Table Of ContentA New Method to Search for CP violation in the Neutrino Sector
J.M. Conrad1 and M.H. Shaevitz2
1 Massachusetts Institute of Technology and
2 Columbia University
Newlow-cost,high-powerprotoncyclotronsopentheopportunityforanovelprecisionsearchfor
CP violation in the neutrino sector. The accelerators can produce decay-at-rest neutrino beams
located at multiple distances from a Gd-doped ultra-large water Cerenkov detector in order to
searchforCP violationinν¯ →ν¯ atshortbaseline. Thisnewtypeofsearchcomplementspresently
µ e
proposedexperiments,providingmeasurementsthatcouldleadtoasubstantiallybetterexploration
of CP violation in the neutrino sector.
PACSnumbers: 14.60.Pq,14.60.St
0 I. INTRODUCTION Theneutrinosourceswouldbebasedoncommercially-
1 developed,small(2.5mdiameter),high-powerprotoncy-
0
With the discovery of neutrino oscillations, particle clotron accelerators that are under development [7]. A
2
physicists have been inspired to develop theories that 250 MeV, 1 mA cyclotron is under construction at MIT
n explain very light neutrino masses. The most popular and a GeV-energy, megawatt-class cyclotron is presently
a
J models invokes GUT-scale Majorana partners which can underdesign. Wheninproduction,becauseofnew,inex-
decay, producing a matter-antimatter asymmetry in the pensive superconducting technology, these machines are
0
3 early universe through the mechanism of CP violation. expected to cost 5% of a conventional proton accelerator
Observation of CP violation in the light neutrino sector (< $20M). These machines will demonstrate the beam
] would be a strong hint that this theory is correct. physics and engineering needed for this experiment.
x
To incorporate CP violation, the light-neutrino mix- This experiment requires accelerators that target 2
e
- ing matrix is expanded to include a CP violating phase, GeV protons at 2.5 mA during a 100 µs pulse every
p δ . Sensitivitytoδ comesthroughmuon-to-electron 500 µs, delivering 9.4×1022 protons per year to a beam
CP CP
e flavor oscillations at the atmospheric mass-squared dif- stop. The result is a high-intensity, isotropic, decay-at-
h
ference, ∆m2 . The oscillation probability, neglecting rest(DAR)neutrinobeamarisingfromthestoppedpion
[ 31
matter effects, is given by [1]: decay chain: π+ → νµ +µ+ followed by µ+ → e+ν¯µνe.
4 The flux, shown in Fig. 1, has an endpoint of 52.8 MeV.
v P =sin2θ23sin22θ13sin2∆13 Each cyclotron produces 4×1022/flavor/year of ν , ν
9 e µ
∓sinδ sin2θ sin2θ sin2θ andν¯ . Theν¯ fractioninthebeamisverylow(∼10−4)
7 cp 13 23 12 µ e
0 ×sin2∆ sin∆ because most π− are captured before decay.
13 12
4 Thisexperimentutilizesanultra-largewaterCerenkov
+cosδ sin2θ sin2θ sin2θ
. cp 13 23 12 detector such as Hyper-K [8], MEMPHYS [9], or the de-
2
1 ×sin∆13cos∆13sin∆12 tector proposed for the Deep Underground Science and
9 +cos2θ sin22θ sin2∆ , (1) Engineering Laboratory (DUSEL) [10]. We use a 300
23 12 12
0 kton DUSEL detector as our model. Water provides a
v: where ∆ij = ∆m2ijL/4Eν, and −(+) refers to neutrinos target of free protons for the inverse beta decay (IBD)
i (antineutrinos). interaction: ν¯e+p→n+e+.
X In Eq. 1, aside from δ , all but two of the parame-
CP IBDinteractionsareidentifiedviaacoincidencesignal.
r ters (θ13 and the sign of ∆m231) are well known. Further The first signal is from the Cerenkov ring produced by
a
precision on these known parameters is expected in the
the positron. The second signal is from capture of the
near future (see Table I). With respect to θ , global fits
13 neutron. The signal from neutron capture on protons,
report a non-zero value at the ∼1σ level [2, 3]. This pa-
which produces only a single 2.2 MeV γ, is too feeble to
rameter drives the amplitude for the CP violating terms
inEq.1andthereforesetstheleveloftechnicaldifficulty
for observing CP violation. The unknown sign of ∆m2 ,
31
referred to as “the mass hierarchy,” affects the sign of
term 3 in Eq. 1. Matter effects modify Eq. 1 and are
sensitive to the mass hierarchy.
