Measuring Active-to-Sterile Neutrino Oscillations with Neutral Current Coherent Neutrino-Nucleus Scattering

1.3 MB·English

by  A. J. Anderson

Measuring Active-to-Sterile Neutrino Oscillations with Neutral Current Coherent
Neutrino-Nucleus Scattering
A.J. Anderson,1 J.M. Conrad,1 E. Figueroa-Feliciano,1 C. Ignarra,1
G. Karagiorgi,2 K. Scholberg,3 M.H. Shaevitz,2 and J. Spitz1
1Massachusetts Institute of Technology, Cambridge, MA 02139, USA
2Columbia University, New York, NY 10027, USA
3Duke University, Durham, NC 27708, USA
Lightsterileneutrinoshavebeenintroducedasanexplanationforanumberofoscillationsignals
at∆m2 ∼1eV2. Neutrinooscillationsatrelativelyshortbaselinesprovideaprobeofthesepossible
new states. This paper describes an accelerator-based experiment using neutral current coherent
neutrino-nucleus scattering to strictly search for active-to-sterile neutrino oscillations. This exper-
iment could, thus, definitively establish the existence of sterile neutrinos and provide constraints
on their mixing parameters. A cyclotron-based proton beam can be directed to multiple targets,
2 producing a low energy pion and muon decay-at-rest neutrino source with variable distance to a
1 singledetector. Twotypesofdetectorsareconsidered: agermanium-baseddetectorinspiredbythe
0 CDMS design and a liquid argon detector inspired by the proposed CLEAR experiment.
2

n
a I. INTRODUCTION search using coherent neutrino scattering that allows for
J pure active-to-sterile oscillation sensitivity.

8 Sterileneutrinomodelshavebeeninvokedtoexplaina Coherent neutrino-nucleus scattering is a well-
1 seriesofintriguingoscillationsignalsat∆m2 ∼1eV2 [1– predicted neutral current weak process with a high cross
4]. These signals have relied on neutrino detection sectioninthestandardmodel,ascomparedtootherneu-
]
h through charged current interactions. In the case of trino interactions at similar energies. Despite this, the
p charged current appearance, the signal is interpreted as coherentinteractionhasneverbeenobservedasthekeV-
- anactiveflavoroscillatingtoanotheractiveflavor,which scale nuclear recoil signature is difficult to detect. The
p
e can occur at these high ∆m2 values if one or more neu- newest generation of ∼10 keV threshold dark matter de-
h trino mass states with m ,... ∼ 1 eV is added to the tectors provides sensitivity to coherent scattering [5] as
4
[ neutrino mass spectrum. The extra mass states are as- the interaction signal is nearly identical to that which is

sumed to participate in neutrino oscillations, and must expected from WIMP interactions.
1
v therefore be small admixtures of weakly-interacting neu- Anactive-to-sterileneutrinooscillationsearchismoti-
5 trinoflavorstates,withtheremainingflavorcomposition vated in Section II. We describe an experimental design
0 being sterile (i.e. non-weakly-interacting). In the case of which makes use of a high intensity pion- and muon-
8 charged current disappearance, the signal is interpreted decay-at-rest (DAR) neutrino source in Section III. The
3 asarisingfromactive-flavorneutrino(e, µ, τ)oscillation coherent scattering process is introduced and the exper-
.
1 to any other neutrino flavor (e, µ, τ, or s, with s being imental design is discussed in Section IV. Sensitivities
0 the sterile flavor). to neutrino oscillations at ∆m2 ∼ 1 eV2 are shown in
2 Theoscillationprobabilitiesforappearanceanddisap- Section V.
1
pearancethroughchargedcurrentsearchesareexpressed
:
v asfunctionsoftheactiveflavorcontentoftheextramass
Xi eigenstate(s) [1, 2]. In this paper, we assume that only II. MOTIVATION FOR AN
one such extra mass state, m4, exists. In that case, the ACTIVE-TO-STERILE OSCILLATION SEARCH
r
a oscillation probabilities are given by
P(ν →ν )=4|U |2|U |2sin2(1.27∆m2 L/E) A decade ago, sterile neutrino oscillation models were
α β(cid:54)=α α4 β4 41 largely motivated by the LSND anomaly [1, 6–9]. This
(1)
resultpresenteda3.8σexcessofν¯ eventsconsistentwith
in the case of active appearance searches, and e
ν¯ →ν¯ oscillations described by Eq. 1 at ∆m2 ∼1 eV2
µ e
P(να →ν(cid:54)α)=4|Uα4|2(1−|Uα4|2)sin2(1.27∆m241L/E) and sin22θµe =4|Ue4|2|Uµ4|2 ∼0.003. The apparent ap-
(2) pearance signal is thus interpreted as indirect evidence
inthecaseofactivedisappearancesearches,whereα,β = for at least one additional neutrino carrying the ability
e,µ,τ; (cid:54)α corresponds to all flavors other than α, includ- to mix with active flavors. Being mostly sterile, an ad-
ing active and sterile; |U |2 corresponds to the α-flavor ditional neutrino avoids conflict with measurements of
α4
contentofthefourthmasseigenstate;andLandE repre- theZ invisiblewidth[10](characteristicofthreeweakly-
senttheneutrinotraveldistanceandenergy,respectively. interacting light neutrino states) and the three-neutrino
Note that neither search case is purely sensitive to the oscillation model established by solar [11–13] and atmo-
sterile neutrino content of the extra neutrino mass state, spheric/accelerator [14–17] experiments.
