We briefly discuss the physics motivation for a neutrino factory with varying
baseline distances of about 1000 to 9000 km. We describe the amount of non
planarity of the storage ring required to service three or four detectors at
once. A novel bowtie storage ring is described that could in part provide these
beams; a preliminary lattice design is given. We give the space angles between
the various detector locations and possible sites for neutrino factories.
Finally we describe detectors at the Gran Sasso Laboratory and at a new
laboratory near Carlsbad, NM to observe the neutrino interactions with wrong
sign leptons.Comment: 8 pages. Presented at the 5th Int. Conf. sponsored by UCLA on the
  Physics Potential and Develoment of mu^+mu^- Colliders (San Francisco,
  December 15-17, 1999) and to be published in the Proceedings by AI

Cline, D. B.

Fukui, Y.

Garren, A.

English

arXiv

D. B. Cline

Crossref

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*Presented at the 5th Int. Conf. Sponsored by UCLA on Physics Potential and Development of µ+µ- Coll iders (San Francisco,
December 15-17, 1999) and to be published in the Proceedings by AIP.
A Neutrino-Factory Muon Storage Ring
to Provide Beams for Multiple Detectors
Around the World*
CAA-0160-2/00
D.B. Cline, Y. Fukui, and A. Garren
Center for Advanced Accelerators
Department of Physics and Astronomy, Box 951547
University of California, Los Angeles, CA  90095-1547 USA
Abstract.  We briefly discuss the physics motivation for a neutrino factory with varying baseline
distances of about 1000 to 9000 km.  We describe the amount of non planarity of the storage ring
required to service three or four detectors at once.  A novel bowtie storage ring is described that could
in part provide these beams; a preliminary lattice design is given.  We give the space angles between
the various detector locations and possible sites for neutrino factories.  Finally we describe detectors
at the Gran Sasso Laboratory and at a new laboratory near Carlsbad, NM to observe the neutrino
interactions with wrong sign leptons.
INTRODUCTION
The physics  potential of a  muon storage-ring neutrino factory is large1-3 and includes
(A)Observation of e  µ at levels of 10
-3; possible detection of e  µ and e  2;
(B)Study of µ   2 and ;µ2
(C)Possible CP violation test for 
 (i) µ   2, ( );µ2
(ii ) e  2, ( ), e  µ, ( );e2 eµ
(D)Possible study of the combined effects to  final states (T violation).µ,µ e,e
In the case (Ci), we expect a very small signal in the three-neutrino “CKM” matrix
formulation.  However, if there are sterile neutrinos, the CP violation could still be very large
in this channel.
One strength of the ICANOE4 detector is the real-time identification of 
2 + N  2 + x
|_
 e,µ
|_
 hadron   .
Using NOMAD-like cuts in addition, the process e  µ, µ + N  µ- + x can be detected
using a magnetized toroid system such as is employed for ICANOE.  We also describe a
magnetized ion detector for a new underground laboratory at Carlsbad, NM.
In order to address the detection of the processes described before and the resulting
background, we need to specify the neutrino factory parameters.
We point out for historical reference that one of the earliest papers on a µ± neutrino
source was by Cline and Neuffer in 1979-80.1  The recent interest in this subject is due to the
probable discovery of neutrino oscill ations by Superkamiokande (SK) using atmospheric
neutrinos.
The current situation in neutrino mass and mixing physics lends itself to some confusion.
We do not know if there are sterile neutrinos or not, and a neutrino factory could be the key
to resolving this issue.
Another key possibly is to operate a neutrino factory below e  2 threshold and then
observe  in the detector.  The detection of e  2  or e  µ will be crucial fore  µ  µ
	
