Table Of ContentProject 8: Using Radio-Frequency Techniques to Measure Neutrino Mass
J.A.Formaggio
FortheProject8Collaboration
LaboratoryforNuclearScience,MassachusettsInstituteofTechnology,Cambridge,MA02139
Abstract
Theshapeofthebetadecayenergydistributionissensitivetothemassoftheelectronneutrino. Attemptstomeasure
1
1 the endpoint shape of tritium decay have so far seen no distortion from the zero-mass form. Here we show that a
0 newtypeofelectronenergyspectroscopycouldimprovefuturemeasurementsofthisspectrumandthereforeofthe
2 neutrinomass. Weproposetodetectthecoherentcyclotronradiationemittedbyanenergeticelectroninamagnetic
n field.Formildlyrelativisticelectrons,likethoseintritiumdecay,therelativisticshiftofthecyclotronfrequencyallows
a ustoextracttheelectronenergyfromtheemittedradiation. Asthetechniqueinherentlyinvolvesthemeasurementof
J
afrequencyinanon-destructivemanner,itcan,inprinciple,achieveahighdegreeofresolutionandaccuracy.
1
3 Keywords: neutrinomass,betadecay,radio-frequency
]
x
e 1. Motivation to approach the inverted or even the hierarchical neu-
- trinomassscaleimpliedbycurrentoscillationmeasure-
l EversinceEnricoFermi’soriginalproposal[1],ithas
c ments. Theproposedtechniquemakesuseoftheradia-
u beenknownthattheneutrinomasshasaneffectonthe
tionemittedduringcyclotronmotioninordertoextract
n kinematics of beta decay. Measurements have always
theenergyoftheelectronejectedintritiumbetadecay.
[
suggestedthatthismasswasverysmall,withsuccessive
As the technique inherently involves the measurement
1 generations of experiments giving upper limits[2][3], of a frequency, it can, in principle, achieve a high de-
v most recently m < 2.3 eV. The upcoming KATRIN
νβ gree of resolution and accuracy. The combination of
7 experiment anticipates having a sensitivity of 0.20 eV
thesetwofeaturesmakesthetechniqueattractivewithin
7
at 90% confidence level[4, 5]. If the neutrino mass is
0 thecontextofneutrinomassmeasurements.
muchbelow0.20eV,itisdifficulttoenvisionanyclas-
6
. sical spectrometer being able to access it. Oscillation
1
experiments,however,telluswithgreatconfidencethat 2. NeutrinoMassviaBetaDecay
0
1 the tritium beta decay neutrinos are an admixture of at
The most sensitive direct searches for the electron
1 least two mass states. Data indicate that the effective
neutrinomassuptonowarebasedontheinvestigation
: mass must satisfy m > 0.005 eV under the normal
v νβ of the electron spectrum of tritium β-decay. The elec-
Xi hierarchy or mνβ > 0.05 eV in the inverted hierarchy. tron energy spectrum of tritium β-decay for a neutrino
These bounds provide a strong motivation to find new,
withcomponentmassesm ,m ,andm isgivenby
r more sensitive ways to measure the tritium beta decay 1 2 3
a
spectrum.
To make advances toward lower and lower masses, dN
∝ F(Z,K )·p ·(K +m )·(E −K )·
it is important to develop techniques that allow for ex- dK e e e e 0 e
e
tremely precise spectroscopy of low energy electrons. (cid:88) (cid:113)
|U |2 (E −K )2−m2·Θ(E −K −m)
Current electromagnetic techniques can achieve order ei 0 e i 0 e i
10−5inprecision,butareatthelimitoftheirsensitivity. i=1,3
Therefore, a new technique must be pursued in order where K denotes the electron kinetic energy, p is the
e e
electronmomentum,m istheelectronmass, E corre-
e 0
(cid:73) sponds to the total decay energy, F(Z,Ke) is the Fermi
Emailaddress:[email protected]() function,takingintoaccounttheCoulombinteractionof
PreprintsubmittedtoElsevier February1,2011
the outgoing electron in the final state, Z is the atomic particleand,consequently,anymeasurementofthisfre-
number of the final state nucleus, and U is the ele- quency stands as a measurement of the electron en-
ei
ment from the PMNS mixing matrix. As both the ma- ergy. Measurements of the relativistic cyclotron fre-
trix elements and F(Z,K ) are independent of the neu- quency shift have been made, but only within the con-
e
trinomass, thedependenceofthespectralshapeonm text of electron traps. Electron energies as low as 16
i
is given solely by the phase space factor. In addition, meV have been measured [7]. In our case, we are in-
theboundontheneutrinomassfromtritiumβ-decayis terested in free-streaming electrons with energies near
independentofwhethertheelectronneutrinoisaMajo- theendpointoftritiumbetadecay. Theseelectronshave
ranaoraDiracparticle. a kinetic energy of 18.6 keV or, equivalently, a boost
Therecurrentlyexiststwotechniquestomeasurethe factorγ(cid:39)1.0365.
