Recent Results from KATRIN Magazine Symmetry Diana Parno, Carnegie Mellon University NuPhys / London / 17 December 2019 The Unbearable Lightness of Neutrinos ◆ Why are neutrinos so light compared to all other fundamental particles? 3 ◆ What is the absolute neutrino mass scale? 2
1
Plot from Luke Kippenbrock
Image from Symmetry Magazine
Diana Parno -- Recent Results from KATRIN -- NuPhys 2019 2 The Plan
◆ Neutrino mass ◆ How the KATRIN experiment works ◆ Modeling the KATRIN spectrum ◆ Closing in on the neutrino mass n
Diana Parno -- Recent Results from KATRIN -- NuPhys 2019 3 Neutrino Mass Scale Agenda for the future◆ Oscillationneutrino experimentsmeasurements give splittings between mass states Neutrino mass ordering? CP violation? ◆What can we say about the offset of
the lightest mass from zeroP(να? →ν β ) ≠ P(να →ν β ) ? Normal hierarchy Baryon asymmetry of the Universe? (eV) i
Are neutrinos Majorana Pre-2019 limit: (taken from R. B. Patterson, Ann Rev Nucl Part particles?mn < 2 eV Sci 65 (2015) 177-192.) (Mainz and Troitsk Neutrinoless Neutrino mass m mass Neutrino experiments) double beta Absolute neutrino mass? Lightest neutrino mass m1 (eV) decay Diana Parno -- Recent Results from KATRIN -- NuPhys 2019 4 Beyond the 3 flavor framework? http://wwwkm.phys.sci.osaka- (Sterile neutrinos?) u.ac.jp/en/research/r01.html 5 Direct Mass Probe Through T Decay
1 mν = 0 1 mν = 1 eV ne - 0.8 3 3 e H He 0.6
◆ Super-allowed decay 0.5 ◆ Q = 18.6 keV 0.4 Probability (arbitrary units) Probability (arbitrary units) ◆ T1/2 = 12.3 yr 0.2
Probability (arb. u.) mn,eff = 1 eV mn,eff = 0 eV ◆ Extract effective neutrino mass from Probability (arb. u.) 00 -5 2000 4000-4 6000 8000-3 10000 -212000 14000-1 16000 180000 spectral shape near endpoint -5 -4 -3 Kinetic -2 Energy Kinetic - -Q-value 1Energy (eV)(eV) 0 b kinetic energy (eV)- Q (eV)
(quasi-degenerate regime) Diana Parno -- Recent Results from KATRIN -- NuPhys 2019 5 The Challenge
1 mν = 0 1 mν = 1 eV
0.8
0.6 -13 0.5 0.4 ~10 of decays Probability (arbitrary units) Probability (arbitrary units) 0.2 mnb = 0 eV mnb = 1 eV 0 0 2000 4000 6000 8000 10000 12000 14000 16000 18000 -5 -4 -3 -2 -1 0 Kinetic Energy (eV) Kinetic Energy - Q-value (eV) ◆ Start with a huge number of decays ◆ Precisely measure energy, rate near endpoint ◆ Somehow ignore all the low-energy decays with no useful information
Diana Parno -- Recent Results from KATRIN -- NuPhys 2019 6 BRIEF ARTICLE BRIEF ARTICLE
THE AUTHOR THE AUTHOR
12 dN G2 m5 cos2 ✓ Advances in High Energy Physics (1) dN = GF2 me5 cos2 ✓C M 2F (Z, E )p E U 2P (E E V ) The MAC-E FilterF e3 7 C nuc 2 e e e ei2 k max e k (1) dEe = 2⇡ 3~ 7 |Mnuc| F (Z, Ee)peEe ⇥ U| ei |Pk(Emax Ee Vk) dEe 2⇡ | broad| beam of electrons fying⇥ almosti,k| parallel| to the magnetic ~ i,kX 12 ◆ Measure integral spectrum with movingfeld threshold lines. Tis is just the oppositeAdvancesX of the in High so-called Energymagnetic Physics 2 ! mirror or2magnetic2 bottle efect. (Emax Ee Vk)2 m2⌫i ⇥(Emax Ee Vk m⌫i) ◆ Magnetic Adiabatic Collimation⇥ (Emax + ElectrostaticEe TVisk) parallel mfilter⌫ beami ⇥⇥ of( electronsEmax isE energeticallye Vk m analyzed⌫i) ΔΩ = ' ⇥ broad beam of electrons⇥ fying almost parallel to the magnetic qq byfeld applying lines. T anis electrostatic is just the opposite barrier created of the so-called by a systemmagnetic of one or more cylindrical electrodes. Terelativesharpness 2 ! mirror or magneticE bottle efect. ($ of this energyE high-pass flter is only given by the ratio of (2)(2) Tµisµ parallel== ?? beam== const const of electrons is energetically analyzed ΔΩ = ' theby minimum applying magnetic anBB electrostaticfeld min barrierreached created at the by electrostatic a system of barrierone or in more the so-called cylindrical analyzing electrodes. planeT anderelativesharpness the maximum ($ magnetic feld between -electron- source and spectrometer of this energy E high-passBmin flter is only given by the ratio of max (3) Electrodes the minimum magnetic= feld min reached at the electrostatic max max Detector E Bmax+ T source barrier in the so-called analyzing plane and the maximum 2 - min )* ) Electrodes+ , magnetic feld between -electron- source and spectrometer(39) T source Analyzing) plane ) Detector) max max Δ. - 2 (without maxfeld) pe (without E field) max It isDetailed benefcial application to place+ the= electronto . source in a magnetic . - min # feld- somewhat lower than the maximum magnetic feld " )* )$ Electrodes+ , SKATRIN: Kleesiek et al., (39) T source ) ) Detector) max max. TusEPJC the magnetic 79 204 mirror(2019)efect based on the adiabatic Δ. - 2 (without feld) invariant-It is ( bene38)hinderselectronswithlargestartinganglesatfcial to place the= electron. source in a magnetic Figure 8:PrincipleoftheMAC-E-Filter.Top:experimentalsetup, -the source and long paths inside. the- source to enter the MAC- bottom:"# momentum$ transformationDiana due toParno adiabatic -- Recent invariance Results from of KATRIN --fNuPhyseld S 2019somewhat lower than the maximum7 magnetic feld E-Filter.. T Onlyus the electronsmagnetic are mirror able toef passect based the pinch on thefeld adiabaticmax the orbital magnetic momentum in the inhomogeneous magnetic whichmax exhibit starting angles at of feld. invariant- (38)hinderselectronswithlargestartinganglesatS S Figure 8:PrincipleoftheMAC-E-Filter.Top:experimentalsetup, ! -the source and long paths inside the source to enter the- MAC- bottom: momentum transformation due to adiabatic invariance of S E-Filter. Only electronssin areS/ able- to pass the pinch feld(40) the orbital magnetic momentum in the inhomogeneous magnetic max Terefore, in the presence of a missed experimental broaden- which exhibit starting angles2 atmax of feld. S - S ing with Gaussian width one expects a shif of the result on (/ )≤ . ! In principle, the pinch magnet could also be installed between- of - S the MAC-E-Filter and thesin detector,S/ - which counts the elec-(40) T2 erefore, in the presence" of a missed experimental broaden- trons transmitted by the MAC-E-Filter,2 max as long as the electron ! (37) - #ing($ with) Gaussian width one expects a shif of the result on transportIn principle, is always the pinch adiabatically. magnet(/ )≤ could Such also an. be arrangement installed between has 2 2 - which givesof rise to a negative! value of [18]. beenthe realized MAC-E-Filter at the KATRIN and the experiment.detector, which counts the elec- Δ# ($ )≈−2 ⋅" , Teexactshapeofthetransmissionfunctioncanbe 2 " 2 trons transmitted by the MAC-E-Filter, as long as the electron ! (37) calculated analytically. For an isotropically emitting monoen- 3.2#.1.MAC-E-Filter.