1. Experimental methods for direct measurements of the Neutrino Mass Part - 1 Como – 30/05/2006

2. 2 Standard model WEAK INTERACTIONS PARTICLE : “ Neutrino ” Pauli (1930) – postulated to reconcile data on radioactive decay of nuclei with energy conservation No Strong or Electromagnetic Interactions (singlet of SU(3) C x U(1) EL ) Non-Sterile Neutrino Has Left – Handed Weak Interactions (SU(2) L )  “Weak” Partner of charged leptons Massless  due to SM gauge group: G SM = SU(3) C x SU(2) L x U(1) Y ) fermions have no bare mass terms (are in chiral representation of gauge group) Charged Fermions Mass arise from Yukawa interactions after spontaneous symmetry breaking Massless neutrino 

3. 3 These currents give all the neutrino interactions within the standard model Measurement of Z 0 weak-decay invisible width (measured at e + - e - annihilation)  only 3 light ( M ≤ M Z / 2 ) neutrinos N = 3.00 ± 0.06 Standard model WEAK INTERACTIONS : Neutrino current interactions terms (mathematically speaking) Charge current Neutral current  

4. 4 Standard model Standard model is not a complete picture of Nature: fine-tuning problem of Higgs mass (supersimm.) gauge coupling unification & many gauge representation (GUT) baryogenesis by heavy singlet fermions (leptogenesis) Gravity (string theories) A true possibility: standard model must be thought as a low energy theory   scale energy  NP under which SM is a valid approximation A possible extension of SM is the seesaw mechanism, where the break of total lepton number and lepton flavour symmetry occurs. The basic assumption is the existence of heavy sterile neutrinos that involves small mass-neutrinos.

5. 5 Standard model extension Neutrino mass pattern & mixing matrix Neutrino oscillations neutrino flavors are superposition of states of definite mass U is unitary  neutrino flavor is not a conserved quantity so  Where: 3 mix angles  13,  23,  12 (s ij and c ij are the respective sin and cosine) (unknown  13 ) 2 Squared mass difference (  m 2 big -  m 2 small ) (from oscillation experiments) CP violating phase  (unknown) 2 Majorana phases  1,  2 (unknown –  - 0 experiments for Majorana neutrinos) Absolute mass scale and hierarchy (normal, inverted or degenerate)

6. 6 No information about the absolute value of the neutrino masses direct measurements Hierarchy or Degeneracy are competitive scenarios M 1  M 2  M 3 M i < M j < M k M (eV) Mass state Standard model extension Electronic neutrino Information on the neutrino mass spectrum:  M Big 2  5 x 10 -3 eV 2  M Small 2  10 -4 eV 2 So, for electronic neutrino:(Majorana terms are not considered)

7. Role of the indirect constraints There are many indirect constraints on the absolute neutrino mass scale We will consider here two of them:  Neutrinoless Double Beta Decay it is a rare nuclear process that, if observed, would imply that  neutrinos are massive  neutrino is a Majorana particle = C present results: M < ~0.5 eV IF neutrino is a Majorana particle  Cosmic Microwave Background measurement WMAP results imply that, assuming neutrino full degeneracy, M < 0.23 eV (assumption of  CDM cosmological model and use of Galaxy Redshift Surveys) necessity of direct measurement at this scale

8. 8 Basic ideas for direct neutrino mass measurement  kinematics of processes involving neutrinos in the final state  +   + +  for M   -  m   + n  0 + v  for M   use dispersion in Time Of Flight of neutrinos from supernova explosion From SN1987A in Small Magellanic Cloud neutrinos were observed. Studying the spread in arrival times over 10 s leads to M e < 23 eV However, not better than 1 eV  uncertainties in time emission spectrum (A,Z)  (A,Z+1) + e - + e for M e use only: E 2 = M 2 c 4 + p 2 c 2  IT IS MODEL INDEPENDENT ! (A,Z) + e - at  (A,Z-1) +  + e for M e electron capture with inner bremsstrahlung not useful to reach the desired sub-eV sensitivity range, due to the high energy of the decay products with respect to the expected neutrino mass scale

9. 9 0.7 - 1 eV 0.5 eV 2.2 eV 0.1 eV 0.05 eV 0.2 eV Present sensitivity Future sensitivity (a few year scale) Cosmology (CMB + LSS) Neutrinoless Double Beta Decay Single Beta Decay Tools Model dependent Direct determination Laboratory measurements Tools for the investigation of the mass scale Neutrino oscillations cannot provide information about a crucial parameter in neutrino physics: the absolute neutrino mass scale

