Experimental methods for direct measurements of the Neutrino Mass Part - 1 Como – 30/05/2006.
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Transcript of Experimental methods for direct measurements of the Neutrino Mass Part - 1 Como – 30/05/2006.
Experimental methods Experimental methods for direct measurements for direct measurements
of the Neutrino Massof the Neutrino Mass
Part - 1Part - 1
Como – 30/05/2006
2
Standard modelStandard 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: GSM= 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
L
ll l
L
,,el
3
These currents give all the neutrino interactions within the standard model
Measurement of Z0 weak-decay invisible width (measured at e+- e- annihilation)
only 3 light ( M ≤ MZ / 2 ) neutrinos
N = 3.00 ± 0.06
Standard modelStandard model
WEAK INTERACTIONS : Neutrino current interactions terms (mathematically speaking)
..cos
..
L
L
CHZg
CHWlg
Llll
WNC
LllCC
0
2
2
Charge current
Neutral current
4
Standard modelStandard 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
Standard model extensionStandard model extensionNeutrino mass pattern & mixing matrixNeutrino mass pattern & mixing matrix
Neutrino oscillations
neutrino flavors are superposition of states of definite mass
ilil U
U is unitary neutrino flavor is not a conserved quantity so 'll
Where:
• 3 mix angles 13, 23, 12 (sij and cij are the respective sin and cosine) (unknown 13)
• 2 Squared mass difference (m2big - m2
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
No information about the absolute value
of the neutrino masses
direct measurements
Hierarchy or Degeneracy are competitive scenarios
M1 M2 M3
Mi < Mj < Mk
M
(eV
)
Mass state
Standard model extensionStandard model extensionElectronic neutrinoElectronic neutrino
Information on the neutrino mass spectrum:MBig
2 5 x 10-3 eV2
MSmall2 10-4 eV2
So, for electronic neutrino:222iei mUm
e
(Majorana terms are not considered)
Role of the indirect constraintsRole 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
Basic ideas for direct neutrino mass measurementBasic ideas for direct neutrino mass measurement
kinematics of processes involving neutrinos in the final state
+ + + for M
- m + n0 + vfor 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
Me < 23 eVHowever, not better than 1 eV uncertainties in time emission spectrum
(A,Z) (A,Z+1) + e- + e for Me
use only: E2 = M2c4 + p2c2 IT IS MODEL INDEPENDENT !
(A,Z) + e-at (A,Z-1) + + e for Me
electron capture withinner bremsstrahlung
not useful to reach the desired sub-eV sensitivity range, due to the high energyof the decay products with respect to the expected neutrino mass scale
9
0.7 - 1 eV
0.5 eV
2.2 eV
0.1 eV
0.05 eV
0.2 eV
Presentsensitivity
Future sensitivity
(a few year scale)
Cosmology (CMB + LSS)
Neutrinoless Double Beta Decay
Single Beta Decay
Tools
Model dependentDirect determinationLaboratory measurements
Tools for the investigation of the Tools for the investigation of the mass scale mass scale
Neutrino oscillations cannot provide information about a crucialparameter in neutrino physics: the absolute neutrino mass scale
10
The nuclear beta decay and the neutrino massThe nuclear beta decay and the neutrino mass
Fermi theory of weak interaction (1932)
(A,Z) (A,Z+1) + e- + e
Q = Mat(A,Z) – Mat(A,Z+1) Ee + E
(Q – Ee) (Q – Ee)2 – M2c4
finite neutrino mass
(Q – Ee)2
dNdp
GF2 |Mif|2 p2 (Q – Ee)2 F(Z,p) S(p,q)
electron momentum distribution
dNdE
GF2 |Mif|2 (Ee+mec2) (Q – Ee)2 F(Z,Ee) S(Ee) [1 + R(Z,Ee)]
electron kinetic energy distribution
zero neutrino mass
only a small spectral region very close to Q is affected
11
The nuclear beta decay and the neutrino massThe nuclear beta decay and the neutrino mass
So, the energy spectrum of emitted electron is:
dE
dN
Phase space term
Coulombian correction term (relativistic, finite size nucleus, no e- shielding)
Form factor term
Radiative electromagnetic correction term
12
Spectral effects of a finite neutrino massSpectral effects of a finite neutrino mass
The more relevant part of the spectrum is a range of the order of [Q – Mc2 , Q]
The count fraction laying in this range is (MQ)3 low Q are preferred
Q
E – Q [eV]
13
Effects of a finite neutrino mass on the Kurie plot Effects of a finite neutrino mass on the Kurie plot