($ ) Tesignifcant# improvement($!) in the transport is always adiabatically. Such an arrangement has 2 2 ergetic source of particles with kinetic energy and charge neutrinowhich gives mass rise sensitivity to a negative by! valuethe Troitsk of and[18 the]. Mainz been realized at the KATRIN experiment. Δ# ($ )≈−2 ⋅" , it readsT aseexactshapeofthetransmissionfunctioncanbe function of the retarding potential as experiments are due to MAC-E-Filters (Magnetic2 Adiabatic Collimation with an Electrostatic Filter). T!is new type of calculated analytically. For an isotropically emitting. monoen-1 3.2.1.MAC-E-Filter.Tesignifcant# improvement($ ) in the ergetic source of particles with kinetic energy2 and charge spectrometer—basedneutrino mass sensitivity on early by work the by Troitsk Kruit and and Read the [69 Mainz]— was developed for the application to the tritium -decay at it reads as function of the retarding potential as experiments are due to MAC-E-Filters (Magnetic Adiabatic 3 (., 2) for Mainz and Troitsk independently [70, 71]. TeMAC-E-Filter . 1 Collimation with an Electrostatic Filter). Tis new type of S combinesspectrometer—based high luminosity on early at low work background by Kruit and and+ Read a high[69]— 0 for .≤12,2 energy resolution, which are essential features to measure { min was developed for the application to the tritium -decay at { the neutrino mass from the endpoint region of a -decay 3 (.{, 2) .−12 - for Mainz and Troitsk independently [70, 71]. TeMAC-E-Filter {1 − √1 − S ⋅ for 12 < . < 12 + Δ., spectrum. = . - S combines high luminosity at low background and+ a high { 1 max for TemainfeaturesoftheMAC-E-Filterareillustrated {{0 .≤12, energy resolution, which are essential features to+ measure {{ - min (41) in Figure 8:twosuperconductingsolenoidsareproducing {{1 − √1 − 1.−12 - .≥12+ Δ.. the neutrino mass from the endpoint region of a -decay {{1 − √1 −- S ⋅ 12 < . < 12 + Δ., aspectrum. magnetic guiding feld. Te -electrons, starting from Figure= 9 shows the. transmission- for function of a MAC-E- { max the tritiumTemainfeaturesoftheMAC-E-Filterareillustrated source in the lef solenoid into the forward Filter at the{ example of the KATRIN experiment at its default + { - (41) hemisphere,in Figure 8 are:twosuperconductingsolenoidsareproducing guided magnetically+ on a cyclotron motion settings (see{1 −Section√1 − 4.4). .≥12+ Δ.. along the magnetic feld lines into the spectrometer yielding { - a magnetic guiding feld. Te -electrons, starting from TFiguree -electrons9 shows are the spiralling transmission around function the guiding of a MAC-E- mag- anthe accepted tritium solid source angle in of nearly the lef .solenoid On the way into of an the electron forward netic feld lines in zeroth approximation. Additionally, in into the center of the spectrometer the magnetic feld Filter at the example of the KATRIN experiment at its default hemisphere, are guided magnetically+ on a cyclotron motion non-homogeneoussettings+ (see Section electrical4.4). and magnetic felds they feel a decreases smoothly by several orders2 , of magnitude keeping along the magnetic feld lines into the spectrometer yielding smallT drief -electrons, which reads are in spirallingfrst order around [70]: the guiding mag- thean magnetic accepted solid orbital angle moment of nearly of the. On electron the way ofinvariant an electron- (equation given in nonrelativistic approximation) netic feld lines in zeroth approximation. Additionally, in into the center of the spectrometer the magnetic feld non-homogeneous: electrical and magnetic felds they( feel42) a ! + decreases smoothly by several orders2 , of magnitude keeping small drif , which reads⊥ in frst|| order [70]: the magnetic orbital momentconst of the electron invariant(38) .×⃗ -⃗ (. +2. ) ⊥ - :⃗ = ( 2 − 3 (-×∇⃗ -))⃗ . (equation given in nonrelativistic⊥ approximation) Te clear advantages of the MAC-E-Filter of large angular . : - >⋅- Terefore nearly all cyclotron! = energy= . is transformed into acceptance and high energy resolution come together with(42) - ! longitudinal motion (see Figure 8constbottom) giving rise to(38 a ) the danger to store⃗ charged⃗ particles⊥ || in Penning, magnetic ⊥ .×2- (. +23. ) ⊥ . Te clear:⃗ = advantages( − of the MAC-E-Filter(-×∇⃗ of-))⃗ large. angular .⊥ - >⋅- Terefore nearly all cyclotron! = energy= . is transformed into acceptance and high energy resolution come together with longitudinal motion (see Figure- 8 bottom) giving rise to a the danger to store charged particles in Penning, magnetic .⊥ A Quick Tour of the Beamline
1 e-/sec
ne 3He 3H 103 e-/sec e- Detect bs
1011 e-/sec Analyze b energy Gaseous
T2 source
Electron transport Calibration + tritium retention Diana Parno -- Recent Results from KATRIN -- NuPhys 2019 8 KATRIN by the Numbers
◆Expected mn sensitivity in 5 calendar years: 0.2 eV at 90% confidence
◆Magnetic field range 3 G – 60,000 G ◆Source activity: 1011 decays every second ◆95% tritium purity ◆Main spectrometer volume: 1240 m3
Diana Parno -- Recent Results from KATRIN -- NuPhys 2019 9 3 Leopoldshafen, Germany 1240 m in Real Life November 2006 Photo: KIT
Diana Parno -- Recent Results from KATRIN -- NuPhys 2019 10 The Plan
◆ Neutrino mass ◆ How the KATRIN experiment works ◆ Modeling the KATRIN spectrum ◆ Closing in on the neutrino mass n
Diana Parno -- Recent Results from KATRIN -- NuPhys 2019 11 Molecular Final-State Distribution ◆ Electronic excitations in T atoms
◆ Additional excitations in T2 gas ◆ Electronic: 20 eV ◆ Vibrational: ~0.1 eV BRIEF ARTICLE ◆ Rotational: ~0.01 eV THE AUTHOR ◆ Beta spectrum depends on excitation energies Vk and on probabilities Pk 2 5 2 dN GF me cos ✓C 2 2 (1) = 3 7 Mnuc F (Z, Ee)peEe Uei Pk(Emax Ee Vk) dEe 2⇡ ~ | | ⇥ | | Xi,k (E E V )2 m2 ⇥(E E V m ) ⇥ max e k ⌫i ⇥ max e k ⌫i q Diana Parno -- Recent Results from KATRIN -- NuPhys 2019 12
