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This document is comprised of a collection of updated preliminary parameters for the key parts of the muon collider. The updated preliminary parameters follow on from the October 2023 Tentative Parameters Report. Particular attention has been given to regions of the facility that are believed to hold greater technical uncertainty in their design and that have a strong impact on the cost and power consumption of the facility. The data is collected from a collaborative spreadsheet and transferred to overleaf.

The International Muon Collider Collaboration (IMCC) [1] was established in 2020 following the recommendations of the European Strategy for Particle Physics (ESPP) and the implementation of the European Strategy for Particle Physics-Accelerator R&D Roadmap by the Laboratory Directors Group [2], hereinafter referred to as the the European LDG roadmap. The Muon Collider Study (MuC) covers the accelerator complex, detectors and physics for a future muon collider. In 2023, European Commission support was obtained for a design study of a muon collider (MuCol) [3]. This project started on 1st March 2023, with work-packages aligned with the overall muon collider studies. In preparation of and during the 2021-22 U.S. Snowmass process, the muon collider project parameters, technical studies and physics performance studies were performed and presented in great detail. Recently, the P5 panel [4] in the U.S. recommended a muon collider R&D, proposed to join the IMCC and envisages that the U.S. should prepare to host a muon collider, calling this their "muon shot". In the past, the U.S. Muon Accelerator Programme (MAP) [5] has been instrumental in studies of concepts and technologies for a muon collider., Comment: This document summarises the International Muon Collider Collaboration (IMCC) progress and status of the Muon Collider R&D programme

Diagnostics based on the polarization properties of the synchrotron emission can provide precious information on both the ordered structure and the random level of the magnetic field. While this issue has been already analysed in the radio, the polarization data recently obtained by the mission IXPE have shown the need to extend this analysis to the X-rays. While our immediate target are young SNRs, the scope of this analysis is wider. We aim at extending the analysis to particle energy distributions more complex than a power law, as well as to investigate a wider range of cases involving a composition of ordered and random magnetic fields. Since only in a limited number of cases an analytical approach is possible, we have devised to this purpose an optimised numerical scheme, and we have directly used it to investigate particle energy distributions in the form of a power law with an exponential, or super-exponential cutoff. We have also considered a general combination of a ordered field plus an anisotropic random component. We have shown that the previously derived analytic formulae, valid for power-law distributions, may be good approximations of the polarization degree also in the more general case with a cutoff, as typically seen in X-rays. We have explicitly analysed the young SNRs SN 1006, Tycho and Cas A. In particular, for SN 1006, we have proved the consistency between the radio and X-ray polarization degrees, favouring the case of predominantly random field, with an anisotropic distribution. In addition, for the power-law case, we have investigated the effect of a compression on both ordered and random magnetic field components, aimed at describing the mid-age radio SNRs. This work allows a more efficient exploitation of radio and X-ray measurements of the synchrotron polarization, and is addressed to present observations with IXPE as well as to future projects., Comment: 14 pages, 21 figures, accepted for publication on Astronomy and Astrophysics

Bent crystal are widely used as optics for X-rays, but via the phenomenon of planar channeling they may act as waveguide for relativistic charged particles beam as well, outperforming some of the traditional technologies currently employed. A physical description of the phenomenon and the resulting potential for applications in a particle accelerator is reported. The elastic properties of the anisotropic crystal lattice medium are discussed, introducing different types of curvature which can enable a wide array of bending schemes optimized for each different case features. The technological development of machining strategy and bending solutions useful for the fabrication of crystals suitable in high energy particle manipulations are described. As well as the high precision characterization processes developed in order to satisfy the strict requirements for installation in an accelerator. Finally, the characterization of channeling phenomenon in bent crystal is described, pointing out several experimental setups suitable to comply each specific case constrains.