10. 10 The nuclear beta decay and the neutrino mass Fermi theory of weak interaction (1932) (A,Z)  (A,Z+1) + e - + e Q = M at (A,Z) – M at (A,Z+1)  E e + E  (Q – E e )  (Q – E e ) 2 – M 2 c 4 finite neutrino mass (Q – E e ) 2 dN dp  G F 2 |M if | 2 p 2 (Q – E e ) 2 F(Z,p) S(p,q) electron momentum distribution dN dE  G F 2 |M if | 2 (E e +m e c 2 ) (Q – E e ) 2 F(Z,E e )S(E e ) [1 +  R (Z,E e )] electron kinetic energy distribution zero neutrino mass only a small spectral region very close to Q is affected

11. 11 The nuclear beta decay and the neutrino mass So, the energy spectrum of emitted electron is: Phase space term Coulombian correction term (relativistic, finite size nucleus, no e - shielding) Form factor term Radiative electromagnetic correction term

12. 12 Spectral effects of a finite neutrino mass The more relevant part of the spectrum is a range of the order of [Q – M c 2, Q] The count fraction laying in this range is  (M  Q) 3  low Q are preferred Q E – Q [eV]

13. 13 Effects of a finite neutrino mass on the Kurie plot The Kurie plot K(E e ) is a convenient linearization of the beta spectrum Q Q–M c 2 Q K(E) zero neutrino massfinite neutrino masseffect of:  background  energy resolution  excited final states K(E)  dN dE G F |M if | 2 (E e +m e c 2 ) F(Z,E e ) S(E e ) [1 +  R (Z,E e )] 1/2  (Q – E e )  (Q – E e ) 2 – M 2 c 4 1/2  Q-  E Q (dN/dE) dE  2(  E/Q) 3

14. 14 Mass hierarchy In case of mass hierarchy:  the Kurie plot  superposition of three different sub - Kurie plots  each sub - Kurie plot corresponds to one of the three different mass eigenvalues The weight of each sub – Kurie plot will be given by |U ej | 2, where | e  =  U ei | Mi  i=1 3 This detailed structure will not be resolved with present and planned experimental sensitivities (~ 0.3 eV) K(E e ) EeEe Q – M 3 Q – M 2 Q – M 1 Q E e K(E e )

15. 15 Mass degeneracy In case of mass degeneracy: the Kurie-plot could be described in terms of a single mass parameter, a mean value of the three mass eigenstates Q – M  K(E e ) Q E e this is the only mechanism which can assure discovery potential to the direct measurement of neutrino mass with the present sensitivities, at least in the “standard” three light neutrino scenario M  =  M i |U ei | 2  |U ei | 2

16. 16 Experimental searches based on nuclear beta decay Requests :  high energy resolution  a tiny spectral distortion must be observed  high statistics in a very narrow region of the beta spectrum  well known response of the detector  spectral output for an energy  function input  control of any systematic effect that could distort the spectral shape Approximate approach to evaluate sensitivity to neutrino mass  M  Require that the deficit of counts close to the end point due to neutrino mass be equal to the Poissonian fluctuation of number of counts in the massless spectrum It underestimates the sensitivity, but it is very useful to understand the general trends and the difficulty of this experimental search  M  1.6 Q 3  E A T M  4 energy resolution total source activity live time

17. 17 electron kinetic energy distribution with zero neutrino mass and background B dN dE  G F 2 |M if | 2 (E e +m e c 2 ) (Q – E e ) 2 F(Z,E e ) S(E e ) [1 +  R (Z,E e )] + B dN dE  G F 2 |M if | 2 (E e +m e c 2 ) (Q – E e ) 2  1 – F(Z,E e ) S(E e ) [1 +  R (Z,E e )] (Q – E e ) 2 M 2 c 4 electron kinetic energy distribution with non-zero neutrino mass Effect of the background G F 2 |M if | 2 (E e +m e c 2 ) (Q – E e ) 2 1+ B G F 2 |M if | 2 (E e +m e c 2 ) (Q – E e ) 2 FS [1 +  R ] FS[1 +  R ] can be re-written as: unaccounted background gives negative neutrino mass squared M 2 c 4  – 2 B G F 2 |M if | 2 (E e +m e c 2 ) FS [1 +  R ] < 0

18. 18 Two complementary experimental approaches  determine electron energy by means of a selection on the beta electrons operated by proper electric and magnetic fields  measurement of the electron energy out of the source  present achieved sensitivity:  2 eV  future planned sensitivity:  0.2 eV  determine all the “visible” energy of the decay with a high resolution low energy “nuclear” detector  magnetic and electrostatic spectrometers  bolometers  present achieved sensitivity:  10 eV  future planned sensitivity:  0.2 eV(5y MARE)  measurement of the neutrino energy source coincident with detector (calorimetric approach)  source separate from detector (the source is always T)  completely different systematic uncertainties

