##  0.3 Physics, detector and accelerator interface

###  0.3.1 Physics and detector needs

#### Overview

The vast physics potential described in Section 0.2 can be translated into
requirements for the machine and the experiments that will harvest data from
it.

The most notable requirements on the machine are: the mitigation of the beam-
induced backgrounds (discussed in Section 0.3.2), the amount of delivered
integrated luminosity and the ability to measure it with permille-level
precision, and a precise determination of the beam energy.

The requirements on the detectors situated at the main interaction points are
set in terms of “baseline” and “aspirational” targets. The latter are aimed at
a muon collider operating at $\sqrt{s}=10$ TeV. They include requirements on
the detector acceptance, particle detection and identification efficiency, as
well as resolutions on the various particle properties inferred by the
instrumental measurements. The baseline requirements are set by the need to
separate collision products from energy depositions from beam-induced
backgrounds and the need to identify and measure particles over a wide range
of energies with a precision at least comparable with the experiments taking
data at the LHC. The aspirational targets are set with the goal of fully
exploiting the physics potential of the machine. They aim at a reconstruction
performances comparable to those targeted by Higgs factories while extending
to significantly higher energies. Furthermore, these requirements are set with
the goal of maintaining sensitivity to unconventional signatures as well as
profiting from the unique potential of muon colliders to use forward muons to
study vector boson fusion processes. The preliminary targets for several key
metrics discussed more in detail in the next Section are reported in Table
0.3.1.

Table 0.3.1: Preliminary summary of the “baseline” and “aspirational” targets for selected key metrics, reported separately for machines taking data at $\sqrt{s}=3$ TeV and $\sqrt{s}=10$ TeV. The reported performance targets refer to the measurement of the reconstructed objects in physics events after, for example, background subtraction and not to the bare detector performance. Requirement | Baseline | Aspirational
---|---|---
|  $\sqrt{s}=3$ TeV |  $\sqrt{s}=10$ TeV |
Angular acceptance | $|\eta|<2.5$ | $|\eta|<2.5$ | $|\eta|<4$
Minimum tracking distance [cm] | $\sim 3$ | $\sim 3$ | $<3$
Forward muons ($\eta>5$) | – | tag |  $\sigma_{p}/p\sim 10$%
Track $\sigma_{p_{T}}/p^{2}_{T}$ [GeV-1] | $4\times 10^{-5}$ | $4\times 10^{-5}$ | $1\times 10^{-5}$
Photon energy resolution | $0.2/\sqrt{E}$ | $0.2/\sqrt{E}$ | $0.1/\sqrt{E}$
Neutral hadron energy resolution | $0.5/\sqrt{E}$ | $0.4/\sqrt{E}$ | $0.2/\sqrt{E}$
Timing resolution (tracker) [ps] | $\sim 30-60$ | $\sim 30-60$ | $\sim 10-30$
Timing resolution (calorimeters) [ps] | 100 | 100 | 10
Timing resolution (muon system) [ps] |  $\sim 50$ for $|\eta|>2.5$ |  $\sim 50$ for $|\eta|>2.5$ |  $<50$ for $|\eta|>2.5$
Flavour tagging |  $b$ vs $c$ |  $b$ vs $c$ |  $b$ vs $c$, $s$-tagging
Boosted hadronic resonance ID |  $h$ vs W/Z |  $h$ vs W/Z | W vs Z

Initial considerations on the interplay between the accelerator complex and
detectors dedicated to the study of neutrino physics are reported in Section
0.3.3.

#### Key challenges

The requirements on a detector that can successfully extract physics from
collision data at a muon collider are set by two categories of constraints:
the rejection of the reducible beam-induced backgrounds (BIB) and the need for
(precision) physics observables. These two categories can lead to conflicting
choices that require an overall optimisation to be performed. A quantitative
assessment of these requirements is being carried out based on a preliminary
set of physics benchmark channels, discussed in the following paragraphs,
which are used to study the overall performance of a detector design on
selected key metrics.

The requirements on the detector acceptance, summarised in terms angular
acceptance and minimum tracking distance, have to balance the need to maximise
the sensitive volume for a high rate SM measurements, retain sensitivity to a
broad range of non-prompt physics, while suppressing the BIB to a manageable
level. For example, the presence of large absorber nozzles located in the
forward region of the detector is key to reducing the high-energy showers from
the beam decays to a soft, diffused, energy contribution in the detector
volume. At the same time, especially when considering a machine operating at a
centre of mass energy of 10 TeV, a sizeable fraction of the interesting events
will include outgoing particles within the uninstrumented volume of the
absorbers. The precision determination of the Higgs boson couplings in single
and multi-Higgs boson production events are used as main benchmark to set the
angular acceptance requirements. The requirements on the minimum tracking
distance will be studied on high-rate Higgs boson studies exploiting flavour-
tagging as well as searches for long-lived particles [1].

Thanks to their highly penetrating nature, muons offer a unique possibility to
discriminate charged and neutral vector boson fusion processes. Dedicated
forward muon ($\eta>5$) detectors that could be placed beyond the detector
shielding and the accelerator components to detect outgoing muons from neutral
vector boson fusion processes. The needs of a comprehensive vector boson
scattering measurement and BSM searches (e.g. extended Higgs sectors)
programme set the goals of measuring not only the presence of the outgoing
muons, but also their momenta with good resolution. A preliminary study of the
placement of the detectors, their technology and the effects of BIB still
needs to be performed.

It is assumed that excellent (>90%) detection efficiencies must be achieved
for energies between $\mathcal{O}(1)$ GeV to $\mathcal{O}(1)$ TeV for all
measured particle species. The requirements on the resolution of the
measurements of transverse momenta and energies are driven by the high rate
Higgs and SM measurements. In particular, these requirements are set by the
need of rejecting irreducible SM backgrounds that share the same final state
signature. Searches for high-mass objects, where searches for heavy vector
triplets (HVT) are being used as a benchmark, contribute with looser
requirements since these are naturally less affected by both BIB and
irreducible SM backgrounds. The same physics benchmarks are currently used for
the determination of the requirements in terms of flavour tagging of hadronic
jets.

The identification of boosted hadronic resonances is an important feature,
required for the full exploration of the SM electroweak sector and several
searches for new heavy particles. In particular, the ability to distinguish
hadronically-decaying Higgs bosons from Z and W bosons in the whole detector
acceptance is crucial. High-mass searches, e.g. searches for HVTs, would
benefit from the ability to distinguish W and Z bosons for centrally-produced
resonances.

The availability of timing information from each of the sub-detectors of a
next-generation collider experiment is taken to be the norm. Requirements on
timing resolutions are set by background suppression considerations. The time
of arrival of BIB particles on the sensitive elements of the detector spreads
over a few ns after the bunch crossing, providing a powerful handle for
rejection. In the future, these requirements could be relaxed when improved
reconstruction algorithms with alternative mitigation strategies (e.g. based
on the event topology) become available. The search for heavy (meta-)stable
massive particles was identified as a benchmark channel that would profit
directly from a precise determination of the time of flight by each of the
detector systems. A minimum goal of retaining sensitivity to slow-moving
particles with a relativistic velocity $\beta\geq 0.5$ was taken as baseline
model-independent benchmark. The use of timing and time-of-flight information
for particle identification is a potentially promising tool that has yet to be
studied.

Unconventional signatures and the search for long-lived states still need to
be explored in detail at a muon collider. However, it is reasonable to assume
that they would impose requirements on the ability to reconstruct displaced
decays using only a subset of the available detector systems. Foreseen
benchmarks are for example a search for anomalous showers in the calorimeter
systems, or searches for displaced decay vertices in the tracking detectors or
the muon system.

The requirements on the detector acceptance and performance are less stringent
when considering an energy stage at $\sqrt{s}=3$ TeV. The differences are
driven by the smaller contribution of vector boson fusion processes to the
total cross-section and by the lower maximum energy of the collision products.

A key part of the physics programme at a muon collider is the measurement of
several cross-sections and branching ratios with percent-level precision. This
immediately sets a stringent requirement on the determination of the delivered
integrated luminosity. The current assumed target is a measurement with an
uncertainty at the permille-level.

#### Recent achievements

Significant progress has been recently made on on the physics requirements of
a muon collider detector. Much of this was documented in the Muon Forum report
[2] and a recent review [3]. There have been two main directions of research
undertaken in the pursuit of better understanding detector needs: those
focused on phenomenological studies and those based on full detector
simulation. Phenomenological studies (discussed in Section 0.2), have been
performed at a variety of levels of sophistication, from background free
studies on truth level events, to fast detector simulation in DELPHES with all
relevant backgrounds. The utility of these studies is that they are able to
cover a large array of physics possibilities and to focus on what is needed
for detectors to disentangle the hard scattering physics backgrounds. The
studies based on full simulation allow one to also quantify the potential in
the presence of beam-induced backgrounds. As focused on in Refs. [2, 3], there
have also been a small amount of studies of the same physics cases, where both
fast and full detector simulations were performed. While ultimately it would
be ideal to have all studies that impacted detector performance requirements
done at a full simulation level, in cases where there is overlap between fast
and full simulation studies good agreement has been found. This in turn gives
confidence in the use of fast simulations to help better delineate the physics
performance goals that have been reported.

Notable highlights were the studies performed on Higgs measurements and dark
matter searches with disappearing tracks.

The Higgs measurements [4, 5] serve as a general purpose benchmark for low-
energy Standard Model processes. These were used to evaluate the effects of
the detector acceptance on the final Higgs boson coupling precision, as well
as to perform an initial study of the resolution and instrumental effects
related to the presence of beam-induced backgrounds.

The search for disappearing tracks [6] is a unique probe to definitively test
the WIMP dark matter paradigm at a collider experiment. The signature consists
of short tracks formed by a few (3-4) tracking detector hits. As such, it is
uniquely sensitive to the detector layout, technology and the levels of beam-
induced background.

Furthermore, recent fast simulation studies [7, 5] have been crucial in
demonstrating the need for not just forward muon tagging, but also the
aspirational goal of forward muon measurements and how these measurements
affect for example the search for exotic Higgs boson decay modes.

#### Planned work

The effort in view of the evaluation report will be focused on extending the
list of preliminary benchmarks mentioned in Section 0.3.1 by assembling a list
of representative benchmarks that will allow judging the physics performance
more globally. As a part of this effort, a broad survey of measurements and
searches will be conducted to identify a list of high-priority benchmarks to
be studied in more detail with full simulation. The result of the survey will
be a prioritised benchmark list. The primary target of the evaluation will be
a collider operating at $\sqrt{s}=10$ TeV. The list should specify for which
benchmarks a dedicated assessment for a lower energy stage at $\sqrt{s}=3$ TeV
should be performed.

The second key task follows directly from the first and consists in performing
the detailed studies for as many of the benchmarks extracted from the
prioritised benchmark list as feasible to update to the requirements on the
key metrics. As a part of this detailed studies, the CLIC-inspired DELPHES
card used for the fast-simulation results will be updated to reflect the
expected detector performance in the “baseline” and “aspirational” scenarios.

The last key task will consist in developing a concept for automating the
evaluation of the prioritised benchmarks to efficiently re-evaluate the
results for any change in assumed detector design or data-taking conditions.

#### Next priority studies and opportunities for additional collaboration

A precise determination of beam energy is necessary for extracting physics
results from the experiments. While it is assumed that techniques foreseen and
used at other collider facilities will be compatible with the requirements,
additional collaborators interest in working on the design of the
instrumentation, the conceptual evaluation of the expected performance and the
evaluation of any interplay with the detectors would be welcome.

Similarly, only preliminary studies have been performed to study luminosity
determination using large-angle Bhabha scattering [8]. The feasibility of
reaching the required precision needs to be systematically assessed, and
possible dedicated detectors need to be designed, if required. New efforts in
this direction would make the current assumptions significantly more robust.

###  0.3.2 Machine-detector interface

#### System overview

The beam-induced background (BIB) poses a significant challenge for the
physics performance of a multi-TeV muon collider. The background is dominated
by the decay of stored muons, with additional contributions from incoherent
electron-positron pair production and possible beam halo losses on the
aperture. These particles interact with surrounding materials and generate a
mixed radiation field composed of secondary electrons, positrons, photons, as
well as hadrons (photo-nuclear interactions) and muons (Bethe-Heitler pair
production). Without dedicated mitigation measures, the beam-induced
background would severely impede the reconstruction of collision events in the
detector and would lead to significant radiation damage in detector
components.

