Studies on a hadronic calorimeter with MPGD technology for a future Muon Collider experiment

In the context of the European strategy for particle physics, the Multi-TeV Muon Collider has emerged as a compelling alternative for advancing our understanding of the Standard Model, after the full exploitation of the High-Luminosity LHC. The physics programme at the Muon Collider includes precise measurements in the Higgs boson sector and the search for new physics at the TeV scale. Achieving these goals relies on accurate full event reconstruction, including the identification and precise four-momentum estimation of various particles. The Particle Flow (PF) algorithm is one of the most suitable approach for this task, exploiting information from tracking, calorimeter, and muon detectors for particle identification and measurements of their momenta/energies. Tracking detectors measure charged particle momenta, while calorimeters provide energy measurements for photons and neutral hadrons. Therefore, a combination of an exceptional tracking system and high-granularity calorimeters is necessary. However, one of the biggest challenges for a future experiment at the Muon Collider is to discriminate the product of the μμ collisions from the intense beam-induced-background (BIB), due to the unstable nature of muons, whose decay products interact with the detector material. To address this, an innovative hadronic calorimeter (HCAL) based on Micro Pattern Gas Detectors (MPGDs) is proposed. MPGDs offer robust technology for high radiation environments and a high granularity for precise spatial measurements. Dedicated studies are needed to assess and optimize the performance of an MPGD-based HCAL, including the development of medium-scale prototypes for performance measurements. The response of HCAL to incoming particles is examined through Monte Carlo simulations using Geant4, comparing the performance of digital and semi-digital readouts, with energy resolution as the figure of merit. The simulated geometry will be integrated into the Muon Collider software to study its impact on jet reconstruction within the full apparatus and in the presence of BIB. The simulation will be also validated through the test of a small-size calorimeter cell equipped with advanced resistive MPGD technologies, namely resistive MicroMegas, resistive μRWELL and RP-WELL.


Introduction
In the field of particle physics, the exploration strategies for seeking new physics are typically divided into two different approaches, each exploiting distinct technologies.Precise measurements are often carried out by colliding electrons/positrons, allowing us to study the interactions of known particles, seeking indirect signs of new physics.On the other hand, high-energy colliders, such as proton-proton colliders, offer the potential for direct discovery of new particles.A muon collider [1], instead, combines the benefits of both electron-positron and proton-proton machines, enable us to explore new physics both directly and indirectly using a single machine.The high mass of the muon mitigates synchrotron radiation emission, a primary limitation in circular electron-positron colliders, allowing for multiple passages through a ring and repeated collisions in another ring.Protons can also be accelerated in rings and collide at very high energy, but they are composite particles, and only a small fraction of the collision energy is available to probe short-distance physics.The center of mass energy reached by a muon collider, therefore, corresponds to that of a proton collider with much higher center of mass energy.
However, the primary challenge in operating a detector at a muon collider stems from the fact that muons are unstable particles.Their decay products interact with the machine components and generate an intense radiation which affects the entire experiment.This radiation, which contaminates what would otherwise be a clean collision environment, is collectively referred to as "Beam Induced Background" (BIB).BIB exhibits two main characteristics: it consists primarily of low-energy particles which arrive at the detector with a broad range of arrival times.Considering this, the primary focus of the detector design is the need to manage and mitigate the effects of the BIB.The large flux of particles sets requirements for the capability to endure radiation exposure over long periods of time; furthermore, distinguishing between the products of beam collisions and BIB particles requires high-granularity measurements in terms of space, time, and energy.

Requirements for HCAL at Muon Collider
The muon collider aims at measuring the physics processes at the energy frontier and this requires excellent resolution, both in energy and space, of collimated high-energy jets.Specifically, for jets above 100 GeV, a jet energy resolution of 3-4% is required.In a multi-TeV muon collider, the knowledge of the BIB distributions and rates in the calorimeter system is crucial to quantify the radiation levels and assess the optimal detector design given the required jet energy resolution.The BIB in the calorimeter region is mainly formed by photons (96%) and neutrons (4%).The simulations show that at 15 kHz bunch crossing a photon flux of ∼ 7.5 kHz/cm 2 is expected at the surface of the hadronic calorimeter [2].An estimation of the radiation doses on the Muon Collider detector was released in [3] assuming a 2.5 km circumference ring, a bunch crossing frequency of 15 kHz and 200 days of operation during a year.In the HCAL, the expected 1 MeV neutron-equivalent fluence is about 10 13 cm −2 per year, with a steeply decreasing radial dependence beyond it.The expected total ionizing dose in the HCAL is ∼ 10 3 kRad per year.
The choice of the technology and the design of the calorimeters is crucial to mitigate the effect of the BIB while maintaining good physics performance.High granularity is required to reduce the overlap of BIB particles in the same calorimeter cell.Time resolution on the order of O(ns) would reject most of the out-of-time components of the BIB.A fine longitudinal segmentation of the calorimeter can contribute in distinguishing between the signal showers and the fake ones produced by the BIB.These requirements are also in line with the high granularity particle flow algorithm approach [4].The goal of this approach is to create an image of the showers induced by various jet fragments, allowing for the correct matching of these showers with the charged particles measured in the tracker, resolving each particle trajectory through the whole detector.This, in turn, enables the accurate identification and measurement of the energy of the showers induced by neutral hadrons.