the use of a neutrino factory to study the neutrino CKM matrix and to search for CP or T
violation.
Backgrounds to Neutrino Oscillation Measurements
The basic concept of the neutrino factory is to detect an oscill ation in the non-µ channel.
For example for a µ
-
 storage ring, µ
-
  e
-
 + µ + .  So we have  in the µ beam,e e
oscill ation into , followed by   µ+ given a "wrong sign lepton."  In the case of ee  µ µ
 2, as we will show, the produced 2 must decay into a µ
± channel to measure the lepton
charge.  
We now discuss the possible level of the signals for neutrino oscill ations at a neutrino
factory.  We can write the transition probably as
   ,Pµ2 
 cos
2
13sin
2 223sin
2 1.27
L
E
û
2m
   ,Pe2 
 sin
2
23sin
2 213sin
2 1.27
L
E
û
2m
where L is in km, E is in GeV, and û2m is in eV2.  The SuperKamiokande results suggest
that 23  45(.  The current limits on µ   e constrain 13 to be less than 20(.  Since we
know nothing about the neutrino CKM matrix, 13 could be very small .  We can express the
e  2 transition as Pe2  Peµ (cos
2 23/sin
2 23).  For 23 w 45(, we find Pe2  Peµ).  Thus for
the issue of background estimates, if 13 is small , then both Pe2 and Peµ will be small .
There are natural sources of wrong sign leptons produced in high-energy neutrino
interactions.  While these backgrounds will not likely affect the detection of e  µ, we will
show that for some parameters this background will be dangerous for e  2 detection.
To show why wrong-sign leptons produced in neutrino interactions may be a limiti ng
background for e  2, we consider the following:
e  2   ,     (Pe2)   ;
2 + N  2
- + X   ,     (12/1all)   ;
2  µ- + X   ,     (P ~ 10-1)   .
(Note that the µ- energy spectrum will be soft.)
The µ± must be detected to identify the "wrong sign 2" from the large rate of production
from  in the neutrino factory beam.  For the parameters Pe2~ 5 × 10
-3, 12/1all ~ 5 × 10
-2.µ2
We find the overall probabilit y to get a  wrong sign µ± from an (e2) oscill ation to be 2.5 ×
10-5.5,6  We will show that this is below some of the "natural" wrong sign production in
neutrino interactions.
The production of charm can lead to wrong sign leptons through the process
µ + N  µ
- + charm
|_
 µ+ +  + X   ,
with the µ- being missed.  (This process was first observed by the HPWF group at FNAL in
1974.)  We do not expect this to be an important background for e  µ because of the high
energy of the resulting µ-.  However, for e  2, the 2 decay into a µ
- channel will result in
a soft µ-, as well as some missing neutrino energy and the same hadronic structure as charm
production. 
A BOWTIE MUON RING LATTICE   FOR NEUTRINO PRODUCTION
This paper also concerns the possible use of a single storage ring to ill uminate three or
more detectors around the world, as shown in Fig. 1.
A bowtie-shaped muon storage-ring lattice is discussed. This planar ring can be designed
and oriented to send neutrino beams to any two detector sites. Bypasses could be added to
send reduced intensity beams to one or two additional sites.   There are several advantages
of the bowtie shape:
 No net bending, so the polarization is preserved,
 With the ring in a tilted plane, both long straight sections point down into the earth, so
neutrinos are sent into two distant detectors. Triangular rings share this advantage.
There are also some disadvantages of the bowtie shape:
 Extra bending required, by 4/3 in this example,
 Geometry constrains the ratio of short and long straight sections, which may increase
circumference,
 Complications due to crossing beamlines.
FIGURE 1.  A scheme to provide neutrino-factory beams to several detectors around the world.
Lattice Description
The lattice contains three parts:  a short straight section, an arc, and a long straight
section. The description follows one quarter of the ring, starting at the center of the short
straight section on the left side of the figure, and ends at the crossing point at the center of
the bowtie (Fig. 2).
Short Straight Section
Half of the short straight section consists of two 14-m arc cells without dipoles. It can
also be configured to provide a 20-m free space for injection. One short straight section may
be used for injection, the other for RF.
Arc
The arc contains eight FODO cells, two without dipoles. The cell phase advances are 60
deg, and the dipole-free cells act as dispersion suppressors. Twelve 5-m long dipoles each
bend the beam 10 deg, so the arc has 120 deg of bending. This angle is needed to cross the
beamlines by 60 deg  (a typical angle, whose exact value depends on the selection of ring and
detector sites).
Long Straight Section