We propose a new method to search for CP violation
bycomparingabsoluteneutrinoratesinasingledetector
that is illuminated by neutrino beam sources at multiple
distances. This method explores the δ dependence
CP
inherentinEq.1inadifferentwayandwithcomparable
precision than the planned long-baseline program. FIG. 1: Energy distribution of neutrinos in a DAR beam
2
Parameter Present: Assumed Future:
Value Uncert. Ref. Value Uncert. Ref.
(±) (±)
∆m2 ×10−5eV2 7.65 0.23 [2] 7.65 — —
21
∆m2 ×10−3eV2 2.40 0.12 [2] 2.40 0.02 [4]
31
sin2(2θ ) 0.846 0.033 [2] 0.846 — —
12
sin2(2θ ) 1.00 0.02 [2] 1.00 0.005 [5]
23
sin2(2θ ) 0.06 0.04 [3] 0.05 0.005 [6]
13
TABLE I: Left: Present values and uncertainties for oscilla-
tion parameters, reported in the references. Right: Future
expectations used in this study.
FIG. 2: Proposed experimental layout. Each phase corre-
sponds to a 5-year data-taking period with each of the three
source sites on for 20% of the time. (Phase 2 is an example;
termined. As an example for phase 2, we have chosen a
thenumberofcyclotronswillbeoptimizedbasedonPhase1
measurements.) design with one, two and seven accelerators. This design
matches the sensitivity of a run of LBNE with 30×1020
protonsontargetinneutrinomodefollowedby30×1020
protons on target in antineutrino mode [10].
be efficiently observed in a large Cerenkov detector. For
that reason, doping with gadolinium (Gd), which has a This design is unique among proposals for CP viola-
high capture rate and a short capture time, is proposed tion searches and complementary to the present plans
[11]. Neutron capture on Gd produces multiple photons [6, 10]. The measurement is done with antineutrinos,
totaling ∼8 MeV which can be observed with 67% ef- whileallexistingproposalsrelyheavilyonneutrinodata.
ficiency [12]. Gd-doping of water is under development The neutrino production systematics are different and
[13]. In IBD events, the energy of the neutrino is related well-controlled. Because of the low energy, the inter-
to the energy of the positron and kinetic energy of the action systematics are also different. Varying L, while
neutron, K, by E =E +(M −M )+K [14]. employing a single detector is novel and reduces system-
ν e+ n p
atics. A two-phase program which allows an optimized
Theacceleratorsareplacedatthreeseparatebaselines,
measurement strategy is powerful and potentially cost-
L, for the ν¯ → ν¯ search (see Fig. 2). Each set of ac-
µ e
saving.
celerators at the three sites runs for a 20% duty factor
interspersedintime; theother40%ofthetimeisusedto
collectbeam-offdata. ThelongestbaselineisL=20km,
where ∼40 MeV ν¯ are at oscillation maximum for the II. EVENT TYPES AND BACKGROUNDS
µ
measured value of ∆m2 . In this case, term 2 of Eq. 1
31
will contribute while term 3 will not. A mid-baseline ac- The energy range of the analysis is 20 < E < 55
ν
celerator site is located at L = 8 km, where term 3 of MeV. The lower cut renders potential backgrounds from
Eq. 1 is non-zero. The shortest baseline accelerator site radioactive decay and spallation negligible. The upper
is at L =1.5 km, directly above the DUSEL detector. cut is chosen because of the 52.8 MeV signal endpoint.
At this location, the neutrino-electron elastic scattering In this energy range, three types of interactions must
ratesaresufficienttoallowprecisionmeasurementofthe beconsidered. FirstistheIBDsignal,withanestimated
neutrino flux normalization as discussed below. We pro- reconstruction efficiency of (cid:15) =67%, based on stud-
recon
pose multiple accelerators at the various locations (see iesforSuper-K[12]. Secondisν +O→e−+F(“ν O”),
e e
Fig. 2), which is feasible because of the low cost per ma- with a suppressed cross section relative to IBD due to
chine. For the L of a given event to be well-determined, nuclear effects [16, 17] and no neutron capture. Third
the beams from each location are staggered in time. is neutrino-electron elastic scattering (ν ES) ν +e− →
e e
Term 3 of Eq. 1 leads to an inherent ambiguity be- ν + e−. This is separable from ν O by angular cuts
e e
tween δ and the mass hierarchy. We assume that on [18, 19] and, so, can be used for the flux normalization.
