Project 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. Electrons will need to be trapped in order to allow [1] E.Fermi,RicercaScient.2,12(1933). sufficient time for a precise determination of their ra- [2] C.Weinheimer, B.Degen, A.Bleile, J.Bonn, L.Bornschein, O.Kazachenko,A.Kovalik,E.W.Otten,Phys.Lett.B460,219 diation frequency. This will be accomplished with a (1999). magneticbottle: thetrappingregionwillbeflankedby [3] TroiskCollaboration(14authors),Phys.Lett.B460,227(1999). regions of increased magnetic field on both ends. The [4] KATRIN Collaboration (52 authors) arXiv:hep-ex/0109033 ratioofthemaximumtotheminimumfieldstrengthde- (2001). [5] T. Thu¨mmler, “Introduction to direct neutrino mass measure- terminestherangeofpitchanglesconfinedinthetrap. mentsandKATRIN”,theseproceedings. Abilitytoswitchthetraponandoffby“opening”either [6] MARECollaboration(15authors),Phys.Rev.Lett.82(1999) end will be necessary in order to limit the number of 513A. electronsinsideandlimitionizationeffects. [7] G.Gabrielse,D.Dehmelt,andW.Kells,Phys.Rev.Lett.54,537 (1985). Thetotalmagnetictrapvolumefortheprototypewill [8] B. Monreal and J. A. Formaggio, Phys. Rev. D80:051301 be approximately 1 mm3 and trap electrons electrons (2009). with near maximal pitch angles (θ ≥ 89o). Though [9] J.Johner,Phys.Rev.A461498(1987). [10] V.N.Aseevetal.,Eur.Phys.J.D1,39(2000). 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