The Neutrino Factory could be an intermediate stage that paves the way to a brand new line of high brilliance muon accelerators. The Muon Collider is a potential experimental development that would take muons and antimuons
to the multi-TeV range and significantly extend the energy reach of current lepton colliders. The point-like nature of muons offers a superior resolution in comparison to composite hadron collisions. The Muon Collider is proposed as an attractive Higgs Factory candidate as well as an energy frontier lepton collider to probe physics beyond the Standard Model.
2.4.1 Facility design
The current energy frontier of modern particle accelerators is restricted by bremsstrahlung ine+ e− colliders and by the strength of bending magnets in hadron colliders. The Large Electron-Positron Collider (LEP) was operated at CERN until 2000 in a 27 km circular tunnel and reached 209 GeV centre-of-mass (COM) energy [133]. Above this energy, the power dissipated through synchrotron radiation overwhelms the accelerating power of the RF cavities.
The straightforward way to circumvent this problem is either to increase the radius of the machine or build a large linear collider. The Future Circular Collider (FCC-eein its electron–positron configuration) collaboration has been assembled to study the potential of a 100 km circular ring in the vicinity of CERN [134]. This ring could take the COM energy of an electron collider up to 365 GeV. The International Linear Collider (ILC) is a proposed 30–50 km linear particle accelerator designed to initially reach 250 GeV COM energy and potentially be upgraded to 1 TeV [135]. Both facilities have a substantial footprint associated with a large cost of construction and operation. The Muon Collider is an elegant alternative that uses the significantly larger mass of muons to limit the synchrotron radiation and reach those energies with a compact machine [16,17,136]. Figure2.15shows the schematics of a proposed layout for a 4 TeV Muon Collider.
Figure 2.15: Schematic of a 4 TeV Muon Collider on the 6×7 km Fermi National Laboratory site [136].
The front-end of the facility shares a lot of its components with the Neutrino Factory. Project X is a code name for the staged upgrade of the Fermi National Laboratory proton driver, necessary for both projects.
The buncher, phase rotator and initial cooling channel would be shared.
The Muon Collider needs a significantly more ambitious cooling system to reach the luminosity required to achieve its physics program [137,138]. The emittance evolution in the cooling and merging channels, as required by the muon collider, is shown in figure 2.16. The small δE requirement of the collider implies that the beam must be cooled to minimal longitudinal emittances. The baseline cooling scenario for a Collider starts with bunch trains from the front-end and cools them both transversely and longitudinally in a sequence of spiral or helical channels, merges the bunches and further cools the beam both transversely and longitudinally, before entering a final cooling section with high-field magnets toward minimal transverse emittances, while the longitudinal emittance increases. For the 125 GeV Collider the cooling scenario would be truncated at minimal longitudinal emittance, where k'1.5 mm and the transverse emittance⊥'0.3 mm. At this longitudinal emittance, the beam would exhibit an energy spread of ∼ 3 MeV, small enough for precision exploration of the Higgs sector.
Figure 2.16:Longitudinal and transverse emittances during the cooling for a muon collider [137].
Following Neutrino Factory designs, muon bunches can be accelerated in a linac and a sequence of recirculating linacs (RLA), where theµ+ andµ− bunches would be inserted into an FFAG collider ring. In the Higgs Factory configuration, a 300 m ring is sufficient to achieve a centre-of-mass energy equal to the Higgs mass, i.e. at the peak of the resonant production. To push the energy frontier with a multi-TeV machine, a larger ring is necessary
but the same accelerating conceptual design is preserved. Studies have been performed for a 100 km ring that would reach 200 TeV in the centre-of-mass frame, almost three orders of magnitude higher than the FCC-ee[139].
2.4.2 Physics
The CERN ATLAS and CMS experiments have discovered a Higgs boson candidate,H, at mH = 125.09±0.24 GeV/c2 [140]. Its mass is consistent with the Standard Model Higgs, which has a small production cross-section and a narrow width of∼4 MeV [141]. Due to the limited energy resolution of hadron colliders, the observed width of the candidate Higgs is of order GeV. A recent study uses the contribution from off-shellH0→ZZ∗ decays to better constrain the width by two orders of magnitude. The current experimental upper limit is ΓH<13 MeV at 95 % confidence level [142]. This estimate relies heavily on simulations produced by strictly using Standard Model physics processes and as such is not sensitive to new physics. A lepton machine is essential to make a direct measurement of the Higgs width with the level of precision achieved on the Z andW widths at LEP. Any deviation from the predicted width could indicate new physics in the form of coupling with BSM particles. In the minimal supersymmetric SM, a precise measurement of the mass, width and cross-section would also constrain some of the other Higgs sector parameters.