19. 19 Historical improvement in T beta spectroscopy with magnetic / electrostatic spectrometers M 2 (eV 2 ) Experimental results on M  n.b.: neutrino mass squared is the experimentally accessible parameter all the experiments but one finds M   Tret’yakov magnetic spectrometers (1983-1993) ITEP (Moscow) (valine source)~ 30 eV Zurich(T 2 implanted source)< 12 eV Los Alamos (T 2 gaseous source)< 9 eV Livermore (T 2 gaseous source) < 7 eV Electrostatic spectrometers (1993-2000) Troitsk (T 2 gaseous source)< 3 eV Mainz (T 2 solid source)< 2 eV

20. 20 Beta spectroscopy with magnetic / electrostatic spectrometers Experimental procedure  T spectrum is scanned by stepping the selected energy from E min to Q  E max > Q to monitor the background  At each E e step, acquisition lasts a time interval  t, with  t increasing with E e Source Electron analyzerElectron counter T2T2 high activity high luminosity L  /4  (fraction of transmitted solid angol) high energy resolution two types:  differential: select E e window  integral: select E e > E th  high efficiency  low background source and spectrometer time stability – excellent live time control

21. 21 The problem of the excited states A good control of molecular excited states is necessary to understand spectral shapes Suppose to have N excited states E i with transition probability W i EeEe K(E e ) Q – E 1 Q – E 2 Q Q’ M > 0 It can be shown that: M 2  – 2(  E i  2 –  E i 2  ) Q’  Q –  E i  spectrum  superposition of N spectra with end point Q-E i, each weighted by W i less kinetic energy available for e and The concavity of the Kurie plot is changed to positive close to Q fake M 2 < 0

22. 22 Excited states and other spectral factors in T Final state distribution is very difficult to calculate for complex molecules Detailed calculations are available only for the process T 2  3 HeT + + e - + Other factors  Spectral shape S(E)=1 foR T (super-allowed transition)  Fermi function F(Z=1,E)  Radiative corrections Looking only at below the last 20 eV should allow to skip excited state problem A fraction of only 3x10 -10 counts lays in the last 10 eV

23. 23 Tritium sources Requests  High specific activity  Low self-absorption and inelastic scattering  Control of excited states  use of molecular tritium T 2 + low inelastic scattering probability + source homogeneity – backscattering from substrate – solid state excitation effects – source charging – surface roughening + highest specific activity + lowest inelastic scattering probability + no backscattering + no source charging + source homogeneity + calibration with radioactive gasses – source strength stability Solid frozen T 2 source Gaseous windowless T 2 source

24. 24 Electrostatic spectrometers with Magnetic Adiabatic Collimation (MAC-E-filter) These instruments enabled a major step forward in sensitivity after 1993 They are the basic devices for next generation experiments aiming at the sub-eV range High magnetic field B max at source and detector. Low field B min at center. All electrons emitted in the forward hemisphere spiral from source to detector In the adiabatic limit E k  / B = constant E k  (center) = E k  (source) (B min /B max ) Since E e = E k  + E k  = constant efficient collimation effect in the center The retarding electric field at the center has maximum potential U 0 and admits electrons with E k  > eU 0 Integral spectrometer Resolving power:  E / E = B min / B max  2 x 10 -4 magnetic bottle  E  4 eV at E  18 keV

25. 25 The experimental beta spectrum with spectrometers R(eU) is fitted with A, Q, B, M 2 as free parameters dN theo dE (Q, M 2 )  F trans (eU-E)  F eloss (E)  F bsc (E)  F charge (E)  F det (E) + B =A R(eU) counting rate for a retarding potential eU theoretical beta spectrum, including radiative corrections and excited final states spectrometer transmission function energy loss in the source backscattering on the source substrate (for frozen source only) potential distribution in the T film (for frozen source only) detector efficiency spectrometer response function r (eU-E) = F trans (eU-E)  F eloss (E)  F bsc (E)  F charge (E) r(eU-E) eU – E (eV) 1 0 ideal response function real response function It is determined experimentally with monochromatic electron sources and at least for some effects it can be determined numerically

26. 26 Experiments with MAC electrostatic spectrometers In the 90’s two experiments based on the same principle improved limit on neutrino mass down to about 2 eV at 95% c.l. Both experiments have reached their final sensitivity KATRIN KArlsruhe TRItium Neutrino experiment new generation experiment aiming at a further factor 10 improvement in sensitivity Mainz (Germany)  frozen T 2 source  complicated systematic in the source solved Troitsk (Russia)  gaseous T 2 source  unexplained anomaly close to the end point collaborations has joined + other institutions (large international collaboration)