|U |2. Inthispaper,wediscussastrictlyneutralcurrent The LSND signal was not present in a similar but less
s4
2
sensitiveν¯ →ν¯ oscillationsearchbytheKARMENex- III. THE NEUTRINO SOURCE
µ e
periment [18]. More recently, however, the MiniBooNE
experiment[19]hasexploredthe∆m2 ∼1eV2parameter A DAR neutrino source can be employed to search for
space and yielded a number of interesting results. Mini- active-to-sterileneutrinooscillationsthroughtheneutral
BooNEfeaturesahigherbeamenergyandlargerdistance current coherent scattering interaction. DAR neutrinos
than LSND but preserves the L/E oscillation probabil- have been identified as an excellent source for neutrino-
ity dependence, allowing for an independent cross check nucleus coherent scattering studies [31–33] because the
of the signal. In searching for νe appearance in a pure neutrinosareproducedinanenergyregion(<52.8MeV)
νµ beam, MiniBooNE has excluded νµ → νe oscillations where the coherent neutrino scattering cross section is
in the LSND ∆m2 range at the 90% CL [20]. However, higher than all others by about one order of magnitude.
MiniBooNE’s search for ν¯µ → ν¯e oscillations in “anti- A search for active-to-sterile oscillations is envisioned
neutrino-mode”isonlyconsistentwiththenooscillation with a series of measurements at different values of L
hypothesis at the 0.5% level [21]. The anti-neutrino re- from the DAR source. In our design, a cyclotron directs
sult is consistent with LSND and ν¯µ →ν¯e oscillations in a proton beam to two graphite targets embedded in a
the ∆m2 = 0.1−1.0 eV2 range. The statistics-limited single iron shield. As the DAR neutrino flavor content
measurementisexpectedtoimprovewithadditionaldata andenergydistributionisdrivenbytheweakinteraction,
being taken through at least 2012. the well understood flux emitted isotropically from each
targetwillbeeffectivelyidentical,barringoscillations,at
Recently, further results for ν¯ disappearance at high
e each baseline L.
∆m2havebeenreportedfromshort-baselinereactoranti-
As discussed in Ref. [5], an ideal neutrino interaction
neutrino experiments. More specifically, a re-analysis of
targetforaDARsourceisadirectdarkmatterdetection
theanti-neutrinospectraproducedbyfissionproductsin
devicesensitivetokeV-scalenuclearrecoils. Weconsider
areactorcore[22]hasledtoaneffecttermed“thereactor
two dark matter detector technologies; a germanium-
anti-neutrino anomaly”, where the ratio of the observed
basedCDMS-styledetector[34]andaliquidargon-based
anti-neutrino rate to the predicted rate deviates below
onesimilartotheCLEAN[35]andCLEAR[33]designs.
unity at 98.6% CL [23]. This can be interpreted as dis-
appearance according to Eq. 2, where charged current
interactions of active flavors other than e are kinemati- A. About decay-at-rest sources
cally forbidden, and/or where the oscillation was into a
non-interacting sterile neutrino. Assuming CPT conser-
IntheDARsourcedescribedhere,neutrinoproduction
vation,whichrequiresthatEq.2holdsforbothneutrinos
begins with 800 MeV protons impinging on a target to
and anti-neutrinos, the strongest limits on ν¯ disappear-
e produce low energy charged pions primarily through the
ance come from a joint analysis of KARMEN and LSND
∆ resonance decay. The pion decay chain π+ → µ+ν ,
ν +12C → 12N +e− scattering events, analyzed for µ
e gs µ+ →e+ν¯ ν ,producestheneutrinofluxshowninFig.1.
evidence of ν disappearance [24]. The reactor-anomaly µ e
e The ν¯ content that arises from π− production and sub-
signalisfoundtobemarginallyconsistentwiththeKAR- e
sequent decay-in-flight (DIF) is well below 10−3 [6, 18]
MEN and LSND ν disappearance results.
e due to π− capture. These features provide an ideal
source for neutrino appearance searches [6, 18, 36, 37],
The above experiments feature a single source, sin-
active-to-sterile searches relying on the charged current
gle detector design. An alternative approach is a near-
interaction [24], and an active-to-sterile neutral current
far detector configuration, where the measured flux in
search [38] as discussed in this paper.
the near detector replaces the first-principles flux pre-
diction. A near-far design removes a significant source
of uncertainty due to the flux prediction, especially if
B. Targeting to allow multiple baselines
the detectors are built to be nearly identical. Using the
near-far technique, the CDHS [25], CCFR [26], and Sci-
BooNE/MiniBooNE [27] experiments have probed neu- A high intensity source of 800 MeV protons is being
trino disappearance at ∆m2 ∼ 1 eV2 using ν charged developed by the DAEδALUS collaboration [37]. This
µ
currentinteractions. Amongtherecentnear-farcompar- design utilizes cyclotron-based accelerators [39, 40] in-
ison data sets, the MINOS experiment has set the only stalledatthreesitesnearaverylargewater-oroil-based
limits on active-to-sterile oscillations using neutral cur- detector. The experiment described here could use one
rent interactions [28]. The resulting limits using both of these DAEδALUS cyclotrons combined with a dual-
charged current and neutral current interactions present target configuration as a neutrino source.
