Recent progress in neutrino factory and muon collider research within the Muon Collaboration

We describe the status of our effort to realize a first neutrino factory and the progress made in understanding the problems associated with the collection and cooling of muons towards that end. We summarize the physics that can be done with neutrino factories as well as with intense cold beams of muons. The physics potential of muon colliders is reviewed, both as Higgs factories and compact high-energy lepton colliders. The status and time scale of our research and development effort is reviewed as well as the latest designs in cooling channels including the promise of ring coolers in achieving longitudinal and transverse cooling simultaneously. We detail the efforts being made to mount an international cooling experiment to demonstrate the ionization cooling of muons.

Figure 1

Muon decays in a straight section per ${10}^7\mathrm{s}$ vs muon energy, with fluxes required for different physics searches assuming a 50 kT detector. Simulated performance of the two studies is indicated.

Figure 2

Schematic of the neutrino factory study-II version.

Figure 3

Fit to muon neutrino survival distribution for $E_{\mu }=30\mathrm{GeV}$ and $L=2800\mathrm{km}$ for ten pairs of ${sin}^{2}2\theta$, $\delta m^2$ values. For each fit, the $1\sigma$, $2\sigma$, and $3\sigma$ contours are shown. The generated points are indicated by the dark rectangles and the fitted values by stars. The SuperK 68%, 90%, and 99% confidence levels are superimposed. Each point is labeled by the predicted number of signal events for that point.

Figure 4

The wrong-sign muon appearance rates for a 20 GeV muon storage ring at a baseline of 2800 km with ${10}^{20}$ decays and a 50 kt detector for (a) ${\mu }^{+}$ stored and negative $\delta m_{32}^2$, (b) ${\mu }^{-}$ stored and negative $\delta m_{32}^2$, (c) ${\mu }^{+}$ stored and positive $\delta m_{32}^2$, (d) ${\mu }^{-}$ stored and positive $\delta m_{32}^2$. The values of $|\delta m_{32}^2|$ range from 0.0005 to $0.0050{\mathrm{eV}}^2$ in steps of $0.0005{\mathrm{eV}}^2$. Matter enhancements are evident in (b) and (c).

Figure 5

The statistical significance (number of standard deviations) with which the sign of $\delta m_{32}^2$ can be determined versus baseline length for various muon storage ring energies. The results are shown for a 50 kt detector, and (a) ${10}^{20}$ ${\mu }^{+}$ and ${\mu }^{-}$ decays and positive values of $\delta m_{32}^2$; (b) ${10}^{20}$ ${\mu }^{+}$ and ${\mu }^{-}$ decays and negative values of $\delta m_{32}^2$; (c) ${10}^{19}$ ${\mu }^{+}$ and ${\mu }^{-}$ decays and positive values of $\delta m_{32}^2$; (d) ${10}^{19}$ ${\mu }^{+}$ and ${\mu }^{-}$ decays and negative values of $\delta m_{32}^2$.

Figure 6

Predicted ratios of wrong-sign muon event rates when positive and negative muons are stored in a 20 GeV neutrino factory, shown as a function of baseline. A muon measurement threshold of 4 GeV is assumed. The lower and upper bands correspond, respectively, to negative and positive $\delta m_{32}^2$. The widths of the bands show how the predictions vary as the $CP$-violating phase $\delta$ is varied from $-\pi /2$ to $\pi /2$, with the thick lines showing the predictions for $\delta =0$. The statistical error bars correspond to a high-performance neutrino factory yielding a data sample of ${10}^{21}$ decays with a 50 kt detector. The curves are based on calculations presented in 72.