The Kurie plot K(Ee) is a convenient linearization of the beta spectrum
Q–Mc2 Q
K(E
)
zero neutrino mass
finite neutrino mass
effect of: background energy resolution excited final states
K(E)
dNdE
GF |Mif|2 (Ee+mec2)F(Z,Ee) S(Ee) [1 + R(Z,Ee)]
1/2
(Q – Ee) (Q – Ee)2 – M2c4
1/2
Q-E
Q
(dN/dE) dE 2(E/Q)3
14
Mass hierarchyMass hierarchyIn 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 |Uej|2, where
|e = Uei |Mi i=1
3
This detailed structure will not be resolved with present and
planned experimental sensitivities(~ 0.3 eV)
K(E
e)
Ee
Q – M3
Q – M2
Q – M1
Q Ee
K(Ee)
15
Mass degeneracyMass 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 Ee
this is the only mechanismwhich 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 = Mi |Uei|2
|Uei|2
16
Experimental searches based on nuclear beta decayExperimental 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 beequal 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 difficultyof this experimental search
M1.6 Q3 E
A TM4
energy resolutiontotal source activity
live time
17
electron kinetic energy distribution with zero neutrino mass and background B
dNdE
GF2 |Mif|2 (Ee+mec2) (Q – Ee)2 F(Z,Ee) S(Ee) [1 + R(Z,Ee)] + B
dNdE
GF2 |Mif|2 (Ee+mec2) (Q – Ee) 2 1 – F(Z,Ee) S(Ee) [1 + R(Z,Ee)]
(Q – Ee) 2
M2c4
electron kinetic energy distribution with non-zero neutrino mass
Effect of the background Effect of the background
GF2 |Mif|2 (Ee+mec2) (Q – Ee)2 1+
B
GF2 |Mif|2 (Ee+mec2) (Q – Ee)2 FS[1 + R]
FS[1 + R]
can be re-written as:
unaccounted background gives negative neutrino mass squared
M2c4 –
2 B
GF2 |Mif|2 (Ee+mec2) FS [1 + R]
< 0
18
Two complementary experimental approachesTwo 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
Historical improvement in T beta spectroscopyHistorical improvement in T beta spectroscopywith magnetic / electrostatic spectrometers with magnetic / electrostatic spectrometers
M2
(eV
2)
Experimental results on M
n.b.: neutrino mass squared is theexperimentally accessible parameter
all the experiments but one finds M
Tret’yakov magnetic spectrometers (1983-1993)
ITEP (Moscow) (valine source) ~ 30 eVZurich (T2 implanted source) < 12 eVLos Alamos (T2 gaseous source) < 9 eVLivermore (T2 gaseous source) < 7 eV
Electrostatic spectrometers (1993-2000)
Troitsk (T2 gaseous source) < 3 eVMainz (T2 solid source) < 2 eV
20
Beta spectroscopy Beta spectroscopy with magnetic / electrostatic spectrometers with magnetic / electrostatic spectrometers
Experimental procedure T spectrum is scanned by stepping the selected energy from Emin to Q Emax > Q to monitor the background At each Ee step, acquisition lasts a time interval t, with t increasing with Ee
Source Electron analyzer Electron counter
T2
high activity
high luminosity L/4(fraction of transmitted
solid angol)
high energy resolutiontwo types: differential: select Ee window integral: select Ee > Eth
high efficiency low background
source and spectrometer time stability – excellent live time control
21
The problem of the excited states 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 Ei with transition probability Wi
Ee
K(E
e)
Q – E1
Q – E2
Q
Q’
M > 0
It can be shown that:
M2 – 2(Ei2 – Ei
2 )
Q’ Q – Ei
spectrum superposition of N spectra with end point Q-Ei, each weighted by Wi
less kinetic energy available for e and
The concavity of the Kurie plotis changed to positive close to Q
fake M2 < 0
22
Excited states and other spectral factors in T 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
T2 3HeT+ + 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 problemA fraction of only 3x10-10 counts
lays in the last 10 eV
23
Tritium sources Tritium sources
Requests
High specific activity Low self-absorption and inelastic scattering Control of excited states use of molecular tritium T2
+ 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 T2 source Gaseous windowless T2 source
24
Electrostatic spectrometers Electrostatic spectrometers with Magnetic Adiabatic Collimation (MAC-E-filter) with Magnetic Adiabatic Collimation (MAC-E-filter)
These instruments enabled a major step forward in sensitivity after 1993They are the basic devices for next generation experiments aiming at the sub-eV range
High magnetic field Bmax at source anddetector. Low field Bmin at center.
