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Ultimate colliders for particle physics: Limits and possibilities

The future of the world-wide HEP community critically depends on the feasibility of the concepts for the post-LHC Higgs factories and energy frontier future colliders. In this paper we overview the accelerator options based on traditional technologies and consider the need for plasma colliders, particularly, muon crystal circular colliders. We briefly address the ultimate energy reach of such accelerators, their advantages, disadvantages and limits in the view of perspectives for the far future of the accelerator-based particle physics and outline possible directions of R&D to address the most critical issues.

43 PARTICLE ACCELERATORS↗

Uniaxial stress induced symmetry breaking for muon sites in Fe

Uniaxial stress was used on Fe single crystals to induce muon precession frequency shifts. The frequency shift for a nominally pure Fe sample at 302K was -0.34 + or - .023 MHz per 100 microstrain along the 100 magnetization axis. This corresponds to a change of magnetic field at the muon of 25.1 + to 1.6G/100 magnetic moment. For an Fe (3wt%Si) single crystal the shifts were -0.348 + or - .008 MHz/100 magnetic moment. The agreement between the shifts for Fe and Fe(3wt%Si) shows the effect to be intrinsic to iron and not strongly impurity sensitive. These shifts and their temperature dependence (1/T) are dominated by the effect of strain inducted population shifts between crystallographically equivalent, but mgnetically inequivalent sites. Their magnitudes are in good agreement ith previous theoretical predictions and by previous extrapolation from calculations on Nb and V especially if both 4T(0) and 1T sites contribute comparably.

Kossler, W. J.↗

Effect of Ni substitution on the fragile magnetic system La 5 Co 2 Ge 3

La 5⁢ Co 2 ⁢Ge 3 is an itinerant ferromagnet with a Curie temperature T C of ~3.8K and a remarkably small saturated moment of 0.1µ B /Co. Here we present the growth and characterization of single crystals of the La 5 ⁢(Co 1–x⁢ Ni x ) 2 Ge 3 series for 0.00 ≤ x ≤ 0.186. Here we measured powder x-ray diffraction, composition as well as anisotropic temperature-dependent resistivity, temperature and field-dependent magnetization along with heat capacity on these single crystals. We also measured muon-spin rotation/relaxation (μ⁢SR) for some Ni substitutions (x = 0.027,0.036,0.074) to study the evolution of internal field with Ni substitution. Using the measured data we infer a low temperature, transition temperature-composition phase diagram for La 5 ⁢(Co 1–x ⁢Ni x ) 2 Ge 3 . We find that T C is suppressed for low dopings, x ≤ 0.014; whereas for 0.036 ≤ x ≤ 0.186, the samples are antiferromagnetic with a Néel temperature T N that goes through a weak and shallow maximum (T N ~ 3.4K for x~0.07) and then gradually decreases to 2.4 K by x = 0.186. For intermediate Ni substitutions, 0.016 ≤ x ≤ 0.027, two transition temperatures are inferred with T N >T C . Whereas the T–x phase diagram for La 5 ⁢(Co 1–x ⁢Ni x ) 2 Ge 3 and the T–p phase diagram determined for the parent La 5 ⁢Co 2 ⁢Ge 3 under hydrostatic pressure are grossly similar, changing from a low-doping or low-pressure ferromagnetic (FM) ground state to a high-doped or high-pressure antiferromagnetic (AFM) state, perturbation by Ni substitution enabled us to identify an intermediate doping regime where both FM and AFM transitions occur.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Production and suppression of delayed light in NaI(Tl) scintillators

Here we investigate a hypothesis that energy accumulation and the subsequent release in NaI(Tl) may lead to pulselike events in the few-keV energy regime, a phenomenon suggested by the crystal manufacturing company Saint-Gobain, who provided the crystals for DAMA/LIBRA. While we observed delayed long-lasting (days) light emission in a 3-inch NaI(Tl) crystal after exposing it to UV light, the delayed light consists primarily of single photons that are uncorrelated with each other. We also observe delayed light emission in NaI(Tl) following gamma radiation and large ionization events like cosmic-ray muons. We found that irradiating the crystal with red light after UV exposure significantly suppressed delayed photon emissions.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Comparison between muon spin rotation and neutron scattering studies on the 3-dimensional magnetic ordering of La2CuO(4-y)

Muon spin rotation and neutron scattering studies on powder and single-crystal specimens of La2CuO(4-y) are compared. The apparent difference between the muon and neutron results for the ordered moment in the antiferromagnetic state is interpreted as the signature of increasingly short-ranged spatial spin correlations with increasing oxygen content.

