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All papers published in this volume have been reviewed through processes administered by the Editors. Reviews were conducted by expert referees to the professional and scientific standards expected of a proceedings journal published by IOP Publishing.• Type of peer review: Single Anonymous• Conference submission management system: Morressier• Number of submissions received: 63• Number of submissions sent for review: 62• Number of submissions accepted: 61• Acceptance Rate (Submissions Accepted / Submissions Received × 100): 96.8• Average number of reviews per paper: 1.02• Total number of reviewers involved: 32• Contact person for queries:Name: Francis PrattEmail: francis.pratt@stfc.ac.ukAffiliation: Science and Technology Facilities Council - ISIS Muons

The SHiP experiment is proposed to search for very weakly interacting particles beyond the Standard Model which are produced in a 400 GeV/c proton beam dump at the CERN SPS. About 10 11 muons per spill will be produced in the dump. To design the experiment such that the muon-induced background is minimized, a precise knowledge of the muon spectrum is required. To validate the muon flux generated by our Pythia and GEANT4 based Monte Carlo simulation (FairShip), we have measured the muon flux emanating from a SHiP-like target at the SPS. This target, consisting of 13 interaction lengths of slabs of molybdenum and tungsten, followed by a 2.4 m iron hadron absorber was placed in the H4 400 GeV/c proton beam line. To identify muons and to measure the momentum spectrum, a spectrometer instrumented with drift tubes and a muon tagger were used. During a 3-week period a dataset for analysis corresponding to ( 3.27 ± 0.07 ) × 10 11 protons on target was recorded. This amounts to approximatively 1% of a SHiP spill.

The use of accelerated beams of electrons, protons or ions has furthered the development of nearly every scientific discipline. However, high-energy muon beams of equivalent quality have not yet been delivered. Muon beams can be created through the decay of pions produced by the interaction of a proton beam with a target. Such ‘tertiary’ beams have much lower brightness than those created by accelerating electrons, protons or ions. High-brightness muon beams comparable to those produced by state-of-the-art electron, proton and ion accelerators could facilitate the study of lepton–antilepton collisions at extremely high energies and provide well characterized neutrino beams 1 – 6 . Such muon beams could be realized using ionization cooling, which has been proposed to increase muon-beam brightness 7 , 8 . Here we report the realization of ionization cooling, which was confirmed by the observation of an increased number of low-amplitude muons after passage of the muon beam through an absorber, as well as an increase in the corresponding phase-space density. The simulated performance of the ionization cooling system is consistent with the measured data, validating designs of the ionization cooling channel in which the cooling process is repeated to produce a substantial cooling effect 9 – 11 . The results presented here are an important step towards achieving the muon-beam quality required to search for phenomena at energy scales beyond the reach of the Large Hadron Collider at a facility of equivalent or reduced footprint 6 . Ionization cooling, a technique that delivers high-brightness muon beams for the study of phenomena at energy scales beyond those of the Large Hadron Collider, is demonstrated by the Muon Ionization Cooling Experiment.

Cosmic ray muon tomography has been recently explored as a non-destructive technique for monitoring or imaging dense well-shielded objects, classically not achievable with traditional tomographic methods. As a recent example of technology transition from high-energy physics to real-world engineering applications, cosmic ray muon tomography has been used with various levels of success in nuclear nonproliferation. However, present muon detection systems have no momentum measurement capabilities and recently developed muon-based radiographic techniques rely only on muon tracking. This unavoidably reduces resolution and requires longer measurement times thus limiting the widespread use of cosmic ray muon tomography. Measurement of cosmic ray muon momenta has the potential to significantly improve the efficiency and resolution of cosmic ray muon tomography. In this paper, we propose and explore the use of momentum-dependent cosmic ray muon tomography using multi-layer gas Cherenkov radiators, a new concept for measuring muon momentum in the field. The muon momentum measurements are coupled with a momentum-dependent imaging algorithm (mPoCA) and image reconstructions are presented to demonstrate the benefits of measuring momentum in cosmic ray muon tomography.

Layered transition metal dichalcogenides (TMDs) are model systems to investigate the interplay between superconductivity and the charge density wave (CDW) order. Here, we use muon spin rotation and relaxation ( μ + SR) to probe the superconducting ground state of polycrystalline 2H-TaS 2 , which hosts a CDW transition at 76 K and superconductivity below 1 K. The μ + SR measurements, conducted down to 0.27 K, are consistent with a nodeless, BCS-like single-gap s -wave state. Fits to the temperature dependence of the depolarization rate and Knight shift measurements support spin-singlet pairing. Crucially, no evidence of time-reversal symmetry breaking (TRSB) is observed, distinguishing 2H-TaS 2 from polymorphs like 4Hb-TaS 2 , where TRSB and unconventional superconductivity have been reported. These findings establish 2H-TaS 2 as a canonical BCS superconductor and provide a reference point for understanding the diverse electronic ground states that emerge in structurally distinct TMD polymorphs.

Cosmic-ray muography uses high-energy particles for imaging applications that are produced by cosmic rays in particle showers in the Earth's atmosphere. This technology has developed rapidly over the last 15 years, and it is currently branching out into many different applications and moving from academic research to commercial application. As in any new sub-field of research and technology, the nomenclature of the field itself is still developing and has not settled yet as new aspects of the field are appearing and with them the terms to describe them. This overview of the field of muography is not going to focus on the physics, on the reconstruction algorithms or on the involved detector technology. Detailed papers on these aspects are included in this issue of Philosophical Transactions A and I will refer to them. Instead, I will give an overview of the field as it is now, in 2018, and try to give an idea of the future directions in this field as I see them. This article is part of the Theo Murphy meeting issue ‘Cosmic-ray muography’.