1 Theory Test: The Odd Observable Out ◆ How often does 3HeT+ stay bound after beta decay?
� HeT+ � = bound � He + T + � He+T+ + � HeT+ + � …
Theory Snell Experiment* Wexler Experiment* HT 0.55 – 0.57 0.932 ± 0.019 0.895 ± 0.011
T2 0.39 – 0.57 0.945 ± 0.006 Jonsell, Saenz, Snell, Pleasanton, Wexler, J. Inorg. Nucl. Froelich, PRC 60, Leming, J. Inorg. Chem. 10, 8 (1958) 034601 (1999) Nucl. Chem. 5, 112 (1957) * = Not really comparable ... Diana Parno -- Recent Results from KATRIN -- NuPhys 2019 13 Tritium Recoil-Ion Mass Spectrometer
◆ TRIMS (at University of Washington) aims to resolve the issue with a modern time-of-flight mass spectrometer ◆ Mass-3 dissociated ions are faster than mass-6 bound ions
HT – T2 gas mix ) keV + H 3He+, T+ 3HeH+ 3HeT+ Ion Energy ( Energy Ion
Plot from Ying-Ting Lin Ion Timing – Beta Timing (ns) Diana Parno -- Recent Results from KATRIN -- NuPhys 2019 14 KATRIN’s Response Function KATRIN, PRL 123 (2019) 221802 ◆ Electrons lose energy via scattering in the gas ◆ Test model with electron gun at upstream end of beamline ◆ Fold into experimental response
Diana Parno -- Recent Results from KATRIN -- NuPhys 2019 15 A Rube Goldberg Background
Rube Goldberg, Collier’s Magazine, 1931 Diana Parno -- Recent Results from KATRIN -- NuPhys 2019 16 A Rube Goldberg Rydberg Background
210Po ◆ Dominant background ◆ Tested with 220Rn source ◆ All daughters are short-lived
Slide credit: Luke Kippenbrock Diana Parno -- Recent Results from KATRIN -- NuPhys 2019 17 Rydberg Backgrounds II: I Want to Believe ◆ Blackbody radiation really can ionize these atoms ◆Simulations reproduce measured rate, dependences Hydrogen binding energies, 8 ≤ n ≤ 40
Intensity (arb. Intensity u.) BBR spectrum, 293 K
Energy Relativebackground reduction (eV) PhD thesis, Nikolaus Trost (KIT) Inner electrode offset Diana Parno -- Recent Results from KATRIN -- NuPhyspotential 2019 (V) 18 The Plan
◆ Neutrino mass ◆ How the KATRIN experiment works ◆ Modeling the KATRIN spectrum ◆ Closing in on the neutrino mass n
Diana Parno -- Recent Results from KATRIN -- NuPhys 2019 19 Spring 2019: KATRIN Takes Off
◆ A few glitches remained
Segmented KATRIN detector KATRIN, PRL 123 (2019) 221802 Rate goes up as voltage drops Diana Parno -- Recent Results from KATRIN -- NuPhys 2019 20 Glitch I: Column Density
◆ Tritium-decay b energy means radiochemistry ◆ Tritiated methane forms in source and freezes in capillary ◆ Ran at 20% nominal column density to control blockage ◆ Now solved via purging and thermal cycling
Diana Parno -- Recent Results from KATRIN -- NuPhys 2019 21 Glitch 2: Backgrounds ◆ Backgrounds 30x higher than design goal! ◆ Two weird sources: Rydberg atoms and Rn decay ◆ But, rates were stable and we have some countermeasures
Diana Parno -- Recent Results from KATRIN -- NuPhys 2019 22 Fitting the Data (in Principle)
◆ A KATRIN spectral fit ideally has four parameters: ◆ Amplitude / intensity ◆ Background rate ◆ Endpoint energy 2 ◆ mn
PhD thesis, Marco Kleesiek (KIT), 2014 Diana Parno -- Recent Results from KATRIN -- NuPhys 2019 23 Fitting the Data (in Practice)
◆ Fit of modeled to measured KATRIN data with 1 error bars 50 1 Fit result spectrum over all data 10 ◆ Treat detector as one uniform pixel 100 ◆ “Stack” similar high-voltage Count rate (cps)
settings ) -40 -30 -20 -10 0 10 20 30 40 ◆ 4 fit parameters: intensity, 2 Stat. Stat. + syst. background, endpoint, 0 -2 neutrino mass Residuals ( -40 -30 -20 -10 0 10 20 30 40 40
20 Time (h) 0 KATRIN, PRL 123 (2019) 221802 -40 -30 -20 -10 0 10 20 30 40 Retarding energy - 18574 (eV) Diana Parno -- Recent Results from KATRIN -- NuPhys 2019 24 Systematics KATRIN, PRL 123 (2019) 221802
Column density
Magnetic fields
Molecular physics
Drifts
Backgrounds
Statistical 0.97
Diana Parno -- Recent Results from KATRIN -- NuPhys 2019 25 The Results KATRIN, PRL 123 (2019) 221802
◆ Extract best-fit value and construct Lokhov-Tkachov* confidence belt . � = −1.0 . eV *Lokhov and Tkachov, Phys. Part. Nucl. 46 347 (2015) � < 1.1 eV (90% C.L.)
Diana Parno -- Recent Results from KATRIN -- NuPhys 2019 26 KATRIN Collaboration
Funding and support from: Helmholtz Association (HGF), Ministry for Education and Research BMBF (05A17PM3, 05A17PX3, 05A17VK2, and 05A17WO3), Helmholtz Alliance for Astroparticle Physics (HAP), and Helmholtz Young Investigator Group (VH-NG- 1055) in Germany; Ministry of Education, Youth and Sport (CANAM-LM2011019), cooperation with the JINR Dubna (3+3 grants) 2017– 2019 in the Czech Republic; and the Department of Energy through grants DE-FG02-97ER41020, DE-FG02-94ER40818, DE- SC0004036, DE-FG02-97ER41033, DE-FG02-97ER41041, DE-AC02-05CH11231, DE-SC0011091, and DE-SC0019304 in the United States. Diana Parno -- Recent Results from KATRIN -- NuPhys 2019 27 Conclusion
◆ We’ve learned a lot about neutrino mass in the last 8 months ◆ Factor of 2 improvement on direct neutrino-mass limit ◆ The KATRIN experiment is up and running in Germany. ◆ Better systematics ◆ More statistics ◆ End goal: 0.2 eV sensitivity at 90% confidence ◆ Stay tuned!
Thank you!