An optimized design of the machine-detector interface (MDI) is hence critical
for minimizing the impact of machine operation on the physics performance
reach, and for reducing the ionizing dose and displacement damage in the
detector. The MDI design must include an elaborate absorber configuration,
consisting of masks inside the final focus region and a conical shielding,
which penetrates deeply into the detector region, up to a few centimeters from
the interaction point. The optimization of these masks and absorbers must be
done jointly with the detector and interaction region (IR) design. A
conceptual MDI layout for a 1.5 TeV muon collider has been devised previously
within the MAP collaboration, by means of the MARS Monte Carlo code [9, 11,
10]. Based on this configuration, first MDI design studies for higher-energy
muon colliders (3 TeV and 10 TeV) were carried out within the IMCC [12, 13,
14] using the FLUKA code [15, 16, 17].

#### Key challenges

The main challenge for the design of the machine-detector interface is the
short lifetime of muons. This intrinsic source of radiation distinguishes a
muon collider from other high-energy colliders. One of the key requirements is
the design of a sophisticated shielding configuration at the interface between
final focus magnets and detector. As shown in previous studies by the MAP
collaboration for 1.5 TeV [9, 11, 10], the number of secondary particles
entering the detector can be suppressed by orders of magnitude by placing
massive absorbers in close proximity of the interaction point (IP). The
innermost part consists of a nozzle-like shielding, which defines the inner
detector envelope and hence the angular acceptance of the detector (10° in
MAP). The shape and material budget of the nozzle determines the entry points,
directions and energy spectrum of particles reaching the detector. The nozzle
must be made of a high-Z material to efficiently shield the electromagnetic
showers induced by muon decay products or by beam halo losses on the aperture.
In addition, it must embed a layer of borated polyethylene or a similar
material to moderate and capture secondary neutrons produced in photo-nuclear
interactions. The nozzle must be carefully optimized for different center-of-
mass energies. Besides the conceptual design, one also faces engineering
challenges including assembly and support of the nozzle, as well as
integration of the nozzle inside the detector. In addition, an adequate
cooling system must be devised, to evacuate the heat deposited by decay
products and beam halo losses.

While the characteristics (e.g. spectra) of the decay and halo-induced
background are mainly determined by the nozzle, the amount of background
particles is also influenced by the interaction region layout, i.e., by the
lattice design and the placement of mask-like absorbers inside IR magnets. For
example, the previous studies by MAP for a 1.5 TeV collider suggested that a
dipolar component in the final focus configuration can be beneficial for
reducing the background flux into the detector [11]. Designing and optimizing
the IR layout is one of the key challenges for the collider design, in
particular for 10 TeV (a 3 TeV and 6 TeV IR design was previously devised
within MAP [18, 19, 20], although no background simulations were published).
Furthermore, the flux of secondary particles is also influenced by the
presence of a solenoid field in the detector region. This concerns not only
the decay-induced background, but also incoherent electron-positron pairs,
which are produced in the vicinity of the IP and are not directly intercepted
by the nozzle. While the choice of the solenoid field strength is primarily
driven by the particle detection efficiency in the detector, it must also take
into account the benefits for background suppression.

Even with an optimized MDI and interaction region design, a suitable choice of
detector technologies and reconstruction techniques is needed to reduce the
effects of the remaining background (see Chapter 0.4). The signatures of
background particles often exhibit distinct differences with respect to
collision products, which can be exploited for background suppression. This
concerns, for example, the arrival time of background particles with respect
to the bunch crossing, as well as the directions of background particles when
they enter the detector. The shielding requirements and MDI design will hence
strongly depend on detector R&D efforts to suppress the effect of background
particles.

#### Recent achievements

A full simulation framework based on the FLUKA Monte Carlo code was developed
for computing the beam-induced background entering the detector. First muon
decay studies for 1.5 TeV, replicating the MAP interaction region, exhibited a
good agreement with the previous MAP results derived with MARS15 [21]. The
studies were further extended to 3 TeV and, in particular, to a higher
collision energy of 10 TeV [12, 13, 14]. At the same time various simulation
techniques were improved, like the sampling of decays from a fully matched
beam phase-space distribution, which provided a more accurate description of
the transverse beam tails. While the 1.5 TeV and 3 TeV studies were still
based on the interaction region lattice from MAP, a new lattice was developed
for the 10 TeV collider, considering a triplet configuration as final focus
scheme [22]. The 10 TeV lattice allows for $\beta^{*}$ values of a few
millimeters and incorporates an adequate chromatic compensation without
sacrificing the physical and dynamic aperture. Using the FLUKA simulation
framework, a comparison of decay-induced background for 1.5 TeV, 3 TeV and 10
TeV were performed [21, 12, 13, 14]. As one of the key findings, these studies
demonstrated that the secondary spectra and multiplicities of particles
entering the detector are not substantially different for a 10 TeV collider.
Figure 0.3.1 illustrates the distribution of arrival times and energy spectra
of decay-induced background particles for 3 TeV and 10 TeV, respectively [14].
The results were obtained with the different IR lattices (MAP lattice for 3
TeV and IMCC lattice for 10 TeV), as described above.

Figure 0.3.1: Left: Distribution of the arrival time of decay-induced
background particles entering the detector. Right: Energy spectra of particles
arriving within the time window $[-1:15]$ ns with respect to the bunch
crossing (photons, electrons and positrons below 100 keV were discarded). The
figures were taken from Ref. [14].

In order to explore the impact of lattice design choices on the decay-induced
background, a series of studies was performed for 10 TeV [12]. Three
alternative triplet layouts were considered, one based on pure quadrupoles,
one based on combined-function dipole-quadrupoles and one using short dipoles
placed between triplet magnets. In the two latter cases, the dipolar component
strongly alters the azimuthal distribution of e-/e+ impact positions on the
vacuum aperture, yet the massive nozzle dilutes any azimuthal dependence of
the particle flux into the detector. In general, the studies showed that the
dipolar component suppresses only marginally the contribution of decays in the
final focus region, but nevertheless is beneficial for reducing the
contribution of distant decays. The latter can yield a non-negligible
contribution if the final focus is followed by a long drift section. Such a
drift might be needed to allow for a a smoother reduction of the beta function
at the end of the final focus scheme. The studies showed that in this case, a
dipolar component in the triplet can help to reduce the background.

In addition to the above studies, the impact of $L^{*}$ on the decay-induced
background was explored for the 10 TeV collider [13]. The solenoid in the
detector region traps the electrons and positrons, which travel in the beam
vacuum until they reach the other side of the interaction region, depositing
their energy in the machine components. As a consequence, muon decays between
the final focus magnets ($s<L^{*}$) contribute several orders of magnitudes
less to the background than those in final focus quadrupoles. A longer $L^{*}$
implies larger beta functions in the magnets, therefore increasing the magnet
aperture. On the other hand, the quadrupole gradient decreases if the maximum
field at the coil aperture is kept the same, thus implying a longer final
focus scheme. A comparative study of two different lattices with $L^{*}=6$ m
and $L^{*}=10$ m showed only a moderate background reduction by a few tens of
percent, but at the expense of a more complex lattice design. Increasing
$L^{*}$ is hence not considered a viable option for reducing the background.

All the studies listed above were still based on the MAP nozzle design, which
was optimized for 1.5 TeV. First attempts to adapt the nozzle for 10 TeV
suggest that there is potential to reduce the decay-induced particle flux into
the detector [13]. For example, the simulations showed that particle flux into
the inner tracker depends on the internal angle of the nozzle tip. The studies
also indicated that changing the external shape of the nozzle and adapting the
placement of the borated polyethylene layer can reduce the neutron and photon
flux. Optimizing the nozzle for 3 TeV and 10 TeV remains one of the key tasks
for future studies.

Preliminary assessments of background sources beyond muon decay were performed
for 10 TeV. In particular, a first comparison of incoherent electron-positron
pairs against decay-induced spectra was carried out [13]. Although some
electrons and positrons from pair production will be trapped by the solenoid,
a non-negligible fraction of particles with energies up to about 1 GeV is
expected to enter the inner tracker. The studies suggest that contribution of
incoherent pairs corresponds to a few ten percent of the total number of
electrons and positrons entering the detector in the vicinity of the IP
(within $\pm$50 cm). On average, the incoherent pairs have a higher energy
than the decay-induced background component since the latter is strongly
diluted by the nozzle.

Through the same simulation framework and by using a simplified model of a
CLIC-like detector as well as the MAP nozzle (for the detector description,
see also Sec. 0.4), the cumulative radiation damage in the detector could be
calculated for different collider energies (so far for muon decay only). Two
quantities were evaluated, the total ionizing dose and the 1 MeV neutron-
equivalent fluence in Silicon. The former describes the ionization damage in
organic materials and compounds, while the latter is related to the
displacement damage. The highest dose values occur around the vertex detector,
reaching about $\sim$200 kGy/year (10 TeV collider). The 1 MeV neutron-
equivalent fluence is highest in the inner tracker due to increased leakage of
neutrons from the nozzle, with a peak value of around $10^{15}$ n/cm2/year (10
TeV collider). Table 0.3.2 provides a summary of the maximum values in
different parts of the detector.

Table 0.3.2: Maximum values of the ionizing dose and the 1 MeV neutron-equivalent fluence (Si) in a CLIC-like detector. All values are per year of operation (10 TeV) and include only the contribution of muon decay. | Dose | 1 MeV neutron-equivalent fluence (Si)
---|---|---
Vertex detector | 200 kGy |  3$\times$1014 n/cm2
Inner tracker | 10 kGy |  1$\times$1015 n/cm2
ECAL | 2 kGy |  1$\times$1014 n/cm2

#### Planned work

One of the key tasks for the evaluation report is the optimization of the
shape and material composition of the nozzle using the FLUKA simulation
framework. The studies will be carried out separately for the 3 TeV and 10 TeV
machines. The optimization will rely on simple key figures (e.g. hit densities
in the vertex detector) in order to avoid the need of a full detector
simulation for each design iteration. For certain reference configurations, a
full evaluation of the background in dedicated detector simulations will be
essential, to provide a feedback for the nozzle design. Where applicable,
alternative optimization techniques (machine learning) will be explored. The
nozzle optimisation will mainly focus on decay-induced beam losses, but the
contribution of other background sources (incoherent pair production and beam
halo losses) will be assessed through the same simulation framework. This
requires input from other codes (GuineaPig) and machine studies (beam dynamics
simulations). In this context, it is foreseen to improve the description of
incoherent pair production by muons in GuineaPig.

Although a full-scale engineering design of the nozzle is out of the scope of
the present studies, it is foreseen to address some of the most important
engineering and integration aspects. This includes in particular the
evacuation of the deposited heat by means of a cooling system, the nozzle
support structure, the nozzle segmentation and assembly, as well as the
integration of the nozzle inside the detector and solenoid. Furthermore, the
feasibility of instrumenting the nozzle will be evaluated in close
collaboration with detector experts.

Another key task will be the optimization of the interaction region layout,
under consideration of the beam-induced background, optics-related
constraints, shielding requirement for magnets (heat load to cold mass,
radiation damage in the coils), as well as magnet technology limitations (coil
aperture versus peak field). The team is prioritizing this optimization for a
10 TeV machine, but will apply lessons learned to a reoptimization of MAP’s 3
TeV interaction region if more resources become available. An important design
specification is the minimum acceptable vacuum aperture in the interaction
region (in terms of transverse beam sigma). A smaller aperture of the masks
embedded in the final focus magnets and the nozzle is beneficial for reducing
the decay-induced background, but can lead to enhanced halo losses in the
interaction region. It is essential to quantify the permissible level of beam
halo losses per bunch crossing, which must remain below the decay-induced
background. Based on these studies, the interaction region aperture will be
revisited and the need of other mitigation measures for halo losses (e.g. halo
scraping system far from the IP) will be assessed.

Complementing the background studies, updated estimates for the cumulative
radiation damage in the detector will be provided for the optimized
interaction region and nozzle layout. These estimates shall include all
background contributions, including incoherent pairs and halo losses, which
have been neglected so far in the radiation damage studies.

#### Important missing effort

Considering the present resources, the MDI and IR studies described in the
previous sub-section will be given priority until the evaluation report
planned for 2026. Although the foreseen design studies will be mainly of a
conceptual nature, they will prepare the path towards a fully integrated MDI
and IR design. With the present resources, integrated engineering can only be
performed for a very limited subset of the systems; however, a detailed design
and integration of all technical systems can be elaborated once more resources
become available. At that stage, important aspects, like the alignment of the
nozzle and correction schemes for possible misalignments, can be addressed in
detail. Furthermore, beam instrumentation like beam position or loss monitors,
as well as luminosity monitoring, can be studied once resources are increased.

