrease since, unlike electrically charged particles, monopole energy loss decreases with velocity. From etch-pit's geometry the particle trajectory, pointing back to the beams’ collision point, can be reconstructed with an accuracy better than 5 mm. Moreover, a check can be made to verify that the particle energy loss is consistent with that expected for a monopole, as it passes through the stack.

In the NTD system the background can arise only from uncorrelated etch-pits caused by nuclear spallation products. The effect of this background is limited by replacing stacks once a year. The large amount of plastic to be scanned with magnifying optical systems constitutes the main analysis challenge. Scanning for etch-pits is performed at a rate of ~ 100 cm² every 10 min at a 20× total magnification. Candidate etch-pits are examined at higher magnification. Advanced image analyses are applied to high-resolution images. In this way, the probability of accidental background coincidence over several foils is completely negligible. This makes discovery possible even on the basis of few, or even only one, event.

4.2 The magnetic monopole trapper system

The second detection system implemented in MoEDAL exploits the fact that slowed-down monopoles can get trapped in ferromagnetic/paramagnetic materials surrounding the interaction region. In MoEDAL, about 800 kg of Al bars are deployed around the interaction point of LHC beams. Aluminium has an enhanced capability to trap monopoles due to its anomalously large nuclear magnetic moment. Aluminium nuclei would bind $\mathcal{M}$s with energies O(100) keV. The presence of a trapped $\mathcal{M}$ in the Al bars would be revealed by the measurement of a persistent current induced when the material is passed through the superconducting coil of a SQUI D magnetometer (see Box 4 in PDF).

4.3 Current results from the MoEDAL experiment

Monopole trapping Al volumes (~ 200 rods 60 cm length and 2.5 cm diameter) were exposed in 2012 to 8 TeV protonproton collisions for an integrated luminosity of 0.7 fb^-1. No magnetic charge was detected in any of the exposed samples when passed through the SQUID system at the ETH Zurich facility. The magnetometer system used for the search is sketched in fig. 7; the minimum magnetic charge detectable by this magnetometer is $0.1 g_{D}$. No signal was detected compatible with the passage of a trapped $\mathcal{M}$.

In the 2015 LHC run, a larger array of Al modules was exposed to 13 TeV proton-proton collisions (integrated luminosity of 0.4 fb^-1) and analyzed. The persistent currents measured during the first passage of the 672 samples through the SQUID magnetometer are shown fig. 8. Twenty samples yielding an absolute value corresponding to the presence of a magnetic charge larger than $0.25 g_{D}$, were set aside and remeasured at least three more times. The monopole hypothesis was excluded for all twenty candidates and new limits have been set on monopole production cross sections, as shown in fig. 4.

5 Conclusions and perspectives

The Standard Model of particle physics has been spectacularly confirmed along the last thirty years by experiments at accelerators and colliders of increasing energy. The last, big achievement was the discovery at the CERN LHC of the missing piece, the Higgs boson. On the other hand, it is largely believed that the Standard Model is incomplete and represents a sort of low-energy limit of a more fundamental and unified theory, which should reveal itself at higher energies. The intriguing requests of a large presence of Dark Matter and Dark Energy in our Universe to explain astrophysical and cosmological observations also point to a revision of the Standard Model. Different extensions of the Standard Model could be tested at accelerators, as, for example, those connected with the neutrino sector or with the search for supersymmetric particles. It is in this context that predictions and searches for magnetic monopoles and other stable massive particles play a fundamental role. We do not know the mass of monopoles (extending up to the GUT scale, $\ge 10^{16}$ GeV/c²), neither if they have an inner structure. The only firm assumption is the one derived from the Dirac relation (1), leading to reasonable predictions for the interactions of $\mathcal{M}$s with matter and detectors.

The omni-purpose LHC experiments are equipped with detectors able to push the search to higher masses and lower $\mathcal{M}$ production cross sections. The in-flight signature of a monopole event in ATLAS or CMS would be rather striking, yielding a large number of signals in the tracker and a localized energy deposition in the electromagnetic calorimeters. Complementary methods are employed in MoEDAL, namely the in-flight detection using NTDs and the detection of trapped monopoles in matter through the induction technique.

Quoting from Joseph Polchinski’s talk at the Dirac Centennial Symposium "...the existence of magnetic monopoles seems like one of the safest bets that one can make about physics not yet seen. It is very hard to predict when and if monopoles will be discovered [...] But we must continue to hope that we will be lucky, or unexpectedly clever, some day". Thus, the searches for monopoles continue with both astroparticle physics projects and accelerator experiments.

Acknowledgments

We would like to thank J. Pinfold, spokesperson of the MoEDAL Collaboration, and our colleagues at INFN Bologna, S. Cecchini, M. Guerzoni, Z. Sahnoun, G. Sirri, V. Togo for their contributions and useful discussions.