Uemura, Y. J.↗

$μ$ $\mathrm{SR}$ study of the dipole-octupole quantum spin ice candidate $\mathrm{Ce_2Zr_2O_7}$

The Ce 3+ pseudospin-1/2 degrees of freedom in Ce 2 Zr 2 O 7 possess both dipolar and octupolar character which enables the possibility of novel quantum spin liquid ground states in this material. In this study, we report muon spin relaxation and rotation (μSR) measurements on single-crystal samples of Ce 2 Zr 2 O 7 in zero magnetic field and in magnetic fields directed along the [1, $\overline{1}$, 0] and [1, 1, 1] crystallographic directions, and for magnetic fields directed both longitudinal and transverse to the direction of muon polarization. Our zero-field results show no signs of magnetic ordering or spin freezing, consistent with earlier zero-field μSR measurements on a powder sample of Ce 2 Zr 2 O 7 , and also with the expectations for a quantum spin ice. However, we measure a more gentle relaxation rate for Ce 2 Zr 2 O 7 in zero field at low temperatures than was previously reported. This difference in relaxation rate is likely due to the low oxidation and, correspondingly, the high stoichiometry of our singlecrystal samples. Longitudinal field measurements confirm that the magnetic dipole moments in Ce 2 Zr 2 O 7 remain dynamic at T = 0.1 K on the microsecond timescale. For both [1, $\overline{1}$, 0] and [1, 1, 1] magnetic fields, our μSR Knight shift measurements show a field-induced leveling off of the magnetic susceptibility at low temperature which is qualitatively consistent with corresponding calculations using the numerical-linked-cluster method in combination with recent estimates for the nearest-neighbor exchange parameters of Ce 2 Zr 2 O 7 .

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Muon spin rotation research program

Data from cyclotron experiments and room temperature studies of dilute iron alloys and iron crystals under strain were analyzed. The Fe(Mo) data indicate that the effect upon the contact hyperfine field in Fe due to the introduction of Mo is considerably less than that expected from pure dilution, and the muon (+) are attracted to the Mo impurity sites. There is a significant change in the interstitial magnetic field with Nb concentration. The Fe(Ti) data, for which precession could clearly be observed early only at 468K and above, show that the Ti impurities are attractive to muon (+), and the magnitude of B(hf) is reduced far beyond the amount expected from pure dilution. Changes in the intersitital magnetic field with the introduction of Cr, W, Ge, and Si are also discussed. When strained to the elastic limit, the interstitial magnetic field in Fe crystals is reduced by 33 gauss, and the relaxation rate of the precession signal increases by 47%.

Stronach, C. E.↗

Mulan: a part-per-million measurement of the muon lifetime and determination of the Fermi constant

The part-per-million measurement of the positive muon lifetime and determination of the Fermi constant by the MuLan experiment at the Paul Scherrer Institute is reviewed. The experiment used an innovative, time-structured, surface muon beam and a near-4 \pi π , finely-segmented, plastic scintillator positron detector. Two in-vacuum muon stopping targets were used: a ferromagnetic foil with a large internal magnetic field, and a quartz crystal in a moderate external magnetic field. The experiment acquired a dataset of 1.6 \times 10^{12} 1.6 × 10 12 positive muon decays and obtained a muon lifetime \tau_{\mu} = 2\, 196\, 980.3(2.2) τ μ = 2 196 980.3 ( 2.2 ) ~ps (1.0~ppm) and Fermi constant G _F = 1.166\, 378\, 7(6) \times 10^{-5} F = 1.166 378 7 ( 6 ) × 10 − 5 GeV ^{-2} − 2 (0.5~ppm). The thirty-fold improvement in \tau_{\mu} τ μ has proven valuable for precision measurements in nuclear muon capture and the commensurate improvement in G _F F has proven valuable for precision tests of the standard model.