The long dispersion-free straight section provides a muon beam whose decaying muons
generate low divergence neutrinos. Two configurations are shown in Figs. 2 and 3. In Fig.
2, the long straight section has quadrupoles in the center (around the crossing point) making
two beam waists, each with 50-m beta function values. In Fig. 3, a 200-m magnet-free
beamline is provided, with a beam waist at the center with 100-m beta values.
FIGURE 2.  Half of a bowtie ring lattice. The center of the figure is a straight section with quadrupoles at its
center, making two beam waists.
Figure 3.  Second configuration for long-straight-section insertion of bowtie ring. There are no quadrupoles
around the center, where the beams cross.
Bypasses
A racetrack ring can be configured to deliver one neutrino beam to an arbitrary detector
site.  A bowtie ring can be configured to deliver neutrino beams from an arbitrary ring site
to two arbitrarily chosen detector sites. This can be done by appropriate choice of the ring
plane, the orientation of the ring in that plane, and the angle at the crossing point between
the two long straight sections (Fig. 4). 
Additional detector sites might be accessible from a single muon storage-ring source by
inclusion of bypasses. A bypass would begin and end on one of the long straight sections,
but lie in a plane that includes the original long straight section but differs from that of the
ring. Its magnets would be powered when one desires to send the muons along the deformed
bypass path rather than along the normal straight path. 
FIGURE 4.  A possible bypass system to provide neutrino beams to off -angle detectors.
In such a bypass, dipoles would produce a roughly triangular path in the bypass plane,
one of whose sides would point to the desired detector. The two necessary degrees of
freedom are provided by the angle between the bypass and ring planes and by the magnitude
of the deflection given by the bypass dipoles. 
Pairs of dipoles should be placed in FODO cells, 180 deg apart, in order to suppress the
dispersion.
SPACE ANGLES FOR THE 
VARIOUS DETECTOR LOCATIONS AROUND THE WORLD
The  oscill ation probabilit y, P,  is given by P = sin2 (2) sin2 (1.27 ûm2 L/E), where
 is the mixing angle,  and ûm2 (eV2)/c4 is the difference of mass squared, L km is the
baseline length, and E (GeV) is the  energy, in a two-flavor  oscill ation model. Assuming
reasonably intense  flux at the far detectors, we obtain wider window ranges of [sin2 (2)
sin2, ûm2] by shooting multiple far  detectors with mixed baseline lengths.
We discuss space angles which are associated with multiple baselines, and  flux as a
function of the polar angle from the straight section axis of a bow-tie storage ring. 
Baseline
Because of the Earth's rotation, the equator radius is longer than the polar radius by 21
km, which corresponds to 0.3% of the average Earth radius.  Figure 5 shows the Earth
surface position as functions of the distance from the equator plane and from the rotation
axis.  The change of the equator radius due to the gravity of the moon and the sun are,
respectively, 0.36 m and 0.17 m, depending on the position relationship of the moon, the sun,
and the Earth.
Table 1 shows baseline length, vertical angle, and the angle to the North direction at the
storage ring site and at the detector site.  The numbers in square brackets are the differences
between a value with an elli ptical radius and a value with a spherical radius.
Space Angles
Figure 5 shows the baselines and vertical angles, and angles to the North direction at
storage rings at Fermilab.
Table. 1.  Baseline Lengths and Surface Angles.
___________________________________________________________________________________
Vertical Angle* to North
Baseline Length  Angle* (deg) (deg)
_______________________________________________________________________________________
Fermilab - Soudan, MN 731.04 [-0.39]  km
    at Fermilab 3.473 [ 0.182]**  -23.625 [ 0.073]
    at Soudan 3.126 [-0.164] 153.597 [ 0.073]
Fermilab - Carlsbad, NM  1748.87 [-0.18]  km
    at Fermilab 7.791 [-0.098] -121.626 [-0.081]
    at Carlsbad 8.009 [ 0.120]    48.689 [-0.075]
Fermilab - Gran Sasso, It 7332.89 [-2.82]  km
    at Fermilab 35.149 [ 0.008]    50.087 [ 0.004]
    at Gran Sasso 35.155 [ 0.005]   -50.749 [-0.006]
Fermilab - Kamioka, Jpn 9133.63 [-1.87]  km
    at Fermilab 45.811 [ 0.008]   -35.178 [-0.016]
    at Kamioka 45.828 [ 0.026]     32.102 [ 0.007]
BNL - Soudan,  MN 1715.25 [-0.87]  km
    at BNL 7.826 [ 0.093]    -56.330 [ 0.076]
    at Soudan 7.665 [-0.081]   110.081 [ 0.076]
BNL - Carlsbad, NM 2903.08 [-0.20]  km
    at BNL 13.118 [-0.048]    -98.421 [-0.053]
    at Carlsbad 13.239 [ 0.065]     62.563 [-0.041]