Diana Parno -- Recent Results from KATRIN -- NuPhys 2019 28 Backup
Diana Parno -- Recent Results from KATRIN -- NuPhys 2019 29 Different Neutrino Mass Probes
n oscillation 0nbb Cosmology Decay kinematics 2 Observable 2 2 2 2 2 2 2 2 Mν = mi m = U m Δmij = mi − mj mββ = ∑Ueimi ∑ νβ ∑ ei i i i i
2 −5 2 Present Δm21 = 7.53(18)×10 eV mββ < (0.2 − 0.4) eV Mν < (0.12 −1) eV 2 −3 2 mνβ < 2 eV knowledge Δm32 = 2.44(6)×10 eV Next 0.01 – 0.05 eV 0.01 – 0.05 eV 0.2 eV generation
Model No mass-scale • d1, d2 phases LCDM • Energy dependence of information • Nucl. matrix • Many conservation mass elements, gA parameters extraction • Majorana ns • H0 tension DianaDiana Parno Parno -- Recent -- Neutrino Results- Massfrom KATRIN Limits -- ThroughNuPhys 2019 Beta Decay 30 ASSESSMENT OF MOLECULAR EFFECTS ON NEUTRINO . . . PHYSICAL REVIEW C 91,035505(2015) ASSESSMENT OF MOLECULAR EFFECTS ON NEUTRINO . . . PHYSICAL REVIEW C 91,035505(2015) Eq. (13)summedoverfinalstatesk becomes TABLE IX. Atomic mass difference and neutrino mass squared ASSESSMENTASSESSMENT OF MOLECULARASSESSMENT OF MOLECULAR EFFECTS OF ON MOLECULAR EFFECTS NEUTRINO ON . EFFECTS NEUTRINO . . ON . NEUTRINO. . . . . PHYSICAL REVIEW PHYSICAL C 91 REVIEW,035505(2015) PHYSICAL C 91 REVIEW,035505(2015) C 91,035505(2015) Eq. (13)summedoverfinalstatesk becomes TABLE IX.extracted Atomic from mass two difference experiments, and neutrino in one mass case squared with the original 1985 dN peEe Ee 2 extracted2 from two experiments, in one case with the original 1985 dN CFpe(EZ,Ee ) Ee 1 W (" E ) . theoretical calculations of the FSD and in the second case with a more CF(Z,E ) 1e 2 W 2(" kE0 )2LANL,. k0 e LLNL and the FSD Eq. (13)summedoverfinalstatesdEe Eq.≃ e (13)summedoverfinalstates2 ASSESSMENTEq.ϵ (013)summedoverfinalstatesk becomes− OFMk00 MOLECULARk becomesk0| e| EFFECTSk becomes−theoreticalTABLE ON NEUTRINO calculations IX. AtomicTABLE . of . . mass the IX. FSD difference AtomicTABLE and in mass the IX.and second difference neutrinoAtomic case PHYSICAL mass mass and with difference neutrino squared a more REVIEW mass and squaredneutrino C 91,035505(2015) mass squared dEe ≃ ϵ − M0 ! | |" k − modern calculation. 0 ! " k # modernextracted(33) calculation. fromextracted two experiments, fromextracted two in experiments, one from case two with in experiments, one the original case with in 1985 the one original case with 1985 the original 1985 dN dN peEe dN EpeeE#e Epe2eEe ◆(33)EAny22e mistake2 in2 the FSD variance2 will shift the mass observable: CF(Z,Ee) CF2 (Z,E1 e) CF2 (Z,E1 Wek)0 (2"k0 1WEke0) .("k0 theoreticalWEek)0 . (" calculationsk0theoreticalEe) . of calculations thetheoretical FSD and of in calculationsthe the FSD second and case of in the the with FSD second a more and case in the with second a more case with a more dE ≃ dE ≃ ϵ Eq.dE− (13M≃)summedoverfinalstatesϵ |− M| ϵ −|− M| k becomes−| | − TABLERobertson IX.LANL Atomic and [15 Knapp,]LLNL[ mass Annu difference. Rev. Nucl. and neutrino16] mass squared e The summatione 0 maye be written00 k in terms0 0 ofk binding0 energieskmodern calculation.modern calculation.LANLmodern [15]LLNL[ calculation. 16] The summation may be written! in terms" ! of binding" energies! " extracted fromPart. Sci two 38, experiments, 185 (1988) in one case with the original 1985 dN # p E# ASSESSMENT(33)E # OF MOLECULAR(33) EFFECTS ON NEUTRINO(33) . . . PHYSICAL REVIEW C 91,035505(2015) and the atomicand the mass atomic difference, mass difference, e e e 2 As published2 .Theory:Fackleret al. [59] CF(Z,Ee) 2 1 As publishedWk0 (".Theory:Facklerk0 Ee) . theoreticalet al. [59] calculations of the FSD and in the second case with a more dEe ≃ ϵ Q−Eq.M (130)summedoverfinalstatesb | | k becomes− LANLTABLE [15 IX.]LLNL[ AtomicLANL mass difference [15 and]LLNL[ neutrinoLANL mass squared [1615]]LLNL[16] 16] 2 0 A Older0 calc.k (Fackler et al. 1985)"00 (eV)extracted from two 18experiments, 570.5(20) in one case with the original 1985 18 568.5(20) The summationThe may summation be writtenThe may summation in be terms written ofQ may bindingA in be termsb0 written! energies ofdN binding in" terms" energies00p ofeE(eV)e bindingEe energies 18 570.5(20)modern calculation. 18 568.5(20) 2 W (Q b 2m ) 1 − CF(Z,E ) 1 W 2(" E )2. W (Q k0 b 2Am ) 01 e #e 2 k0 k0 e theoretical calculations of the FSD and in the second case with a more k0 A 0 e − dEModerne ≃ calc. ϵ(Saenz− etM 0al. 2000)Q|A (eV)| (33)− 18 588.6(20) 18 586.6(25) and the atomicand mass the| atomic difference,| and mass the− difference, atomic+ mass difference,− 2M0 QA 0(eV)! " k 18 588.6(20)modern calculation. 18 586.6(25) | | − + − 2M0 As published#.Theory:FacklerAs published(33) .Theory:FacklerAset published al. [59] .Theory:Fackleret al. [59] et al. [59] k k $ ! " 2 2 2 2 #$ ! " m (eV ) mν (eV ) 147(79) 147(79)LANL [15]LLNL[LANL130(25) [1615] ]LLNL[130(25) 16] # 2 The2 summation may2QA beb written0 TheQ inA summation termsb0 may"ν of00 be writtenQ(eV) bindingA in termsb0 energies"of binding00 (eV) energies 18 570.5(20)"00 (eV) 18− 570.5(20) 18 18 568.5(20) 570.5(20) 18− 568.5(20) 18 568.5(20) Wk0 (QA Wbk00 2 2(QmAe) W1bk002 2(mQ−eA) 1b0 and2 them− atomice) mass1 difference, − − − m b meandE b the(f )k atomicEe mass difference,(34) Q(34)A (eV)QA (eV) 18As 588.6(20)Q publishedA (eV).Theory:Fackler 18 588.6(20)et al. [59] 18 18 586.6(25) 588.6(20) 18 586.6(25) 18 586.6(25) | e| (f )k |− |e+ −| −|+ 2M0 − −+ 2M0 Re2 − evaluated2M0 Re. Theory:QA evaluatedb0 SaenzAs."Theory:00et(eV) published al. [8] Saenz.Theory:Fackler 18 570.5(20)et al. [8] 18et 568.5(20) al. [59] k $ −k + $ k− ! $ ! " W!k0 "(Q2A b0 2 2me) 1 "2 − 2 Q 2(eV)2 18 588.6(20) 18 586.6(25) − + − | | m (eV− +) −m−2M(eV0 ) 147(79)mA (eV ) 147(79) 130(25)147(79) 130(25) 130(25) −ν ν ν 2 # # # k "$ (eV)QA b!"0 00 (eV)" 18 571.2(20)"m2 00(eV (eV)) 18 571.2(20)147(79) 18 18 569.2(20) 570.5(20)130(25) 18 569.2(20) 18 568.5(20) 2 2 2 2 2 2 2 2 # 00 − ν − − −− − − − W (δ Wbk0% (δ E )bW(,f )k%k0 E(Qe)A, b0 (35)2me) 1 (35) −2 mek0 b(f )k (mfE)eke b(fe)k mEe b(f )k Ee(34) me b(f )k(34)Ee (34)(34) ReQ evaluated(eV). Theory: Saenz et al. [8] 18 588.6(20) 18 586.6(25) ≡ | ≡| +| | − + | |− − + − QRe+A−(eV)−evaluated2M0 QReA. (eV)Theory:evaluated 18 Saenz 589.3(20)Re.−Theory:Aet al.evaluated[8 18] Saenz 589.3(20). Theory:et al. [8 18] Saenz 587.3(25)et al. [8] 18 587.3(25) − + −− + −− + − 2 2 "00 (eV) 18 571.2(20) 18 569.2(20) k k k $ ! W2k0 −(δ 2b(f )%k Ee) , "2 − 2 (35) 2− 2 ≡ | | + − mQA (eV)(eV ) 18 589.3(20)147(79) 18 587.3(25) 130(25) # k m"(eV(eV))m"(eV(eV)) 18 20(79) 571.2(20)"ν (eV) 18 20(79) 571.2(20) 18 18 37(25) 569.2(20) 571.2(20) 18 569.2(20) 37(25) 18 569.2(20) # #2 2 2 2 2 2 ν 00 ν 00 m2 (eV00 2) 20(79) 37(25) Wk0 (δ b(fW)%kk0 E(δe) ,b(fW)%k k0 E(δe) ,b(f(35))%k2 E#e) , (35) (35) ν − − where termswhere of ordertermsb of(f )k orderme/Mb0(fhave)kme/M beenm0 have droppedb been andEwhere dropped a terms of order andQAb(f(eV))k ame/M0 have beenQA dropped(eV)(34) and 18a 589.3(20)QA (eV) 18 589.3(20) 18 587.3(25)589.3(20) 18 587.3(25) 18 587.3(25) ≡ | | ≡ + | −| ≡+ |e −|(f )k+ eparameter− δ (the extrapolated end-point energy for zero final- Re evaluated. Theory: Saenz et al. [8] k k −k + − 2 Bodine,2 DSP, Robertson,2 2 Phys. Rev.2 C 912 , 035505 (2015) parameterparameterδ (the# extrapolatedδ (the# extrapolated end-point energy# end-point for zero energy final-state for binding) zero hasm final- beenν (eV defined) for brevity.mν The(eV summation)and 20(79)mν LLNL−(eV experiments) 20(79) as originally reported, 37(25) 20(79) both having 37(25) 37(25) 2 may then be carried2 out, been"00 analyzed(eV) with the theory of Fackler 18et al. 571.2(20)[59]. While 18 569.2(20) % Diana Parno -- Recent Results from KATRIN -- NuPhys 2019 31 statewhere binding) termsstatewhere hasbinding) of order been termsb hasdefined(f )kwhere ofm beene order/M for terms0 definedhaveb brevity.