In addition to the MDI and IR design studies, it will be important to design a
collimation or scraping system, which reduces the halo-induced background in
the detector and also protects the interaction region in case of accidental
beam losses. Multi-turn tracking studies will be needed to assess the
efficiency of collimation techniques. In addition, it might be necessary to
explore novel collimation schemes. The studies described in the previous sub-
section will provide the necessary input concerning the acceptable amount of
halo losses in the interaction region. It will therefore establish
specifications for future design studies of a halo cleaning system, which can
be addressed once more resources become available.

###  0.3.3 Neutrino beams

The collider target parameters foresee a single bunch of $N_{\pm}=1.8\times
10^{12}$ muons (and one of anti-muons) injected in the 10 TeV muon collider
every $1/f_{r}=0.2\leavevmode\nobreak\ {\textrm{sec}}$. Assuming
$10^{7}\,{\textrm{sec}}$ of operation per year, this corresponds to a current
of $9\times 10^{19}$ muons per year. The muons circulate until they decay, and
those that decay in a straight section of the collider ring give rise to a
collimated beam of neutrinos that could be used for physics measurements in a
dedicated detector. The fraction of usable muons is the length $L$ of the
straight section divided by the collider circumference, of 10 km, and a region
of at least $L=10$ m without fields is required for the installation of the
detector close to the Interaction Point (IP). This gives $9\times 10^{9}$
neutrinos of each species per second and $9\times 10^{16}$ per year at the 10
TeV collider. At the 3 TeV collider, a similar estimate gives $2.4\times
10^{10(17)}$ neutrinos per second (year). Notice that our estimate only
accounts for the muons that decay in the detector region. The total length of
the straight section is about 100 m in the current versions of the collider
lattice design, and most of the muons decaying in this longer region should
produce usable neutrinos. At the real collider we could thus expect few or 10
times more neutrinos than our estimate.

The neutrinos are very collinear to the decaying muons, with an angle that is
typically below $0.1\leavevmode\nobreak\ {\textrm{mrad}}$ already at the 3 TeV
MuC, and even smaller at 10 TeV because of the larger muon energy (see e.g.
Ref. [23]). The muon beam angular divergence is typically much above
$0.1\leavevmode\nobreak\ {\textrm{mrad}}$, hence the distribution of the
neutrino angle relative to the beam axis is driven by the dynamics of the muon
beam and it cannot be estimated without reference to the lattice design, which
is still preliminary. Fortunately, the beam angular divergence in the detector
region equal to $0.6\leavevmode\nobreak\ {\textrm{mrad}}$, both for the 3 and
10 TeV colliders is a rather robust design parameter because it is directly
related to the luminosity at fixed emittance. Our estimate of the neutrino
angle (and energy) distribution thus assumes a constant
$0.6\leavevmode\nobreak\ {\textrm{mrad}}$ angular spread444Specifically, we
smear $p_{x,y}/p_{z}$, with $p$ the muon momentum, by independent Gaussians
with $\sigma=6\times 10^{-4}$. for the decaying muons, and nominal beam energy
of $1.5$ and 5 TeV for the 3 and 10 TeV muon collider, respectively. This
simplified simulation of the neutrino angle and energy distribution has been
found in qualitative agreement with the complete simulation based on a
preliminary design of the lattice.

The relevant parameter for physics studies is the rate of neutrino
interactions, which in turn depends on the geometric acceptance and on the
mass per unit area of the neutrino target. There are good perspectives to
attain order-one geometric acceptance: around 30% of the neutrinos would
intercept a small 10 cm radius cylindrical target placed at a realistically
large (200 m) distance from the IP. The target mass is harder to estimate,
because it is intertwined with the capabilities of the detector to record the
products of the neutrino interactions. Two options are considered in Section
0.2.2, and the resulting interaction rates reported in Fig. 0.2.4.

Despite the promising potential discussed in Section 0.2.2, no resources are
currently available within IMCC for the design of dedicated neutrino
detectors. We instead plan to refine the estimation of the neutrino flux from
updated accelerator lattice designs.

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##  0.4 Detector

###  0.4.1 Concepts

#### System overview

The detector concept for a $\sqrt{s}=3$ TeV muon collider is based on the
detector design proposed by CLIC [1], modified to adapt it to the machine-
detector interface. The forward calorimeters (luminometer) have been replaced
with the shielding nozzles designed by MAP. This structure is constituted by
two double-cone made of tungsten and borated polyethylene having an opening
angle of $10^{\circ}$, which are necessary to mitigate the impact of the beam-
induced background. The nozzles are placed along the beam axis, in the region
between 6 and 600 cm away from the interaction point. As a consequence of
that, the inner openings in the endcap region of the tracking detector,
calorimeter and muon stations have been increased to host the nozzles. In
addition to that, the spatial configuration of the vertex detector has been
optimised to minimize the occupancy in the region of the tip of the nozzles.
Finally, the magnetic field has been set to 3.57 T for consistency with the
magnetic field assumed in the MARS15 simulation of the BIB particles. The
detector is structured as follow. The innermost system closest to the beam-
pipe is a full-silicon tracking system, that includes a vertex detector made
of silicon pixels with double layers, and inner and outer trackers
respectively composed of silicon macropixels and microstrips. The tracking
system is surrounded by a calorimeter system consisting of an electromagnetic
(ECAL) and a hadronic (HCAL) calorimeter, the former composed of alternating
layers of tungsten absorber and silicon sensors, and the latter having
alternating layers of steel absorber and scintillating pads. A solenoid with
an inner bore of 3.5 m radius, provides a magnetic field of 3.57 T, whose flux
is returned by a magnet iron yoke instrumented with muon chambers (resistive
plate chambers). A scheme of the full detector is shown in Fig. 0.4.1.

Figure 0.4.1: Muon collider detector concept. From the innermost to the
outermost regions, it includes the nozzles (cyan), the tracking system (light
green), the electromagnetic calorimeter (yellow green), the hadronic
calorimeter (red), the superconducting solenoid (light blue), and muon
detectors (light green and blue).

#### Key challenges

As for the accelerator, the main technological challenges for the detector
arise from the short lifetime of muons. In fact the beam-induced background
produced by the decay in flight of muons in the beams and subsequent
interactions potentially poses a serious limitation to detector operations.
All kinds of particles are produced, like photons, electrons, and neutrons,
that can be partially mitigated by a proper design of the machine-detector-
interface, as described in Section 0.3.2. Nevertheless, of the order of
$10^{8}$ particles enter the detector at this center of mass (CoM) energy,
therefore the detector design, the technology choices, and the reconstruction
strategies must primarily take into account the beam-induced-background
impact.

It is important to study the features of the beam-induced background by using
simulation, to take the proper directions for the detector development. Figure
0.4.2 shows two key distributions, the arrival time with respect to the bunch
crossing time currently set to zero, and the energy of the beam-induced
background particles when they enter the detector. These distributions have
been obtained by using MARS15 simulation at $\sqrt{s}=$1.5 TeV [22]. It can be
seen that a large part of beam-induced background particles are asynchronous
with respect to the bunch crossing, and they usually have low energy.
Therefore timing measurements and appropriate energy thresholds are important
handles to suppress them at the detector level.

Figure 0.4.2: Energy and arrival time, with respect to the bunch crossing
time, of the beam-induced background particles when they enter the detector.

The following general requirements have been identified for the detector,
driven by the necessity of suppressing the beam-induced background and keeping
the signal efficiencies as high as possible:

  * •

time measurements with excellent resolution: at this CoM energy resolutions
ranging from 30 to 60 ps for the tracking system, and around 100 ps for the
calorimeters are evaluated to be appropriate with the detector technologies
available at the time of HL-LHC; the time resolution due to the primary vertex
uncertainty has not been studied yet, but a resolution below 10 ps can be
easily assumed by considering the beam size in $z$;

  * •

energy measurements, to apply a proper threshold for rejecting the beam-
induced background soft component;

  * •

high granularity, to reduce the overlaps between beam-induced background and
signal hits, and consequently reducing the occupancy;

  * •

radiation hard devices, since the radiation level is similar to what is
expected at the High-Luminosity LHC (HL-LHC) [2].

The research and development for these technologies will be performed in
synergy with the existing programs, from HL-LHC to other future colliders.

The muon collider detector should ensure the physics reaches from low energy
(_e.g._ Higgs and standard model physics) to the highest achievable energy
scale for new physics searches (Section 0.3.1). This is particularly
challenging in the detector for $\sqrt{s}=10$ TeV collisions and beyond, where
particle momenta from few GeV to several TeV have to be measured. The detector
layout and design should satisfy physics requirements, and at the same time,
it has to accommodate the MDI requirements and geometry. In this context, the
magnetic field value plays an important role. High magnetic fields, around 5
T, could help in improving tracking momentum resolution of high energy
particles but it could generate inefficiencies for those with low momentum. In
addition, there are significant challenges to achieve the mechanical and
electrical stability of the superconductive solenoids needed to reach such
values of the field, including the technology transfer from previous HEP
projects and the availability of experts.

Another challenge is the simulation of the detector for reconstruction and
performance studies. The propagation of millions of beam-induced background
particles through the detector volume, done with software based on Geant4 [4],
is heavily CPU-time consuming. Dedicated software and algorithms that tackle
this problem in the proper way have to be developed since the muon collider
environment is different from that of other well-known collider machines.
Adequate computing resources should also be allocated for the detector
studies.

#### Work progress since the publication of the European LDG roadmap

An important progress since the the publication of the European LDG roadmap is
the initiation of the studies for the design of the detector at $\sqrt{s}=$10
TeV. To properly understand the requirements, three major macro-categories of
physics processes for muon collisions at $\sqrt{s}=$10 TeV have been
identified:

  * •

low energy: typical examples are electroweak (EW) and Higgs boson production,
with energy in the range of a few hundreds of GeV; a sample of Higgs bosons
decaying to $b\bar{b}$ jets is used for the studies;

  * •

high energy: New physics (NP) processes can create heavy resonances at the
order of TeVs; simulated Z′ boson with a mass of 9.5 TeV is taken as a
representative case with physics objects with energies up to $\approx 5$ TeV;

  * •

unconventional signatures such as long-lived particles, disappearing tracks
and emerging jets are just a few examples.

The transverse momenta, $p_{\mathrm{T}}$, of the decay products of Higgs and
Z′ bosons are shown in Fig. 0.4.3 to illustrate the difference among them.

Figure 0.4.3: Left: $p_{\mathrm{T}}$ distributions of $b$-quark coming from
the $H\rightarrow b\bar{b}$ decays at $\sqrt{s}=3$ and 10 TeV, as obtained at
generator level. Right: distribution of leptons and jets $p_{\mathrm{T}}$
coming from the decay of a Z′ boson produced at $\sqrt{s}=10$ TeV with a mass
of 9.5 TeV, as obtained at generator level.

The requirements set on the detector by the selected physics benchmarks at
$\sqrt{s}=$10 TeV are determined by optimizing the different sub-detectors.
For the tracking system, a parametric study has been done looking at the
relation between the depth of the tracking system and the magnetic field.
Figure 0.4.4 (left) shows the results of momentum resolution for tracks with a
transverse momentum $p_{\mathrm{T}}\sim 5000$ GeV, as a function of the
maximum tracker radius for different magnetic field values where it is evident
that a deeper tracker with an high magnetic field value is necessary to keep a
good track reconstruction resolution. A preliminary discussion with experts on
detector magnets has been organized with a dedicated workshop [11], that set
the basis for the studies.

Studies with photon/protons/pions particle guns have been performed to
determine the calorimeter characteristics. Deeper calorimeters to contain high
energy particles showers are necessary as shown in Fig. 0.4.4 (right), where
it is visible that a fraction of photon energy (with energies greater than 1
TeV) leaks into HCAL. For the muon reconstruction, studies on muons with
$p_{\mathrm{T}}\sim 5000$ GeV have shown that more inclusive algorithms that
also use calorimeters information should be used in order to collect the
energy released by muons.

Figure 0.4.4: Left: track momentum resolution for muons with $p=5$ TeV and
$\theta=\pi/2$, as a function of the tracker radius ($R_{max}$) and for
different values of magnetic field ($B$). Right: fraction of photon energy
measured in HCAL with respect to the total energy measured in ECAL+HCAL, as a
function of the true photon energy.