BNL - Gran Sasso, It 6526.73 [-2.30]  km
    at BNL 30.825 [ 0.011]     56.812 [ 0.002]
    at Gran Sasso 30.830 [ 0.001]    -59.240 [-0.010]
BNL - Kamioka, Jpn 9635.70 [-1.66]  km
    at BNL 49.157 [ 0.014]    -24.150 [-0.012]
    at Kamioka 49.169 [ 0.027]     22.571 [ 0.008]
CERN - Soudan,  MN 6568.46 [-4.40]  km
    at CERN 31.053 [ 0.000]    -48.743 [ 0.007]
    at Soudan 31.043 [-0.009]     50.750 [ 0.000]
CERN - Carlsbad, NM  8135.78 [-1.88]  km
    at CERN 39.677 [-0.013]    -53.679 [-0.028]
    at Carlsbad 39.730 [ 0.041]     41.287 [-0.008]
CERN - Gran Sasso, It 727.58 [-0.37]  km
    at CERN 3.120 [-0.107]   122.679 [ 0.089]
    at Gran Sasso 3.437 [ 0.114]    -52.084 [ 0.089]
CERN - Kamioka, Jpn 8737.07 [-2.91]  km
    at CERN 43.301 [-0.007]     37.574 [ 0.016]
    at Kamioka 43.333 [ 0.029]    -31.479 [ 0.003]
_______________________________________________________________________________________
  *positive =  North/East; negative = West
** [elli ptic Earth - spherical Earth]
FIGURE 5.  Baselines and surface angles at Fermilab.
DETECTORS AT THE GRAN SASSO AND CARLSBAD SITES
We assume that distances of 2000 to 7000 km are useful to study neutrino oscill ations,
matter effects, and possibly CP violation.  We also assume that the detectors must be located
underground, because of the enormous backgrounds from cosmic rays.  Finally, we assume
that existing underground faciliti es will be used for the detector.  In this section, we discuss
detector locations of ~ 2000 to 3000 km from either FNAL or BNL and 6000 to 7000 km to
the LNGS.
We discuss two detectors:
(1) ICANOE at the LNGS [Fig. 6(A) and (B)] and
(2) A magnetized Fe detector at the Carlsbad Underground Laboratory (Fig. 7).
These two detectors are in a sense the extremes of the detectors one may use for a neutrino
factory.  The ICANOE detector will have excellent electron identification and can observe
µ,2  e, whereas the Carlsbad detector will li kely be used for wrong-sign muon
identification, i.e.,   µ+ in the detector.  To search for CP violation, both detectorseµ
will  have to use µ± sign determination, since we have to way to measure the electric charge
of the “e” -li ke signals.
We will first address the issue of the crossing angle of the neutrino beam on the detector.
This will not be a problem for a new hall as can be constructed at the Carlsbad site, but as
shown in Fig. 6(B), it could be a problem for a fixed laboratory like the LNGS.  It is possible
that part of the ICANOE detector can be reconfigured to fit this space angle.
SUMMARY
We considered the option of shooting multiple far detectors with intense  beam from
a bow-tie storage ring. The base line lengths, surface angles, and space angles were
calculated with both elli ptical and spherical Earth models.  The transverse angle of the
muons in the straight section of a bow-tie storage ring is demonstrated to be much smaller
than the HWHM (half width half maximum) of the  angle from the axis.  We also discussed
the important neutrino physics that can be carried out with detectors at LNGS (ICANOE) and
at Carlsbad, NM.
                                 (A)                                                                           (B)
FIGURE 6.  (A) Schematic of the ICANOE detector to be constructed at the LNGS; (B) Detector crossing
of the LBL beam from FNAL for the ICANOE detector at LNGS.
FIGURE 7.  Possible neutrino-factory detector at the WIPP site in Carlsbad, NM.
ACKNOWLEDGEMENTS
We wish to thank J. Gallardo, R. Nelson, R. Palmer, and F. Sergiampietri for their help
and encouragement.
REFERENCES
[1] Cline, D. and Neuffer, D., in Physics Potential and Development of µ+µ- Colliders (Proc., Second
Workshop, Sausalito, CA, Nov. 1994), AIP Conference Proceedings No. 352, ed. D. B. Cline (American
Institute of Physics, Woodbury, NY, 1996), pp. 10-11 (reprinted from 1981).
[2] Geer, S., FNAL, private communication (1999).
[3] CERN Study of the Neutrino Factory, CERN report No. 99-02 (1999).
[4] ICARUS and NOE Collaboration, “ ICANOE:  A Proposal for a CERN-GS Long Baseline and
Atmospheric Neutrino Oscill ation Experiment,” CERN/SPSC 99-25 (August 30, 1999).
[5] Cline, D., "The Neutrino Physics Potential of the ICARUS Detector Program," UCLA Report No. PPH-
0079-9/99, in Proc., 23rd Johns Hopkins Wksp. on Current Problems in Particle Theory (Johns Hopkins
U., Baltimore, MD, June 12–12, 1999), World Scientific Publishing (in press).
[6] Cline, D., “Wrong-Sign Muon Appearance with an ICARUS-like Detector at a Neutrino Factory,” in
Proc., Neutrino Factories Based on Muon Storage Rings, NuFact’99 (ICFA/ECFA, Lyon, France, July
1999) Nucl. Instrum. Meth. A (in press).