a challenge in fitting sterile neutrino oscillation mod- In a baseline scenario, the cyclotron-based beam will
els [29]. bedivertedbetweenthetwotargetssothatnotargetre-
ceives more than 1 MW average power. The beam will
Theaforementionedresultsunderscoretheexperimen- be directed at 90◦ with respect to the detector, so as to
tal and theoretical need for acquiring further data in ad- minimize DIF backgrounds. Notably, a multi-target de-
dressing the possibility of sterile neutrinos [30]. sign can also be exploited for a charged current neutrino
3
interaction oscillation measurement with a common de- the number of neutrons, number of protons, and weak
tector and multiple baselines. The main technical issue mixingangle,respectively];M isthenucleartargetmass;
in the two-target cyclotron design is maintaining a good T is the nuclear recoil energy; and E is the incoming
ν
vacuum in the two-prong extraction line. The beam will neutrino energy. The ∼5% cross section uncertainty, the
be “painted” across the face of each target in order to actual value depending on the particular nuclear target
prevent hot spots in the graphite, an effect which will employed, is dominated by the form factor [42].
dominatethe±25cmuncertaintyontheexperimentalL Coherent neutrino scattering is relevant for the under-
from each neutrino source. The targets will be arranged standingoftypeIIsupernovaevolutionandthefuturede-
in a row enveloped within a single iron shield, with the scription of terrestrial supernova neutrino spectra. Mea-
detectorlocated20mdownstreamoftheneartargetand suringthecrosssectionoftheprocessalsoprovidessensi-
40 m downstream of the far target. This configuration tivity to non-standard neutrino interactions (NSI) and a
has been found to provide the best overall sensitivity to sin2θ measurement at low Q [31]. Cross section mea-
W
the LSND allowed region. surements as a function of energy on multiple nuclear
The analysis below exploits the L dependence of neu- targets can allow the cross section dependence on NSI
trino oscillations. Therefore, the flux of protons on each andθ tobeisolatedandunderstood. Asdemonstrated
W
target must be well understood in time; standard proton here, neutrino oscillations can also be cleanly probed us-
beammonitorsallowa0.5%measurementprecision. The ing coherent scattering.
absolute neutrino flux is less important, as sensitivity to Thedifficultyofcoherentneutrinoscatteringdetection
the oscillation signal depends on relative detected rates arisesfromtheextremelylowenergyofthenuclearrecoil
at the various distances. The systematic uncertainty as- signature. For example, a 20 MeV neutrino produces a
sociated with the flux normalization is 10% if there is no maximum recoil energy of about 21 keV when scattering
large water or oil detector available and 1.1% if such a on argon. Both a CDMS-style germanium detector [34]
detectordoesexist[36]. Ahighstatisticsν-electronscat- and a single phase liquid argon detector, such as the one
tering measurement at a large water detector provides a proposed for the CLEAR experiment [33], are consid-
precise determination of the flux normalization. ered in this paper for detecting these low energy events.
Other dark matter style detector technologies, especially
those with ultra-low energy thresholds, can be effective
IV. DETECTING COHERENT NEUTRINO for studying coherent neutrino scattering as well.
SCATTERING
Coherent neutrino-nucleus scattering, in which an in-
A. Experimental Setup
coming neutrino scatters off an entire nucleus via neu-
tral current Z exchange [41], has never been observed
The envisioned experimental setup is consistent with
despite its well predicted and comparatively large stan-
thecurrentDAEδALUSacceleratorproposalandfollows
dard model cross section. The coherent scattering cross
a realistic detector design. A single DAEδALUS cy-
section is
clotron will produce 4×1022 ν/flavor/year running with
dσ G2 (cid:18) MT(cid:19) a duty cycle between 13% and 20% [37, 39]. A duty cy-
= FQ2 M 1− F(Q2)2 , (3)
dT 4π W 2E2 cle of 13% and a physics run exposure of five total years
ν
are assumed here. With baselines of 20 m and 40 m,
where GF is the Fermi constant; QW is the weak charge thebeamtimeexposuredistributionatthetwobaselines
[QW = N − (1 − 4 sin2θW)Z, with N, Z, and θW as is optimal in a 1 : 4 ratio: one cycle to near (20 m),
four cycles to far (40 m). Instantaneous cycling between
targets is important for target cooling and removes sys-
tematics between near and far baselines associated with
0.035 ⌫µ ⌫µ detectorchangesovertime. Theacceleratoranddetector
0.030 location is envisioned inside an adit leading into a sharp
units 0.025L 3ta0k0e,ftinriSseouatthtDheakSoatan.foTrdheRneeseuatrrcinhoFflaucxilintyoramtaHlizoamtieosn-
Arb. 0.020 ⌫e uncertainty at each baseline is conservatively expected
x 0.015H at 1.5%. We assume the flux has been constrained to
u
Fl 0.010 this level by an independent measurement of ν-electron
scattering with a large water-based Cerenkov detector
0.005
also assumed to be in operation at Sanford Labs. The
0.000 1.5% uncertainty estimate takes into consideration the
0 10 20 30 40 50
theoretical uncertainty in the ν-electron scattering cross
NeutrinoEnergy MeV
section and the statistics achievable with a large water
FIG.1: EnergydistributionofneutrinosfromaDARsource. detector. The flux normalization correlation coefficient
H L between the near and far baselines is conservatively set
4
ν source 4×1022 ν/flavor/year matter searches [44]. The detection efficiency above a
Dutyfactor 13%
10 keV threshold is set to 0.67 with a 3% energy reso-
Baselinecorrelation 0.99
lution near the threshold. These assumptions are rea-
ν fluxnorm. uncertainty 1.5%
Uncorr. sys. uncertainty 0.5% sonablyconservativeandconsistentwithfutureexpecta-
Distancesfromν source 20m,40m tions [45, 46].