Figure 7

Three-sigma error ellipses in the $[N(e^{+}),N(e^{-})]$ plane, shown for ${\nu }_{\mu }\to {\nu }_e$ and ${\overline{\nu }}_{\mu }\to {\overline{\nu }}_e$ oscillations in a NuMI-like high-energy neutrino beam driven by a 1.6 MW proton driver. The calculation assumes a liquid-argon detector with the parameters listed in 28, a baseline of 2900 km, and 3 years of running with neutrinos, 6 years running with antineutrinos. Curves are shown for different $CP$ phases $\delta$ (as labeled), and for both signs of $\delta m_{32}^2$ with $|\delta m_{32}^2|=0.0035{\mathrm{eV}}^2$, and the sub-leading scale $\delta m_{21}^2={10}^{-4}{\mathrm{eV}}^2$. Note that ${sin}^{2}2{\theta }_{13}$ varies along the curves from 0.001 to 0.1, as indicated [79].

Figure 8

Three-sigma error ellipses in the $[N(\mu +),N(\mu -)]$ plane, shown for a 20 GeV neutrino factory delivering $3.6\times {10}^{21}$ useful muon decays and $1.8\times {10}^{21}$ antimuon decays, with a 50 kt detector at $L=7300\mathrm{km}$, $\delta m_{21}^2={10}^{-4}{\mathrm{eV}}^2$, and $\delta =0$. Curves are shown for both signs of $\delta m_{32}^2$; ${sin}^{2}2{\theta }_{13}$ varies along the curves from 0.0001 to 0.01, as indicated [79].

Figure 9

Summary of the $3\sigma$ level sensitivities for the observation of ${\nu }_{\mu }\to {\nu }_e$ at various MW-scale superbeams (as indicated) with liquid-argon “A” and water-Cerenkov “W” detector parameters, and the observation of ${\nu }_e\to {\nu }_{\mu }$ in a 50 kt detector at 20, 30, 40, and 50 GeV neutrino factories delivering $2\times {10}^{20}$ muon decays in the beam-forming straight section. The limiting $3\sigma$ contours are shown in the ($\delta m_{21}^2,{sin}^{2}2{\theta }_{13}$) plane. All curves correspond to 3 yr of running. The grey shaded area is already excluded by current experiments.

Figure 10

Number of events and statistical errors in the $b\overline{b}$ final state as a function of $\sqrt{s}$ in the vicinity of $m_{h_{\mathrm{SM}}}=110\mathrm{GeV}$, assuming $R=0.003\%$, and $ϵL=0.00125{\mathrm{fb}}^{-1}$ at each data point.

Figure 11

Separation of $A$ and $H$ signals for $\tan \beta =5$ and 10. From Ref. 116.

Figure 12

AGS proton driver layout.

Figure 13

FNAL proton driver layout from Ref. 125.

Figure 14

Target, capture solenoids, and mercury containment.

Figure 15

Cross section of the induction cell and transport solenoids.

Figure 16

Evolution of the beam distribution in the phase rotation section. The graphs show the distribution before the phase rotation, after the first induction linac (top row, left to right), after minicooling, and after the second and third induction linacs (bottom row).

Figure 17

Evolution of beam in buncher. Plots are at the beginning of the buncher (top left), and at the ends of the three bunching stages (top right, bottom left, and bottom right, in that order).

Figure 18

Two cells of the 1.65 m cooling lattice.

Figure 19

The transverse (filled circles, in mm) and longitudinal (open circles, in cm) emittances, as a function of the distance down the cooling channel.

Figure 20

Muons per incident proton in the cooling channel that would fall within a normalized transverse acceptance of 15 mm (open circles) or 9.75 mm (filled circles).

Figure 21

Accelerating system layout.

Figure 22

Layouts of short (left), intermediate (middle), and long (right) cryomodules. Blue lines are the SC walls of the cavities. Solenoid coils are indicated in red.

Figure 23

Layout of an RLA linac period.

Figure 24

Three-dimensional view of the storage ring magnets.

Figure 25

Top view and cross section through 20 GeV ring and berm. The existing 110 m tower, drawn to scale, gives a sense of the height of the ring on the BNL landscape.

Figure 26

Muons per incident proton in the study-II neutrino factory front end.

Figure 27

Schematic of a 20 GeV neutrino factory at BNL.

Figure 28

Schematic of a 50 GeV neutrino factory at Fermilab.

Figure 29

A possible 50 kt steel-scintillator-PDT detector at WIPP.