A muon collider is the ideal machine to achieve a resolution of order MeV on the Higgs width [19]. Thes-channel production, represented on the left panel of figure2.17, is the only process through which the width can be measured directly. The mass of the muon couples to the Higgs (mµ/me)2 more strongly than electrons to achieve a resonant production cross-section of ∼40 pb, comparable to the LHC cross-section at 14 TeV COM energy.
With a nominal luminosity of 1031cm−2/s,∼4000 Higgs are produced each operational year. A scan over the Higgs mass with a small-δE collider would resolve the mass and width to high accuracy, higher than any alternative H0 studies. The right panel of figure2.17represents the production cross-section forµ+µ− colliders. The cross section for a machine with a resolution R= 0.003 % yields a significantly larger cross section than ane+e− collider as represented by the Next Linear Collider (NLC) curve.
With an energy reach extended to the TeV scale, the Muon Collider could probe supersymmetric extensions of the standard model. It is ideally suited for the study of heavy H/A scalars, cousins of the Higgs boson found in two-Higgs-doublet models and required in supersymmetric models [144]. The Natural Supersymmetry model has a 1.5 TeVH/Awith a small mass splitting of 10 GeV, easily resolved by a muon collider. At the high energy frontier, a 3 to 4 TeV machine is ideally suited for the study of scalar supersymmetric particles and extra Z-bosons or strongW W scattering. Historically, hadron
µ − µ +
∼mµ
H
0 ∼mb¯ b
b
Figure 2.17: (Left) Leading-order Higgs production to decays-channel process.
(Right) Production cross-section as a function of the centre-of-mass energy√
sµµ[143].
colliders have always been discovery machines. If the LHC is to see any hint of physics beyond the standard model, the Muon Collider is the ideal facility to make subsequent precision measurements.
The Muon Collider could also significantly extend the current limits achieved on heavy neutrino couplings and mass scale [20]. More exotic propositions have been made to collide neutrino beams from storage rings to produce and observe high energyνν¯interactions [145].
CHAPTER 3
Muon Ionization Cooling Experiment
Intense muon sources are required for a future Neutrino Factory or Muon Collider [122,146]. At production, muons occupy a large phase space volume (emittance), which makes them difficult to accelerate and store. Therefore, the emittance of the muon beams must be reduced, i.e the muons must be
“cooled”, to maximise the muon flux delivered to the accelerator. Conventional cooling techniques applied to muon beams would leave too few muons to be accelerated since the muon lifetime is short (τµ ∼2.2µs) [147]. Simulations indicate that the ionization-cooling effect builds quickly enough to deliver the flux and emittance required by the Neutrino Factory and the Muon Collider [17,118, 148]. The Muon Ionization Cooling Experiment (MICE) experiment has been designed to study ionization cooling in detail and demonstrate the feasibility of the technique [22].
3.1 Intent
Muon cooling is the most novel accelerator physics technique required to build the front-end of future muon accelerators. Ionization cooling was proposed in the late 1960s by G. I. Budker and A. N. Strinsky and later developed and promoted by D. Neuffer [149]. It adds an order of magnitude in intensity to a Neutrino Factory and reduces its cost by as much as 20 % [122,150].
Cooling of minimum-ionizing muons has never been observed experimentally.
The MICE collaboration has set out to demonstrate the viability of ionization cooling as a technique by which to reduce the phase space volume
of muons to fit the acceptance of an accelerator. The group consists of accelerator physicists, experimental particle physicists and engineers from Europe, Japan, the US, China and Korea. The specific goal of the experiment is to build a section of a cooling channel that gives the desired performance for a Neutrino Factory and expose it to a variety of test beams.
The aim is not to demonstrate theprincipleof ionization cooling, which is expected to result if all components work as specified, but rather to learn how to operate a functional cooling channel [22]. The experiment was conceived to observe a 10 % reduction in transverse geometric emittance. It was built with a comprehensive set of particle detectors to measure the emittance upstream and downstream of an absorber with a resolution of 0.1 % or better. To achieve this resolution, MICE was designed as a single-particle experiment.
The particle rate is such that the trajectory and momentum of each muon are reconstructed individually. A muon crosses the experiment on average every 10µs over a period of 1 ms every second. The muons are combined into an ensemble at the reconstruction level to compute the beam parameters.
The accelerator physics behind the principle of ionization cooling and the design of the MICE cooling channel are described in detail.