Exposure 5years: 1near,4far Two classes of background events are considered for a
Depth 300ft
germanium detector:
TABLE I: The experimental configuration assumptions.
1. Misidentified electronic recoils - Electronic recoils
can be produced by photons and beta parti-
cles interacting with the active detection medium.
Misidentification of such events is particularly
to 0.99, its deviation from unity being dominated by dif-
problematic near the detector surfaces, where
ferences between the two beam dumps. An uncorrelated
the collection of electron-hole pairs is suppressed
systematic uncertainty of 0.5% at each baseline, is also
and discrimination is less effective. Existing ex-
included. The general experimental assumptions can be
periments have demonstrated an electronic recoil
seen in Table I.
misidentification rate of less than 1 event per
Wealsoconsidera“dedicated”physicsrunscenarioin
100 kg·days exposure [34]. Upgrades to detector
which the duty factor is raised from 13% to 50% for all
designareexpectedtoimprovediscriminationbya
five years. With the instantaneous power achievable re-
factor of 104 [46]. The assumed rate of radiogenic
maining constant, this change leads to an average power
background detection (∼2 events/year) is negligi-
increase of a factor of 4. Steady-state and beam-related
ble.
backgrounds also increase by this factor in a dedicated
scenario. The nominal duty factor of 13% is driven by
2. Cosmogenic neutrons - Single scatter neutrons can
therequirementthatthevariousDAEdALUSaccelerator
produce a signal identical to a coherent neutrino
baseline beam windows do not overlap in time. A dedi-
scatteringevent,andtherateoftheseeventswould
catedscenarioispossibleinconsiderationofmaintaining
be significant at a shallow site. As a point of ref-
sufficient target cooling and the phased DAEδALUS de-
erence for surface experiments, the CDMS exper-
ployment timeline. The timeline calls for a cyclotron or
iment located at the Stanford Underground Fa-
set of cyclotrons installed exclusively at a single “near”
cility with 16 m.w.e. of overburden measured a
baseline, close to a large water detector, for at least
neutron background of 0.67 events/(kg·day) [47].
five years [37]. With a 13% duty factor only required
This figure could be significantly reduced with
whenallbaselineshaveoperationalaccelerators,alonger
additional active and passive shielding and the
duty factor and higher average power seems possible in
larger overburden envisioned for the DAEδALUS
DAEδALUSsingle-baseline-onlyoperation. Notethatal-
site. A cosmogenic-induced background of 0.1 de-
though only two targets are required for the experimen-
tected events/(10 kg·day), after correcting for effi-
tal design described here, supplementing the beamline
ciencyandduringbeam-on,isassumed. Thisvalue
with more targets can ensure optimal use of beam time
is considered a design goal and can be met with a
in consideration of cooling requirements and ultimately
300 ft overburden and modest active and passive
increase neutrino oscillation sensitivity.
shielding.
Inthisstudy,theestimatedradiogenicandcosmogenic
1. Germanium detector – signal and backgrounds background rates are distributed evenly across the ger-
manium nuclear recoil energy range considered, 10 keV
A low-threshold germanium-based detector, such as to 100 keV.
CDMS,measuresphononsandionizationfromelectronic
and nuclear recoils [43]. A CDMS detector consists of a
large germanium crystal (0.25−1 kg) operated at cryo- 2. Liquid argon detector – signal and backgrounds
genictemperatures(∼100mK)withthousandsofsuper-
conducting transition-edge sensors (TESs) photolitho- Asinglephaseliquidargondetectorcanbeusedtode-
graphically patterned on the top and bottom surfaces. tectthescintillationlightcreatedbyWIMP-orcoherent
TheTESsarewiredinparalleltoformfourreadoutchan- neutrino-induced nuclear recoils. Such detectors employ
nels on each surface, which measure phonons created in alarge,homogeneousliquidargonvolumesurroundedby
particle interactions. The particle-induced ionization is photomultiplier tubes (PMTs). Inner detector surfaces
also measured by electrodes on the crystal surface. The as well as the PMTs themselves are usually covered in a
ratio of the energy in these two channels is a powerful wavelengthshiftingsubstancewhichconvertsthe128nm
discriminator between nuclear and electronic recoils. scintillation light into the visible spectrum for detection.
