The MoEDAL experiment at Point 8 of the LHC ring is the seventh and newest LHC experiment. It is dedicated to the search for highly-ionizing particle avatars of physics beyond the Standard Model, extending significantly the discovery horizon of the LHC. A MoEDAL discovery would have revolutionary implications for our fundamental understanding of the Microcosm. MoEDAL is an unconventional and largely passive LHC detector comprised of the largest array of Nuclear Track Detector stacks ever deployed at an accelerator, surrounding the intersection region at Point 8 on the LHC ring. Another novel feature is the use of paramagnetic trapping volumes to capture both electrically and magnetically charged highly-ionizing particles predicted in new physics scenarios. It includes an array of TimePix pixel devices for monitoring highly-ionizing particle backgrounds. The main passive elements of the MoEDAL detector do not require a trigger system, electronic readout, or online computerized data acquisition. The aim of this paper is to give an overview of the MoEDAL physics reach, which is largely complementary to the programs of the large multipurpose LHC detectors ATLAS and CMS.

Anti-Hermitian mass terms are considered, in addition to Hermitian ones, for $\mathcal{P}\mathcal{T}$-symmetric complex-scalar and fermionic field theories. In both cases, the Lagrangian can be written in a manifestly symmetric form in terms of the $\mathcal{P}\mathcal{T}$-conjugate variables, allowing for an unambiguous definition of the equations of motion. After discussing the resulting constraints on the consistency of the variational procedure, we show that the invariance of a non-Hermitian Lagrangian under a continuous symmetry transformation does not imply the existence of a corresponding conserved current. Conserved currents exist, but these are associated with transformations under which the Lagrangian is not invariant and which reflect the well-known interpretation of $\mathcal{P}\mathcal{T}$-symmetric theories in terms of systems with gain and loss. A formal understanding of this unusual feature of non-Hermitian theories requires a careful treatment of Noether’s theorem, and we give specific examples for illustration.

MoEDAL is designed to identify new physics in the form of long-lived highly ionizing particles produced in high-energy LHC collisions. Its arrays of plastic nuclear-track detectors and aluminium trapping volumes provide two independent passive detection techniques. We present here the results of a first search for magnetic monopole production in 13 TeV proton-proton collisions using the trapping technique, extending a previous publication with 8 TeV data during LHC Run 1. A total of 222 kg of MoEDAL trapping detector samples was exposed in the forward region and analyzed by searching for induced persistent currents after passage through a superconducting magnetometer. Magnetic charges exceeding half the Dirac charge are excluded in all samples and limits are placed for the first time on the production of magnetic monopoles in 13 TeV $pp$ collisions. The search probes mass ranges previously inaccessible to collider experiments for up to five times the Dirac charge.

An extension of QED is considered in which the Dirac fermion has both Hermitian and anti-Hermitian mass terms, as well as both vector and axial-vector couplings to the gauge field. Gauge invariance is restored when the Hermitian and anti-Hermitian masses are of equal magnitude, and the theory reduces to that of a single massless Weyl fermion. An analogous non-Hermitian Yukawa theory is considered, and it is shown that this model can explain the smallness of the light-neutrino masses and provide an additional source of leptonic \( \mathcal{C}\mathcal{P} \) violation.

We demonstrate the extension to parity-time ($\mathcal{PT}$)-symmetric field theories of the Goldstone theorem, confirming that the spontaneous appearance of a field vacuum expectation value via minimization of the effective potential in a non-Hermitian model is accompanied by a massless scalar boson. Laying a basis for our analysis, we first show how the conventional quantization of the path-integral formulation of quantum field theory can be extended consistently to a non-Hermitian model by considering $\mathcal{PT}$ conjugation instead of Hermitian conjugation. The extension of the Goldstone theorem to a $\mathcal{PT}$-symmetric field theory is made possible by the existence of a conserved current that does not, however, correspond to a symmetry of the non-Hermitian Lagrangian. In addition to extending the proof of the Goldstone theorem to a $\mathcal{PT}$-symmetric theory, we exhibit a specific example in which we verify the existence of a massless boson at the tree and one-loop levels.

MoEDAL is designed to identify new physics in the form of stable or pseudostable highly ionizing particles produced in high-energy Large Hadron Collider (LHC) collisions. Here we update our previous search for magnetic monopoles in Run 2 using the full trapping detector with almost four times more material and almost twice more integrated luminosity. For the first time at the LHC, the data were interpreted in terms of photon-fusion monopole direct production in addition to the Drell-Yan-like mechanism. The MoEDAL trapping detector, consisting of 794 kg of aluminum samples installed in the forward and lateral regions, was exposed to $4.0{\mathrm{fb}}^{-1}$ of 13 TeV proton-proton collisions at the LHCb interaction point and analyzed by searching for induced persistent currents after passage through a superconducting magnetometer. Magnetic charges equal to or above the Dirac charge are excluded in all samples. Monopole spins 0, $½$, and 1 are considered and both velocity-independent and-dependent couplings are assumed. This search provides the best current laboratory constraints for monopoles with magnetic charges ranging from two to five times the Dirac charge.