(f )k ofm beene for order/MW Thek0 brevity.droppedhaveb summation(δ(f )km beenb( Thee andf/M)k dropped0 a summationhaveEe)and, been and LLNL dropped a experimentsand LLNL and(35) a experiments asa originallyfull reanalysis would as reported, be desirable, originally it is both possible reported, tohaving estimate both having dN peEe Ee QA (eV) 18 589.3(20) 18 587.3(25) ≡ | | + − CF(Z,E ) 1 (δ b E )2 the changes that would be produced with the use of a more k e 2 (f )k e 2 2 mayparameter then beδ carried(theparameter extrapolated out, δ (theparameter extrapolatedend-pointδ (the energy end-point extrapolated for zero energy final- end-pointdEe for≃ zerobeen energy final-ϵ0 analyzed− forM0 zero+ with⟨ final-⟩− the theorymodern oftheory Fackler such as that ofet Saenz al.et[ al.59[8].]byapplying While may then be carried out, # ! been" analyzedm withν (eV the) theory of Fackler 20(79)et al. [59]. While 37(25) σ 2 Eqs. (36) and (37). The results are shown in the lower half of the state binding)state has binding) been definedstate has binding) been for brevity. defined has Thebeen for brevity. summation defined The for summation brevity.a1 and full LLNL reanalysis Theb summation experiments.and would LLNL(36) be experiments as desirable,and originally LLNL it asis experiments reported, possible originally both to as reported, estimate having originally both reported, having both having where terms of order b(f )kme/M0 have been droppeda2 full and reanalysis a table. would There is excellent be desirable, agreement between it the is atomic possible mass to estimate dN peEe Ee × + (δ b(f )k Ee) may then bedN carriedmay then out, be carriedmayp theneE out,e be carriedEe out, 2 $thebeen2 changes+ ⟨ analyzed⟩− that& been with would analyzed the be theorybeenfrom produced withβ decay analyzedof the and Fackler from with theory ion cyclotron with theet of al. use resonance, the Fackler[59 of theory 18]. a 589.8(12) While moreet of al. Fackler[59]. Whileet al. [59]. While CF(Z,Ee) parameter1 δ ((theδ extrapolatedb(f )k Ee) end-point energy for zero final- eV, and the large negative value of m2 is eliminated in both CF(2Z,Ee) 1 (δ bThe(f ) meank bindingEe energy) b(f )k actsthe as a shift changes in the extrap- that would be producedν with the use of a more dE ≃ ϵ − M2 + ⟨ ⟩− ⟨ ⟩ 2 2 2 e 0 0 olated end pointmodernaδ,andthevariance full reanalysis theoryσba full suchb(f would)k reanalysis asb(f )k that beaexperiments, desirable, fullof would Saenz reanalysis subject be it toet is thedesirable, al. possiblelimitations would[8]byapplying of the beit to approximations is desirable,estimate possible toit is estimate possible to estimate dEe ≃ state! binding)ϵ0 " − hasM been0 defined+ ⟨ for⟩− brevity. The summationmodern= ⟨ ⟩−⟨ theory⟩ and such LLNL as that experiments of Saenz aset originally al. [8]byapplying reported, both having dN dN peEe dN Epee!Ee "EpeeEe of2 the (full)Ee binding-energy2 distribution enters the2 expression used. These results provide a striking measure of experimental CF(Z,Ee) CF(2Z,E1 e) CF(δ(Z,E1 be()f )k (δE1eas) ab shape(f )k distortionEqs.the(δE neare ( changes)36 theb) end(f and) point.k ( thatthe Hence,37E).e changes both Thewould) the results first be thatbeentheconfirmation produced are changes would analyzed shown of the calculationsbe with in that produced the with the would of lower Saenz the useet al.halfwithbe theory of, especially produced a of the more the of in use Fackler withof a more theet al. use[59 of]. a While more 2 σmayb then be22 carried out, 2 and the second moments of the final-stateEqs. distribution (36) can and be (37the difficult). The regime results of electronic are excited shown states. in the lower half of the dEe ≃ 1 dEe ≃ ϵ0 dE−e M≃ϵ0σ0b. +−⟨ M0ϵ⟩−0 +(36)−⟨ M0⟩− + ⟨ ⟩− et al. et al. ! 2 " ! " ! extracted from"table. datamodern for comparison There theory with is theory.modern excellent such Table VIII astheorylists agreement thatamodern full such of Saenzreanalysis as theory between that of such would the Saenz[8]byapplying as atomic be thatet desirable, al. of mass[ Saenz8]byapplying it is possible[8]byapplying to estimate × + (δ 1b E ) . the first three moments(36) of the binding-energytable. distributions There for is excellent agreement between the atomic mass (f )k dN2 e 2 2peEe 2 Ee Eqs. (36) andEqs. (37). ( The36) and results (Eqs.37). are4. ( The Branching36 shown) resultsand ratios ( in to37 molecular the are). The lower shown and results atomic half inspecies the ofare the lower shown half in the of the lower half of the $ ×+ ⟨ + σ(⟩−δ b(fCF&)k σ(Z,EEe)) σ1two theories. from(δ β bdecay andE from)2 ionthe cyclotron changes resonance, that would 18 be 589.8(12) produced with the use of a more $ b + ⟨ ⟩−b e & 2 b In practice, experiments are(f ) notk from analyzedeβ in thisdecay way. andThe from branching ion ratio2 to cyclotron the bound molecular resonance, ion can be 18 589.8(12) 1 1 .1 . (36) table.. (36) There istable. excellent(36) There agreement istable.extracted excellent from There the between theory agreement is in excellent a straightforward the atomicbetween agreement way with mass cer- the atomic between mass the atomic mass The mean binding energy b(f )dEk actse ≃ as2 a shift in theϵ20 extrap-Rather,− M the0 FSD2eV, from+ andtheory⟨ is the used⟩− to large generate negativethe spectrum modern value of theorymν is eliminated such as that2 in of both Saenz et al. [8]byapplying The× mean+ binding(δ ×b(f energy)k+ (δEeb)×(fb()fk )k+acts(δE ase) ab shift(f!)k inE thee)" extrap- eV, and the largetain assumptions. negative Two 1950s value mass-spectrometry of m experimentsis eliminated in both ⟨ ⟩ 2 2 to be2 fitted to data,from from whichβ decay valuesfrom for andQA and fromβ mdecayν can ionfrom and cyclotron fromβ decay ion resonance, cyclotronand from 18 ion resonance, 589.8(12)ν cyclotron 18 resonance, 589.8(12) 18 589.8(12) olated end point$ δ,andthevariance+ ⟨ $ ⟩− +⟨ σ⟨b&$⟩ ⟩−b(f )k+2⟨& b(f2⟩−)2bek extracted. Inexperiments,& addition,2 only three experiments subject have to used theEqs.measured limitations (36 this) branching and of (37 ratio the). for The approximations HT [ results78,79]; one are of the shown in the lower half of the σ experiments also measured2 the branching ratio2 for T [79]. 2 olated end point δ,andthevariance= ⟨ σ⟩−⟨b b (gaseousf⟩)k tritium,b and(f the)k most modernexperiments, of these (Troitsk [23]) subject to the limitations of the2 approximations ofThe the mean (full) bindingbinding-energyThe mean energy bindingThe distributionb(f ) meank energyacts binding as entersb a1(f shift)k energy theacts in expression the asb a extrap-(f shift)k acts in the asused.eV,. extrap-a shift and These in the theresults largeeV, extrap- and(36) providenegative the large aeV,The value striking experimental and negative of the measurem resultsν large valueis are eliminated consistent negative of of experimental withmν eachis value in other eliminated both but of mν is in eliminated both in both = ⟨ has a scattering⟩−⟨2 contribution⟩ to the spectrum at energies more table. There is excellent agreement between the atomic mass of the (full) binding-energy⟨ ⟩ × distribution⟨2 +⟩(δ2 entersb⟨(2f )k the⟩2E2 expressione) 2 22 used. These2 resultsdisagree starklyprovide with the a theoretical striking prediction. measure of experimental asolated a shape end distortion pointolatedδ,andthevariance near end point theolated endδ,andthevariance point. end pointσ Hence,b δ,andthevarianceb(f both)k σ theb b( firstfthan)bk( 10f eV)k belowconfirmationσexperiments,b theb end(f ) point.kb(f However,)k ofexperiments, subject the theb two(f ) remainingk calculations to theexperiments, subject limitations of to Saenz the of subject limitationset the al. approximations, to especially the of limitations the inapproximations of the approximations $ + ⟨ ⟩−experiments, LANL& [15]andLLNL[16], used differential fromCalculationsβ decay of the dissociation and from likelihood ion rely cyclotron on the resonance, 18 589.8(12) as a shape distortion near the end= point.