Carey, Rebecca↗

The Mu2e crystal calorimeter

The Mu2e experiment at Fermilab will search for the charged-lepton flavour violating conversion of negative muons into electrons in the coulomb field of an Al nucleus, planning to reach a single event sensitivity of about $3\cdot10^{−17}$, four orders of magnitude beyond the current best limit.The conversion electron has a clear monoenergetic signature at 104.967 MeV, slightly below the muon rest mass, and will be identified by a complementary measurement carried out by a high-resolution tracker and an electromagnetic calorimeter (EMC). The calorimeter is composed of 1348 pure CsI crystals, each read by two custom UV-extended SiPMs, that are arranged in two annular disks. The EMC should achieve better than 10% energy resolution and 500 ps timing resolution for 100 MeV electrons and maintain extremely high levels of reliability and stability and in a harsh operating environment with high vacuum, 1 T B-field and radiation exposures up to 100 krad and $10^{12} \rm{n}_\rm{1MeVeq}/\rm{cm}^{2}$.The calorimeter technological choice, along with the design of the custom front-end electronics, cooling and mechanical systems were validated through an electron beam test on a large-scale 51-crystals prototype (Module-0) and extensive test campaigns that characterised and verified the performance of crystals, photodetectors, analogue and digital electronics. This included hardware stress tests and irradiation campaigns with neutrons, protons, and photons.The production and QC phases of all calorimeter components is completed apart for the digital electronics that has been revised for improving its resilience to SEU and SEL. A series of vertical slice tests with the final electronics is being carried out on the Module-0 at LNF along with the implementation and validation of the calibration procedures. The first disk has been assembled in 2022 while the second disk is under assembly at the moment of writing. Status of construction will be summarised, along with plans for commissioning and first calibration of the fully assembled disks.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

Studies of Cherenkov photon production in PbF 2 crystals using proton beams at Fermilab

Future lepton colliders such as the FCC-ee, CEPC, ILC, or a muon collider will collect large data samples that allow precision physics studies with unprecedented accuracy, especially when the data is collected by innovative state-of-the-art detectors. An electromagnetic calorimeter based on scintillating crystals, designed to separately record Cherenkov and scintillation light, can achieve precision measurements of electrons and photons without sacrificing jet energy resolution, given adequate light collection efficiency and separation. This paper presents initial measurements from a program aimed at developing such a calorimeter system for future colliders. Finally, we focus on using PbF 2 crystals to enhance the understanding of Cherenkov light collection, marking the first step in this endeavor.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

Study of the Mu2e sensitivity to the $\mu^-\rightarrow e^+$ conversion process

The Mu2e experiment at Fermilab (Batavia, IL) will search for the coherent neutrinoless conversion of a muon into an electron in the electric field of an aluminum atom. The conversion process results in a monochromatic electron with energy slightly below the muon rest mass ($E_e= 104.97$ MeV). The experiment goal is to improve the previous measurement by four orders of magnitude and reach a single event sensitivity of $3 \times 10^{-17} $ on the conversion rate with respect to the muon capture rate. \\ The experiment will deliver a very intense pulsed negative muon beam to an aluminum target to achieve a total number of $10^{18}$ stopped muons in three years of running. Production and transport of the muons are accomplished with a sophisticated magnetic system comprised of a Production, a Transport and a Detector solenoid, with the last one hosting a Straw-tube Tracker and a Crystal Calorimeter. The entire detector region is surrounded by a Cosmic Ray Veto system. Mu2e is und er construction at the Muon Campus of Fermilab. \\ The INFN italian group is responsible for the design and construction of the crystal calorimeter, which plays a crucial role in the Mu2e measurement, providing particle identification capabilities fundamental for the rejection of the different background sources that can mimic a conversion electron. The calorimeter information allows also to improve the tracking performances it provides a fast standalone trigger for the experiment.\\ After a long R\&D phase, the final drawings see a calorimeter comprised of 1348 pure CsI crystals arranged in two annular disks. Each crystal is readout by two custom UV-extended Silicon Photomultipliers (SiPMs). Performances of the selected components were verified with an electron beam test, carried out in 2017 at the Beam Test Facility (BTF) at the National Laboratories of Frascati, on a large size prototype of 51 crystals and 102 SiPMs, confirming excellent energy ($\sigma_{E}/E = \mathcal{O }(10\%)$) and timing ($\sigma_{T} <500$ ps) resolutions in a! greement with the Mu2e specifications.\\ In the first chapters of this thesis, I describe my involvement in the calorimeter activities, with particular emphasis on the data analysis of the prototype energy response and resolution, that I was personally leading. Moreover, a description of the tuning of the simulation and the careful data-MC comparison is also reported.\\ An auxiliary measurement that can be performed with Mu2e is the search for a Lepton Number Violation (LNV) process where the negatively charged muon converts, without neutrinos, into a positron, $\mu ^{-} +N(A,Z) \rightarrow $ e$^+ +N(A,Z-2)$. At the moment of writing, Neutrinoless Double Beta Decay (0$\nu \beta \beta$) has set the most stringent limit on the LNV processes (T$^{0\nu \beta \beta}_{1/2} > 1.1 \times 10^{26} $ yr at 90$\%$ CL) with the GERDA experiment. In 0$\nu \beta \beta$ a pair of free electrons is created in the transformation from a nucleus $(A, Z)$ into its daughter $(A, Z + 2)$, namely: $(A,Z)\rightarrow (A, Z+2) =2 e^-$. Similar transitions could proceed through the emission of a pair of positrons, double electron capture (EC), or EC and single emission of a positron, with the nucleus changing from $(A, Z)$ to $(A, Z - 2)$. All these variations are equally interesting when discussing of new Physics, since they all manifest a non-conservation of the number of leptons.\\ Moreover, recent studies show that, because of flavor effect, off-diagonal processes, such as the $\mu^- -e^+$ conversion, can have their rate enhanced with respect to processes occurring in the $e-e$ sector.\\ Mu2e will search for $\mu^- + Al(27,13) \rightarrow e^+ +Na(27,11)$, only considering ground state transition, producing a conversion positron with energy $E_{e^+}= 92.32 $ MeV.\\ This thesis is focused on this search. In particular, I developed an algorithm to account for the radiative corrections to be applied to the conversion positrons that resulted in a few percent reduction in s ignal acceptance.\\ One of the most prominent background to ! this sear! ch is the Radiative Muon Capture (RMC) $ \mu+ N(Z,A)\rightarrow \gamma + \nu_{\mu} + N(Z-1,A)$. The produced photon can convert, virtually or in the detector materials (in the following referred as internal or external conversion respectively) in an electron-positron pair, producing positrons with energies approaching the expected conversion energy. Experimental results from previous experiments indicate the RMC endpoint ($\kmax$) to be of $\sim$ 90 MeV. A precise modeling of this background is relevant due to the proximity of the photon spectrum endpoint to the positron conversion energy. The calorimeter group is obviously interested to reconstruct the RMC distribution having also the opportunity to improve the current knowledge of the process. \\ A toy MC has been developed to evaluate the number of $e^+$ from external RMC background in the signal window. Knowing this value and ev...

