Measuring the mass of a sterile neutrino with a very short baseline reactor experiment

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by  D. C. Latimer

Measuring the mass of a sterile neutrino with a very short baseline reactor experiment
D. C. Latimer1, J. Escamilla2 and D. J. Ernst2
1 School of Liberal Arts and Sciences, Cumberland University, Lebanon, Tennessee 37087 and
2 Department of Physics and Astronomy, Vanderbilt University, Nashville, Tennessee 37235
(Dated: February 7, 2008)
An analysis of the world’s neutrino oscillation data, including sterile neutrinos, (M. Sorel, C. M.
Conrad, and M. H. Shaevitz, Phys. Rev. D 70, 073004) found a peak in the allowed region at a
2 ∼ 2
mass-squareddifference∆m =0.9eV . Wetraceitsorigin toharmonicoscillations intheelectron
survivalprobability Pee asafunction of L/E, theratio of baseline toneutrinoenergy,asmeasured
2 ∼ 2
in the near detector of the Bugey experiment. We find a second occurrence for ∆m = 1.9 eV .
Wepoint out thatthephenomenonof harmonic oscillations of Pee as afunction of L/E, asseen in
theBugeyexperiment,canbeusedtomeasurethemass-squareddifferenceassociated withasterile
neutrino in the range from a fraction of an eV2 to several eV2 (compatible with that indicated
7 by the LSND experiment), as well as measure the amount of electron-sterile neutrino mixing. We
0 observe that the experiment is independent, to lowest order, of the size of the reactor and suggest
0 thepossibility of a small reactor with a detector sitting at a veryshort baseline.
2
PACSnumbers: 14.60.Pq
n Keywords: neutrinooscillations,sterileneutrino
a
J

4 Present data demonstrate that neutrinos change their

flavorwhile propagatingin vacuum and through matter. 30
1
The evidence comes fromsolar neutrino experiments [1],
v
4 a long baseline reactor experiment [2], atmospheric ex-
0 periments[3],andalongbaselineacceleratorexperiment 20
0 [4]. These experiments, together with the constraint im- 2χ
1 ∆
posed by the CHOOZ reactor experiment [5], provide a
0 quantitative [6] determination of the mixing parameters 10
7
and mass-squared differences for three neutrino oscilla-
0
/ tions. Moreover,as the data becomes ever more precise,
x 0
alternativeexplanationsofthedataarecontinuallybeing
e
- ruled out [7]. 0.1 1
p The lone datum that does not fit into the scenario of ∆m2 (eV2)
e
h three neutrino mixing is the appearance result from the
: LSND experiment [8]. An oscillation explanation of this FIG. 1: The value of ∆χ2 = χ2 −χ2min versus ∆m2. The
v solid (green) straight lineistheresult forathree-neutrinofit
result requires a neutrino mass-squared difference of at
i
X least 10−1 eV2 while the world’s remaining data is com- to data from Refs. [1, 2, 3, 4, 5, 8, 16]. The solid (blue)
curveis theresult of a four-neutrino fit to this data, and the
r patible withtwo mass-squareddifferences of the orderof
a 8×10−5 eV2 and2×10−3 eV2. The additionofa sterile d[1a5s]h.eTdh(erezde)rocuforvrethisetvheertriecsaulltsciaf,lein(χa2mddinit)ioisn,arwbeitardardy.Bugey
neutrinoorneutrinos[9]hasbeenproposedinanattempt
toincorporateLSNDintoananalysisthatwouldbecon-
sistentwiththeworld’sdata. Otherphysicalmechanisms
have also been proposed as possible explanations [10]. measuretheassociatedmass-squareddifferenceandmix-
Restrictingourdiscussiontosterileneutrinos(withCP ing angle. For simplicity, we introduce only one sterile
andCPTconserved),the simplestextensionis the inclu- neutrino;however,ourmethodscanbeeasilygeneralized
sionofasinglesterileneutrino[11]. Suchmodelsfallinto to include additional sterile neutrinos. For the baselines
oneoftwoclasses. The3+1schemeaddsthe fourthneu- and energies of interest here, only the mass-squared dif-
trinowhosemassseparationismuchlargerthantheother ferences involving the extra neutrino will contribute to
three. In the 2+2 scheme, the LSND mass-squared dif- the oscillations. The mass of the three usual neutrinos
ference separates two pairs of neutrinos with the smaller can be taken as degenerate so that oscillations will be
mass-squareddifferences. Currentanalysesindicate that governedby only one mass-squareddifference ∆m2.