A 100 kg active mass of germanium is considered for A 456 kg active mass of liquid argon with a flat effi-
the experiment described here, similar to proposed dark ciency of 0.50 above a 30 keV energy threshold is con-
5
sidered for the experiment described here. The detec-
tion volume and efficiency are consistent with the pro-
g105
posed CLEAR design [33]. An 18% energy resolution k Measured (4.85 pe/keVee)
0
ntheaanrtwhrheasthowldouilsdubseed,exapsseucmteidngfrroemsolpuhtiootnoeslleigchtrtolynwPoorisse- ar / 10104 Theoretical (6 pe/keVee)
e
son statistics [48], 6 photoelectrons/keVee light collec- y
tion, and a quenching factor of 0.25 [49]. Vr / 103
e
There are three primary sources of background that s / k102
are considered for a single phase liquid argon detector: nt
e
v
E
1. Cosmogenic neutrons - The muon-induced neu- 10
tron background is contingent on the geometry of
the site, overburden, and active/passive detector 1
shielding. Muon events and muon-induced neu-
tronscanbevetoedwithhighefficiencyandlowde- 10-1
tectordeadtimeinaliquidargondetectornearthe
surface [33]. The target design cosmogenic back- 10-2
20 30 40 50 60 70 80 90 100
ground is 0.1 detected events/(10 kg·day). Recoil energy (keVr)
2. 39Ar contamination - 39Ar is a naturally occurring FIG. 2: The expected 39Ar background energy spectrum un-
der two sets of assumptions. The line labeled “Measured”
radioisotopewithanisotopicabundanceof39Ar/Ar
corresponds to an ERC that was obtained in a detector with
=8×10−16, corresponding to a specific activity of
4.85 photoelectrons/keVee. The line labeled “Theoretical”
1.01Bq/kg[50]. Theisotopeisabetaemitterwith
is the ERC simulated in an ideal detector with 6 photoelec-
an energy endpoint of 565 keV.
trons/keVeeandrepresentsthebackgroundERCusedforthis
Pulse-shape discrimination (PSD) can be used to study. Bothlinescorrespondtoa50%efficiencyfordetecting
separate the 39Ar-induced electronic recoils from nuclear recoils in the fiducial volume.
the nuclear recoils produced in WIMP and coher-
ent neutrino scattering events [51]. The electronic
recoil contamination (ERC) of the nuclear recoils tector surface area to yield 1.3×104 events/year.
decreases exponentially as the number of photo- However, this rate may be substantially reduced
electrons detected increases. Reference [52] mea- by the use of cleaner materials, scrubbing of the
sures the ERC for PSD in the single phase liq- surface, and fiducialization. A surface background
uid argon DEAP-1 detector (4.85 photoelectrons contamination of 100 detected events/year is as-
perkeVee)andalsoprovidesa“theoretical”Monte sumed here and can be considered a design goal.
Carlo estimate of the ERC attainable for an ideal
The 30 keV energy threshold employed here is larger
detector with 4π PMT coverage and 6 photoelec-
than the oft-chosen 20 keV threshold in single phase liq-
trons/keVee. Both scenarios correspond to a 50%
uidargondetectorsinordertomitigatethesteeplyfalling
efficiencyfornuclearrecoildetectioninthefiducial
39Ar contamination. If 39Ar discrimination improves in
volume. Note that, according to Ref. [53], the Mi-
a future design, adjusting the threshold to (e.g.) 20 keV
croCLEAN experiment has achieved 6 photoelec-
trons/keVee sensitivity. The abundant 39Ar back- wouldallowa60%largersignalsample. Inthisstudy,the
estimated surface and cosmogenic background rates are
ground could further be alleviated with the use of
distributed evenly across the argon nucleus recoil energy
depleted argon from underground sources, which
has an isotopic abundance of 39Ar that is <5% of range considered, 30 keV to 200 keV.
One additional possibility that would significantly re-
natural argon at the surface [54]. Figure 2 shows
the rate of 39Ar after PSD with 13% on-time, for ducethenon-beam-relatedbackgroundwouldbetousea
pulsedsourceofneutrinos,suchasattheSpallationNeu-
twoassumptionsofERCreportedinRef.[52]. The
tron Source (SNS). The SNS produces protons in very
theoretical ERC with non-depleted liquid argon is
short bunches of <750 nsec at a rate of about 60 Hz,
employed for this study.
so that the time window for expected signal events is a
3. Surface contamination - Radioactive impurities on small fraction of the total running time. Combining a
the detector surfaces can decay and contribute to pulsedDARbeamstructurewithaliquidargondetector
the background. These surface backgrounds have waspreviouslyproposedbytheCLEARexperiment[33],
been measured in the DEAP-1 detector and were allowingthemtoclaimanadditionalrejectionof6×10−4
foundtohaveanactivityof1.3×10−4 Bq[55]. De- for steady-state, non-beam-related backgrounds using a
pending on the origin of these events, the scaling timingcut. AlthoughtheDAEδALUSproposaldoesnot
and resulting background prediction can differ. If include this timing structure, the experimental concept
theeventsaredueexclusivelyto210Pbsurfacecon- described here could be employed at other facilities.
tamination,theDEAP-1figurecanbescaledbyde- The detector-specific assumptions are summarized in
6
76Ge 40Ar tector far enough from the source that the beam-related
Activemass 100kg 456kg neutron flux is negligible.