betadecayspectrumwithsufficientsensitivitytoextract Sincetherelativisticboostfortheenergiesbeingcon-
neutrino masses at the eV or sub-eV scale. Calorimet- sidered is close to unity, the radiation emitted is rela-
ric techniques, such as those employed by the MARE tivelycoherent. Eachelectronemitsmicrowavesatfre-
collaboration[6],measurethetotalenergydepositedby quencyωandatotalpowerwhichdependsontherela-
thedecay. Insuchcryogenicmeasurements,thesource tivisticvelocityβ[9]:
and detector are one and the same, providing a more
favorablescaling. Theuseofextremelylong-livediso- 1 2q2ω2 β2
P(β,θ)= c ⊥ (2)
topes,however,makesrealizingsufficientratesdifficult. 4π(cid:15) 3c 1−β2
0
Spectrometer techniques, such as those in use by the
KATRIN experiment[4] and its predecessors, separate where q is the electron charge, (cid:15) is the permittivity of
thesourcefromthedetectorinordertomeasuretheen- free space, and c is the speed of light. For a mag-
ergy of the electron to very high precision. KATRIN neticfieldstrengthof1Tesla,theemittedradiationhas
veryefficientlyremovesthebulkofthelowenergyspec- a baseline frequency of 28 GHz. This frequency band
trum. However, the separation of the electron and the iswellwithintherangeofmostcommerciallyavailable
sourcerequiresalarge-scaleapparatus.KATRINiscur- radio-frequency antennas and detectors. It is conceiv-
rentlyatthelimitofsuchspectroscopictechniques,with able, therefore, to make use of radio-frequency detec-
aprojectedmasssensitivityof200meV. tiontechniquesinorderachieveprecisionspectroscopy
We propose a third approach to neutrino mass mea- of electrons. The typical power emitted by these elec-
surements,usingradio-frequencytechniquestomeasure tronsissufficientlyhightoenablesingle-electrondetec-
thebetadecayenergyspectrum. Thetechniquehasthe tion.
potential of retaining the high resolution available in Consider the arrangement shown in Fig. 1. A low-
spectroscopicmeasurementswhileremovingtheneces- pressuresupplyoftritiumgas(electronsource)isstored
sity of extracting the electron from the source. A de- in a uniform magnetic field generated by a solenoid
scriptionofthetechniqueisgivenbelow. magnet. Tritium decay events release electrons with
0 < E < 18575eV(andvelocity0 < β < β where
e max
β = 0.2625) in random directions θ relative to the
max
3. DescriptionofTechnique field vector. The electrons follow spiral paths with a
velocity component (β ) parallel to the magnetic field.
||
Each electron emits microwaves at frequency ω as de-
Imagine a charged particle, such as an electron cre-
fined in Eq. 1 and a total power which depends on the
ated from the decay of tritium, traveling in a uniform
perpendicularandparallelvelocitycomponents,β and
magnetic field B. In the absence of any electric fields, (cid:107)
β ;respectively.Bydetectingtheradiationandmeasur-
⊥
theparticlewilltravelalongthemagneticfieldlinesun-
ingitsfrequencyspectrum,oneobtainsωandhencethe
dergoing simple cyclotron motion. The characteristic
energyoftheelectron.
frequencyωatwhichitprecessesisgivenby
Although the emitted radiation is narrowband with
frequency ω, the signal seen in a stationary antenna is
eB ω ω
ω= = c = c , (1) morecomplicated;generallyitincludesaDopplershift
γme γ 1+ Ke due to β , some dependence on the electron-antenna
mec2 (cid:107)
distance, and the differential angular power distribu-
where (ω ) is the cyclotron frequency and γ is the rel- tionoftheemission. Thedetectedsignalthusdepends
c
ativistic boost factor. The cyclotron frequency, there- on the antenna configuration, and may have a nontriv-
fore, is shifted according to the kinetic energy of the ial frequency content. Nevertheless, one can consider
2
a long array of evenly-spaced antennae oriented trans- toprocessthesedecayswithoutunreasonablepileup.