neither provides a compelling explanation of the data In Fig. 4 of Ref. [13], there is a narrow peak in the
[12, 13]. As four neutrinos do not seem to be sufficient, allowed region which occurs at ∆m2 ∼=0.9 eV2. We can
five neutrino scenarios have been investigated [13, 14]. trace this peak to the Bugey reactor experiment [15],
Here we assume the existence one sterile neutrino in which is an electron anti-neutrino disappearance exper-
a 3+1 scheme and propose a new way to experimentally iment with detector baselines of 15, 40, and 95 m. We
2
constructa modelofthe aforementionedneutrino exper- 1.05
iments. This analysis [17] produces mixing angles for
three neutrino oscillations that are very similar to those
of Ref. [6]. In Fig. 1, we present χ2 versus the mass-
1
squared difference, ∆m2, for three cases.
Thehorizontalsolid(green)lineistheresultofathree- e
Pe
neutrino analysis of the data from Refs. [1, 2, 3, 4, 5],
LSND [8], and KARMEN [16]. The χ2 contains the no 0.95
oscillation contribution from LSND and KARMEN. By
definition the three neutrino results do not depend on
∆m2 yielding a straight line. The solid (blue) curve is
the result of a 3+1 analysis. As expected, the nonzero 0.9 4 6 8 10
LSND data utilizes ∆m2 and the additional mixing an- L/E (m/MeV)
gles θ14 and θ24 (the results are essentially independent
of θ34) to lower the χ2. For ∆m2 < 0.03 eV2 the fourth FIG. 2: The electron survival probability Pee versus L/E.
Thedataarefromtheneardetector,L=15m,oftheBugey
neutrino does not contribute to the LSND or KARMEN
[15] experiment. The solid (red) curve results from a ster-
experiment, and the χ2 reverts to the three neutrino re- ile neutrino associated with ∆m2 = 0.9 eV2 and the dashed
sult as it must. The exact values of these two curves are (violet) curveresults from ∆m2 =1.9 eV2.
irrelevantforthediscussionathand. Weincludethemto
provide a reasonablebackgroundfor the dashedcurve in
which we add the Bugey experiment [15] to the previous
analysis, following exactly the analysis in Ref. [15]. For dashed (violet) curve for ∆m2 = 1.9 eV2. Although the
∆m2 < 0.2 eV2, the dashed curve merges with the solid statisticsarepoor,onecanseethatthere is anharmonic
curve as Bugey does not contribute in this region. Be- oscillation in the data at frequencies which generate the
yond this, the dashed curve contains fluctuations. This dips in the χ2. The dips correspondroughly to a change
isbecausetheparametersareinaregionthatrunsalong in χ2 of ten. Whether these dips are real or statistical
the edge of the Bugey excluded region where the χ2 is fluctuations is not the question. The point is that with
notsmooth. This phenomena is alsopresentin Ref.[13]. improvedstatisticstheexistenceofasterileneutrinowith
These curves do not indicate the existence of a sterile ∆m2 in the appropriate range would produce a measur-
neutrino. The addition of the CDHS [18], CCFR84 [19], able narrow minimum in the χ2. The Bugey experiment
andNOMAD [20]experiments werefoundin Ref.[13] to is an existence proof for the validity of such an experi-
largely offset the LSND indication of a sterile neutrino. ment.