Efficiency 0.67(flat) 0.50(flat)
A precise estimate of the neutron flux would require
Threshold 10keV 30keV
∆E atthreshold 3% 18% detailed knowledge of the experimental site, beam con-
E
Radiogenicbackground 2/year Seetext figuration, and shielding. The neutron flux is estimated
Cosmogenicbackground 0.1/(10kg·day) 0.1/(10kg·day) withaMonteCarlosimulationoftheexperimentalgeom-
Beam-relatedbackground 0/year 0/year etry consistent with the DAEδALUS proposal [37] and
several simplifying assumptions. Instead of simulating
TABLEII:Theassumptionsrelevantforthespecificdetector
the passage of neutrons through the beam dump shield-
technologies considered.
ing, we simply assume that a cubic shield with sides of
length 6 m is sufficient to reduce the escaping neutron
flux to a level consistent with safety regulations. Also,
Table II and the expected signal and background rates we assume that this cube of shielding is adjacent to a
are shown in Fig. 3. rock (SiO2) cliff. The maximum permissible annual dose
for workers in a restricted area with a neutron beam is
100 mRem [56]. The neutron flux escaping the shielding
is set to a rate equivalent to an exposure of 100 mRem
kg Ge coherent signal in 40 hours.
ar/100 102 GAArre cbboaahcckekgrgerrnootuu snniddgnal jecUtesdingatatGheeaendtg4e-boafsetdhesimshuielaldtiinong [c5u7b],en.eTuthreonnseaurteroinns-
e
y are simulated in energy bins from 0-30 MeV. The flux
eVr/ 10 is tallied at 20 cm intervals into the rock cliff, and the
k
s/ fluxes beyond 1 m into the cliff are fit to the functional
nt
eve 1 form
d
cte Ae−z/λ
Dete10-1 Φ(z)= z2 , (4)
where A and λ are fit parameters, and z is the distance
10-2 from each flux tally point to the DAR source. The neu-
tron fluxes are in reasonable agreement with this func-
10-3 tional form. The fit function is then used to extrapolate
0 20 40 60 80 100 120 140 160 180 200 thefluxtoafullyearofrunningandlargerdistancesfrom
Recoil energy (keVr) thesource. Asimulationisalsoemployedtoestimatethe
FIG. 3: The expected non-oscillated signal and total back- fraction of incident neutrons that produce single-scatter
ground rates at a 20 m baseline for the two detector tech- nuclear recoils in the detection volume. Less than 0.2
nologies considered in the baseline physics run scenario. The beam-related events are expected per year for a 456 kg
ratescorrespondtowhatisexpectedforonefullyearofnear- liquid argon detector at a 12 m baseline. The beam-
target-only operation at 13% duty factor. relatedbackgroundat20mfromthesource,theshortest
relevant detector baseline considered here, is therefore
assumed to be negligible.
3. Neutron flux from the source V. MEASUREMENT STRATEGY AND
SENSITIVITY
DAR sources produce a large flux of neutrons, aris-
ing from spallation reactions of protons with the beam A. Overall strategy
dump material. For the DAR source considered here,
the neutrons have energies up to 800 MeV. In a 1 MW Neutrinooscillationsdependuponneutrinoenergyand
beam, the neutron production rate is ∼1016/s and at- distance traveled. Since the neutrino energy cannot be
tenuation lengths may be as high as tens of centimeters. reconstructedpreciselywiththecoherentinteraction,our
Single scatter neutrons can produce elastic recoils in the sensitivity to the oscillatory behavior arises mainly from
detectorvolumethatareindistinguishablefromcoherent L,avaluewhichiswelldeterminedbythelocationofthe
neutrino scattering on an event-by-event basis. More- target being used at any given time and its distance to
over, because the neutron flux is attenuated by matter, the common detector. In the case that a disappearance
underestimating the neutron background in the detec- signal is detected, the target exposure priorities for the
torcouldmimicadeviationfromthe1/r2-dependenceof two baselines can be optimized to maximize sensitivity.
theneutrinoflux,similartowhatisexpectedforneutrino The purely neutral current experiment described is
disappearance. It is therefore essential to locate the de- sensitive to the effective disappearance of all three types
7
of neutrinos present in the beam, ν , ν¯ , and ν , into tween the two baselines and different recoil energy bins.
µ µ e
ν . We assume this disappearance can be approximated NotethatthebackgroundcontributionstoP andN can-
s i i
by a two-neutrino oscillation driven by a ∆m2 in the cel. The background-contributed statistical uncertainty,
LSND allowed region, and that the oscillation proba- however,isaccountedforinM . Thebackgroundcontri-
ij
bility under the approximation is the same for neutri- butioncanbemeasuredwithhighstatisticsduringbeam-
nos and anti-neutrinos. The baselines for the experi- offcycles,andsosystematicuncertaintiesassociatedwith
ment, 20 m and 40 m, have been chosen in order to backgroundaresmallrelativetostatisticaluncertainties.