MPGD-based HCAL
The CALICE collaboration contributed to the development of calorimeter concepts for highly granular detectors used in particle flow [5].The collaboration focused on developing calorimeters with gaseous detectors as the active element, which can achieve higher granularity compared to more traditional scintillator-based calorimeters, being at the same time more economic competitive.Historically, Resistive Plate Chambers (RPCs) have been considered due to their intrinsic digital nature and excellent time resolution, down to few hundred ps.Recently, Micro Pattern Gas Detectors (MPGD), such as resistive Micromegas [6,7], and the newest technologies like rwell [8] and RP-WELL [9], have been proposed for semi-digital calorimeters.They are expected to outperform RPCs due to their higher rate capability, good energy resolution, high detector stability, uniformity and low pad multiplicity.

Design strategy for HCAL
The strategy we are following to design an MPGD-based HCAL begins with a standalone simulation in GEANT4 [10].This first step aims at studying the calorimeter response to a single pion shower and optimizing its geometry for full shower containment.The simulation have to be validated by testing a small size HCAL cell employing MPGDs as active layers with pion beam.The simulation will be extended within the Muon Collider software in order to study the impact of the technology on the performance of the Pandora Particle Flow algorithm for particle reconstruction.

GEANT4 simulation
A calorimeter cell has been studied using GEANT4, in order to assess the response and shower containment under a pion beam irradiation.The geometry implemented in GEANT4 consists of a sampling calorimeter composed of layers with 2 cm of iron (G4_Fe) as the absorber and 5 mm of pure argon (G4_Ar) as the active layer, simulating the MPGD.The response to the shower has been studied using a pion gun with energies of 20 GeV, 40 GeV and 60 GeV hitting the calorimeter surface perpendicularly.The QGSP_BERT physics list is used.Figure 1 shows the structure of one layer of the sampling calorimeter on the left and an event display of a cascade generated by a  − with 20 GeV energy within the calorimeter on the right.
The shower containment is studied in both the transversal and longitudinal direction relative to the pion beam line, for different values of the number of layers and the transversal size.Figure 2 shows the longitudinal shower containment as a function of the depth for a lateral surface dimension of 1 × 1 m 2 .The shower containment is expressed in terms of fraction of deposited energy and the depth is expressed in units of nuclear interaction length   ; for iron, the value of   ∼ 16.8 cm is used.Approximately, 90% of the energy is contained within ∼ 14   , which corresponds to 100 layers in our geometry.
Figure 3 shows the shower containment in the transverse plane with respect to the  − direction expressed in terms of fraction of energy deposited inside cylinders of increasing radius having the axis aligned with the pion direction, as a function of the cylinder radius, in unit of nuclear interaction length   .This plot is obtained with a number of layers equal to 100.The 90% of the energy is contained within a cylinder of radius ∼ 3   .