⟨ ⟩−⟨ Hence,= ⟨ both⟩ ⟩−⟨ the= first⟨ ⟩ ⟩−⟨confirmation⟩ oftheoretical the calculations dissociation energy of 1.897 of Saenz eV and assumeet that al., especially in andof the the second(full) binding-energyof moments the (full) of binding-energyof the distribution the final-state (full) binding-energy enters distribution distribution the expression enters can distributionspectrometers be the expression andtheused. enters magnetic-field difficult These the configurations regime expression resultsused. designed Theseof provide electronic for resultseV,used. a striking and excited Theseprovide the measure results large states. a striking negative provide of experimental measure valuea striking of of experimentalm measure2 is eliminated of experimental in both The mean binding energy b(f )abroadspectralreach.Thetwoexperimentswereingoodk acts as a shift in the extrap- all electronic excited states are dissociative, i.e., that there are ν as a shapeand distortion theas a second shape near distortion moments theas a end shape near point. of distortion the the Hence, final-state end point. near both distributionthe⟨ theHence, end first⟩ point. both canconfirmation2 the Hence, be first2 boththeconfirmation of the difficult the first calculations2 regimeconfirmation ofno fast the radiative of of calculations electronic Saenz transitions ofet between the al. of excited calculations, the Saenz especially excited states. stateset al.and of in, especially Saenz et al. in, especially in extracted from data for comparisonolated withend point theory.δ,andthevariance Table VIII listsagreement withσ each other,b but, as is well known,b(f both)k found experiments, subject to the limitations of the approximations an unexpected excessb of events(f in) thek end-point region, which bound states [54]. Under these assumptions, and working theand first the threeextracted second momentsand moments the from second of data the ofand for binding-energy the moments the comparison final-state second of the moments distribution distributionswith final-state theory. of the can distributionis Table for expressed final-state be VIII numericallythe can=lists distribution difficult as⟨ be a negative⟩−⟨m regimethe2.Theyalsoyielded can difficult be of⟩ electronic regimethenear the difficultβ of excitedend electronic point, regime Jonsell states.et excited ofal. [54 electronic] have states. calculated excited states. of the (full) binding-energy distribution enters4. the Branching expressionν ratios toused. molecular These and results atomic provide3 species a striking measure of experimental concordant values for Q ,butonlyrecentlyhasanaccurate abranchingratiotothebound HeT+ molecular ion of extractedthe from firstextracted data three for moments from comparisonextracted data offor with the comparison from binding-energy theory. data for Table with comparison theory.VIII distributionslists Table withVIII theory. forAlists Table VIII lists 0.39–0.57, depending on whether the quasibound states above two theories. as a shape distortion near the enddetermination point. of Q Hence,A by a non-β-decay both method, the ion first4. cyclotron Branchingconfirmation ratios to of molecular the calculations and atomic of Saenz specieset al., especially in the firsttwo three theories.the moments first three of thethe moments binding-energy first three of the moments binding-energy distributions of the binding-energyresonance distributionsfor in the SmiletrapThe for distributionsapparatus branching [53], become ratio for available tothe the binding bound energy dissociate. molecular An absolute uncertainty ion can of 0.2%, be In practice, experimentsand are the not second analyzed moments in this of the way.for final-state comparison. Table distributionIX shows4. Branching the results can of the4. be ratios LANL Branching tothederived molecular difficult from ratios4. requiring Branching and regimeto that molecular atomic the FSD of ratios integrate specieselectronic and to to molecular atomic 100%, is excited species and states. atomic species The branchinggiven for ratio calculation to of the the entire bound spectrum but molecular no explicit ion can be Rather,two theories. the FSDIntwo practice, from theories. theory experimentstwo is used theories. to generate are not the analyzed spectrum in thisextracted way. from the theory in a straightforward way with cer- extracted from data for comparison with theory.The Table branchingVIIIThelists ratio branching touncertainties theThe bound ratio are branching indicated to molecular the for the bound branching ratio ion ratios. to molecular the can bound be ion molecular can be ion can be In practice,Rather, theIn experiments practice, FSD from experimentsIn are theory practice, not isanalyzed used experimentsare to not in generate analyzed this are way.TABLE the not in VIII.spectrumtain thisanalyzed Comparison assumptions. way. of zeroth, in first,extracted this and second Two way. moments from 1950s theAcalculationofthedifferentialspectrumasafunctionof mass-spectrometry theory in a straightforward experiments way with cer- to be fitted to data, from whichthe first values three for momentsQA and of themν binding-energycanof theoretical final-state distributions distributions [10]. for electron energy4. would Branching permit a more ratios stringent test to of molecular the theory and atomic species measuredextracted this fromtainextracted branching the assumptions. theory from ratioextractedthan in the a the Two straightforward for energy-averaged theory 1950s HT from in [78 branching the a mass-spectrometry, straightforward79 theory]; way ratio. one Experimentally, with in of a straightforwardcer-the way experiments with cer- way with cer- Rather, the FSDRather, from the theory FSDRather, is from used the theory to FSD generate is from used thetheory to spectrum generate is used the to spectrum generate the spectrum2 2 be extracted.to be In fitted addition, to data, only from three which experiments values have for Q usedReferenceA and mν Excitationcan energy Wk0 b(f )k σb two theories. k | | ⟨ ⟩ the ability to distinguish between dissociation products (e.g., experimentstainrange assumptions. (eV) alsotain (eV) measured assumptions. Two (eV2 1950s) tain the mass-spectrometry assumptions. Two3 branching 1950s3 mass-spectrometry ratio Two for experiments 1950s T [ mass-spectrometry79]. experiments experiments to be fitted toto data, be fitted from toto which data, be fitted valuesfrom to which for data,Q values fromand whichm for Qcan valuesand m for canQ andmeasuredm can thisbetween branchingTheHe+ branchingTand ratioHe T+)allowsastrongertestthan ratio for HT to2 the [78 bound,79]; one molecular of the ion can be gaseous tritium,be extracted. and the In most addition, modernIn practice, only of these three experiments (TroitskA experiments [ areν23])A not have analyzed usedν A in' thisν way. + + Fackler et al. [59]0to1650.9949measured thismeasured branching17.71 611.04 thismeasuredasimplemeasurementofthedissociationlikelihood,yielding