provide the best sensitivity to the LSND allowed param- The oscillations-predicted spectra, P , are obtained by
i
eter space, given the neutrino energy spectrum of each summingoverallneutrinoflavorspredictedineachrecoil
flavor in the beam. The experiment described here pro- energybinoftheunoscillatedspectrum,andreweighting
vides indirect sensitivity to the LSND allowed param- each neutrino according to its flavor α = e,µ by the
eter space by simultaneously measuring terms describ- following “active” survival probability
ing the amplitude of active neutrino mixing to a sterile
neutrino: 4|Ue4|2|Us4|2 in the case of νe in the beam, P(να →νactive) = 1−P(να →νs)
and 4|Uµ4|2|Us4|2 in the case of νµ and ν¯µ in the beam. = 1−sin22θαssin2(1.27∆m2L/E)(,6)
These terms are then translated to the appearance am-
plitude measured by LSND, sin22θµe = 4|Ue4|2|Uµ4|2. where νactive can be any active state including να, and
Sensitivity to sin22θ , along with simultaneous sensi- sin22θ = 4|U |2|U |2. By unitarity assumptions,
µe αs α4 s4
tivity to sin22θee = 4|Ue4|2(1−|Ue4|2) and sin22θµµ = |Us4|2 is a function of (cid:80)α=e,µ,τ|Uα4|2,
4|U |2(1−|U |2), are considered the figures of merit
µ4 µ4
(cid:88)
here, as they can be easily compared to existing charged |U |2 =1− |U |2 . (7)
s4 α4
current appearance and disappearance measurements.
α=e,µ,τ
Of course, distinguishing between sin22θ and sin22θ
ee µµ
in the case of an observed disappearance is not possi- During the fit, we vary |U |, |U |, and ∆m2. For sim-
e4 µ4
ble in a flavor-blind experiment. Therefore, we rely on plicity, however, we assume |U | = 0. Note that a non-
τ4
marginalizing over the full parameter space of |Uµ4| and zero |Uτ4| would increase the active survival probability
|Ue4| explored, in the most conservative case possible, for any given |Ue4| and |Uµ4|, and would therefore make
when drawing sensitivity contours for each case. this search slightly less sensitive to oscillations in terms
The sensitivity to any particular set of oscillation pa- of sin22θ . On the other hand, if non-zero |U | and
µe e4
rameters is obtained by simultaneously fitting the ex- |U |weretobeestablishedindependentlybyothershort
µ4
pected flavor-summed coherent signal events as a func- baseline experiments, the type of neutral current search
tion of recoil energy at the near and far baselines. The outlined in this paper may offer sensitivity to U , de-
τ4
eventsateachbaselinearedistributedamongbinsofnu- pending on the sizes of |U |, |U | and |U |.
e4 µ4 τ4
clear recoil energy (1 bin/10 keV); however, the sensitiv- Figures 4, 5 and 6 show the expected sensitivity to
ity results are largely insensitive to the number of recoil the LSND allowed region with a germanium detector in
energy bins used in the comparison. the baseline and dedicated physics run scenarios and an
argon detector in the baseline scenario, respectively. In
obtaining the sensitivity curves, the 3D search grid is
B. Sensitivities reduced from (∆m2, |U |2, |U |2) to a 2D space of
e4 µ4
∆m2 and sin22θ = 4|U |2|U |2. Note that a non-
µe e4 µ4
The signal predictions are evaluated for each set of os- zero sin22θ requires both ν and ν disappearance.
µe e µ
cillation parameters, ∆m241 ≡ ∆m2, |Uµ4|, and |Ue4|. A The sin22θµe sensitivity curves are obtained using a
χ2 is calculated by comparing the oscillations-predicted raster scan in ∆m2 space. That is, each curve maps out
spectra, including backgrounds, to the no-oscillations the maximum sin22θ = 4|U |2|U |2 which satisfies
µe e4 µ4
prediction. χ2 ≤ ∆χ2 at a given confidence level, for each point
The χ2 is constructed as in ∆m2. Tcuhte 90%, 99%, and 3σ confidence level curves
shown in this paper correspond to ∆χ2 =1.64, 6.63,
χ2 =N(cid:88)bins(P −N )(P −N )M−1 , (5) and 9.00 for a one degree of freedom, counte-sided raster
i i j j ij scan(90%),andaonedegreeoffreedom,two-sidedraster
i,j=1
scan (99% and 3σ), respectively.
where i and j denote the energy bins at the near and Figure 7 shows the oscillation sensitivity for a germa-
farbaselines,respectively;P istheoscillations-predicted nium detector in terms of the disappearance amplitudes
i
eventspectrumasafunctionofN =1,...,10,11,...,20 which would be accessible in charged current searches,
bins
bins, corresponding to (e.g.) 10 energy bins for the two sin22θ =4|U |2(1−|U |2)andsin22θ =4|U |2(1−
ee e4 e4 µµ µ4
baselines appended side by side; N is the correspond- |U |2) overlaid with the region allowed by LSND at
i µ4
ing no-oscillations spectrum; and M−1 is the inverse co- 90% CL, assuming the LSND best-fit ∆m2 = 1.2 eV2.
ij
variance matrix including statistical and systematic un- The curves are obtained using a one-sided raster scan
certaintiesandnormalizationsystematiccorrelationsbe- in sin22θ with the ∆χ2 values defined above. The
ee cut
8
4) 4)
c c
2/V 2/V
e e
2| (m 2| (m
10 10
D| D|
1 1
90% CL sensitivity 90% CL sensitivity
99% CL sensitivity 99% CL sensitivity
3s CL sensitivity 3s CL sensitivity
LSND best fit LSND best fit
10-1 10-1
LSND 90% CL LSND 90% CL
10-4 10-3 10-2 10-1 10-4 10-3 10-2 10-1
sin2(2q ) sin2(2q )
m e m e
FIG. 4: Sensitivity to the LSND 90% CL allowed parameter FIG. 6: Sensitivity to the LSND 90% CL allowed parameter
space with a germanium-based detector under the baseline spacewithanargon-baseddetectorunderthebaselinephysics
physics run scenario. run scenario.
current oscillation search correspond to sin22θ < 0.1
µµ
at 90% CL, for ∆m2 =1.2 eV2 [28].