Recent studies have shown that the electromagnetic shower induced by a high-energy electron, positron or photon incident along the axis of an oriented crystal develops in a space more compact than the ordinary. On the other hand, the properties of the hadronic interactions are not affected by the lattice structure. This means that, inside an oriented crystal, the natural difference between the hadronic and the electromagnetic shower profile is strongly accentuated. Thus, a calorimeter composed of oriented crystals could be intrinsically capable of identifying more accurately the nature of the incident particles, with respect to a detector composed only of non-aligned crystals. Since no oriented calorimeter has ever been developed, this possibility remains largely unexplored and can be investigated only by mean of numerical simulations. In this work, we report the first quantitative evaluation of the particle identification capability of such a calorimeter, focusing on the case of neutron-gamma discrimination. We demonstrate through Geant4 simulations that the use of oriented crystals significantly improves the performance of a Random Forest classifier trained on the detector data. This work is a proof that oriented calorimeters could be a viable option for all the environments where particle identification must be performed with a very high accuracy, such as future high-intensity particle physics experiments and satellite-based gamma-ray telescopes., Comment: 13 pages, 9 figures

We observed a substantial increase of the scintillation light output of lead tungstate (PbWO$_4$) at a small incidence angle with respect to two main lattice axes. This reflects the acceleration of electromagnetic shower development that occurs in the crystalline Strong Field. We measured the scintillation light generated by $120$-$\mathrm{GeV}$ electrons and $10$-$100$-$\mathrm{GeV}$ $\gamma$ rays on thick samples. This result deepens the knowledge of the shower development mechanisms in crystal scintillators and could pave the way to the development of innovative accelerator- and space-borne calorimeters.

Using the newly developed 530 MeV positron beam from the Mainz Microtron MAMI and employing a bent silicon crystal, we demonstrate the first successful manipulation with high efficiencies of the trajectories of positrons through planar channeling and volume reflection. This uncovered the presence of fine structure within the angular distribution of charged particles when they are channeled between the planes of bent crystals. The alignment of our experimental findings with simulation results not only demonstrates a deeper understanding of the interactions between charged particle beams and bent crystals but also signals a new phase in the development of innovative methodologies for slow extraction in circular accelerators operating in the GeV range, with implications for worldwide accelerators. Our results also mark a considerable progression in the generation of advanced x-ray sources through the channeling process in periodically bent crystals, rooted in a comprehensive understanding of the interactions between positron beams and such crystals.

Context. We propose that the X-ray filaments emerging from selected bow shock pulsar wind nebulae are due to a charge-separated outflow of electrons and/or positrons escaping the nebula and propagating along the local Galactic magnetic field. Aims. The X-ray brightness, length, and thickness of filaments are all accounted for if a nonresonant streaming instability is excited. Methods. This is possible if particles are released in the interstellar medium as a collimated beam, as would be expected in a reconnection region between the nebular and interstellar magnetic fields. Results. We successfully test this idea on the Guitar Nebula filament and discuss other cases. Conclusions. These filaments provide the best diagnostics available for particle escape from evolved pulsar wind nebulae, a process essential to assessing the contribution of these sources to cosmic ray positrons. The same phenomenology might govern the occurrence of TeV halos and their importance for cosmic ray transport., Comment: 8 pages, 2 figures, 2 tables

It has been known since decades that the alignment of a beam of high-energy electrons with particular crystal directions involves a significant increase of bremsstrahlung radiation emission. This enhancement lies at the conceptual foundation of innovative positron source schemes for future lepton colliders. In particular, the so-called hybrid scheme makes use of a heavy-metal radiator in crystalline form, which is then followed by an amorphous metallic converter for positron generation from electrons by means of a two-step electromagnetic process. This work presents the most recent simulation results obtained on the development of a hybrid positron source for the FCC-$ee$ from the standpoint of the features of both the crystalline radiator and the amorphous converter.

We present the first continuous operation in a surface lab of BULLKID, a detector for searches of light Dark Matter and precision measurements of the coherent and elastic neutrino-nucleus scattering. The detector consists of an array of 60 cubic silicon particle absorbers of 0.34 g each, sensed by cryogenic kinetic inductance detectors. The data presented focusses on one of the central elements of the array and on its surrounding elements used as veto. The energy spectrum resulting from an exposure of 39 hours to ambient backgrounds, obtained without radiation shields, is flat at the level of $(2.0\pm0.1\,{\rm stat.}\pm0.2\,{\rm syst.})\times10^6$ counts / keV kg days down to the energy threshold of $160\pm13$ eV. The data analysis demonstrates the unique capability of rejecting backgrounds generated from interactions in other sites of the array, stemming from the segmented and monolithic structure of the detector.