#### Work planned for next evaluation report

The magnet layout and magnetic field intensity will be one of the first items
to be tackled for the next activities. This choice will drive the design of
the detector sub-systems. The tracking, calorimeter, and muon detector system
geometries will be defined, considering the available space (limited by the
magnet, MDI, and cavern dimensions).

The assessment of the beam-induced background effects on the detector at
$\sqrt{s}=10$ TeV is another important activity for the upcoming Evaluation
Report. It will include the study of incoherent electron-positron production,
a physics process that could become relevant at high center-of-mass energies,
such as 10 TeV. Once the simulation samples of the beam-induced background
described in Section 0.3.2 are validated, the studies at the detector level
will start. First, the interactions of the beam-induced background with the
detector have to be simulated; a preliminary detector design will be used,
considering different configurations and values of the magnetic field. Several
important physics quantities, like detector occupancy and distributions of hit
position, time, and energy will be studied, including the determination of the
radiation levels. The detector requirements will be reviewed, to verify if
important changes for the layout and the technology choices are necessary,
with respect to the $\sqrt{s}=3$ TeV concept. The reconstruction performance
of the main physics objects will be studied. Initially, using the same
algorithms reported in Section 0.4.2, and subsequently, with algorithms tuned
specifically for the $\sqrt{s}=10$ TeV case. Feedback will be provided to the
MDI study group to assess the possibility of improving the detector acceptance
(_e.g._ , reducing the nozzle angle) while maintaining excellent
reconstruction performance. The technology choice will be made by considering
physics requirements and costs.

A first detector concept description at $\sqrt{s}=10$ TeV will be delivered
and made available in one of the next releases of the muon collider simulation
framework and will serve as the starting point for all future studies. The
simulation of the beam-induced background in this detector will be provided,
along with a version of the reconstruction algorithms with an initial tune
specifically tailored for this concept.

#### Next priority activities and collaboration opportunities

Among the future activities, it will be important to study how to reconstruct
and identify very forward muons, with angle below $10^{o}$ with respect to the
beam pipe. These muons are emitted outside the detector acceptance, mainly in
the nozzles. Their identification is important in several processes. For
example, muons from $Z^{0}Z^{0}$ fusion processes are mainly emitted in these
regions, therefore their detection could be employed to tag such events and
distinguish them from the $W^{+}W^{-}$ fusion. These muon detectors have to be
placed along the beam line, where also the accelerator magnets are placed. The
propagation of the very forward muons through the magnetic fields
configuration due to the accelerator components is not trivial, and a
dedicated study with FLUKA has to be performed.

###  0.4.2 Performance

This section presents an overview of the performance of the 3-TeV detector
concept for the reconstruction of the primary physics objects in the presence
of beam-induced background.

#### Overview of the physics object reconstruction

The high levels of beam-induced background in the detector pose unprecedented
challenges for the reconstruction and identification of the particles produced
in muon collisions, which are referred to as physics objects. To fully exploit
the physics potential of a muon collider and accomplish its physics program,
it is essential to reconstruct all the physics objects with high efficiency
and determine their properties with the greatest precision, even in the
presence of beam-induced background.

A campaign of studies, based on a detailed detector simulation, was carried
out to assess the effects of the background on the detector response and
possibly develop the appropriate mitigation measures. The outcome was that the
reconstruction algorithms for all the considered physics objects required
revision or fine-tuning. However, the results indicate that the background
effects on the detector response can be minimized to a degree that does not
compromise the detector performance. This performance was then estimated
reconstructing a set of benchmark Higgs boson channels at a 3 TeV muon
collider.

The beam-induced background causes very high hit multiplicities in the
detector’s tracking system, making the track finding process highly
challenging, since the number of hit combinations to be considered increases
exponentially, and a uniform diffuse energy deposition in the calorimeters,
which makes it difficult to identify and accurately measure the energy of
particles from collisions.

In general, the physics object reconstruction involves combining information
from different detector sub-systems. Tracks, calorimeter clusters, and muon
detector hits are combined to achieve an optimal performance in terms of
identification efficiency, background rejection, and momentum resolution. For
this purpose, a particle flow algorithm is employed, PandoraPFA [7], which
takes as an input the reconstructed tracks and the hits of the calorimeters
and muon detectors.

Figure 0.4.5: Left: Invariant mass distribution of the muon pairs produced in
the $\mu^{+}\mu^{-}\to
H\nu_{\mu}\bar{\nu}_{\mu}\to\mu^{+}\mu^{-}\nu_{\mu}\bar{\nu}_{\mu}$ process
without the beam-induced background (red line) and with the beam-induced
background overlaid to the physics events (blue line). Right: Transverse
momentum resolution as a function of transverse momentum for the reconstructed
muons entering in the plot on the left with the beam-induced background (BIB)
overlaid.

The initial focus of the detailed simulation studies was on muons, electrons,
photons, and jets. Muons are identified by matching tracks with hits in the
muon detector system. This sub-detector, located far from the beamline, is not
significantly affected by the beam-induced background, except for the forward
and backward regions with respect to the beam direction. Electrons and photons
are reconstructed by matching tracks with clusters in the electromagnetic
calorimeter. Isolated clusters are classified as photons, while clusters
matched with a track are classified as electrons. The energy of electrons and
photons is corrected to take into account inefficiencies and radiation losses.
The reconstruction efficiency of the electromagnetic objects as a function of
the energy reaches around 95$\%$ for high energy but drops at low energies due
to the beam-induced background. For the jet reconstruction, tracks and
calorimeter hits are filtered to remove the beam-induced background
contamination and then are given as input to the PandoraPFA algorithm. The
particles reconstructed by PandoraPFA are used as input to the jet clustering
algorithm, which aims to group together particles produced in the
fragmentation process of the same quark or gluon, by exploiting their
correlations. The resulting jet energy is corrected to recover the losses due
to particles escaping the detector, detector inefficiencies, and also for
beam-induced background contamination. The jet reconstruction algorithm has
been tested with simulated samples of different jet flavours: gluons and $u$,
$d$, $s$, $c$, and $b$ quarks. Despite the presence of the beam-induced
background throughout the detector, the efficiency ranges between 80$\%$ and
95$\%$, with a negligible fake jet probability. In order to identify the jets
originating from heavy quarks, secondary vertices compatible with the decays
of $b$\- and $c$-hadrons are reconstructed by combining tracks. A jet is
identified as a heavy-flavour jet if one of these secondary vertices is
reconstructed within the jet cone. The $b$-jet identification probability is
approximately 45$\%$ at low $p_{\mathrm{T}}$ (20 GeV) and increases to 70$\%$
at 120 GeV, while keeping a misidentification rate of about $20\%$ for
$c$-jets and from $1\%$ to $5\%$ for light jets. This level of performance is
similar to what is currently achieved at hadron colliders. At lepton
colliders, a higher efficiency can be expected. The current algorithm is
mainly limited by the presence of the beam-induced background. In the future,
artificial intelligence-based methods will be implemented to minimize the
effects of BIB and further enhance efficiency.

The physics objects described above were used to reconstruct the Higgs boson
decay modes into the final states $b\bar{b}$, $\gamma\gamma$, $\mu^{+}\mu^{-}$
and derive the reconstruction performance in the momentum range defined by
these processes. The invariant mass depends on the magnitude and the direction
of the decay particle momenta. The peak position at the nominal mass of the
Higgs boson indicates a well-calibrated energy of the objects, while the peak
width reflects the accuracy with which the object properties are measured.
Figure 0.4.5 (left) shows the distribution of Higgs boson reconstructed mass
for $\mu^{+}\mu^{-}\to H\nu_{\mu}\bar{\nu}_{\mu}$ with $H$ decaying into
$\mu^{+}\mu^{-}$. The reconstruction of high-energy muons produced in this
decay, namely above 10 GeV (see Fig. 0.4.5 on the right), is not significantly
affected by the beam-induced background, as shown in the figure. The width of
the mass peak is 0.4 GeV, comparable to electron-positron colliders. Figure
0.4.5 (right) demonstrates that relatively high-energy muons are reconstructed
with high momentum resolution. In Fig. 0.4.6, the invariant mass of the
$H\to\gamma\gamma$ for the $\mu^{+}\mu^{-}\to H\nu_{\mu}\bar{\nu}_{\mu}$
process is plotted. As for the muons, high-energy photon reconstruction is not
heavily impacted by the beam-induced background. In fact, the di-photon mass
distribution has a peak with a width of 3.2 GeV, with a small tail at higher
masses that does not have an impact on the $H\to\gamma\gamma$ measurements.
These events are then used to evaluate the energy resolution achieved with the
current calorimeter. This range of energy is dominated by the constant term,
which is about $3\%$.

Figure 0.4.6: Invariant mass distribution of the photon pairs produced in the
$\mu^{+}\mu^{-}\to
H\nu_{\mu}\bar{\nu}_{\mu}\to\gamma\gamma\nu_{\mu}\bar{\nu}_{\mu}$ process with
the beam-induced background overlaid to the physics events.

The case is different for hadronic jets where an important contribution is
given by low-energy (from 500 MeV to GeV) objects. The reconstruction
performance of low-momentum, around GeV, tracks and low-energy calorimeter
clusters is impacted by the beam-induced background. The di-jet mass
resolution is critical, for example, to separate the $H$ and $Z$ peaks as
shown in Fig. 0.4.7(left). The current value of the Higgs boson mass
resolution is about $18\%$, being dominated by beam-induced background
effects, i.e. the energy thresholds set on the calorimeter hits. The di-jet
mass resolution is sufficient for determining the Higgs and Z bosons yields on
a statistical basis, but in the future improving the jet energy resolution
will be fundamental for several measurements. This can be achieved by
optimizing the filters for removing the beam-induced background contamination,
and subsequently by lowering the calorimeter energy thresholds. Fig. 0.4.7
(right) [8] shows the invariant mass distribution of two jets originating from
the leading Higgs boson in a $HH$ samples, compared with that of
$q_{h}\bar{q}_{h}$ in a $\mu^{+}\mu^{-}\to q_{h}\bar{q}_{h}q_{h}\bar{q}_{h}$
events sample without beam-induced background. It’s important to emphasize
that the degraded energy resolution when including beam-induced background is
due to the limited performance of the reconstruction algorithm which is
currently being improved.

Figure 0.4.7: Left: Invariant mass distribution of the jet pairs produced in
the $\mu^{+}\mu^{-}\to H\nu_{\mu}\bar{\nu}_{\mu}\to
b\bar{b}\nu_{\mu}\bar{\nu}_{\mu}$ process with the beam-induced background
overlaid to the physics events: the reconstructed mass peak of the Higgs boson
is indicated in red, while the background from $Z\to b\bar{b}$ and $Z\to
c\bar{c}$ is in green. Right: Di-jets invariant mass of the leading Higgs
candidate in the sample of $HH$ events compared to that one of
$q_{h}\bar{q}_{h}q_{h}\bar{q}_{h}$ events, in samples reconstructed without
the BIB.

A review of the Higgs precision measurement at a muon collier at $\sqrt{s}=3$
TeV can be found [8]. The analysis of the different decay final states allowed
to determine the detector performance in an energy range of few GeV up to
hundred of TeV, summarized in table 0.4.1. This performance can be considered
the requirements to be competitive on Higgs physics.

Object | Requirements
---|---
muons | $\frac{\Delta p_{T}}{p_{T}}=0.4\%$
photons | $\frac{\Delta E}{E}=3\%$
jets | $\frac{\Delta p_{T}}{p_{T}}=15\%$
$b$-jets | $\frac{\Delta p_{T}}{p_{T}}=15\%$
|  $b$ efficiency = 60 %
|  $c$ mistag = 20 %
$b$-jets | $\frac{\Delta p_{T}}{p_{T}}=10\%$
(for $\lambda_{3}$) |  $b$ efficiency = 76 %
|  $c$ mistag = 20%
Table 0.4.1: Detector and reconstruction requirements for Higgs physics at the
muon collider, determined with the detailed simulation studies. The values
have been obtained for objects with $p_{T}$ of about 100 GeV, that is the
average transverse momentum of the particles from the 2-body decay of the
Higgs boson with $\sqrt{s}=3$ TeV. The first set of requirements is intended
for single Higgs boson measurements, while more stringent requirements are
presented for the trilinear coupling determination with the four-$b$-jet final
state. Taken from [8]

#### Key challenges

The first studies with the detailed detector simulation have shown that the
effects of the beam-induced background on high-energy objects in the central
region of the detector are negligible. One of the key challenges in event
reconstruction is dealing with physics objects that have low energy and
physics objects that are in the forward or backward regions of the detector.