4) Figures 4 and 6 show that, despite the difference in
c
2/V fiducial mass, the 100 kg germanium detector performs
e
2| (m slightly better than the 456 kg liquid argon one. The
10 difference is in part due to the difference in nuclear re-
D|
coil energy threshold; 10 keV for germanium, 30 keV
for argon. This emphasizes the fact that a low detec-
tor energy threshold is important for obtaining a high-
statistics sample of coherent neutrino scattering events
as the rate is dominated by events with very low energy
1
recoils ((cid:46)10 keV).
In a baseline physics run scenario, an experiment fea-
90% CL sensitivity turingagermanium-orargon-baseddetectorcanexclude
99% CL sensitivity the LSND best-fit mass splitting (∆m2 = 1.2 eV2) at
3s CL sensitivity
3.8σ or3.4σ,respectively. TheLSNDbest-fitmasssplit-
LSND best fit
10-1 LSND 90% CL ting is excluded at 4.8σ in the dedicated, germanium-
based physics run scenario considered. For sensitivity in
10-4 10-3 10-2 10-1 terms of sin22θee and sin22θµµ, a germanium-based ex-
sin2(2q m e) perimentinthebaselinescenariocouldexcludenearlyall
FIG. 5: Sensitivity to the LSND 90% CL allowed parameter oftheavailable90%CLLSNDparameterspaceatthe3σ
space with a germanium-based detector under the dedicated level and large portions of the available reactor anomaly
physics run scenario. allowed region, assuming ∆m2 ∼1.2 eV2.
VI. CONCLUSIONS
figure also shows the approximate region of sin22θ val-
ee
ues allowed at 90% CL by fits to the reactor anomaly This paper has described a method to search for
andgalliumexperimentcalibrationdatasetsinRef.[23]. active-to-sterile neutrino oscillations at relatively short
The “reactor” allowed contour is for ∆m2 (cid:38)1.5 eV2 and baselinesusingneutralcurrentcoherentneutrino-nucleus
is relatively independent of ∆m2 in this region. As a scattering. Detection of such a process could definitively
reference, limits on sin22θ from the MINOS neutral- establish the existence of sterile neutrinos and measure
µµ
9
their mixing parameters.
An experiment that relies on the high statistics de-
)ee1 9900%% CCLL sseennssiittiivviittyy,, DD mm22==11..22 eeVV22 tection of an as-yet-undetected process is obviously dif-
q2 33ss CCLL sseennssiittiivviittyy,, DD mm22==11..22 eeVV22 ficult. However, all of the technology required for such
2(sin LRLRSSeeNaNaccDDtt oo99rr00 99%%00 %%CCLL CC,, LLDD ,,mm DD 22mm==2211>>..2211 ..ee55VV ee22VV22 an experiment either exists or has been proposed with
realistic assumptions. A cyclotron-based proton beam
can be directed to a set of targets, producing a low en-
ergyneutrinosourcewithmultiplebaselines. Thisallows
a measurement of the distance dependence of an oscil-
lation signal without moving detectors or instrumenting
10-1 multiple devices. Both a germanium-based detector in-
spired by the CDMS design and a liquid argon detector
inspired by the proposed CLEAR experiment would be
effective for performing these measurements.
Along with relevance in understanding Type II super-
nova evolution and supernova neutrino detection, coher-
entneutrino-nucleusscatteringcanprovidesensitivityto
non-standard neutrino interactions, the weak mixing an-
10-1 1 gle, and, as shown in this paper, neutrino oscillations
sin2(2q m m ) at ∆m2 ∼1 eV2. Depending on the detector technology
andrunscenario,theexperimentdescribedissensitiveto
FIG. 7: Sensitivity to disappearance amplitudes accessible
with charged current searches, assuming the LSND best-fit the LSND best-fit mass splitting at the level of 3-5σ and
∆m2 =1.2eV2. Thesensitivitycorrespondstoagermanium- canprobelargeregionsoftheLSNDandreactoranomaly
based detector under the baseline physics run scenario. The allowedregions. Theexperimentoffersapureandunique
LSNDbandrepresentsthe90%CLallowedvaluesofsin22θ analysis of neutrino oscillations that is complementary
µe
at∆m2 =1.2eV2. “Reactor”referstotheresultreportedin to charged current-based appearance and disappearance
Ref. [23] and indicates the range of sin22θee values preferred searches.
by a joint fit to reactor and gallium experiment calibration
measurements. The reactor result is nearly independent of
∆m2, for ∆m2 values near and above 1.5 eV2. Acknowledgments
We thank the National Science Foundation and Depart-
ment of Energy for support.
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