The vast majority of Pulsar Wind Nebulae (PWNe) present in the Galaxy is formed by middle-aged systems characterized by a strong interaction of the PWN itself with the supernova remnant (SNR). Unfortunately, modelling these systems can be quite complex and numerically expensive, due to the non-linearity of the PWN-SNR evolution even in the simple 1D / one-zone case when the reverse shock of the SNR reaches the PWN, and the two begin to interact (and reverberation starts). Here we introduce a new numerical technique that couples the numerical efficiency of the one-zone thin shell approach with the reliability of a full ``lagrangian'' evolution, able to correctly reproduce the PWN-SNR interaction during the reverberation and to consistently evolve the particle spectrum beyond. Based on our previous findings, we show that our novel strategy resolves many of the uncertainties present in previous approaches, as the arbitrariness in the SNR structure, and ensure a robust evolution, compatible with results that can be obtained with more complex 1D dynamical approaches. Our approach enable us for the first time to provide reliable spectral models of the later compression phases in the evolution of PWNe. While in general we found that the compression is less extreme than that obtained without such detailed dynamical considerations, leading to the formation of less structured spectral energy distributions, we still find that a non negligible fraction of PWNe might experience a super-efficient phase, with the optical and/or X-ray luminosity exceeding the spin-down one., Comment: 12 pages, 2 tables, 5 figures

A Mathematical Program with Equilibrium Constraints (MPEC) is formulated to capture the relationships between multiple Mobility Service Providers (MSPs) and the users of a multi-modal transport network. The network supply structure is defined through a novel supernetwork approach where users' daily trip chains are represented to model the mobility services used to reach each destination. At the upper level, a profit maximization formulation is introduced to describe each MSPs' behaviour. At the lower level, users within a class choose minimum cost routes, according to Wardrop's first equilibrium principle. To consider the interactions between modes, non-separable costs between supernetwork links are defined, and users' equilibrium conditions are formulated as a Variational Inequality (VI). To solve the MPEC, an iterative solution algorithm based on a Modified Projection Method is proposed. Numerical examples are presented to illustrate properties of the model, and to examine scenarios showcasing cooperation or competition strategies between MSPs.

Electromagnetic processes of charged particles interaction with oriented crystals provide a wide variety of innovative applications such as beam steering, crystal-based extraction/collimation of leptons and hadrons in an accelerator, a fixed-target experiment on magnetic and electric dipole moment measurement, X-ray and gamma radiation source for radiotherapy and nuclear physics and a positron source for lepton and muon colliders, a compact crystalline calorimeter as well as plasma acceleration in the crystal media. One of the main challenges is to develop an up-to-date, universal and fast simulation tool to simulate these applications. We present a new simulation model of electromagnetic processes in oriented crystals implemented into Geant4, which is a toolkit for the simulation of the passage of particles through matter. We validate the model with the experimental data as well as discuss the advantages and perspectives of this model for the applications of oriented crystals mentioned above., Comment: 18 pages, 9 figures

During its early evolution, a pulsar wind nebula (PWN) sweeps the inner part of the supernova ejecta and forms a thin massive shell. Later on, when the shell has been reached by the reverse shock of the supernova remnant, the evolution becomes more complex, in most cases reverting the expansion into a compression: this later phase is called "reverberation". Computations done so far to understand this phase have been mostly performed in the thin-shell approximation, where the evolution of the PWN radius is assimilated to that of the swept-up shell under the effect of both the inner pressure from the PWN, and the outer pressure from the supernova remnant. Despite the thin-shell approach seems rather justifiable, its implementations have so far been inaccurate, and its correctness, never tested. The outer pressure was naively assumed to be scaled according to the Sedov solution (or a constant fraction of it) along the entire evolution. The thin-shell assumption itself fails along the process, being the shell no longer thin in comparison with the size of the PWN. Here, through a combination of numerical models, dimensional arguments, and analytic approximations, we present a detailed analysis of the interaction of the PWN with the supernova remnant. We provide a new analytic approximation of the outer pressure, beyond the Sedov solution, and a revised "thin-shell" able to reproduce results from numerical simulations. Finally, we compute the efficiency by which the PWN is compressed during reverberation over a wide population of sources., Comment: 23 pages, 20 figures

