Neutrino masses and Double Beta Decay Andrea Giuliani University of - - PowerPoint PPT Presentation
Neutrino masses and Double Beta Decay Andrea Giuliani University of Insubria (Como) and INFN Milano-Bicocca Italy 21 July: introduction and discussion of the experimental approaches 22 July: status and prospects of the experimental
Andrea Giuliani
University of Insubria (Como) and INFN Milano-Bicocca Italy
Neutrino masses and Double Beta Decay
Outline of the lectures
21 July 22 July
Neutrino flavor oscillations
neutrinos are massive
Premise
Flavor eigenstates ≠ Mass eigenstates
Weak interaction Propagation
Neutrino flavor oscillations what we presently know from neutrino flavor oscillations
Neutrino mixing and masses
given the three ν mass eigenvalues M1, M2, M3 we have approximate measurements of two ∆Mij
2
∆M12
2 ~ (9 meV)2 Solar
|∆M23
2 | ~ (50 meV)2
Atmospheric
(∆Mij
2 ≡ Mi 2 – Mj 2)
ν1 ν2 ν3 νe νµ ντ
approximate measurements and/or constraints on Ulj
elements of the ν mixing matrix
< 0.2 TBM mixing
Summary of our present knowledge
Nσ solar atmospheric < 0.031 = 1/3 = 0 = 1/2 TBM: cij=cosθij sij=sinθij δ: CP violating phase Majorana CP violating phases
…in another form
Neutrino flavor oscillations and mass scale
what we do not know from neutrino flavor oscillations: neutrino mass hierarchy
direct inverted
absolute neutrino mass scale
degeneracy ?
(M1~M2~M3 )
DIRAC or MAJORANA nature of neutrinos
ν ≠ ν ν ≡ ν
Tools for the investigation of the ν mass scale
0.5 - 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
Complementarity of cosmology, single and double β decay
Cosmology, single and double β decay measure different combinations
In a standard three active neutrino scenario:
i=1 3
cosmology simple sum pure kinematical effect
2 |Uei|2
i=1 3 1/2
beta decay incoherent sum real neutrino
i
i=1 3
double beta decay coherent sum virtual neutrino Majorana phases
Present bounds Σ [eV] 〈Mββ〉 [eV] 〈Mβ〉 [eV]
The three constrained parameters can be plot as a function of the lightest neutrino mass Two bands appear in each plot, corresponding to inverted and direct hierarchy The two bands merge in the degenerate case (the only one presently probed)
Combined information
For simplicity, a two neutrino scenario with degenerate masses The two masses are over-constrained ⇒ Majorana phases
M1 [meV] M2 [meV] ∆m2
solar
right value
phase
S.R. Elliott, J. Engel, J.Phys. G30 (2004) R183
M2 [meV] M1 [meV] ∆m2
solar
wrong value
phase
S.R. Elliott, J. Engel, J.Phys. G30 (2004) R183
Combined information: three neutrinos
M1 M2 M3
S.R. Elliott, J. Engel, J.Phys. G30 (2004) R183
Neutrino: some basic ingredients Neutrinos and antineutrinos look distinct particles
Two ways to explain this phenomenology:
νe produces electrons when interacting with matter via charge currents
νe e-
target fermion
νe produces positrons when interacting with matter via charge currents
νe e+
target fermion
νe and νe have different lepton numbers: L(νe,e-) = 1; L(νe,e+) = -1
lepton number, like charge, is rigorously conserved
νe is a DIRAC particle → νe ≠ νe νe and νe have different helicities: H(νe) = -1; H(νe) = +1
p s p s
νe is a MAJORANA particle → νe ≡ νe
νe
RH
νe
LH
preferred by theorists
Dirac and Majorana neutrinos, neutrinos and antineutrinos
Probability to produce a charged lepton
Neutrino: DIRAC or MAJORANA particle? (1) “gedanken” experiment: DIRAC and MAJORANA neutrinos have different behaviors mν ≠ 0 Helicity depends on the reference frame, while Lepton number does not.
1 GeV, 1 eV mass RH antineutrino Interacts with a rest proton a positron is produced via charge currents
rest proton 1 GeV antineutrino
will an electron or will a positron be produced ? MAJORANA’s answer: H counts. DIRAC’s answer: L counts.
High energy proton
The same antineutrino is pursued by a very energetic proton It is seen as a 1 Gev, LH particle by the fast proton
(2) “gedanken” experiment s
Let’s put a muon neutrino at rest in the middle of the room with spin down
Ceiling Floor If accelerated at relativistic energy upwards, it will produce a negative muon interacting with the wall
µ− µ+
If accelerated at relativistic energy downwards, it will produce
with the wall if Majorana
Majorana Dirac
Why most physicists think that MAJORANA is better…
Origin of the charged fermion masses in the Standard Model
M
Particles bump on the Higgs field pervading all the empty space and acquire a mass
because they are neutral and do not interact with the Higgs field
mass because they do not have a right-handed component and the left-handed component propagate freely
How can we give a mass to neutrinos?