The beam-induced background mitigation measures must be refined and perfected
to improve the reconstruction of the low-energy objects. For instance, the
energy thresholds on the calorimeter hits affect the energy resolution of jets
and low-energy photons and electrons. In the detector forward and backward
regions closer to the beamline, the beam-induced background levels are higher.
At multi-TeV collision energies, all the standard model particles are highly
boosted in the forward region and their decays may produce particles that are
very close to each other in space or even overlapping in the detector.
Dedicated algorithms must be developed for those cases.

#### Work progress since the publication of the European LDG roadmap

Since the publication of the European LDG roadmap, an assessment has been
performed of the reconstruction performance for tracks, muons, electrons,
photons, and jets in the presence of the beam-induced background with a
detailed detector simulation at a 3 TeV collider, as discussed in Section
0.4.2. The reconstruction algorithms of the physics objects were revised and
fine-tuned to preserve their reconstruction efficiency and the accuracy in the
determination of their properties.

Moreover, such physics objects were used to carry out sensitivity studies on
the Higgs boson production cross sections at a 3 TeV collider. This paper
reports only a small subset of all the results collected in the review by
Casarsa et al. [9], where it is demonstrated that the achieved outcomes are
competitive compared to the corresponding comprehensive estimates from the
CLIC Collaboration at the same collision energy.

#### Work planned for next evaluation report

The work plan for the evaluation report follows two main directions: the
completion of the physics objects studies at the 3 TeV center-of-mass energy
and a preliminary evaluation of the reconstruction performance for the main
physics objects at a $\sqrt{s}=10$ TeV collider.

At 3 TeV center-of-mass energy, a refinement of the electron and photon
reconstruction is planned: the energy resolution is currently limited at low
energies by the high thresholds set for the electromagnetic calorimeter hits
and at high energies by the spillage of the electromagnetic showers into the
hadronic calorimeter; electron reconstruction would also benefit from the
recovery of the radiated bremsstrahlung photons. Furthermore, the tau leptons
are still missing to complete the set of available physics objects and their
reconstruction algorithms must be studied. In addition, only preliminary
studies were conducted on the missing energy determination due to the issues
on the calorimeter object reconstruction. The improvements already discussed
on this sub-detector will open the possibility also to tackle the missing
energy resolution.

#### Next priority activities and collaboration opportunities

The detector performance has been determined for the most critical and
important objects. Additional efforts are needed to get a complete picture at
3 TeV and to have a full set of reconstructed objects to be used in physics
studies:

  * •

a study of the reconstruction algorithms for tau leptons with the beam-induced
background and an assessment of their performance;

  * •

an optimization of the jet reconstruction, taking advantage of an improved
reconstruction of low-momentum objects and possibly the identification of jet
substructure;

  * •

development of dedicated algorithms to reconstruct and identify boosted
physics objects;

  * •

an improvement of the jet flavour identification, exploiting more
sophisticated algorithms based on artificial-intelligence techniques;

  * •

an assessment of the most suitable particle identification techniques and
algorithms in the muon collider environment.

Neverthless, the next steps will be the study of the detector performance
at$\sqrt{s}=10$ TeV following the same priority list used for the $\sqrt{s}=3$
TeV. The algorithms studied for the 3 TeV case will optimized and adapted
where needed, to the higher center-of-mass energy. New methods may be
developed to reconstruct physics objects that exhibits different properties at
high energy.

###  0.4.3 Technologies

#### System overview

The detector concept described earlier serves as a starting point for
evaluating the expected detector performance in different physics scenarios by
building an efficient full-simulation workflow to study various beam-induced
background mitigation strategies. At this conceptual stage, only general
assumptions about the relevant detector parameters were made, such as
dimensions, material composition, granularity, and spatial and time
resolution. This approach simplifies the process of iterative variations
towards an optimised detector design for which specific technology details can
be implemented at a later stage. These studies allow the identification of the
key features of different sub-detectors at a muon collider experiment, which
are summarised in the recent review for Snowmass 2021 on the promising
detector technologies and R&D directions [10].

From the technology perspective the present $\sqrt{s}=3$ TeV detector model
can be divided into six sections ordered by increasing distance from the
interaction point:

  1. 1.

Vertex detector (VXD): Si sensors with $25\times 25$ µm2 pixels and time
resolution of $\sigma_{\text{t}}=30$ ps arranged in double layers with 2 mm
spacing.

  2. 2.

Inner (IT) and outer (OT) tracker: Si sensors with 50
µm$\,\times\leavevmode\nobreak\ 1$ mm (IT) and 50
µm$\,\times\leavevmode\nobreak\ 10$ mm (OT) macro-pixels and time resolution
of $\sigma_{\text{t}}=60$ ps.

  3. 3.

Electromagnetic calorimeter (ECAL): sampling design with W absorber and Si
sensors arranged in $5\times 5$ mm2 tiles.

  4. 4.

Hadronic calorimeter (HCAL): sampling design with steel absorber and plastic-
scintillator tiles arranged in $30\times 30$ mm2 cells.

  5. 5.

Superconducting solenoid: magnetic field strength of 3.57 T with a Fe return
yoke.

  6. 6.

Muon detector: resistive plate chambers (RPC) divided into $30\times 30$ mm2
cells interleaved in the magnet’s return yoke.

Description of this geometry is implemented in the DD4hep [5] framework, which
provides interface to Geant4 [4] simulation software and to Marlin [6]
framework for detector digitization and event reconstruction. Two generic
types of hits are used in the detector simulation:

  * •

Tracker hit: corresponds to a single energy deposited by a particle in the
sensitive volume, with associated energy, time and position of the deposit
within the volume.

  * •

Calorimeter hit: corresponds to the integrated energy deposited by one or more
particles in the sensitive volume during the fixed integration time, with only
the total energy and time assigned to the hit associated with the volume.

Tracker-type hits are used for VXD, IT and OT detectors, while calorimeter-
type hits are used for the ECAL, HCAL and muon detectors, which have the
actual granularity implemented in the geometry.

#### Key challenges

High-intensity beam-induced background that survives after passing through the
MDI nozzles poses significant challenges for most of the sub-detectors by
inducing high levels of radiation and by creating excessive amount of
background hits. Projected levels of total ionizing dose (TID) and neutron
fluence at Muon Collider are comparable to those expected at HL-LHC, while the
background hits have signatures unique to Muon Collider and require dedicated
treatment in each sub-detector to achieve the necessary physics performance.

In the tracking detectors, the beam-induced background causes very high hit
density, up to $5\times 10^{3}$ hits/cm2 in the innermost layers of VXD, when
integrating over a 15 ns readout window. Combinatorial background arising from
such a large number of hits makes track reconstruction unfeasible unless the
amount of background hits entering the pattern recognition algorithm is
significantly reduced. The primary beam-induced background suppression methods
in the tracking detectors are:

  1. 1.

Timing: rejection of hits outside of a very narrow time window of about 100 ps
(exploiting the characteristic time distribution of beam-induced background
hits, as shown in Fig. 0.4.8.

  2. 2.

Direction: rejection of hits inconsistent with pointing at the interaction
region by estimating their direction from a stub of two hits in a double-
layer.

  3. 3.

Cluster shape: rejection of beam-induced background hits represented by wider
clusters of pixels due to crossing the sensors at a shallower angle.

  4. 4.

Goodness of fit: rejection of fake track candidates due to bad $\chi^{2}$.

Considering these aspects, the great challenge for tracking-detector
technology is to provide extreme time resolution and on-detector hit filtering
while maintaining low material budget and high radiation tolerance. A low
material budget indirectly requires low power density of the readout
electronics such that it can be cooled without introducing additional heat-
exchanging materials. We should also note that these beam-induced background
suppression methods could potentially limit the performance of long-lived
particles, for which a dedicated strategy should be defined in the future.

Figure 0.4.8: Time distribution of hits in the tracking detector corrected for
the expected photon’s time of flight from the interaction point. Hits from the
beam-induced background (BIB) are shown by solid lines, while hits from single
muons smeared by corresponding time resolutions are shown by filled areas.

In the ECAL and HCAL sub-detectors beam-induced background contribution comes
primarily from low-energy photons and neutrons respectively, which have a
relatively uniform angular distribution across the detector volume. Yet, their
distribution in time and depth is different from the shower signatures
produced by the hard collision, as shown in Fig. 0.4.9. Given that the beam-
induced background contribution partially overlaps with the signal hits, with
the current configuration and technology of the calorimeters, it can’t be
excluded from the readout completely and has to be subtracted instead at a
later stage. To minimise the effect of such beam-induced background
subtraction on the resulting energy resolution the corresponding detector
should possess high spatial granularity and time resolution, allowing to
measure the corresponding time and depth profiles of the shower. In particular
fine depth segmentation implies a large number of sensitive layers in the
detector, making the cost of the technology also an important factor. Thus,
the main challenge for the ECAL and HCAL technologies is to provide excellent
time resolution in a finely segmented detector at a low cost, while being
compatible with the radiation-hardness requirements.

Figure 0.4.9: Difference between the time (left) and depth (right) of the hits
produced by beam-induced background (BIB) and signal b-jets.

The muon system is relatively unaffected by the beam-induced background
contribution except for the very forward region, where high-energy neutrons
and photons create hits near the MDI nozzles. While this does not pose any
serious challenge for muon detection itself, it is nevertheless important to
have high spatial and time resolution to allow matching of standalone muon
tracks with hits in the tracking detector. Such seeding of muon tracks from
the muon system would greatly improve muon-reconstruction speed given the high
combinatorial background in the tracking detector.

#### Work progress since the publication of the European LDG roadmap

Several developments have been done for different sub-detectors towards a
better definition of their technical characteristics.

A realistic digitization algorithm for pixel sensors of the tracking detectors
has been implemented and integrated into the Muon Collider simulation
software. With a configurable pixel pitch for the sensor together with other
readout parameters like noise and threshold it provides realistic pixel
clusters that can be used for beam-induced background suppression. On the
hardware side several technologies have the potential to meet the requirements
of the tracking detectors, such as AC- and DC-coupled LGAD, trench-isolated
LGAD, as well as MAPS technology thanks to its particularly low material
budget. Estimates of the data rate, mainly due to the beam-induced background
hits, underline the importance of fast and radiation-hard data-transfer links,
such as LpGBT, and careful design of the data acquisition logic. Reduction of
the amount of data directly in the readout chip is particularly important in
this respect.

For ECAL a new conceptual design has been implemented in the simulation based
on Crilin technology [19], which is a semi-homogeneous calorimeter with finely
segmented Cherenkov-radiating crystals providing high time resolution at
relatively low cost. A semi-homogeneous calorimeter is expected to have a
better energy resolution with smaller fluctuations, which can help to minimize
the effect of the beam-induced background. After showing a good performance in
Muon Collider simulation studies some physical prototypes have been built and
tested to experimentally validate this technology and the expected
performance. The latest beam test [20] of a multi-layer prototype at CERN
demonstrated a time resolution of $\mathcal{O}$(20 ps), as shown in Fig.
0.4.10, which gives confidence that reaching $\sim 100$ ps on the final
detector would be possible.

Figure 0.4.10: Left: two out of three detection layers of the Crilin prototype
proposed for Muon Collider calorimeter tested at CERN teast beam. Right:
Distribution of the time difference between two neighbouring layers of the
prototype measured obtained with test beam data.

For HCAL the use of micro-pattern gas detectors (MPGD) [17] as an active layer
is under study, which offers good energy and time resolution at high rate and
low cost for instrumenting such a large area. The corresponding design has
been implemented in the detector geometry for full-simulation studies, which
showed performance comparable to that of the current baseline. The
technologies being considered are µRWell, RPWell and MicroMegas, for which
initial digitization logic for digital readout has been implemented in the
simulation software. Physical prototypes for each technology have been also
produced and two test-beam campaigns have been carried out at CERN during 2023
(see Fig. 0.4.11), which showed good results in terms of MIP detection
efficiency.

Figure 0.4.11: Left: MPGD-based HCAL prototype tested at CERN having multiple
layers built with different technologies. Right: measured MIP-detection
efficiency of different MicroMegas layers as a function of the applied high
voltage.