ratio branching for HT this ratio [ branching78,79 for]; HT one ratio [78 of,79 the for]; HT one [ of78, the79]; one of the The experimentalexperiments− results also areextracted consistent measured from with the the theorybranching each other in a ratio straightforwardbut for T2 [79 way]. with cer- hasbe a extracted. scatteringgaseousbe In contribution extracted. tritium, addition, andRather,be only In to extracted. theaddition, three spectrum most the FSD experiments only modern In from addition, at three energies theory of experiments have these only more isSaenz used used(Troitsk threeet al. [ to8]0to2400.9988 have experiments generate [23 used]) the have spectrum18.41 used 694.50 information about how the electronic states are populated gaseous tritium,gaseous and the tritium, mostgaseous and modern the tritium, most of these and modern the (Troitsk most of these [ modern23]) (Troitskdisagree ofexperiments these [23]) starkly (TroitskTheexperiments also with− experimental [23 measured]) the theoretical alsotainexperimentsafter theβ decay. assumptions. resultsmeasured branching prediction. are also the consistent ratio Two measured branching for1950s T2 with the mass-spectrometry ratio[79 branching]. each for T other2 [ ratio79 but]. experiments for T2 [79]. than 10 eVhas below a scattering the end contribution point.to be However, fitted to to the data, the spectrum two from remaining which at energies values more for QA and mν can TheCalculations experimentalThe of experimental results the035505-15 dissociation areThe consistent experimental results likelihood are with consistent results each rely other are on with consistent the but each other with but each other but experiments,has a scattering LANLhas contribution a scattering [15]andLLNL[behas to contribution extracted. a the scattering spectrum16 In], to contribution addition, used the at energies spectrum differential only to more theat three energies spectrum experiments more at energiesdisagree have more used starklymeasured with the this theoretical branching prediction. ratio for HT [78,79]; one of the than 10 eV below the end point. However, the two remainingtheoreticaldisagree starkly dissociationdisagree with the starkly energy theoreticaldisagree with of 1.897 the starkly prediction. theoretical eV with and the assume prediction. theoretical that prediction. spectrometersthan 10 eV belowthan and magnetic-field 10 the eV end belowgaseousthan point. 10the configurations However, eV tritium, end below point. andthe the However, two the designed end mostremaining point. the modern for However, two remaining of these the two (Troitsk remainingCalculations [23]) experiments of the dissociation also measured likelihood the branching rely on ratio the for T2 [79]. experiments, LANL [15]andLLNL[16], used differentialall electronicCalculations excitedCalculations of the states dissociation areCalculations of dissociative, the dissociation likelihood of i.e., the that rely likelihood dissociation there on are the rely likelihood on the rely on the abroadspectralreach.Thetwoexperimentswereingoodexperiments,experiments, LANL [15]andLLNL[hasexperiments, LANL a scattering [15]andLLNL[16 LANL], contribution used [15 differential]andLLNL[16 to], theused spectrum differential16], usedat energies differentialtheoretical more dissociationThe experimental energy of results 1.897 are eV consistent and assume with that each other but spectrometers and magnetic-field configurations designednotheoretical fast for radiative dissociationtheoretical transitions energy dissociationtheoretical between of 1.897 energy dissociation the eV excited of and 1.897 assume states energy eV and that and of 1.897 assume eV that and assume that agreementspectrometers withspectrometers andeach magnetic-field other,than but,spectrometers and as 10 magnetic-field is configurations eV well below and known, the magnetic-field configurations end designed both point. found for However, configurations designed the for two designedall remaining electronic for exciteddisagree states starkly are with dissociative, the theoretical i.e., that prediction. there are abroadspectralreach.Thetwoexperimentswereingoodabroadspectralreach.Thetwoexperimentswereingoodabroadspectralreach.Thetwoexperimentswereingoodabroadspectralreach.Thetwoexperimentswereingoodboundall electronic statesall [ excited54 electronic]. Under statesall excited these areCalculations electronic dissociative, assumptions, states excited are of dissociative,i.e., the and states that dissociation working there are i.e., dissociative, are that likelihood there i.e., are that rely there on the are an unexpectedagreement excess with of events eachexperiments, in other, the end-point but, LANL as is region, well [15]andLLNL[ known, which bothno16 found], fast used radiative differentialnono fast fast transitions radiative radiativeno between fast transitions transitions radiative the between between excited transitions states the the between excited excited and states thestates excited and and states and agreement withagreement each other, withagreement but, each as other, is wellwith2 but, known, each as other, is well both but, known, found as is both wellnear found known, the β bothend found point, Jonselltheoreticalet al. dissociation[54] have energy calculated of 1.897 eV and assume that is expressed numerically asspectrometers a negative mν and.Theyalsoyielded magnetic-field configurationsbound states designedboundbound [54]. for states Under states [bound54 [ these54].]. Under Under states assumptions,3 these [these54]. Under assumptions, assumptions, and working these assumptions, and and working working and working an unexpectedan unexpectedan excess unexpected of excess eventsan excess unexpected of in events the of events end-point in excess the in the end-point region, of end-point events which in region, the region, end-pointabranchingratiotothebound which which region, which all electronicHeT+ excitedmolecular states are ion dissociative, of i.e., that there are concordant values for QA,butonlyrecentlyhasanaccurateabroadspectralreach.Thetwoexperimentswereingoodnear the β end point, Jonsell et al. [54] have calculated 2 2 2 near2 the β endnear point, the β Jonsellendnear point, theet al.β Jonsellend[54] point, haveet al. Jonsell calculated[54] haveet al. calculated[54] have calculated is expressedis expressed numericallyis expressed numerically as numericallyis a expressed negative as a asm numerically negative a.Theyalsoyielded negativemν as.Theyalsoyieldedm a.Theyalsoyielded negative0m.39–0.Theyalsoyielded.57, depending on whetherno fast the radiative quasibound transitions3 states above between the excited states and determination of QA by a non-agreementβ-decay with method,ν each ion other, cyclotronν but, as is wellabranchingratiototheboundν known, bothabranchingratiototheboundabranchingratiotothebound found abranchingratiotothebound3HeT molecular3HeTHeT+ ionmolecularmolecular of3HeT ion ionmolecular of of ion of concordantconcordant valuesconcordant for valuesQ values,butonlyrecentlyhasanaccurateconcordant for Q forA,butonlyrecentlyhasanaccurateQ values,butonlyrecentlyhasanaccurate for Q ,butonlyrecentlyhasanaccuratethe binding energy dissociate.bound An absolute states [+ uncertainty54]. Under of+ these 0.2%, assumptions,+ and working resonance in the SmiletrapAan apparatus unexpected [53A ], excess become of events availableA in the end-point0.39–0.57, region,0 depending.039–0.39–0 which.57,.57, on depending depending whether0.39–0. the57, on on quasibound depending whether whether the the on states