Following what is done with the other fermions in a straight-forward way Dirac mass where νR are new fields insensitive to the gauge interactions Destroy RH neutrino – create LH neutrino Create LH neutrino – destroy RH neutrino
x νR νL
However, we are authorised to add a new mass term: Majorana mass which involves fields of equal chiralities possible only for neutral particles! Destroy RH neutrino – create LH neutrino Destroy RH antineutrino – create LH antineutrino
x (ν)R νL
In matrix notation:
νR νR νL νL
Provides the Dirac and Majorana mass terms defined before
Neutrino mass matrix
In order to find the physical states and masses, this matrix must be diagonalized in order to put the Lagrangian in the form:
See-saw mechanism Eigenvalues:
m1 ~ - mD
2 / MR
mD must be of the same order of the charged lepton masses (Higgs mechanism) MR can be everywhere (GUT scale) → the condition MR >> mD can naturally explain the small neutrino masses
m2 ~ MR + mD
2 / MR
Eigenvectors:
ν1 ~ νL+νL
c- (mD / MR)(νR+νR c)
ν2 ~ νR+νR
c+(mD / MR)(νL+νL c)
Light Majorana neutrinos Heavy Majorana neutrinos, usually named N
Leptogenesis
If there is a source of CP violation in the lepton sector (δ or Majorana phases), the heavy Majorana neutrinos N can violate CP too and decay with different rates to e+ and e-
Different rates Unequal number of leptons and anti-leptons in the early Universe Sphaleron process (violate B and L, but conserves B-L)
The asymmetry is transferred to baryons
Decay modes for Double Beta Decay (A,Z) → (A,Z+2) + 2e- + 2νe
2ν Double Beta Decay allowed by the Standard Model already observed – τ ≥ 1019 y
(A,Z) → (A,Z+2) + 2e-
neutrinoless Double Beta Decay (0ν-DBD) never observed (except a discussed claim) τ > 1025 y
(A,Z) → (A,Z+2) + 2e- + χ
Double Beta Decay with Majoron (light neutral boson) never observed – τ > 1022 y
Three decay modes are usually discussed: Processes and would imply new physics beyond the Standard Model violation of total lepton number conservation They are very sensitive tests to new physics since the phase space term is much larger for them than for the standard process (in particular for ) interest for 0ν-DBD lasts for 70 years !
Goeppert-Meyer proposed the standard process in 1935 Racah proposed the neutrinoless process in 1937
Double Beta Decay and elementary nuclear physics
Weiszaecker’s formula for the binding energy of a nucleus MASS Z DBD
βX
Even-even Odd-odd Nuclear mass as a function of Z, with fixed A (even) Odd-odd Even-even Q-value
How many nuclei in this condition?
Double Beta Decay to excited states
Less probable but experimentally interesting
Double Beta Decay and neutrino physics
Diagrams for the three processes discussed above: Standard process two “simultaneous” beta decays 0ν-DBD a virtual neutrino is exchanged between the two electroweak lepton vertices DBD with Majoron emission A Majoron couples to the exchanged virtual neutrino
DBD is a second order weak transition
very low rates
Neutrino properties and 0ν-DBD d d u u e- e-
W- W-
νe
a LH neutrino (L=-1) is absorbed at this vertex
νe
a RH antineutrino (L=1) is emitted at this vertex
in pre-oscillations standard particle physics (massless neutrinos), the process is forbidden because neutrino has not the correct helicity / lepton number to be absorbed at the second vertex
Helicities can be accommodated thanks to the finite mass, BUT Lepton number is rigorously conserved
0ν-DBD is forbidden
Helicities can be accommodated thanks to the finite mass, AND Lepton number is not relevant
0ν-DBD is allowed
SUSY λ’111,λ’113λ’131,….. (V+A) current <mν>,<λ>,<η>
Other more exotic processes for 0ν-DBD
mν ≠ 0 ν ≡ ν
Observation of 0ν-DBD
Schechter-Valle theorem
Generic process inducing neutrinoless double beta decay Majorana mass term
Electron sum energy spectra in DBD
The shape of the two electron sum energy spectrum enables to distinguish among the three different discussed decay modes
The Majoron spectrum is a continuum with maximum close to Q
(phase space for a particle decaying to three light objects)
Q ~ 2-3 MeV for the most promising nuclides
additional signatures:
sum electron energy / Q
two neutrino DBD continuum with maximum at ~1/3 Q neutrinoless DBD
peak enlarged only by the detector energy resolution
Majoron signature
Light neutrino exchange V+A current
Electron minimum energy spectrum Angular distribution between the 2 electrons
MeV MeV
Cosθ Cosθ