All electrons emitted in the forward hemisphere spiral from source to detector
In the adiabatic limit
Ek / B = constant
Ek(center) = Ek(source) (Bmin/Bmax)
Since Ee = Ek + Ek= constant efficient collimation effect in the center
The retarding electric field at the center hasmaximum potential U0 and admits electrons with
Ek> eU0
Integral spectrometer
Resolving power: E / E = Bmin / Bmax 2 x 10-4
magnetic bottle
E 4 eV at E 18 keV
25
The experimental beta spectrum with spectrometers The experimental beta spectrum with spectrometers
R(eU) is fitted with A, Q, B, M2 as free parameters
dNtheo
dE(Q, M
2) Ftrans(eU-E) Feloss(E) Fbsc(E) Fcharge(E) Fdet(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) = Ftrans(eU-E) Feloss(E) Fbsc(E) Fcharge(E)
r(eU-E)
eU – E (eV)
1
0
ideal response function
real response function
It is determined experimentally with monochromatic electron sourcesand at least for some effects it can be determined numerically
26
Experiments with MAC electrostatic spectrometersExperiments 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
KATRINKATRINKAKArlsruhe rlsruhe TRITRItium tium NNeutrino experimenteutrino experiment
new generation experiment aiming at afurther factor 10 improvement in sensitivity
Mainz (Germany)Mainz (Germany) frozen T2 source complicated systematic in the source solved
Troitsk (Russia)Troitsk (Russia) gaseous T2 source unexplained anomaly close to the end point
collaborations has joined + other institutions (large international collaboration)
27
MAC electrostatic spectrometer withwindowless gaseous T2 source
240 days of measurement(from Jan 1994 to Dec 1999)
Troitsk experiment: the set-upTroitsk experiment: the set-up
Differentially pumped gaseous T2
source with magnetic transportL = 3 m - = 50 mmp = 10-2 mbarT = 26 – 28 KT2 : HT : H2 = 6 : 8 : 2
L = 6 m - = 2 mP = 10-9 mbar
28
Troitsk experiment: the calibrationTroitsk experiment: the calibration
Energy resolution: EFW = 3.5 – 4 eV
Monochromatic 0.5 eV energy-spread electrons from electron gun
eU0 (eV)
Careful measurement of theresponse function, without T2 gas
and with T2 gas at different pressures
r
eU – E (eV)
29
Troitsk experiment: the anomalyTroitsk experiment: the anomaly
eU0 (eV)
Rat
e
Elow (eV)
M2
(eV
2)
relative intensity: 6x10-11
peak position change with time
collected data present an anomalyintegral spectrum must be fitted
with a step function 5-15 eV below Q
a peak in the differential spectrum
without step function M2 is negative
and not compatible with 0
with step function included in the fit:
M2 = -1.9 3.4 2.2 eV2
M < 2.5 eV (95% c.l.)
30
Troitsk experiment: the speculationTroitsk experiment: the speculation
13 orders of magnitude higher thanforeseen 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 – Estep changes periodicallywith T = 0.5 y between 5 and 15 eV
attempts to correlate with Mainzmeasurement mostly failed
neutrino density ~ 0.5 x 1015 cm-3
exotic explanation
e + T 3He + e-
= 0.77 x 10-44 cm2
Q
Q + M - EbQ + M
Q + M – Ebound Q + M
Q
31
MAC electrostatic spectrometer with frozen solid T2 source
Mainz experiment: the set-upMainz experiment: the set-up
Segmented Si detector to help background
rejection
L = 2 m - = 0.9 mp = 0.5 x 10-10 mbarBmin = 5x10-4 T
T2 film quench-condensedon a graphite substrate Tsource = 1.86 K thickness = 45 nm 130 mL area = 2 cm2
activity = 20 mCi
32
Mainz experiment: control of the systematicMainz experiment: control of the systematic
systematic constantly improved M2, 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 inducedby the quench condensed source
Source roughening (which induces dispersion in energy losses) is reduced by cooling the T2 film down to 1.2 K
The source charging and the related potential profile is modeled and included in the analysis Fcharge
Energy loss in the source was studied with different source thicknesses Feloss
r
eU0 (keV)
33
Mainz experiment: the resultsMainz experiment: the results
M2 = -1.2 2.2 2.1 eV2 M < 2.2 eV (95% c.l.)
Final experimental sensitivity reached
Rat
e
eU0 (keV)
sourcecharging
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 M2 ~ 0
M2
(eV
2)
Elow (keV)
100 eV
34
Next generation of MAC spectrometer:Next generation of MAC spectrometer:the KATRIN proposalthe KATRIN proposal
Strategy better energy resolution EFW ~ 1 eV higher statistic stronger T2 source – longer measuring times better systematic control in particular, improve background rejection
Goal: to reach sub-eV sensitivity on M
letter of intenthep-ex/0109033
Double sourcecontrol of systematic
Pre-spectrometerselects 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
KATRIN sensitivityKATRIN sensitivity
In addition, no excited states below 27 eV
Simulation to evaluate sensitivityE = 1 eV spect = 7 m (10 m) Background = 11 mHz Source: area 29 cm2
column density 5 x 1017 molecule/cm2
Sensitivity on M2: 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 possiblein T2 with energy loss lower than 12 eV
The response function is flat forQ – 12 eV < eU0 < Q
Use small region below end-pointof the order of 20 eV
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.