quasibound quasibound whether above the states states quasibound above above states above determinationdeterminationdetermination of QA by of aQ non-determination ofA byQβA-decay aby non- a non- method,β of-decayQβ-decayA by ion method, a cyclotron method,non-β ion-decay ion cyclotronderived cyclotron method,2 from ion cyclotron requiring thatnear the the FSDβ integrateend point, to Jonsell 100%, iset al. [54] have calculated for comparison. Table IX isshows expressed the results numerically of the as LANL a negative mtheν .Theyalsoyielded bindingthe energythe binding binding dissociate. energy energythe An binding dissociate. dissociate. absolute energy uncertainty An An dissociate. absolute of uncertainty uncertainty 0.2%, An absolute3 of of uncertainty 0.2%, 0.2%, of 0.2%, resonanceresonance inresonance the Smiletrap in the in Smiletrapresonance the apparatus Smiletrap apparatus in [53 the apparatus], Smiletrap become [53 [],53 available become apparatus], become available [given available53], become for calculation available of theabranchingratiotothebound entire spectrum but no explicit HeT+ molecular ion of concordant values for QA,butonlyrecentlyhasanaccuratederived fromderivedderived requiring from from thatderived requiring requiring the FSD from that that integrate requiring the the FSD FSD to that 100%,integrate integrate the is FSD to to 100%, integrate 100%, is is to 100%, is for comparison.for comparison.for comparison. Table IX Tabledeterminationforshows comparison.TableIX theshowsIX results ofshowsQ Table the ofby the results theIXa non- resultsshows LANLβ of-decay of the the theuncertainties LANL method, results LANL of ion the arecyclotron LANL indicated for0.39–0 the branching.57, depending ratios. on whether the quasibound states above TABLE VIII. Comparison of zeroth, first, and secondA moments given for calculationgivengiven for for calculation of calculation thegiven entire for of of spectrum calculation the the entire entire but of spectrum spectrum no the explicit entire but but spectrum no no explicit explicit but no explicit resonance in the Smiletrap apparatus [53Acalculationofthedifferentialspectrumasafunctionof], become available the binding energy dissociate. An absolute uncertainty of 0.2%, of theoretical final-state distributions [10]. uncertaintiesuncertaintiesuncertainties are indicated are areuncertainties for indicated indicated the branching for arefor the indicated ratios. branching branching for the ratios. ratios. branching ratios. for comparison. Table IX shows theelectron results energy of the would LANL permitderived a more from stringent requiring test of the that theory the FSD integrate to 100%, is TABLETABLE VIII.TABLE Comparison VIII. VIII. Comparison of ComparisonTABLE zeroth, ofVIII. first, zeroth, of and Comparison zeroth, second first, first, and moments of and second zeroth, second moments first,than moments andAcalculationofthedifferentialspectrumasafunctionof the second energy-averaged momentsAcalculationofthedifferentialspectrumasafunctionofAcalculationofthedifferentialspectrumasafunctionofgiven branchingAcalculationofthedifferentialspectrumasafunctionof for calculation ratio. Experimentally, of the entire spectrum but no explicit of theoretical final-stateof theoretical distributions final-stateof theoretical [10 distributions]. final-state2 [10 distributions]. 2 [10]. Referenceof theoretical Excitation final-state energy distributionsWk0 [10].b(f )k σ electron energyelectronelectron would energy energy permitelectron would would a more permit energy permit stringent awould a more test permit stringentof stringent the theory a more test test of stringent of the the theory theory test of the theory k | | ⟨ ⟩ b the ability to distinguish betweenuncertainties dissociation are indicated products for (e.g., the branching ratios. range (eV) (eV) (eV2) than the3 energy-averagedthan the3 energy-averagedthan branching the energy-averaged ratio. branching Experimentally, ratio. branching Experimentally, ratio. Experimentally, TABLE VIII. Comparison2 of zeroth,2 first,between and2 secondHethan momentsTand the energy-averagedHe AcalculationofthedifferentialspectrumasafunctionofT )allowsastrongertestthan branching ratio. Experimentally, ReferenceReference ExcitationReference energy Excitation' W energy Excitationb W energy2 σ 2 b W 2σ 2 b + σ 2 + Referenceof Excitation theoretical energyk final-statek0 distributions(Wf )kkk0 k0 bb [(f10)k(].f )kk theσk0 abilityb (f to)kthe distinguish+ abilityb to betweenthe distinguish+ ability dissociation to between distinguish products dissociation between (e.g., products dissociation (e.g., products (e.g., Fackler et al. [59]0to1650.9949| | 17.71⟨k | |⟩ | 611.04| ⟨ 2 ⟨ ⟩ asimplemeasurementofthedissociationlikelihood,yielding⟩| b| 2 ⟨ the⟩ ability2 to distinguishelectron energy between would dissociation permit a more products stringent (e.g., test of the theory range (eV)rangerange (eV) (eV)range (eV) (eV) (eV (eV)) (eV)between (eV (eV2) ) (eV)3Hebetween (eVTand)3 3He3HebetweenTandT )allowsastrongertestthan3He33He TTand)allowsastrongertestthan3He T )allowsastrongertestthan ' − ' 'informationbetween about+ howHe the++than electronicTand the+ energy-averagedHe+ statesT+ are)allowsastrongertestthan populated branching+ ratio. Experimentally, Saenz et al. [8]0to2400.9988'18.41 694.50 2 + 2 ++ + + + Fackler et al. [Fackler59]0to1650.9949et al. [59ReferenceFackler]0to1650.9949et al. [59]0to1650.9949 Excitation− 17.71 energy 611.0417.71k asimplemeasurementofthedissociationlikelihood,yieldingW 611.04k0 b17.71(f )kasimplemeasurementofthedissociationlikelihood,yielding 611.04σb theasimplemeasurementofthedissociationlikelihood,yielding+ ability to distinguish+ between dissociation products (e.g., Fackler et al. [59]0to1650.994917.71after 611.04| β| decay.⟨ asimplemeasurementofthedissociationlikelihood,yielding⟩ 2 −range (eV)− information− (eV)information about (eV how) the aboutinformation electronic how3 the about states electronic how are3 thepopulated states electronic are populated states are populated Saenz et al. [8]0to2400.9988Saenz et al. [8]0to2400.9988Saenz et al. [8]0to2400.998818.41 694.50− 18.41 694.50 18.41information 694.50 aboutbetween howHe the+ electronicTand He statesT+)allowsastrongertestthan are populated Saenz et al. [8]0to2400.9988− 18.41− ' 694.50after β −decay.after β decay.after β decay. + + Fackler et al. [59]0to1650.9949−035505-15 17.71after 611.04β decay. asimplemeasurementofthedissociationlikelihood,yielding Saenz et al. [8]0to2400.9988−18.41 694.50 information about how the electronic states are populated 035505-15 035505-15− 035505-15 035505-15 after β decay.
035505-15 Rydberg: Does This Really Make Sense? ◆ Dominant background is homogeneously distributed in the volume ◆ Background electrons are created with very low energy (< 1 eV) ◆ Rate dependence on temperature, inner-electrode offset, bakeout
Diana Parno -- Recent Results from KATRIN -- NuPhys 2019 32 Radon-Induced Backgrounds
simulation
measurement
clustered events
“single” events
◆ 219Rn emanates from NEG pumps ◆ Shakeoff electrons are magnetically trapped and ionize residual gas molecules ◆ Detected electrons show motion pattern of progenitors Slide credit: Florian Fränkle, KIT Diana Parno -- Recent Results from KATRIN -- NuPhys 2019 33 Suppression: Radon-Induced Background ◆ LN-cooled baffle at each pump port ◆ ~97% suppression with all three baffles cold ◆Testing optimal regeneration strategy Total background rate Total (cps)
Rate of events in clusters (cps) PhD thesis, Fabian Harms (KIT) Diana Parno -- Recent Results from KATRIN -- NuPhys 2019 34