For muon detector, the Picosec technology [18] is being studied as a better-
performing alternative to the RPC layers. It uses a crystal Cherenkov
radiator, coupled to a UV-transparent photocathode and a two-stage
amplification by Micromegas, providing a time resolution comparable to that of
the tracking detector. This would be of great importance for rejecting out-of-
time beam-induced background hits, especially in the forward region of the
muon system where the rates are high. Several prototypes have been tested with
different photocathode materials and gas mixtures, with very promising
preliminary results, as shown in Fig. 0.4.12. Finally, the tested Picosec
geometry has been interfaced with the full-simulation framework to study its
performance in the forward region in the presence of beam-induced background.

Figure 0.4.12: Time resolution obtained by the Picosec prototypes as a
function of the mean signal amplitude compared for different photo-cathode
materials (left) and gas mixtures (right).

The community of the IMCC Detector and Physics is deeply involved in the ECFA
DRD collaboration. In some of the study, like the calorimeter one, the efforts
are lead by the IMCC people. In addition to that, the muon collider community
participates to the DRD activities, making sure that all the mentioned
technologies relevant for each subdetector are included in the corresponding
DRD collaboration roadmaps. Similar efforts are also taking place within CPAD.
A comprehensive list of all the relevant technologies can be found in [10].

#### Work planned for next evaluation report

A number of developments are planned to progress towards a well-defined
conceptual detector design. Important input is expected from experimental
tests of the first production batches of DC-RSD sensors [21], which is a
promising technology for the tracking detector. In particular its ability to
achieve low occupancy by controlling the extent of charge sharing will be
validated and implemented in the simulation software. R&D on the technologies
considered for the ECAL, HCAL and muon detector will continue according to
their working plans, which are part of the coordinated DRD and CPAD efforts in
Europe and U.S. respectively.

#### Next priority activities and collaboration opportunities

Current available technologies allow competitive physics measurement at muon
collider if the detector were to be built in the next few years. With the new
generation of the detector, the performance can be greatly improved, as the
preliminary studies on the calorimeter systems is showing.

The development of an ad hoc tracking detector needs to be better pursued.
Here, the technology is at a very early stage and multiple technical aspects
need to be addressed. These include the possibility of having long pixels in
the inner and outer trackers, where hit density is lower, which is challenging
to implement in DC-RSD technology. Different possible readout implementations
can have great impact on the sensor’s efficiency, granularity of the timing
information and the resulting power consumption. An integrated approach to the
tracker design that also includes the mechanics and cooling will be very
important in the future.

The integration of all sub-detectors, currently missing, will be studied once
the technology for each individual sub-detector is defined.

###  0.4.4 Software and computing: Concepts

#### System overview

The muon collider software framework [3] is based on CLIC’s iLCSoft. It
includes the DD4hep toolkit [5] to model the detector geometry, the Geant4 [4]
program to simulate the detector response, and the Marlin package [6] for the
event digitization and reconstruction. Stable particles are generated by
external packages and given as input to the aforementioned software. Signal
and physics backgrounds events are produced by users with common packages like
Whizard [13] and MadGraph [14]. The beam-induced background bunch-crossings,
instead, are produced by using the FLUKA [15] and FlukaLineBuilder [16], as
described in Section 0.3.2. The programs workflow proceeds as:

  * •

generation of $\mu^{+}\mu^{-}$ interactions and beam-induced background bunch
crossings;

  * •

simulation of the interaction of the generated particles with the passive and
active elements of the detector; the results are stored as SimHits;

  * •

overlay of beam-induced background SimHits to the $\mu^{+}\mu^{-}$ interaction
events;

  * •

reconstruction of the energy deposits in each sub-detectors, i.e. tracker,
calorimeters, muon system producing RecHits;

  * •

reconstruction of high-level physics objects e.g. charged particle tracks,
jets, secondary vertices, muons, electrons, etc.

The physics objects are then used in the analysis measurements, as presented
in Section 0.4.2. The software infrastructure is currently supported and
maintained by two INFN experts.

The computing infrastructure is formed by:

  * •

CPU: accessed via cloud services provided by INFN and CERN;

  * •

storage: disk space of about 600 TB at INFN sites and about 100 TB at CERN.

#### Key challenges

The major challenges identified so far are the following:

  * •

production of the beam-induced background bunch-crossing events, see Section
0.3.2 for a description;

  * •

simulation of the beam-induced background particles in the detector; this task
requires a significant amount of CPU time, in Ref. [3] such a time is
quantified depending on the configuration used to track particles throughout
the material;

  * •

the overlay of the beam-induced background hits with the $\mu^{+}\mu^{-}$
interactions particle hits; this process demands a significant amount of
computing memory (RAM) per event, for a detailed discussion see Ref. [3];

  * •

tracks and calorimeter object reconstruction from RecHits including the beam-
induced background; it can be performed only under particular conditions, for
example by filtering tracker hits depending on their arrival time on the
sensor and subtracting a tuned amount of energy in the calorimeter cells.

#### Work progress since the publication of the European LDG roadmap

The software has been improved significantly since the publication of the
roadmap to reduce the amount of computing resources and the time necessary to
simulate and reconstruct a complete bunch-crossing event. A complete
description of the improvements can be found in Ref. [3]. The notable
optimisations include the early exclusion of irrelevant beam-induced
background particles from Geant4 simulation by filtering tracker-hit
collections based on the arrival time on the sensor, as well as the
integration of ACTS (A Common Tracking Software) track-reconstruction
framework [12].

Another important step forward is the transition to the common Key4hep
software stack that is almost completed, but not yet in production.

From the point of view of the code distribution to the users, two major
software releases have been done since the publication of the roadmap, in June
2022 and April 2023. The software is available with its distribution via
docker images and CERN CVMFS.

#### Work planned for the evaluation report

The major activities currently in progress and likely to be ready at the time
of the evaluation report are:

  * •

complete transition to Key4hep and distribution of a production release,
depending on the person-power available;

  * •

definition of the release validation workflow;

  * •

definition of a user support, with voluntary personnel, to help newcomers to
use the software structure;

  * •

expansion of computing infrastructure to include additional European and US
sites.

#### Next priority activities and collaboration opportunities

The computing infrastructure is distributed in different sites, a federation
is needed with an authentication and an authorization method common to the
IMCC. A similar problem is present on data management, where different
architectures are used by different sites and within IMCC there is no data
management system in place. Both these activities are not pursued due to the
lack of person-power.

The usage of advanced artificial intelligence methods for physics object
reconstruction like tracks and jets and their identification could
significantly improve the performance by helping to minimize the impact of the
beam-induced background. These activities require a significant increase of
the person-power.

## References

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##  0.5 Accelerator design

This chapter describes the whole accelerator chain of the proposed muon
collider complex. The challenge of the proton complex is to provide the few MW
proton with very short bunch lengths of a few ns and low repetition rate of 5
Hz. The muon production cooling part consists of a target inside an as high as
possible magnetic field and standing the drive beam power, a decay channel
with decreasing magnetic fields and comprising a chicane to remove unwanted
particles, a section for longitudinal capture of the muons and, finally,
several ionization cooling channels interleaved with a section merging several
muon bunches into one bunch. The acceleration to high energy has to be fast
requiring large average RF gradients at all stages; the baseline solution
consists of a sequence of recirculating linacs followed be very rapid cycling
synchrotrons accelerating the beam within a few tens of turns. Finally, the
muons are injected into the muon collider ring, which has to provide
sufficient luminosity leading to a challenging design with $\beta^{*}$ and rms
bunch length of a few mm and large rms momentum spread of around $1\cdot
10^{-3}$.

###  0.5.1 Proton complex

#### System overview

The proton complex is the first piece in the muon collider complex. It
comprises of a high power acceleration section; an accumulator and compressor;
and a target delivery section. The high power acceleration section can take
many shapes as shown in Fig. 0.5.1. In our baseline design we will study a
final energy linac. This section is responsible for delivering high power,
high intensity bunches to the accumulator and compressor section. At the end
of the high power acceleration section the pulse total charge is distributed
among a high number of bunches with a small energy spread. Such a long train
of bunches do not reach the desired instantaneous power for intense pion
production on the target.

Figure 0.5.1: Schematic layouts for the proton complex section. Our baseline
design is the schematic 1 on the figure. The bunch density as the proton
travels thought the complex is also depicted. The closer to the target the
highest the bunch charge density and at the point where is collides with the
target. To reach high densities is one the the main challenges in the design
of the part of the muon collider.

In order to achieve the high proton intensities in a short pulse, an
Accumulator and Compressor ring will be used to combine and compress the
protons into very short bunch, with a length of the order of $\sim 2$ ns rms.
The first storage ring, the Accumulator, accumulates the protons via charge
stripping of the incoming H- beam from the linac section, preserving the
energy spread. The incoming beam is chopped to allow a clean injection into
the ring circumference. The second storage ring, the Compressor, accepts
between 1 and 6 intense bunches from the Accumulator and performs a 90°-bunch
rotation in longitudinal phase space, shortening the bunches to the limit of
the space-charge tune shift just before extraction. The Compressor ring must
have a large momentum acceptance to allow the storage of the beam with a
momentum spread of a few percent, which arises as a consequence of the bunch
rotation.

The target delivery section transports the final intense short bunches from
the compressor to the target, ensuring that neither the transverse nor
longitudinal properties of the beam are compromised in the process. To achieve
optimal luminosity, the final collider will work in single bunch colliding
mode. Therefore, in the multi-bunch solution, short bunches extracted from the
Compressor must be recombined and hit the pion production target
simultaneously.

The primary requirement of the proton complex is to enable the production of a
high number of useful muons at the end of the decay channel after the target.
The production rate, to good approximation, is proportional to the primary
proton beam power, and (within the 5–15 GeV range) only weakly dependent on
the proton beam energy. Considering a conversion efficiency of about 0.013
muons per proton-GeV, a proton beam in the 1–4 MW power range at an energy
between 5 GeV and 10 GeV will provide the sufficient number of muons required.

#### Key challenges

The critical challenges for the proton complex include the determination of
proton final energy on the target with significant implications for particle
creation, the layout of the high power acceleration section, and the choice of
target material and size. Two final proton beam energies, 5 GeV and 10 GeV,
will be investigated during the length of the grant.

A comprehensive study is required to identify key parameters for the Proton
Complex, including a compression scheme and the final number of bunches, thus
influencing the layout of compressor ring lattice and the required number of
turns for compression. The minimum number of bunches needed will affect the
layout of the ring-to-target delivery design. The beam parameters on the
target surface will impact the design of the expense beam dump, which can be
challenging due to target geometries and constraints.

Determining the linac chopping scheme is another key parameter, which will
directly influence the linac pulse length and current, and subsequently, the
accumulator and further accelerator design.

Other important challenges include the design of the accumulator lattice for
both energies to be studied, investigation of the instability thresholds in
the accumulator and compressor rings, error analysis across the entire complex
with a focus on bunch recombination at the target delivery system, and
continuous development of the H- source to meet the needed pulse current and
length for the muon collider’s requirements, including potential upgrades.

#### Recent achievements

A baseline lattice for the accumulator and compressor for the 5 GeV case,
based on the studies for the neutrino factory at CERN, was revised and ported
to XSuite and PyOrbit. A campaign to cross benchmark of both codes, specially
for high space charge conditions, is ongoing. Basic beam physics parameters
are being collected and compiled and a parametric study is underway. A first
look at the transport between ring and target of a 2 ns high current bunch has
started. A compilation of the literature on past projects, with special
attention to US Muon Acceleration Program (MAP) [2, 1] results, was done.

Since both the accumulator and compressor rings are strongly space charge
limited machines, an evaluation of available codes for space charge dominated
beam simulation is under way. In order to complement this evaluation a
collection of data from CERN PS bunch rotation and Booster bunch
recombination, both with high density bunches, was carried out. Data analyses
and further plans are underway.

#### Planned work

The majority of the planned work for the following year is concentrated on the
compressor lattice design, refinement, and target delivery parameters. We plan
to explore possibilities at a beam energy of 5 GeV, including the definition
of minimum number of bunches possible and a rotation scheme. Also for the 5
GeV case, we plan to narrow down the beam parameters that are possible to be
delivered to the target. A second step in the process will be the design of a
10 GeV compressor ring and the re-design of the target delivery section, in
case the 5 GeV solution is unable to achieve the required beam quality.