CP
the timescale of the measurements presented here, the Forν Oandν ESevents, weestimate(cid:15) =75%[18].
e e recon
mass hierarchy will be measured using LBNE[10] or at- Beam-off backgrounds arise from three sources: atmo-
mospheric neutrino measurements.[15]. For the sensitiv- spheric ν p scatters with muons below Cerenkov thresh-
µ
ity estimates, we choose the normal hierarchy as the ex- old which stop and decay (“invisible muons”), atmo-
ample model. spheric IBD events, and diffuse supernova neutrinos.
We present a two-phase experiment, where the design These are all examples of correlated backgrounds; acci-
has flexibility in the second phase. In our case, each dentalbeam-offbackgroundsareestimatedtobenegligi-
phase represents five years. The first phase explores the ble. Theratesofthesecorrelatedbackgroundsarescaled
oscillation space at ∼3σ and requires one accelerator at fromanalysesfortheGADZOOKSexperiment[11]. The
the near location, two at the mid-location and three at interaction rates of the beam-off backgrounds are well-
thefarlocation. OnceasignalforCP violationhasbeen measured during the 40% beam-off running fraction.
localized, the strategy for the second phase can be de- The beam-on backgrounds have both accidental and
3
Event Type 1.5 km 8 km 20 km
IBD Oscillation Events (E >20 MeV)
ν
δ =00, Normal Hierarchy 763 1270 1215
CP 180
” , Inverted Hierarchy 452 820 1179
δ =900, Normal Hierarchy 628 1220 1625
CP 120
” , Inverted Hierarchy 628 1220 1642
δ =1800, Normal Hierarchy 452 818 1169
CP 60
” , Inverted Hierarchy 764 1272 1225
δ =2700, Normal Hierarchy 588 870 756
CP ” , Inverted Hierarchy 588 870 766 δCP 0
IBD from Intrinsic ν (E >20 MeV) 600 42 17
e ν 3 sigma Phase I
IBD Non-Beam (Eν >20 MeV) -60 5 sigma
atmospheric νµp “invisible muons” 270 270 270 3 sigma Phase II
atmospheric IBD 55 55 55 -120 5 sigma
diffuse SN neutrinos 23 23 23
ν −e Elastic (E >10 MeV) 16750 1178 470 -180
e ν
ν −Oxygen (E >20 MeV) 101218 7116 2840 0.0001 0.001 0.01 0.1
e ν
sin2(2θ )
13
TABLEII:Eventsamplesforthecombinedtwo-phaserunfor
sin22θ =0.05 and parameters from Table I (future).
13
FIG. 3: Phase 1 and Combined-phase sensitivity to θ (cid:54)= 0
13
at 3σ and 5σ.
correlated sources. The accidental backgrounds arise
fromtheν inthebeamwhicharefollowedbyaneutron-
e
likeevent. Thisbackgroundisestimatedtobeverysmall
using the measurements from the Super-K Gd-doping
study[12]. Correlated backgrounds are produced by the
intrinsicν¯ contentofthebeam. Thisisreducedbycare-
e
fuldesignofthebeamstop. Weassumealongwatertar-
get embedded in a copper absorber, surrounded by steel
foreachcyclotron. Wetargetat100degreesfromthede-
tector to reduce decay-in-flight (DIF) backgrounds. For
2 GeV protons on target, the pion yields, π+/p (π−/p),
are 0.43 (0.056). with a π+ (π−) DIF fraction of 0.017
(0.025). Thedecaysofµ−’sarefurtherreducedbyafac-
tor of 8.3 since the µ− will be captured before decaying.
The compact design decreases the ν¯ production com-
e
pared to LAMPF/LANCE by a factor of 1.7. The beam
has a ν¯e/νe ratio of 4×10−4. FIG.4: Correlatedsensitivity(1and2σcontours)toδCP and
sin22θ for the combined two-phase running.
13
III. SYSTEMATIC ERRORS Thelargestsystematicerrorsarisefromtheν ESsam-
e
ple used to determine the absolute normalization of the
The multiple-DAR-source design is an elegant choice flux. Theerroronthiscrosssectionis0.5%duetoa0.7%
for precision oscillation physics because the beam and uncertainty from the NuTeV sin2θ measurement [20].