A timely and long-term programme of kaon decay measurements at a new level of precision is presented, leveraging the capabilities of the CERN Super Proton Synchrotron (SPS). The proposed programme is firmly anchored on the experience built up studying kaon decays at the SPS over the past four decades, and includes rare processes, CP violation, dark sectors, symmetry tests and other tests of the Standard Model. The experimental programme is based on a staged approach involving experiments with charged and neutral kaon beams, as well as operation in beam-dump mode. The various phases will rely on a common infrastructure and set of detectors., Comment: Letter of Intent submitted to CERN SPSC. Address all correspondence to hike-eb@cern.ch

We introduce BULLKID, an innovative phonon detector consisting of an array of dices acting as particle absorbers sensed by multiplexed Kinetic Inductance Detectors (KIDs). The dices are carved in a thick crystalline wafer and form a monolithic structure. The carvings leave a thin common disk intact in the wafer, acting both as holder for the dices and as substrate for the KID lithography. The prototype presented consists of an array of 64 dices of 5.4x5.4x5 mm$^3$ carved in a 3" diameter, 5 mm thick silicon wafer, with a common disk 0.5 mm thick hosting a 60 nm patterned aluminum layer. The resulting array is highly segmented but avoids the use of dedicated holding structures for each unit. Despite the fact that the uniformity of the KID electrical response across the array needs optimization, the operation of 8 units with similar features shows, on average, a baseline energy resolution of $26\pm7$ eV. This makes it a suitable detector for low-energy processes such as direct interactions of dark matter and coherent elastic neutrino-nucleus scattering.

We determine a DG-Lie algebra controlling deformations of a locally free module over a Lie algebroid $\mathcal{A}$. Moreover, for every flat inclusion of Lie algebroids $\mathcal{A}\subset \mathcal{L}$ we introduce semiregularity maps and prove that they annihilate obstructions, provided that the Leray spectral sequence of the pair $(\mathcal{L},\mathcal{A})$ degenerates at $E_1$.

Scintillating homogeneous detectors represent the state of the art in electromagnetic calorimetry. Moreover, the currently neglected crystalline nature of the most common inorganic scintillators can be exploited to achieve an outstanding performance boost in terms of compactness and energy resolution. In fact, it was recently demonstrated by the AXIAL/ELIOT experiments that a strong reduction in the radiation length inside PWO, and a subsequent enhancement in the scintillation light emitted per unit thickness, are attained when the incident particle trajectory is aligned with a crystal axis within $\sim 1^\circ$. A SiPM-based system has been developed to directly probe this remarkable effect by measuring the scintillation light emitted by a PWO sample. The same concept could be applied to full-scale detectors that would feature a design significantly more compact than currently achievable and unparalleled resolution in the range of interest for present and future experiments.

An intense positron sources is a demanding element in the design of future lepton colliders. A crystal-based hybrid positron source could be an alternative to a more conventional scheme based on the electron conversion into positron in a thick amorphous target. The conceptual idea of the hybrid source is to have two separate objects, a photon radiator and a photon-to-positron converter target. In such a scheme an electron beam crosses a thin axially oriented crystal with the emission of a channeling radiation, characterized by a considerably larger amount of photons if compared to Bremsstrahlung. The net result is an increase in the number of produced positrons at the converter target. In this paper we present the results of a beam test conducted at the DESY TB 21 with 5.6 GeV electron beam and a crystalline tungsten radiator. Experimental data clearly highlight an increased production of photons and they are critically compared with the outcomes of novel method to simulate the number of radiated photons, showing a very good agreement. Strong of this, the developed simulation tool has been exploited to design a simple scheme for a positron source based on oriented crystal, demonstrating the advantages in terms of reduction of both deposited energy and the peak energy deposition density if compared to conventional sources. The presented work opens the way for a realistic and detailed design of a hybrid crystal-based positron source for future lepton colliders.