verse to the magnetic field. Any single transverse an- Themaintoolforseparatingsignalfrombackground
tenna may see the electron passing by, resulting in a is the high-resolution and high-linearity nature of fre-
complex, broadband“siren”signalwhichsweepsfrom quency domain analysis. Electrons with E = 0
e
blueshift to redshift. However, the coherent sum sig- will generate fundamental signals at 27.992490 GHz;
nalfromalloftheantennaeinthearraymustbequasi- 18.575 keV electrons will emit fundamentals at about
periodic. If the antennae signals are mixed appropri- 27.010643 GHz; as each 1 eV analysis bin is about 50
ately,almostallofthecomplexDopplereffectssumin- kHzwidethefullregion-of-interest(ROI)isperhaps1
coherently while the unshifted cyclotron frequency re- MHz wide. Detecting a narrow signal in the endpoint
mains coherent. The final summed periodic signal ap- ROI is, by itself, insufficient to identify confidently an
pearsasa“carrierwave”atfrequencyωwith(a)anam- endpoint electron, since this band is also populated by
plitudemodulation,becausetheantennaresponsevaries thelow-frequencysidebandsofthemuchmorenumer-
periodically along the electron’s path, and (b) possibly ouslow-energyelectrons;wewillneedtodetectatleast
a small residual frequency modulation due to the rela- twospectrallines,possiblythree,inordertoconfidently
tivistic “beaming” of the cyclotron radiation (see Fig- identify an electron. In principle, any possible confu-
ure2(b)). Amorein-depthdescriptionofthetechnique sion source has a lower power than a real ROI source
canbefoundinRef[8]. atthesamefrequency,butpowermeasurementsareex-
In order to measure the electron energy to a preci- pectedtobefairlynoisyinthissystem.
sion ∆E, we need to measure the frequency to a rela- Several other parameters conspire to reduce the im-
tive precision of ∆f/f = ∆E/m . For ∆E = 1 eV this pact of sideband confusion. In order for a low-energy
e
implies ∆f/f = 2 × 10−6. In order to achieve a fre- electrontoputanysidebandatallintotheROI,itmust
quency precision of ∆f, we need to monitor the signal havealargeβ togeneratetheDopplershift;however,a
(cid:107)
for t = 1/∆f, according to Nyquist’s theorem. This largeβ alsoleadstoaquickexitfromthespectrometer
min (cid:107)
is a key number for several aspects of the experiment; (and consequently a broad signal) and to lower emit-
for concreteness, we discuss a reference design with a ted power. Accidental coincidences may still occur. If
1 T magnetic field and a ∆E = 1.0 eV energy resolu- the detection criterion requires simply two high-power
tion. First,wewantthebetaelectronstohavemeanfree spectral peaks in coincidence, we estimate that a T
2
flighttimeslongerthant (30µsinthereferencede- sourcestrengthof10,000Bqwouldgiveanaccidental-
min
sign). Due to T -e− scattering, this places a constraint triggerratecomparabletoKATRIN’sbackgroundevent
2
onthedensityofthesource.TheT -e−inelasticscatter- rateofoneper1013effectivesourcedecays.Requiringa
2
ingcrosssection[10]at18keVisσ=3×10−18cm2,so thirdspectralpeakraisesthisallowablesourcestrength
in order to achieve the appropriate mean free path the toapproximately109Bq.
T density cannot exceed ρ = (t βcσ)−1. It also It is important that single electrons can be detected
2 max min
places a constraint on the physical size of the appara- well above the noise level; first of all, to avoid false
tus; we presume that our measurement ends when the eventsfromnoisefluctuations;secondly,inordertoap-
particlereachestheendofsomeinstrumentedregion. If proach as nearly as possible the Nyquist limit on the
wewanttobeabletomeasureparticleswithminimum frequency resolution; thirdly, to increase the precision
pitchangleθ ,theinstrumentedregionneedstobeof of total-power measurements and start/stop time esti-
min
lengthl = t βc·cos(θ )long;inpractice,engineer- matesforeachdetectedelectron. Forourreferencede-
min min
ingconstraintsonlmaysetθ .Finally,t alsoplaces signwithB=1T,∆E =1eV,eachresolutionbincovers
min min
aconstraintonthemagneticfield. Theelectroncontin- 50kHz.Thisbandwidthshowsathermalnoisepowerof
uouslylosesenergyviacyclotronradiation;wewantto 6.5×10−19W/K,comparedwithapossiblesignalpower
completeourfrequencymeasurementbeforeithaslost intheneighborhoodof10−14 W.Inthisfrequencyband
energy∆Eduetoradiativeemission. thereexistamplifierswhichpossess10-20Knoisetem-
One great advantage of the MAC-E filter technique peratures.