W
detector systematics are low. The shape of the DAR We assume a 2.1% energy scale error [21] which leads to
flux with energy is known to high precision and is com- a 1% error on the DAR flux when a E >10 MeV cut
vis
mon among the various distances, thus shape compar- on the events is applied. The ν events on oxygen and
e
isons will have small uncertainties. The neutrino flux IBDeventswithamissingneutroncanbeseparatedfrom
from the three distances is accurately determined from the ν ES sample since the angular distribution of ν ES
e e
the direct measurement of the π+ production rate using events is very forward-peaked, while these backgrounds
ν ES events from the near accelerator. Existing proton have a broad distribution [19]. We take the uncertainty
e
rate monitors assure that relative proton intensities are fromcontaminationbytheseeventstobenegligible. The
understood to 0.1%. The interaction and detector sys- uncertaintyoftheelectron-to-free-protonratioinwateris
tematic errors are low since all events are detected in a also very small. Adding the ν ES systematics in quadra-
e
single detector. The IBD cross section for the signal is ture, the systematic error on the IBD flux is expected to
well-known [14]. The fiducial volume error on the IBD be 1.1%. For the total error on the IBD flux, one must
eventsisalsosmallduetotheextremevolume-to-surface- then add the ν ES statistical error in quadrature, which
e
area ratio of the ultra-large detector. depends on the running period.
4
sin22θ13/δCP -180 -90 0 90 135 thatofLBNE,butisinvertedinitsδCP dependence[10].
0.01 52.5 47.2 29.0 38.8 48.5 The combined two-phase running yields a 4.1σ mea-
0.05 21.6 21.9 19.5 25.6 30.4 surement of δ at the test point of sin22θ =0.05 and
CP 13
0.09 18.3 19.9 17.6 23.8 26.3
δ =−900,asshowninTableIII(top). Thecorrelated
0.01 51.3 45.5 26.9 36.7 46.9 CP
measurement uncertainties are shown in Fig. 4 for 1 and
0.05 19.9 21.2 18.2 24.2 29.6
2σ contours. Table III (bottom), which providesthe sta-
0.09 16.8 19.2 16.5 22.6 25.3
tistical uncertainty, indicates that the measurement is
TABLEIII:The1σmeasurementuncertaintyonδ forvar- statistics-limited.
CP
iousvaluesofsin2θ forthecombinedtwo-phasedata. Top:
13
Systematic and statistical errors. Bottom: Statistics only.
V. CONCLUSIONS
The other significant systematic error is on the effi-
ciency for neutron detection in IBD events. To reduce
uncertainties,neutronsaretaggedviatimingratherthan We have described a novel experiment to search for
position reconstruction. This leads to an inefficiency for CP violation in the neutrino sector. This experiment
neutronsoutsideofthetimingwindowwithasystematic is relatively low cost, employing multiple high-powered
uncertainty of 0.5% [12]. compact cyclotrons located at L = 1.5 km, 8 km and
20 km from a large water Cerenkov detector. Using the
exampleoftheDUSELdetector,forsin22θ =0.05,the
13
IV. OSCILLATION SENSITIVITIES CP violationparameterδCP canbemeasuredtothelevel
of LBNE (>4σ) in a 2-phase 10-year run.
Sensitivity estimates were made by calculating the χ2 Thecomplementarynatureofthismeasurementmakes
for a given set of predicted events and investigating the itacompellingadditiontotheprogram. Thisexperiment
χ2 minimization and excursion, using a method simi- will probe for CP violation with antineutrinos, unlike
lar to Ref. [6]. Matter effects were included in the fit, the present program which relies heavily on neutrino in-
but are negligible due to the short baseline. System- teractions. The systematics are also quite different and
atic uncertainties (see Sec. III and Table I) were con- low compared to present planned experiments. As a re-
strainedbypull-termcontributionstotheχ2 oftheform sult,thisexperimentwillprovideapowerfulinputtoour
(k −1)2/σ2,whereσ2 aretheuncertainties. Resultsare global search for new physics in the neutrino sector.
i i i
given for two scenarios (see Fig. 2): Phase 1 and Phase
1+2 combined. Table II gives the event samples associ- Acknowledgments
ated with the combined phases, for the various classes of
oscillation, background, and calibration events. The authors thank the DAEδALUS group for discus-
Thesensitivityforobservinganon-zerovalueforθ at sions, especially Timothy Antaya, William Barletta and
13
the 3 and 5σ CL as a function of δ is shown in Fig. 3 William Louis. We thank the National Science Founda-
CP
for combined two-phase running. This sensitivity meets tion for support.
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