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

The Mu2e Crystal and SiPM Calorimeter: Construction Status

The Mu2e experiment at Fermilab searches for the neutrino-less conversion of a negative muon into an electron, with a distinctive signature of a mono-energetic electron with an energy of 104.967 MeV. The calorimeter is made of two disks of pure CsI crystals, each read out by two custom large-area UV-extended silicon photomultipliers (SiPMs). It plays a fundamental role in providing excellent particle identification capabilities and an online trigger filter while improving the track reconstruction, requiring better than 10% energy and 500 ps timing resolutions for 100 MeV electrons. In this article, we present the status of construction and the quality control (QC) performed on the produced crystals and photosensors, the development of the rad-hard electronics, and the most important results of the irradiation tests. Construction of the mechanics is also reported. Status and plans for the calorimeter assembly and its first commissioning are described.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

Ubiquitous spin freezing in the superconducting state of UTe 2

In most superconductors electrons form Cooper pairs in a spin-singlet state mediated by either phonons or by long-range interactions such as spin fluctuations. The superconductor UTe 2 is a rare material wherein electrons are believed to form pairs in a unique spin-triplet state with potential topological properties. While spin-triplet pairing may be mediated by ferromagnetic or antiferromagnetic fluctuations, experimentally, the magnetic properties of UTe 2 are unclear. By way of muon spin rotation/relaxation (μSR) measurements on independently grown UTe 2 single crystals we demonstrate the existence of magnetic clusters that gradually freeze into a disordered spin frozen state at low temperatures. Our findings suggest that inhomogeneous freezing of magnetic clusters is linked to the ubiquitous residual linear term in the temperature dependence of the specific heat (C) and the low-temperature upturn in C/T versus T. The omnipresent magnetic inhomogeneity has potential implications for experiments aimed at establishing the intrinsic low-temperature properties of UTe 2 .

36 MATERIALS SCIENCE↗

Nature of the ferromagnetic-antiferromagnetic transition in Y 1- x La x TiO 3

In this work, we explore the magnetically ordered ground state of the isovalently substituted Mott insulator Y 1- x La x TiO 3 for x≤ 0.3 via single-crystal growth, magnetometry, neutron diffraction, x-ray magnetic circular dichroism, muon spin rotation, and small-angle neutron scattering (SANS). We find that the decrease in the magnetic transition temperature on approaching the ferromagnetic-antiferromagnetic phase boundary at the La concentration xc ≈ 0.3 is accompanied by a strong suppression of both bulk and local ordered magnetic moments, along with a volume wise separation into magnetically ordered and paramagnetic regions. The thermal phase transition does not show conventional second-order behavior since neither a clear signature of dynamic critical behavior nor a power-law divergence of the magnetic correlation length is found for the studied substitution range; this finding becomes increasingly obvious with increasing La substitution. We find no evidence for a spin-glass phase. Finally, from SANS and magnetometry measurements, we discern a crossover from easy-axis to easy-plane magnetocrystalline anisotropy with increasing La substitution. These results indicate complex changes in magnetic structure upon approaching the phase boundary.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Entanglement between a muon spin and $I>\frac{1}{2}$ nuclear spins

We report on the first example of quantum coherence between the spins of muons and quadrupolar nuclei. We observe this effect in vanadium intermetallic compounds which adopt the A15 crystal structure, and whose members include all technologically dominant superconductors. The entangled states are extremely sensitive to the local structural and electronic environments through the electric field gradient at the quadrupolar nuclei. This case-study demonstrates that positive muons can be used as a quantum sensing tool to probe also structural and charge related phenomena in materials, even in the absence of magnetic order.