usedbyexperimentssuchasMainz[2],Troitsk,[3]and Asecondnoisesourcecomesfromtheincoherentsig-
KATRIN is the ability to reject effortlessly extremely nals of non-endpoint and/or low-pitch beta electrons.
largefluxesoflow-energyelectrons,andtoactivatethe For our 1-T, 30 µs-analysis-period reference design,
detectorandDAQonlyforthesmallfractionofdecays each 50 kHz analysis bin near 27 GHz will show ap-
near the endpoint. A cyclotron emission spectrometer proximately10−24 W/Bqoftritiumnoise. Thisiscom-
willbeexposedtoallofthetritiumdecaysinitsfieldof patible with robust signal detection in the presence of
view(Fig. 2); therefore,itisimportantthatwebeable the 108–109 Bq source allowed by pileup limitations.
3
Wenote, however, thepossibilitythatthisnoisepower 4. NextSteps
willhavenon-Gaussianfluctuations.
Thistechniquepresentsaverydifferentsystematicer- We will initially operate a prototype system in a 1
T field, which corresponds to a baseline cyclotron fre-
ror budget than MAC-E filter experiments. The spec-
quencyof27.997GHz. Aconceptualdesignofthepro-
trometeriscontinuouslymonitoringalldecayenergies,
totypeenvisionedisshowninFigure3.Eachpartserves
and thus is immune to slow source strength drifts. We
one of two basic functions, or both functions in some
anticipate using an essentially static tritium gas whose
cases. The first function is as a part of the technology
electrostatic potential is fixed at both ends; this pre-
tobeproven, i.e., theabilitytodetectthecyclotronra-
cludeslargesystematicsduetosourcecharging,voltage
supplystability,flow-relatedDopplershifts,andT− ion diation of interest. The second function is as part of a
systemofcalibrationsandcrosscheckstoverifyourun-
traps. Microwave frequency measurements are easily
stabilizedagainstdriftsatthe10−12level. derstandingofanysignalsobserved,ortodiagnoseour
inabilitytoobservesignalsinthecaseofnullmeasure-
ments.
Superconducting magnet coils
phasedelay loops Vacuum Pump
amplifiers Fill Lines
transverse antenna array mdeitxeecrtsors ETMeliermrcotprro SCneo Dnnsetrotoerlsctor (cid:0)(cid:1)S(cid:0)(cid:1)ource ControRleceiver
Warm Amplifiers
endcap
radiation antenna
T gas
2
source
decay electron
decay electron
transverse antenna array Baffles
~30
inches
Superconducting magnet coils
(cid:0)(cid:1)(cid:0)(cid:1)
(cid:0)(cid:1)(cid:0)(cid:1) Electron Source
(cid:0)(cid:1)(cid:0)(cid:1)
Figure1:Schematicofahypotheticaltritiumbetadecayexperiment. (cid:0)(cid:1)(cid:0)(cid:1)
A chamber encloses a diffuse gaseous tritium source under a uni- (cid:0)(cid:1) Cold Amplifiers
(cid:0)(cid:1) Main Magnet
form magnetic field. Electrons produced from beta decay undergo
cyclotronmotionandemitcyclotronradiation,whichisdetectedby Antenna
anantennaarray. Magnetic Mirrors
(cid:0)(cid:1)(cid:0)(cid:1)(cid:0)(cid:1)(cid:0)(cid:1)(cid:0)(cid:1) Electron Detector
(cid:0)(cid:1)(cid:0)(cid:1)(cid:0)(cid:1)(cid:0)(cid:1)(cid:0)(cid:1)(cid:0)(cid:1)(cid:0)(cid:1)(cid:0)(cid:1)(cid:0)(cid:1)(cid:0)(cid:1)
(cid:0)(cid:1)(cid:0)(cid:1)(cid:0)(cid:1)(cid:0)(cid:1)(cid:0)(cid:1)
(cid:0)(cid:1)(cid:0)(cid:1)(cid:0)(cid:1)(cid:0)(cid:1)(cid:0)(cid:1) Cooling Liquid Space
(cid:0)(cid:1)(cid:0)(cid:1)(cid:0)(cid:1)(cid:0)(cid:1)(cid:0)(cid:1)
(cid:0)(cid:1)(cid:0)(cid:1)(cid:0)(cid:1)(cid:0)(cid:1)(cid:0)(cid:1)
ower (arb. units) 456 10−11 tritium endpoint Fisnoigguurmcreea3gca:nneStcbheenetmcraaas2pte piinscechdoaefsactnohdledspt(ro4or.pe4odKs.)eAdrersgeeisroeinaerscwohhf.ewAreirlaeerlgaencettrseounnpnsearsfcroponrmodvutichdtee-