Other planned work regarding the proton complex includes:

  * •

Compilation of linac technologies and main parameters

  * •

Study on H- source capabilities (current and pulse length)

  * •

Study on H- stripping for injection into the Accumulator

  * •

Definition of a possible chopping scheme for the linac and final accumulator
setup

  * •

Definition of RF requirements for bunch rotation

  * •

Initial study of main instabilities in the accumulator and compressor rings

#### Next priority studies and opportunities for additional collaboration

Several studies with lower priority are at present not planned and could
represent great opportunities for future collaborative work. Notably, the
study proposal does not encompass work on the accumulator or further
acceleration (beyond the linac final energy of 5 GeV), alternative rotation
schemes and in-depth error and instability studies in various sections of the
complex. All these topics would be of interest to further optimise the proton
complex scheme and could be envisaged with additional resources and
collaborators. On a more technical side, integrated engineering activities, as
well as the detailed RF design for the rotation scheme, will be lacking. In
depth work on the linac lattice design and many R&D topics regarding H- source
development, H- stripping, high efficient acceleration and design of high-
gradient super conducting (SC) cavities will be either partially covered or
not at all developed at this stage, and we will use already proven schemes and
setups for the SC linac in the baseline design. Other area that represents
further opportunities for knowledge exchange and collaboration are tests in a
established machine that can achieve space charge levels similar the the final
bunches in the proton complex, such measurements can further our knowledge of
the extreme space charge effects and help benchmarks the codes used for design
and simulations.

###  0.5.2 Muon production and cooling

#### System overview

Figure 0.5.2: Schematic of the muon production system. Protons are incident
onto the target on the left of the figure, while the cooled muon beam leaves
on the right of the figure, entering into the low energy acceleration system

The muon production and cooling system comprises several subsystems, as shown
in Fig. 0.5.2. The protons provided by the proton complex intersect a target
to produce pions. The target is immersed in a 20 T solenoid field, yielding a
high pion flux. The field is rapidly tapered to 1.5 T. Pions and muons
traverse a solenoid-focused chicane where high momentum beam impurities are
removed followed by a Beryllium absorber which ranges out remnant low energy
protons. The remaining beam passes through a longitudinal drift where any
remaining pions decay. The beam is then captured longitudinally. A multi-
frequency RF system that captures the beam into 21 bunches is required owing
to the initially large longitudinal beam emittance. Another solenoid chicane
system splits the beam by charge species, in preparation for the ionisation
cooling system.

The ionisation cooling system comprises a series of solenoids, which focus the
beam onto energy absorbers where the beam momentum is removed. The momentum is
restored longitudinally using RF cavities resulting in a reduction in the
beam’s emittance (volume in position-momentum space). An initial rectilinear
cooling system, Rectilinear A, reduces the beam emittance sufficiently that
the many initial bunches can be merged into one single bunch. The beam is then
cooled further to the final emittance, using a continuation of the rectilinear
cooling system, Rectilinear B, followed by a sequence of high field solenoids
operated ultimately with a low momentum (non-relativistic) beam. The beam is
finally reaccelerated to semi-relativistic speeds so that it can be delivered
to the acceleration system.

#### Key challenges

Critical challenges have been identified in the muon production and cooling
system.

  * •

An outline cooling system was prepared by the US Muon Accelerator Program
(MAP) [1] that yielded an emittance that did not meet our requirement by a
factor of two. The MAP system used conservative equipment parameters, but more
demanding parameters may yield improved performance while remaining practical.
Significant risk was identified associated with heating in the final cooling
absorbers. The MAP system must be assessed and optimised to get a better
understanding of the potential system performance including thorough
assessment of engineering challenges.

  * •

A detailed design for the pion production target, solenoid and surrounding
infrastructure must be performed. This target is as demanding as state-of-the-
art horn-based pion production targets. Solenoid focusing at high beam powers
in this environment has not yet been done in practice. Assessment of the
associated issues must be performed, building on the work done by MAP,
including detailed assessment of solenoid feasibility accounting for radiation
and thermal loads in liaison with the magnet team. Handling of the spent
proton beam must be studied in detail.

Other important challenges have been identified.

  * •

A system to separate the charge species has not been designed. In the baseline
design the system must accommodate very large emittance which is not readily
manageable using a conventional system, while maintaining the bunch structure.

  * •

A design for the longitudinal capture system exists. In order to enable pion
yield optimisation studies to continue, the sensitivity to incident beam
parameters must be understood.

  * •

A design for the bunch merge system was done but the lattice is no longer
available. A new lattice must be generated and sensitivity to parameters must
be performed.

  * •

It is very likely that the overall system performance may be greatly increased
by looking at alternative designs to the baseline described above. This could
dramatically improve the facility performance.

#### Recent achievements

Figure 0.5.3: Target assembly radial build showing different azimuthal regions
from the target the axis up to the SC solenoid coils.

The target team have designed a baseline radial build for the pion production
target, taking into account radiation flux into the surrounding solenoid, heat
load on the graphite target itself and appropriate cooling systems for the
target and shielding (detailed in 0.6.4 and 0.6.5). The radial build is shown
in Fig. 0.5.3. A 3D FLUKA model for the target area has been constructed and
the pion and muon yield through the target system has been assessed. The
magnet team have identified HTS technology as having greater tolerance to
radiation issues. The target team have updated the design with reduced
shielding. Preliminary concepts for the spent proton beam handling have been
studied.

Figure 0.5.4: System performance of the muon cooling system, including an
updated rectilinear and final cooling system. Optimisation continues; in
particular the rectilinear cooling system final emittance has not been
integrated with the final cooling system.

Beam physics designs have been made for the ionisation cooling systems. Two
cooling systems have been studied, the rectilinear cooling system, used at
high and intermediate emittances, and the final cooling system, used for low
emittances. The optical parameters of the solenoid system have been assessed
and parameter dependencies established, including non-linear optics
dependencies on momentum and transverse emittance. Possible lattices using
different RF technologies have been assessed. A preliminary system
optimisation for both lattices has been performed yielding potentially
improved performance. The current performance estimate for the ionisation
cooling system is shown in Fig. 0.5.4. The performance of both the rectilinear
and final cooling systems have been improved yielding significantly smaller
transverse and longitudinal emittance compared to previous baselines.
Optimisation continues and it is expected that the simulated performance will
improve further.

#### Planned work

The target design will continue with increasing detail. Systems for cooling of
the shielding, moderation and absorption of neutrons will be refined. Improved
models for the incident proton beam will be considered and the design for the
upstream beam window will be updated. Preliminary studies for the handling of
the spent proton beam have been envisaged but a detailed design does not
exist. The existing beam physics design for the chicane and proton absorber
will be refined and an engineering design for handling of the significant
spent proton beam in this region will be developed. The 1.5 T solenoid field
in this region will likely require superconducting technology. An appropriate
collimation and shielding system will be designed to protect the solenoids in
this region.

The intermediate emittance rectilinear cooling system design will be further
optimised. The optimisation will be extended to include the high emittance
rectilinear cooling system. The optimisation will be refined to include a more
detailed assessment of the limitations of solenoid and RF fields, taking into
account the required field profiles and highly compact nature of the lattice.
An integrated design will be completed for a small subset of the cooling
lattices that are proposed.

The final cooling system design will be further optimised. The lattice design
will be refined in collaboration with magnet and RF experts. Absorber heating
increases rapidly at lower beam emittance and lower momentum characteristic of
the downstream end of this system. Schemes to mitigate the impact on the
liquid hydrogen will be assessed. Impact of misalignment and field errors will
be assessed. Other collective effects will be assessed. The final cooling
system will be integrated with the final emittance of the rectilinear cooling
system. A system to reaccelerate the beam to relativistic speeds will be
studied.

Limitations arising from space charge and beam loading will be assessed to
estimate a maximum beam current that can traverse the cooling system. A
preliminary estimate of tolerances to alignment will be performed. A
preliminary design for the absorber will be made including a preliminary heat
load assessment. A preliminary assessment of radiation load from muon decays
will be performed and collimation systems will be considered. Beam
instrumentation requirements will be considered. Simulation in alternate codes
will be performed to validate the performance estimates.

For all systems, a future R&D path will be developed including an assessment
of necessary equipment tests. Detailed studies of a rectilinear cooling
channel cell for a cooling Demonstrator are described below.

#### Next priority studies and opportunities for additional collaboration

Several studies with lower priority will not be carried out, assuming current
resource levels continue. In the target region, effects of misalignments and
field errors will not be studied. Mitigation schemes, to handle the case that
the baseline design can not accommodate the required beam power or the
requirements change, will not be studied in detail. Equipment tests will not
be possible but a plan will be developed.

Integrated engineering will be performed for only a representative subset of
the rectilinear cooling cells. Beam instrumentation will not be studied in
detail, but is expected to be feasible based on existing facilities.
Correction schemes for misalignments will not be studied. Low frequency
acceleration systems such as induction linacs, that may be advantageous for
the final cooling system, will not be studied.

Integration systems, key for a start-to-end simulation, will not be developed.
Consequently the muon production system will carry significant performance,
risk, cost and power uncertainty. These integration systems are unconventional
and technically challenging. In particular, the charge separation system,
which has no current design, will not be developed. This system must separate
muon charge species before cooling, where the beam that has transverse and
longitudinal emittances that are expected to be too large for a conventional
dipole-based scheme to manage without significant beam degradation.

The longitudinal capture and bunch merge system, which have beam physics
designs, will not be developed further. Both of these systems have complex
arrangements of RF cavities, operating at several frequencies, for
simultaneous manipulation of several bunches. The schemes would benefit from
analysis of the challenges in the RF systems. The bunch merge system
additionally incorporates a challenging transverse funnel.

The baseline subsystems were chosen as they have the most mature design.
Alternative schemes are likely to improve performance significantly, but have
lower Technology Readiness Level. For example an emittance exchange scheme,
employing a wedge absorber and dipole, could yield better performance compared
to the final cooling scheme with simpler technology. A combined ‘HFoFo’
channel would be capable of cooling two charge species simultaneously,
potentially yielding a more cost- and power-efficient cooling system.
Frictional cooling, ring coolers, Parametric Ionisation Cooling channels and
helical cooling channels may all yield improved cost, power or luminosity
performance. None of these alternatives will be studied.

###  0.5.3 Acceleration

#### Low-energy acceleration

##### System overview

The low energy section involves three superconducting linacs operating at 352
MHz and 1056 MHz: a single pass linear pre-accelerator (PA) followed by a pair
of multi-pass ‘Dogbone’ recirculating linacs (RLA). In the presented scenario,
acceleration starts after final cooling at 255 MeV/c and proceeds to 63 GeV,
where the beam is going to be injected into a first rapid cycling synchrotron.
A schematic of the low energy section is shown in Fig. 0.5.5. The 352 MHz
linac, which has a large aperture, is sufficient to transmit a beam that has
received relatively little cooling. The 1056 MHz cavities linearise the RF
waveform to minimise the growth of uncorrelated energy spread in the beam.

Figure 0.5.5:  Layout of a two-step-Dogbone RLA complex. Pre-accelerator,
Dogbone I and Dogbone II are stacked up vertically; $\mu^{\pm}$ beam can be
transferred between the accelerator sections by the vertical dogleg.

##### Key challenges

To ensure that the survival rates of muons are sufficient, the acceleration
must be done at high average gradient. Since muons are generated as a
secondary beam they occupy large phase-space volume. In addition to providing
high average gradient, the accelerator must have very large transverse and
longitudinal accelerator acceptances.

For the given longitudinal emittance, in order to accelerate of the muon beam
within the given transverse and longitudinal emittance tolerances, the
beamline must be designed to minimize transverse chromatic effects, thus tight
focusing in bending plane with weak quadrupoles. In addition to preservation
of the longitudinal emittance, the bunch length needs to be precisely
controlled in the arcs.

The weak FODO channel chosen to minimize chromatic effects for first passages
(where the beam energy is low) will lead to large betatron amplitudes at high
energies, making the linac vulnerable to transverse wakefield effects.
Considering the high bunch charge to be accelerated, the initial offset of the
beam needs to be controlled precisely.

Another key challenge is the beam loading effect due to the high bunch charge.
The following bunch will always gain less energy due to the beam loading
effect of the the preceding bunch. Since both bunches will be recirculating in
the same arc, the energy difference will lead to a transverse orbit deviation
from the reference orbit in the arc, which will in turn lead to a transverse
beam offset in the following linac pass. This offset will create a wakefield
in the linac that will amplify the beam offset and potentially lead to beam
loss or degradation. Therefore the beam loading effect needs to be controlled
either by exchanging bunch positions or some other methods.