Bonfà, Pietro↗

Fast Muon Capture Monitoring in Mu2e with the CAPHRI Detector

The Mu2e experiment at Fermilab will search for the charged lepton flavor violating (CLFV) process of a neutrinoless muon-to-electron conversion in the field of an aluminum nucleus. Reaching the experiment’s target sensitivity requires precise normalization of the physics signal through accurate monitoring of the muon capture rate on the stopping target. For this purpose, the Calorimeter Precise High-Resolution Intensity detector (CAPHRI) has been developed. The detector is composed of four LYSO crystals installed in the upstream disk of the Mu2e calorimeter and read out with the standard calorimeter readout. CAPHRI measures the muon capture rate by detecting the characteristic 1.8~MeV gamma emission line of the $^{27}Al(\mu^−, \nu n \gamma) ^{26}Mg$ nuclear reaction. The fast, precise response enables injection-by-injection monitoring of proton beam intensity fluctuations. We report on the commissioning and performance characterization of CAPHRI. The response of each channel is calibrated at two SiPM overvoltages using both the intrinsic self-emission of the LYSO crystals and cosmic ray signals. In parallel, Monte Carlo simulations are used to evaluate the detector acceptance and the expected signal-to-background ratio under realistic running conditions. Preliminary results show a crystal light yield consistent with expectations and a channel inter-calibration at the 2--4% level. Simulation studies indicate that the detector acceptance and background rejection satisfy the requirements for physics operations, with about 1000 detected events per beam injection at a beam power of 1.5~kW. These results demonstrate that CAPHRI is an effective tool for beam monitoring and signal normalization in Mu2e.

Ciccarella, V. [Frascati; U. Rome La Sapienza (mai↗

Structural, magnetic, and electronic evolution of the spin-ladder system BaFe 2 S 3-x Se x with isoelectronic substitution

We reWe report experimental studies of a series of BaF e 2 S 3 - x Se x ( 0 ≤ $x$ ≤ 3 ) single crystals and powder specimens using x-ray diffraction, neutron-diffraction, muon-spin-relaxation, and electrical transport measurements. A structural transformation from $C$ $mcm$ ( BaFe 2 Se 3 ) to $P$ $nma$ ( BaFe 2 Se 3 ) was identified around $x$ = 0.7 - 1 . Neutron-diffraction measurements on the samples with $x$ = 0.2, 0.4, and 0.7 reveal that the Néel temperature of the stripe antiferromagnetic order is gradually suppressed from ~120 to 85 K, while the magnitude of the ordered Fe 2+ moments shows very little variation. Similarly, the block antiferromagnetic order in BaFe 2 Se 3 remains robust for 1.5 ≤ $x$ ≤ 3 with negligible variation in the ordered moment and a slight decrease of the Néel temperature from 250 K ( $x$ = 3 ) to 225 K ( $x$ = 1.5 ). The sample with $x$ = 1 near the $C$ $mcm$ and $P$ $nma$ border shows coexisting, two-dimensional, short-range stripe- and block-type antiferromagnetic correlations. The system remains insulating for all $x$ , but the thermal activation gap shows an abrupt increase when traversing the boundary from the $C$ $mcm$ stripe phase to the $P$ $nma$ block phase. The results demonstrate that the crystal structure, magnetic order, and electronic properties are strongly coupled in the BaFe 2 S 3-x Se x system.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

The IDEA detector concept for FCC-ee

A detector concept, named IDEA, optimized for the physics and running conditions at the FCC-ee is presented. After discussing the expected running conditions and the main physics drivers, a detailed description of the individual sub-detectors is given. These include: a very light tracking system with a powerful vertex detector inside a large drift chamber surrounded by a silicon wrapper, a high resolution dual readout crystal electromagnetic calorimeter, an HTS based superconducting solenoid, a dual readout fiber calorimeter and three layers of muon chambers embedded in the magnet flux return yoke. Some examples of the expected detector performance, based on fast and full simulation, are also given.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