27. 27 MAC electrostatic spectrometer with windowless gaseous T 2 source 240 days of measurement (from Jan 1994 to Dec 1999) Troitsk experiment: the set-up Differentially pumped gaseous T 2 source with magnetic transport L = 3 m -  = 50 mm p = 10 -2 mbar T = 26 – 28 K T2 : HT : H2 = 6 : 8 : 2 L = 6 m -  = 2 m P = 10 -9 mbar

28. 28 Troitsk experiment: the calibration Energy resolution:  E FW = 3.5 – 4 eV Monochromatic 0.5 eV energy-spread electrons from electron gun eU 0 (eV) Careful measurement of the response function, without T 2 gas and with T 2 gas at different pressures r eU – E (eV)

29. 29 Troitsk experiment: the anomaly eU 0 (eV) Rate E low (eV) M 2 (eV 2 ) relative intensity: 6x10 -11 peak position change with time collected data present an anomaly integral spectrum must be fitted with a step function 5-15 eV below Q a peak in the differential spectrum without step function M 2 is negative and not compatible with 0 with step function included in the fit: M 2 = -1.9  3.4  2.2 eV 2 M < 2.5 eV (95% c.l.)

30. 30 Troitsk experiment: the speculation 13 orders of magnitude higher than foreseen by standard cosmology hypotheses:  neutrinos are bound in the solar system in a cloud  the binding energy varies within the cloud  semiannual effect probably, experimental artifact position Q – E step changes periodically with T = 0.5 y between 5 and 15 eV attempts to correlate with Mainz measurement mostly failed neutrino density ~ 0.5 x 10 15 cm -3 exotic explanation e + T  3 He + e -  = 0.77 x 10 -44 cm 2 Q Q + M - E b Q + M Q + M – E bound Q + M Q

31. 31 MAC electrostatic spectrometer with frozen solid T 2 source Mainz experiment: the set-up Segmented Si detector to help background rejection L = 2 m -  = 0.9 m p = 0.5 x 10 -10 mbar B min = 5x10 -4 T T 2 film quench-condensed on a graphite substrate  T source = 1.86 K  thickness = 45 nm 130 mL  area = 2 cm 2  activity = 20 mCi

32. 32 Mainz experiment: control of the systematic systematic constantly improved  M 2, significantly negative at the beginning, is now statistically compatible with zero Signal to background ratio – improved by:  background reduction  maximization of source strength Detailed study of the systematic induced by the quench condensed source  Source roughening (which induces dispersion in energy losses) is reduced by cooling the T 2 film down to 1.2 K  The source charging and the related potential profile is modeled and included in the analysis  F charge  Energy loss in the source was studied with different source thicknesses  F eloss r eU 0 (keV)

33. 33 Mainz experiment: the results M 2 = -1.2  2.2  2.1 eV 2 M < 2.2 eV (95% c.l.) Final experimental sensitivity reached Rate eU 0 (keV) source charging effect Clear improvement in signal-to-background ratio from 1994 set-up to 1998-2001 set-up To reduce systematic uncertainties, only the final 70 eV are used  M 2 ~ 0 M 2 (eV 2 ) E low (keV) 100 eV

34. 34 Next generation of MAC spectrometer: the KATRIN proposal Strategy  better energy resolution   E FW ~ 1 eV  higher statistic  stronger T 2 source – longer measuring times  better systematic control  in particular, improve background rejection Goal: to reach sub-eV sensitivity on M letter of intent hep-ex/0109033 Double source control of systematic Pre-spectrometer selects electrons with E>Q-100 eV (10 -7 of the total) Better detectors:  higher energy resolution  time resolution (TOF)  source imaging Main spectrometer  high resolution  ultra-high vacuum (p<10 -11 mbar)  high luminosity

35. 35 KATRIN sensitivity In addition, no excited states below 27 eV Simulation to evaluate sensitivity   E = 1 eV   spect = 7 m (10 m)  Background = 11 mHz  Source: area 29 cm 2 column density 5 x 10 17 molecule/cm 2 Sensitivity on M 2 : 0.35 eV with  spec = 10 m sensitivity down to 0.25 eV Schedule:  2003: proposal + pre-spectrometer  2004: application for funds  2007: start No electron inelastic scattering is possible in T 2 with energy loss lower than 12 eV The response function is flat for Q – 12 eV < eU 0 < Q Use small region below end-point of the order of 20 eV

36. 36  Neutrino is at the frontier of particle physics Its properties have strong relevance in cosmology and astrophysics  Absolute mass scale, a crucial parameter, is not accessible via flavor oscillations  Direct measurement through single beta decay is the only genuine model independent method to investigate the neutrino mass scale Conclusion  Neutrino needs more research and researchers, even if it cannot interact with.