Figure 0.5.6:  Start-to-end Twiss functions along RLA2

##### Work progress since the publication of the European LDG roadmap

We created a preliminary lattice design for RLA2. We used a FODO focusing
structure in the linac to reduce chromatic effects at low energy. Several
lattice configurations were considered for the recirculating arcs including
FODO, Triplet, Theoretical Minimum Emittance (TME) and Double Bend Achromat
(DBA). The DBA showed better performance. An initial bunch with 100 mm.rad
longitudinal and 40 mm.mrad transverse emittance could be accelerated from 5
GeV to 63 GeV while preserving longitudinal emittance, a 25% increase in
transverse plane, and a better than $90$% muon survival rate. Figure 0.5.6
shows the linear lattice functions along the RLA2. Because the quadrupole
gradients in the linac are the same for each linac pass, the increasing beam
energy in later passes leads to large beta functions in later passes. Table
0.5.1 contains the main parameters for the simulated RLA2 and the predicted
RLA1.

Table 0.5.1: Preliminary parameters for low energy acceleration. Parameter | Unit | PA | RLA1 | RLA2
---|---|---|---|---
Injection energy | [GeV] | 0.255 | 1.25 | 5
Ejection energy | [GeV] | 1.25 | 5 | 63
RF Frequency | [MHz] | 352 | 352 | 1056 | 352 | 1056
Number of cavities | # | 30 | 25 | 2 | 320 | 56
RF gradient | [MV/m] | 25 | 25 | 30 | 25 | 30
Energy gain / pass | [GeV] | 0.955 | 0.8 | 11.6
Passes | # | 1 | 5 | 5

##### Work planned for the evaluation report

The following works are planned as a next step as voluntary effort and
provided resources can be made available.

  * •

No work has been performed for PA and RLA1. Our next step will be to create
designs for these lower energy parts. The large acceptance of especially in
PA, requires large apertures and tight focusing. Combined with moderate beam
energies, this favors solenoid rather than quadrupole focusing for the entire
PA linac.

  * •

We have made significant progress with the lattice design in RLA2. However,
the design still does not meet our performance requirements (see above) even
without machine imperfections. We will therefore continue to improve this
design until it meets our requirements.

  * •

The gradients estimated in simulations are somewhat optimistic. All
simulations will be repeated for lower acceleration gradients: 16 MV/m for 352
MHz, 30 MV/m for 1056 MHz.

  * •

The impact of machine imperfections and operation strategies balancing
contradicting requirements will be implemented in simulations

##### Next priority studies and opportunities for additional collaboration

The expected gradient and balancing beam loading effect for the accelerating
gradient plays a main role on the muon survival rate in the low energy
section.

An initial 6D phase space distribution is essential for performing more
realistic simulations in the low energy acceleration chain of muon collider.
Our simulations have thus far assumed a Gaussian distribution, but the
upstream systems could deliver a beam very different from that. Simulations
that provide that distribution will not be available during this study, if for
no other reason than the systems upstream of the PA will not be fully
designed.

#### High-energy acceleration

##### System overview

For the high-energy acceleration from $63\text{\,}\mathrm{GeV}$ to the TeV
range, a chain of rapid cycling synchrotrons (RCS) is foreseen to accelerate
the two counter-rotating bunches with a repetition rate of
$5\text{\,}\mathrm{Hz}$. One option, inspired by the US Muon Acceleration
Program (MAP) [2, 1], includes intermediate stages of
$0.30\text{\,}\mathrm{TeV}$, $0.75\text{\,}\mathrm{TeV}$ and
$1.5\text{\,}\mathrm{TeV}$ to finally reach $5\text{\,}\mathrm{TeV}$ before
injecting the muons into the separate collider ring. This scenario is
illustrated in Fig. 0.5.7.

Figure 0.5.7: Sketch of the chain of rapid cycling-synchrotrons for the high-
energy acceleration complex. From Ref. [3].

The first two RCS share the same tunnel, meaning that they have the same
circumference and layout [4]. The bending in the first RCS is provided by
normal conducting magnets. The RCS2 to RCS4 are planned as hybrid RCSs where
strong fixed-field, superconducting magnets are interleaved with normal
conducting magnets cycling from $-B_{\mathrm{nc}}$ to $+B_{\mathrm{nc}}$. This
combination allows for a large energy swing combined with a high average
bending field to minimize the radius and thus the travel time and decay of the
muons.

##### Key challenges

To keep decays acceptably low, the RCSs must have high average gradients
$G_{\text{avg}}$, as high as
$2.4\text{\,}\mathrm{M}\mathrm{V}\mathrm{/}\mathrm{m}$. The average gradient
is the energy gain in one turn divided by the circumference; since most of the
ring does not contain RF, the gradient in the RF sections must be
significantly higher than that average gradient. Assuming a survival rate of
90% per RCS, ultra-fast acceleration with tens of GeV energy gain per turn is
required. The RF voltage has therefore to be provided by hundreds of
superconducting cavities. To both provide large gradients, ILC-like
$1.3\text{\,}\mathrm{GHz}$ cavity structures, also known as TESLA cavities
[5], have been assumed for the simulations. As a result of the tens of GV of
RF voltage, the number of synchrotron oscillations per turn is much larger
than the conventional stability limit for stable synchrotron oscillations and
phase focusing of $1/\pi$ [6] in a synchrotron with one or few localized RF
sections. As a consequence, the RF system must be distributed over the entire
RCSs in order to reduce the synchrotron tune between two consecutive RF
stations to a value much smaller than that instability limit.

As a direct result of the decay and ultra-fast acceleration, the acceleration
times are in the millisecond range and the number of turns in each RCS is
between 17 and 66. In the RCS chain, the ramp rate of the normal conducting
magnets is on the so far unprecedented order of kT/s, a particular challenge.
Further, due to the hybrid structure of the three downstream RCSs, beam orbits
and radii are not constant anymore, but change locally, as depicted in Fig.
0.5.8.

Figure 0.5.8: Trajectories in a half-cell of RCS2. The injection/extraction
orbits are respectively in the inner/outer side (in blue/cyan). From Ref. [7].

Special attention is therefore being paid to the lattice design in order to
minimize the orbit length change during acceleration. Fast cavity detuning on
the kHz scale to match the RF frequency with the changing revolution frequency
have to be developed.

With the special beam structure of counter-rotating, intense single µ+ and µ-
bunches, large transient beam loading for both fundamental and higher-order
modes must be expected.

##### Recent achievements

To simulate longitudinal beam dynamics, we use the longitudinal macroparticle
tracking code BLonD [8, 9]. The code was successfully extended to model multi-
turn wakefields in the multiple RF stations per ring. A plot of the
longitudinal phase space at injection for RCS1 is displayed in Fig. 0.5.9(a).

Tracking simulations on the influence of the number of RF stations on the
longitudinal emittance and beam stability have been performed for all RCSs. As
shown in Fig. 0.5.9, their minimum number is around 32 RF stations for RCS1
and RCS4, and 24 stations for RCS2 and RCS3 [3].

Figure 0.5.9: (a) Longitudinal phase space for a $\mu^{+}$ bunch in RCS1 for
$n_{\mathrm{RF}}=32$ at injection. The red line indicates the separatrix (with
continuous energy approximation) for
$f_{\mathrm{RF}}=$1.3\text{\,}\mathrm{GHz}$$.
(b) Relative emittance growth at the end of the cycle of each RCS with respect
to the emittance at injection versus $n_{\mathrm{RF}}$ for RCS1 to RCS4 from
simulations without intensity effects.

This allows to keep the longitudinal emittance growth close to the required 5%
level (not taking into account intensity effects nor phase and energy errors
at injection).

A first lattice of the RCS2 has been developed with Xsuite [10]. In the
current version (see Fig. 0.5.10, the RCS2 consists of 26 arcs. 24 out of the
26 insertions between the arcs host some cavities. The two remaining
insertions will be dedicated to injection and extraction. The arc half-cells
house three dipoles: two superconducting dipoles ($10\text{\,}\mathrm{T}$) on
the outside, and a pulsed normal conductor with a peak field of
$1.8\text{\,}\mathrm{T}$ in the middle.

Figure 0.5.10: Twiss functions in one out of 26 arcs of RCS2.

Simulations that include the intensity effects of the single but intense muon
bunch show the effect of short-range and long-range induced voltages. The
short range wakefields, calculated once following the theory of K. Bane [11]
and once using a resonator model for all fundamental and higher-order modes of
an ILC-like cavity, show induced voltages on the order of
$1\text{\,}\mathrm{MV}$ per meter (and per cavity), i.e., stay below 10% of
the cavity voltage without beam. The effect of multi-turn wakefields due to
HOMs (higher-order modes) on the longitudinal stability was investigated and
the power which is induced into these HOMs was studied as a function of their
quality factors [12].

The orbit length variation $\Delta\mathcal{C}$ has been minimized by
optimizing the layout of the FODO cells [7] so as to reduce the range of
tuning required for the RF cavities and their power sources. With the current
design, values reach $\Delta\mathcal{C}/\mathcal{C}\cdot
f_{\text{RF}}\approx$2\text{\,}\mathrm{kHz}$$ in RCS2, resulting in a tuning
requirement of
$\Delta\mathcal{C}/\mathcal{C}\approx$1.5\text{\times}{10}^{-6}$$, equivalent
to a peak tuning speed of approximately
$10\text{\,}\mathrm{M}\mathrm{Hz}\mathrm{/}\mathrm{s}$.

At this state, giving some tolerances on the magnets and thus
$\Delta\mathcal{C}$ becomes very challenging. Due to the fast acceleration, it
becomes very difficult to correct any dynamic errors like a jitter on the
powering of the magnets. The lattice should enable some passive mitigation of
this jitter. The task is even more challenging because it should work also for
a counter-propagating beam. A main concern is the eddy currents generated in
the pulsed magnets like the normal conducting dipoles.

##### Planned work

The longitudinal tracking and RF studies are well advanced for a single beam,
but the transient beam loading in the RF cavities due to the counter-rotating
beams remains to be investigated. The impact of fundamental and higher-order
mode voltages induced in the RF cavities on the longitudinal beam dynamics
will be studied in detail. We will not place RF cavities at points where the
two opposite sign muon beams cross to prevent the short range wakefield
induced in the cavities by one beam from affecting the other one.

The present parameter set for the RCS chain (Table 0.6.3) has been derived
assuming the same muon survival rate for each of the stages. This results in
very different requirements for the total RF voltages. While the first RCS
must be equipped with almost $21\text{\,}\mathrm{GV}$, the RF voltage is
smaller for the following two stages, despite the fact that RCS3 is
significantly larger than the first two accelerators. Parameter optimization
of the sequence of RCSs, in particular with respect to survival rate and the
energy levels at which beam is transferred, will be performed to reduce the
overall RF voltage installed in the entire chain and to maintain the same
average accelerating gradient through the entire RCS chain.

The required RF voltage for a given transmission is smallest for a perfectly
linear energy ramp. This would require that the current driving the pulsed
magnets in the RCS varies linearly with time. While a close approximation to
this is possible, that would require a very costly power source for the
magnet. It would be less costly to drive the magnets with a current pulse that
is closer to a portion of a sine wave. However, a nonlinear rise of the field
must be compensated by additional RF voltage to reach the same muon survival.
First discussions on cost models for the RF system and the bending magnets
with their power converter have started, but there are not yet at the level of
detail and consistency to allow cost optimization. This effort will continue
in 2024, adding also software tools to extract cost estimates.

The work on RCS lattice, started only recently, will be continued and extended
to cover the whole RCS chain and possible limitations. Special emphasis will
be to ensure a sufficient energy acceptance and a careful evaluation of
possible synchro-betatron resonances The effect of deviations in the magnetic
field strength of fast ramping magnets on the beam and possible mitigation
method have to be studied. Code development will be pushed to enable start-to-
end simulations and integrate the magnetic ramp. Such simulations will give a
first estimate of the emittance growth during the acceleration.

##### Next priority studies and opportunities for additional collaboration

While the RCS injection chain accelerates the bunch to the energy required for
the collider ring, its current design does not deliver the longitudinal bunch
parameters required. The short bunches required pose tight constraints on the
longitudinal emittance growth in the entire RCS chain. Scenarios where the
longitudinal bunch parameters for the collider are not achieved during the
normal course of acceleration in the final RCS should be designed and
simulated (for example, a longitudinal phase space rotation could be performed
on the bunch in less than one turn).

Furthermore, the present RF frequency for the muon acceleration of
$1.3\text{\,}\mathrm{GHz}$ has been taken as an assumption, as detailed cavity
designs are available for the International Linear Collider (ILC). Although