Muons are particles with a spin of ½ that can be implanted into a wide range of condensed matter materials to act as a local probe of the surrounding atomic environment. Measurement of the muon’s precession and relaxation provides an insight into how it interacts with its local environment. From this, unique information is obtained about the static and dynamic properties of the material of interest. This has enabled muon spin spectroscopy, more commonly known as muon spin rotation/relaxation/resonance (μSR), to develop into a powerful tool to investigate material properties such as fundamental magnetism, superconductivity and functional materials. Alongside this, μSR may be used to study, for example, energy storage materials, ionic diffusion in potential batteries, the dynamics of soft matter, free radical chemistry, reaction kinetics, semiconductors, advanced manufacturing and cultural artefacts. This Primer is intended as an introductory article and introduces the μSR technique, the typical results obtained and some recent advances across various fields. Data reproducibility and limitations are also discussed, before highlighting promising future developments.Muon spin spectroscopy examines how muons interact with their local environment through measurement of the muon’s precession and relaxation. This provides unique information about the static and dynamic properties of a material. This Primer gives an introductory overview to muon spin spectroscopy, describing how muons are produced and used experimentally in various applications.

The discovery of superconductivity in Nd 0.8 Sr 0.2 NiO 2 (ref. 1 ) introduced a new family of layered nickelate superconductors that has now been extended to include a range of strontium doping 2 , 3 , praseodymium or lanthanum in place of neodymium 4 – 7 , and the five-layer compound Nd 6 Ni 5 O 12 (ref. 8 ). A number of studies have indicated that electron correlations are strong in these materials 9 – 15 , a feature that often leads to the emergence of magnetism. Here we report muon spin rotation/relaxation studies of a series of superconducting infinite-layer nickelates. Regardless of the rare earth ion or doping, we observe an intrinsic magnetic ground state arising from local moments on the nickel sublattice. The coexistence of magnetism—which is likely to be antiferromagnetic and short-range ordered—with superconductivity is reminiscent of some iron pnictides 16 and heavy fermion compounds 17 , and qualitatively distinct from the doped cuprates 18 . Measurements of four different infinite-layer nickelates show that magnetic behaviour coexists with superconductivity. This is different from what is seen in cuprates, giving a strong distinction between the two classes of oxide superconductors.

The observation of superconductivity in La 3 Ni 2 O 7– δ under pressure, following the suppression of a high-temperature density wave state, has attracted considerable attention. The nature of this density wave order was not clearly identified. Here we probe the magnetic response of the zero-pressure phase of La 3 Ni 2 O 7– δ as hydrostatic pressure is applied, and find that the apparent single density wave transition at zero applied pressure splits into two. The comparison of our muon-spin rotation and relaxation experiments with dipole-field numerical analysis reveals the magnetic structure’s compatibility with a stripe-type arrangement of Ni moments, characterized by alternating lines of magnetic moments and non-magnetic stripes at ambient pressure. When pressure is applied, the magnetic ordering temperature increases, whereas the unidentified density wave transition temperature falls. Our findings reveal that the ground state of the La 3 Ni 2 O 7– δ system is characterized by the coexistence of two distinct orders—a magnetically ordered spin density wave and a lower-temperature ordering that is most probably a charge density wave—with a notable pressure-enhanced separation between them. The density wave transition in a superconducting nickelate is shown to split when hydrostatic pressure is applied, indicating that it is composed of both a spin density wave and another form of ordered state.

There is considerable evidence that the superconducting state of Sr 2 RuO 4 breaks time reversal symmetry. In the experiments showing time reversal symmetry breaking, its onset temperature, T TRSB , is generally found to match the critical temperature, T c , within resolution. In combination with evidence for even parity, this result has led to consideration of a d x z  ±  i d y z order parameter. The degeneracy of the two components of this order parameter is protected by symmetry, yielding T TRSB  =  T c , but it has a hard-to-explain horizontal line node at k z  = 0. Therefore, s  ±  i d and d  ±  i g order parameters are also under consideration. These avoid the horizontal line node, but require tuning to obtain T TRSB  ≈  T c . To obtain evidence distinguishing these two possible scenarios (of symmetry-protected versus accidental degeneracy), we employ zero-field muon spin rotation/relaxation to study pure Sr 2 RuO 4 under hydrostatic pressure, and Sr 1.98 La 0.02 RuO 4 at zero pressure. Both hydrostatic pressure and La substitution alter T c without lifting the tetragonal lattice symmetry, so if the degeneracy is symmetry-protected, T TRSB should track changes in T c , while if it is accidental, these transition temperatures should generally separate. We observe T TRSB to track T c , supporting the hypothesis of d x z  ±  i d y z order. Two possible scenarios of the superconducting order parameter in Sr 2 RuO 4 remain difficult to distinguish. Here, the authors observe that the onset temperature of time reversal symmetry breaking tracks the superconducting transition temperature in Sr 2 RuO 4 , supporting a d x z  ± i d y z order parameter.