P
26 26.05 26.1 26.15 26.2 the coupling to the cyclotron frequency. Signals are amplified and
senttothereceiverelectronics. Anelectrondetectorisinstalledfor
3
21 tritium endpoint17572 eV = 1.565! mthoeTniehtonereinrsggtayprutrriepngogsieopsn.oionftiinstetroeshtawvehiscohuarcreeswoeflleulencdterorsntsooidn
priortotheiruseinthisprototype. Thesimplestsource
205.6 25.8 26 26.2 26.4 26.6 26.8 27 27.2
Frequency (GHz) willgeneratesingleelectronsinanarrowrangeofener-
giesandangleswithrespecttothemagneticfield. The
Figure 2: Simulated microwave spectrum, showing the cyclotron energy and angle should be independently controllable
emissionof105tritiumdecaysover30µsina10mlonguniformmag-
so that the response can be mapped as a function of
net(ω0=27GHz,B∼1T)withafinely-spacedtransverseantenna
array. e−-T2 scattering is neglected. The short arrow points out a both variables. Work to create an electron gun with
tripletofspectralpeaksgeneratedbyanindividualhigh-energy,high these capabilities is ongoing. In principle, the infor-
pitchangleelectron.Thelog-scaleinsetzoomsinonthiselectronand mation gained from the simplest source is sufficient to
theendpointregion.
computetheresponsetoanymorecomplicatedsource.
Theisotope83mKrisanisotropicallyemittingsourceof
4
monoenergeticconversionelectronswithE =17.8keV. rangeofthistechnique.
Theobservationanddetailedquantitativeunderstanding
oftheresponsetoagaseous83mKrservesasanexcellent
template to extrapolate to the more complex spectrum
References
expectedfromtritiumbetadecay.
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diation frequency. This will be accomplished with a
(1999).
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Thetotalmagnetictrapvolumefortheprototypewill
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this is a considerable reduction in the allowed phase
space, it optimizes the signal-to-noise ratio to facili-
tateelectrondetection. Asmalltwo-wireantennapopu-
latesthetrapvolumeforRFdetection. Signalsarecar-
riedtoalownoisecryogenicamplifierthatcanoperate
in the K -band. The amplified signals are then trans-
a
portedoutsidethemainvolumeandmixedtolowerfre-
quencyforreadydetection. Inadditiontotheobserva-
tionoftheircyclotronradiation,wealsorequireacon-
ventional method of detecting electrons, so as to mon-
itor the 83mKr activity present in the test cavity. This
will allow the verification of the functionality of elec-
tronsourcesandtheeffectivenessofthemagnetictrap.
Energyandtimeresolutionarenotcriticalrequirements
for this detector since its main purpose is to tag elec-
tronsandverifywhetherornottheywereinthetrapat
aparticulartime. Itmaybeusefulinearlystagestouse
thisdetectorasatriggertoinitiatethesearchforasignal
of cyclotron radiation. However, another primary goal
ofthisprototypeistodemonstratethatthesignalofcy-
clotronradiationisrecognizablewithoutanyadditional
detectionmethods. Amicrowavesourceinsidethepro-
totypeisalsoenvisionedtoserveasapower-frequency
calibration.
5. Summary
Radio-frequency techniques are new in the field
of neutrino mass measurements, but their application
mayprovideapathtoaccesssensitivitylevelscomple-
mentary to those already available from calorimetric
and spectroscopic techniques. An R&D program is
underway to determine the feasibility and sensitivity
5