Plasma wakefield acceleration (PWFA) has shown illustrious progress and resulted in an impressive demonstration of tens of GeV particle acceleration in meter-long single structures. To reach even higher energies in the 1 TeV to 10 TeV range, a promising scheme is channeling acceleration in solid-density plasmas within crystals or nanostructures. The E336 experiment studies the beam-nanotarget interaction with the highly compressed electron bunches available at the FACET-II accelerator. These studies furthermore involve an in-depth research on dynamics of beam-plasma instabilities in ultra-dense plasma, its development and suppression in structured media like carbon nanotubes and crystals, and its potential use to transversely modulate the electron bunch., Comment: submitted to Snowmass'2021 Accelerator Frontier (AF6), 16 pages, 9 Figs

We have observed a significant enhancement in the energy deposition by $25$--$100~\mathrm{GeV}$ photons in a $1~\mathrm{cm}$ thick tungsten crystal oriented along its $\langle 111 \rangle$ lattice axes. At $100~\mathrm{GeV}$, this enhancement, with respect to the value observed without axial alignment, is more than twofold. This effect, together with the measured huge increase in secondary particle generation is ascribed to the acceleration of the electromagnetic shower development by the strong axial electric field. The experimental results have been critically compared with a newly developed Monte Carlo adapted for use with crystals of multi-$X_0$ thickness. The results presented in this paper may prove to be of significant interest for the development of high-performance photon absorbers and highly compact electromagnetic calorimeters and beam dumps for use at the energy and intensity frontiers.

Positron sources are the key elements for the future and current lepton collider projects such as ILC, CLIC, SuperKEKB, FCC-ee, Muon Collider/LEMMA, etc., introducing challenging critical requirements for high intensity and low emittance beams in order to achieve high luminosity. In fact, due to their large production emittance and constraints given by the target thermal load, the main collider parameters such as the peak and average current, the emittances, the damping time, the repetition frequency and consequently the luminosity are determined by the positron beam characteristics. In this paper, the conventional positron sources and their main properties are explored for giving an indication to the challenges that apply during the design of the advanced accelerator concepts. The photon-driven positron sources as the novel approach proposed, primarily for the future linear colliders, are described highlighting their variety and problematic.

We present the results of an experimental study of multiple scattering of positively charged high energy particles in bent samples of monocrystalline silicon. This work confirms the recently discovered effect of a strong reduction in the rms multiple scattering angle of particles channeled in the silicon (111) plane. The effect is observed in the plane orthogonal to the bending plane. We show in detail the influence of angular constraints on the magnitude of the effect. Comparison of the multiple scattering process at different energies indicates a violation of the law of inverse proportionality of the rms angle of channeled particles with energy. By increasing the statistics, we have improved the results of multiple scattering measurements for particles moving, but not channeled, in silicon crystals., Comment: arXiv admin note: text overlap with arXiv:1910.00250 minor fixes

Pulsar wind nebulae (PWNe) represent the largest class of sources that upcoming {\gamma}-ray surveys will detect. Therefore, accurate modelling of their global emission properties is one of the most urgent problems in high-energy astrophysics. Correctly characterizing these dominant objects is a needed step to allow {\gamma}-ray surveys to detect fainter sources, investigate the signatures of cosmic-ray propagation and estimate the diffuse emission in the Galaxy. In this paper we present an observationally motivated construction of the Galactic PWNe population. We made use of a modified one-zone model to evolve for a long period of time the entire population. The model provides, for every source, at any age, a simplified description of the dynamical and spectral evolution. The long term effects of the reverberation phase on the spectral evolution are described, for the first time, based on physically motivated prescriptions for the evolution of the nebular radius supported by numerical studies. This effort tries to solve one of the most critical aspects of one-zone modeling, namely the typical overcompression of the nebula during the reverberation phase, resulting in a strong modification of its spectral properties at all frequencies. We compare the emission properties of our synthetic Pulsar Wind Nebulae population with the most updated catalogues of TeV Galactic sources. We find that the firmly identified and candidate PWNe sum up to about 50% of the expected objects in this class above threshold for detection. Finally, we estimate that CTA will increase the number of TeV detected PWNe by a factor$\geq3$., Comment: 15 pages, 8 figures, 2 tables. Accepted for publication in Monthly Notices of the Royal Astronomical Society

We introduce the notion of Chern-Simons classes for curved DG-pairs and we prove that a particular case of this general construction provides canonical $L_\infty$ liftings of Buchweitz-Flenner semiregularity maps for coherent sheaves on complex manifolds., Comment: V2 introduction and references expanded, V3 corrected typos and minor changes