The first important feature of the dashed curve is the For a reactor, the neutrino spectrum and technology
narrowdipnear0.9eV2. Thiscorrespondstothepeakin set the range of detectable neutrino energies to lie be-
the allowedregionfound in Fig.4 ofRef. [13]. Note that tween approximately 1 to 5 MeV. At a baseline of 15 m,
wealsofindasecondnarrowdipnear1.9eV2. Thislarger the ratio L/E ranges from 3 to 15 m/MeV. Oscillations
mass-squareddifference is also present in Ref. [13]; how- have undergone one cycle when φ = π. For a ∆m2 of
ever, in their analysis, the inclusion of other null result 0.9 (1.9) eV2, the oscillation length is 2.7 (1.3) m/MeV
shortbaselineexperiments[18,19,20]almostcompletely which results in approximately 5 (10) cycles in the al-
suppressesthis dip’s significance. Clearlythe narrowdip lowed range.
inthe χ2 hereandthe narrowpeak inthe allowedregion Theamplitude oftheoscillationsfortheBugeydatais
in Ref. [13] originates from the Bugey experiment. about 1.25%. Twice this (peak to trough) is somewhat
To understand the source of this dip, we turn to the less than the average error bar thus giving the low sta-
in vacuo neutrino oscillation probability. Using a stan- tistical significance to these dips. If the statistical error
dard extension of the MNS mixing matrix, the electron bars were one fourth this (sixteen times the data) an os-
neutrino survival probability at these short baselines is cillation pattern of this same magnitude would be very
approximately significant. This could be achieved by running longer
Pee(L/E)∼=1−sin2(2θ14)sin2φ, (1) and/or building a larger detector and/or using a more
powerful reactor.
with φ = 1.27∆m2L/E where ∆m2 is in eV2, the base- Another consideration is the energy resolution, or the
line L is in m, and the energy E is in MeV. We can use minimum size of the bin in E. In order to cleanly de-
this to determine which data in the Bugey experiment fine the oscillation length in L/E, four data points per
yield the dips in χ2. Fig. 2 contains a plot of Pee versus cycle are needed, or a resolution of 0.7 (0.33) m/MeV
L/E from the Bugey near detector located at L = 15 for ∆m2 = 0.9 (1.9) eV2. This corresponds to an en-
m. The solid (red) curve is for the best fit parameters ergy resolution of 10% (5%). For ∆m2 = 0.9 eV2, this
withamass-squareddifferenceof∆m2 =0.9eV2andthe resolutionis less stringentthan that ofthe Bugey exper-
3
iment by about 25%. For ∆m2 = 1.9 eV2, the needed imum mass-squared difference which can be probed re-
2
resolution is about double that in the Bugey experiment mainsaround3 eV . Theminimum andmaximumvalue
thus requiring a total 32 fold increase in counts relative of L/E shift to 2.2 and 10.3 m/MeV, respectively. The
to Bugey. midpoint for L/E moves to 5.1 m/MeV, and the mea-
Weestimatedthesenumbersforanaverageenergyneu- surement would cover 4 (7) cycles for ∆m2 = 0.9 (1.9)
trino. TheresultwillapproximatelyholdforsmallerL/E eV2. To reach 3 eV2, a resolution of 4% in the energy
as can be seen in Fig. 2. Focusing on an L/E below 5 would be required. By lowering the maximum value of
m/MeV, one could combine two bins into one wider bin, L/E the minimum sensitivity is raised,here to 0.06eV2.
reducing the error bars so that they become comparable Going to a smaller baseline increases the flux by L2, but
totheothererrorbars,whileretainingtherequisitenum- the size of the reactor, hence its power, would necessar-
berofdatapointsperoscillation. However,forthelarger ily decrease by L3. This produces a smaller number of
values of L/E equalspacing in E yields wider spacingin cycles such that the number of energy bins decreases by
L/E, and the ideal spacing is not achieved. an additional factor of L. The overall result is that the
Thereisanabsolutemaximummass-squareddifference experiment, to lowest approximation, is independent of
that can be reached by this type of experiment. This is the size of the reactor. This is true if you are searching
setbythephysicalsizeofthe reactor. Ifonegetstoare- for the existence of a sterile neutrino. Since the accu-
gionwherethelengthofasingleoscillationiscomparable racy of the measured mass-squared difference would be
tothedimensionsofthereactorcore,thenneutrinosfrom increasedbyobservingadditionalcycles,thelastfactorof
the backofthe reactorareincoherentwiththe neutrinos Lwouldnotapply ifthe goalwereafixederroron∆m2.