Shower digitization and energy resolution
In order to take into account the geometrical constraints imposed by the experiment, the studies on energy resolution are conducted considering a calorimeter cell consisting of 50 layers of alternating iron (corresponding to approximately 7   ) and gaseous argon with a lateral surface of 1×1 m 2 .In the simulation, the cell is irradiated with a pion gun of energy spanning from 5 GeV to 80 GeV.With this geometry and energy range, approximately 80% of the energy is expected to be released in the calorimeter cell (see figures 2 and 3).
-3 -  The active layer is divided into cells with an area of 1 cm 2 to achieve high granularity.Pion energy reconstruction is studied simulating two different types of readout: digital and semi-digital.Their performance are compared in terms of energy resolution.In both cases, energy reconstruction is based on the total number of hits registered in the active layers of the calorimeter.A 'hit' is defined on the base of the energy deposited by particles in each cell of the active layer.
For the digital readout, a hit is defined applying a single threshold on the energy deposited in each cell.Figure 4 shows a shower initiated by a 20 GeV negative pion inside the calorimeter, digitized according to this criterion.
The energy of the primary pion is then reconstructed by counting the number of hits.The distribution of the number of hits is built with 30 thousand events for several values of the hitting pion energy and the mean value and the width of the distributions are used to build the calorimeter response function, which gives a analytic relationship between the energy of the showering pion and the mean total number of hits.The inverse response function is used to build the distribution of the reconstructed energies.
-4 - To simulate the semi-digital readout, three different threshold of increasing value are applied to each cell, expressed in units of MIP (i.e. the energy released by a MIP in the active layer), defining three different regions of hits:  1 represents the number of hits with energy deposited between the first (0.0.1 MIP) and second threshold (4 MIP);  2 represents the number of hits with energy deposited between the second and the third threshold (12 MIP);  3 represents the number of hits with energy deposited above the third threshold.The purpose of this more refined definition is to provide a better estimate of the number of particles that deposit energy inside each cell.Figure 5 shows a shower initatied by a 20 GeV negative pion inside the calorimeter digitized with the semi-digital readout: the hits passing the second and the third threshold mostly concentrate around the core of the shower, where higher hit density is expected.-5 -Finally, the energy resolution curves for both the digital (in green) and semi-digital (in red) readouts are compared in figure 6.In the case of the digital readout, the resolution saturates at approximately 40 GeV.This effect is related to the loss of proportionality in the response function at high energy.For a 80 GeV pion, the resolution reaches a value of approximately 8% for the semi-digital readout, approximately 14% for the digital one.Furthermore, the resolution of the semi-digital readout with a larger cell dimension (3×3 cm 2 ) is also obtained and compared with the one obtained with 1×1 cm 2 cell size in figure 7, applying the same thresholds for the hit definition in both cases.This comparison is worth making because a larger cell size would reduce the number of channels in the front-end electronics, consequently lowering costs and power consumption.It can be observed that at approximately 60 GeV the resolution with the larger cell size exhibits saturation effects.However, this preliminary study requires further refinement of the thresholds.-6 -

JINST 19 C05037 7 Conclusions
Some preliminary results on the simulated performances of a MPGD-based HCAL are shown, in terms of shower containment and energy resolution.Further and more realistic improvements will come from the implementation of the hit detection efficiency and the effect of charge spreading among adjacent cells.In order to have a more realistic description of the muon collider environment, the BIB contribution will be accounted by including the neutron and photon flux.The same geometry has to be described in the context of the full apparatus in the framework of the Muon Collider software, to study the impact on the jet energy reconstruction.
Besides, the results of the simulation will be compared with real data.In fact, as a proof of concept, a real prototype of a calorimeter cell has been built and tested in August 2023 at CERN PS facility, with pion beam of energy ranging from 3 GeV to 10 GeV.The prototype consisted of 8 layers with alternating stainless steel absorber and MPGD, reaching a depth of approximately 1   .The active layers have been instrumented with resistive MicroMegas, rwell and RP-WELL.A preliminary test beam with muon beam of 150 GeV was conducted at CERN SPS in July 2023 on the detectors alone to assess their performance.At the time of the conference, the analysis of the test beam data is still ongoing.The experimental results will then complement the simulation studies presented in this contribution.

Figure 1 .
Figure 1.On the left: sketch showing one layer of the calorimeter made of 2 cm of iron for the absorber(in blue) and 5 mm of argon for the active layer (in yellow).On the right: event display of a 20 GeV  − developing a shower inside the calorimeter.Reprinted from [11], Copyright (2023), with permission from Elsevier.

Figure 2 .
Figure 2. Longitudinal shower containment, expressed in terms of fraction of deposited energy, as a function of the depth in unit of nuclear interaction length   , for three different values of the  − energy.This plot is obtained with lateral surface dimension of 1×1 m 2 .Reprinted from [11], Copyright (2023), with permission from Elsevier.

Figure 3 .
Figure 3. Lateral shower containment, expressed in terms of fraction of deposited energy, as a function of the cylinder radius in unit of nuclear interaction length   , for three different values of the  − energy.This plot is obtained with 100 layers.Reprinted from [11], Copyright (2023), with permission from Elsevier.

Figure 4 .
Figure 4. Digitized shower initiated by a 20 GeV negative pion, with digital readout.The pion travels in the z-direction.

Figure 5 .
Figure 5. Digitized shower initiated by a 20 GeV negative pion, with semi-digital readout.The pion travels in the z-direction.

Figure 6 .
Figure 6.Comparison between energy resolutions obtained in the case of the digital readout, in green, and the semi-digital one, in red.

Figure 7 .
Figure 7.Comparison between energy resolutions obtained in the case of the semi-digital readout for a cell size of 1×1 cm 2 , in red, and for a cell size of 3×3 cm 2 one, in blue.