Figure 30

Block schematic of the UNO detector, including initial design parameters.

Figure 31

Comparative sizes of various proposed high-energy colliders compared with the FNAL and BNL sites. The energies in parentheses give for lepton colliders their CoM energies and for hadron colliders the approximate range of CoM energies attainable for hard parton-parton collisions.

Figure 32

Schematic of a muon collider.

Figure 33

Plan of a 0.1-TeV-CoM muon collider, also known as a Higgs factory.

Figure 34

Layout and parameters of the solenoid based ring cooler. Circumference: 36.963 m; nominal energy at short straight section: 250 MeV; bending field: 1.453 T; normal field gradient: 0.5; maximum solenoid field: 5.155 T; rf frequency: 205.69 MHz; accelerating gradient: 15 MeV$/$m; main absorber length: 128 cm; LiH wedge absorber: 14 cm; gradient of energy loss: 0.75 MeV$/$cm.

Figure 35

The figure shows a computer model of a 52 cm radius dipole with index $n=-\frac{1}{2}$ and the calculated field components radially 10 cm off axis.

Figure 36

Evolution of the beam emittance/transmission at the ring cooler. After 15 turns, the transverse emittances are reduced from 1.2 to 0.21 cm and the longitudinal emittance is reduced from 1.5 to 0.63 cm. The 6D emittance is therefore reduced from 2.2 to $0.028{\mathrm{cm}}^3$, giving a 6D cooling factor of 79. The transmission without decay is 71%, and the transmission with decay is 48%. The resulting merit factor is 38.

Figure 37

Layout of an RFOFO cooling ring.

Figure 38

Three cells of the RFOFO lattice; (a) plan, (b) side.

Figure 39

Transmission, normalized transverse emittance, normalized longitudinal emittance, normalized 6-dimensional emittance, and the merit factor, as a function of distance.

Figure 40

Schematic diagram of half of a $22.5°$ bending cell. A wedge absorber is located in the middle of the cell.

Figure 41

The ${\beta }_x$, ${\beta }_y$, and $D$ (dispersion) in a $22.5°$ bending cell. SYNCH calculations (solid curves) and beam parameters from an ICOOL simulation (marked points) are compared.

Figure 42

Top view of a sixteen cell muon-cooling ring.

Figure 43

The evolution of $x$, $y$, $z$ normalized emittances in 32 full turns.

Figure 44

The transmission and the figure of merit factor as a function of the arc length in 32 full turns.

Figure 45

Cut view of a straw-man detector in Geant for the Higgs factory with a Higgs $\to b\overline{b}$ event superimposed. No backgrounds shown. The tungsten cones on either side of the interaction region mask out a $20°$ area.

Figure 46

Conceptual layout of MICE upstream spectrometer: following an initial TOF measurement, muons are tracked using detector planes located within a solenoidal magnetic field. Although in principle three $x,y$ measurements as shown suffice to determine the parameters of each muon’s helical trajectory, in practice additional measurement redundancy will be employed; for example, a fourth measurement plane can be used to eliminate very-low-momentum muons that would execute multiple cycles of helical motion. A similar spectrometer (but with the time-of-flight measurement at the end) will be used downstream of the cooling apparatus.

Figure 47

Schematic layout of the MICE apparatus.

Figure 48

A possible MICE tracking-detector configuration.

Figure 49

Distribution of ratios of output to input 6-dimensional emittance for 1000 simulated experiments, each with 1000 accepted muons. The top figure shows the distribution of this ratio for the emittances as generated by simulation; the bottom figure, as “measured” in the simulated experiments. The curves are Gaussian fits to the points.

Figure 50

Results from ICOOL simulation of MICE: normalized transverse (top) and longitudinal (bottom) emittances vs distance.

Figure 51

Simulation results for 88-MHz variant of MICE apparatus: (a) output emittance vs input emittance, with $45°$ line (dashed line) superimposed; (b) beam transmission vs input emittance; (c) cooling performance (see text) vs input emittance for various beam kinetic energies (top to bottom: 140, 170, 200, and 230 MeV).