fromthe frontofthe reactor. Usingascalefactorforthe The larger width in the energy binning also reduces the
reactorcoreof3mandanaverageenergyof3.5MeV,we resolution needed. For L = 11 m, the required resolu-
find the maximum achievable mass-squareddifference to tion increases to 6 (13)% for ∆m2 = 0.9 (1.9) eV2. For
be roughly 3 eV2. This number depends on the shape of a discovery experiment, a small research reactor with a
thereactorcore,thelocationofthedetectorwithrespect smalldetectorsitting verynear the coreis aninteresting
to the orientation of the cylindrical core, and the power optionto consider. The detectormightevenbe wrapped
distribution within the core. A straightforward calcula- around the core to increase the count rate.
tionforagivenexperimentisnecessarytogetmorethan Theargumentdoesrequirethatthetechnologyforneu-
a crude estimate. Unfortunately, this number is smaller trino detection scales nicely as the size of the detector.
than the 10 eV2 that is the lower end of a presently al- The technical issues for doing this experiment and those
lowed region found in Ref. [13]. To reach this maximum involvedwith using short baseline neutrino detectors for
sensitivity, an energy resolution of 3% is required. nonproliferation monitoring [21] are related.
To determine the lower limit on the measurable mass- We have shown that a very short baseline reactor ex-
squared difference, we require that the oscillation phase periment can be used to measure the mass-squared dif-
reach at least φ = π/4. From this phase, one could de- ference associated with a sterile neutrino should it lie in
termine the oscillation parameters without knowledge of therangeoflessthanatenthofaneV2 uptoseveraleV2
theabsoluteflux. Thisgivesalowerlimitof∆m2 =0.05 by measuring the oscillations in the data over a number
eV2 for L=15 m. of oscillation lengths. A Fourier transform analysis of
Themeasurementof∆m2isinsensitivetotheabsolute such data would be an efficient way of extracting the os-
normalization of the data; the oscillation length derived cillationfrequencies;however,suchmethods arenotfun-
from the harmonic oscillations in the data determines damentally different from fitting oscillation parameters
∆m2. The amplitude of these oscillations determines di- to the data as a function of the mass-squared difference
rectly sin2(2θ14) which is also independent of the abso- ∆m2. The experiment also measures sin2(2θ14) through
lute flux if several oscillation cycles are measured. How theamplitudeoftheoscillations. Wesuggestthatasmall
this worksout in the data analysis canbe seen in Fig. 2. reactor with a very short baseline be investigated. The
For small values of L/E, the data are coherent and thus experimentisnotsensitivetotheabsolutenormalization
the peak is quite near Pee = 1. The uncertainty in the of the data and thus holds the possibility of being more
normofthedatawillnecessarilybesufficienttoallowthe accurate than alternatives.
datatobeuniformlyadjustedsuchthatthefitcurvewill The MiniBooNE experiment [22] will soon confirm or
havethe peakforsmallL/E alsoquite nearPee =1,the contradict the LSND experiment. The experiment pro-
required physical value. A great advantage of the pro- posed here could play a significant role independently
posed experiment is that the normalization of the data, of that outcome. Should MiniBooNE leave the situation
usually the largestsystematic errorin a neutrino oscilla- ambiguous,theproposedexperimentcouldprovideacost
tion experiment, is nearly irrelevant. effective, accurate, and independent way to resolve the
The above utilized a baseline L = 15 m. Doubling situation. Should MiniBooNE confirm the existence of
the flux by moving to L = 11 m would be attractive. a sterile neutrino(s), then this experiment mightprovide
We repeat the analysis for this value of L. The max- a more accurate measurement of the mass-squared dif-
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