Other observables
parameter containing the physics what the nuclear theorists try to calculate what the experimentalists try to measure
0ν-DBD: parameters determining the rate 1/τ = G(Q,Z) |Mnucl|2〈Mββ〉 2
neutrinoless Double Beta Decay rate Phase space Nuclear matrix elements Effective Majorana mass
how 0ν-DBD is connected to neutrino mixing matrix and masses in case of process induced by mass mechanism 〈Mββ〉 = ||Ue1 | 2M1 + eiα1 | Ue2 | 2M2 + eiα2 |Ue3 | 2M3 | < 0.2
1 2
〈Mββ〉 = ||Ue1 | 2M1 + eiα1 | Ue2 | 2M2 + eiα2 |Ue3 | 2M3 | Effects of the Majorana phases: graphic representation
From where we start…
76Ge claim
excluded by CUORICINO , NEMO3
…and where we want to go
Approach the inverted hierarchy region in a first phase (〈m〉>50 meV) Exclude the inverted hierarchy region in a second phase (〈m〉>15 meV) There are techniques and experiments in preparation which have the potential to reach these sensitivities
The size of the challenge
∼ 100 - ∼ 1000 counts / y ton ∼ 1 - ∼ 10 counts / y ton ∼ 0.1 - ∼ 1 counts / y ton
76Ge claim
50 meV 20 meV
Background requirements
To start to explore the inverted hierarchy region
Sensitivity at the level of 1-10 counts / y ton
To cover the inverted hierarchy region
Sensitivity at the level of 0.1 -1 counts / y ton
The order of magnitude of the target bakground is ~ 1 counts / y ton
Common to all tecnhiques and experiments Cooperation
Background sources
(source itself, surrounding structures)
Levels of < 1 µBq / kg are required for some materials at the ton scale Understanding U/Th and 210Pb contamination Purification techniques Quality control procedure to establish: diagnostic is a problem by itself (traditional gamma counting not sufficient) Improve alternative techniques:
(BiPo detector) Two main sources
(α, n) processes ⇒ [0,10] MeV spectrum ⇒ can be shielded
complicated problem ⇒ depth ⇒ appropriate shielding / coincidence techniques ⇒ reliable simulations ⇒ “Ad hoc” experiments at muon accelerators could be useful Choice of materials Storage of materials underground Partial or full detector realization underground (Ge diodes) Crucial for all experiments and techniques cooperation (in Europe, ILIAS) Critical in the low energy resolution techniques
100 100 Mo
Mo
136 136 Xe
Xe
76 76 Ge
Ge
130 130 T e
T e
energy resolution [%] 1000 100 10 1 0.1 0.01 0.001 sensitivity to 〈m〉 [meV] 1 2 3 4 present sensitivity Inverted hierarchy
A challenge for the space-resolving techniques, which normally have low energy resolution (~ 10 %) δ=∆E/Q
Experimental strategies
Detect and identify the daughter nuclei (indirect search) geochemical experiments radiochemical experiments
it is not possible to distinguish the decay channel important in the 70s-80s – no more pursued now
Detect the two electrons with a proper nuclear detector (direct search) desirable features
a peak must be revealed over background (0ν-DBD) shield cosmic rays (direct interactions and activations) underground very radio-pure materials
238U – 232Th ⇒ τ ~ 1010 y
signal rate ⇒ τ > 1025 y present more sensitive experiments: 10 - 100 kg future goals: ~ 1000 kg ⇒ 1027 – 1028 nuclides
Experimental approaches to direct searches
Two approaches:
e- e-
Source ≡ Detector (calorimetric technique)
very large masses are possible demonstrated: up to ~ 50 kg proposed: up to ~ 1000 kg with proper choice of the detector, very high energy resolution
Ge-diodes bolometers
in gaseous/liquid xenon detector, indication of event topology constraints on detector materials in contradiction neat reconstruction of event topology it is difficult to get large source mass several candidates can be studied with the same detector
e- e-
source detector detector
Source ≠ Detector
Experimental sensitivity to 0ν-DBD
sensitivity F: lifetime corresponding to the minimum detectable number
background level
F ∝ (MT / b∆E)1/2
energy resolution live time source mass
F ∝ MT
b ≠ 0 b = 0
b: specific background coefficient [counts/(keV kg y)] importance of the nuclide choice
(but large uncertainty due to nuclear physics)
sensitivity to 〈M〉 ∝ (F/Q |Mnucl|2)1/2 ∝
1 b∆E MT Q1/2
1/4
|Mnucl|
Isotopic abundance (%)
48Ca 76Ge 82Se 96Zr 100Mo116Cd130Te136Xe150Nd20 40 Transition energy (MeV)
48Ca 76Ge 82Se 96Zr 100Mo116Cd130Te136Xe150Nd2 3 4 5
Choice of the nuclide
Nuclear Matrix Element Sign of convergence!
No super-favoured isotope !
C [y-1]
82Se 100Mo 116Cd 130Te 136Xe 150Nd
C = |M0ν|2 • G0ν [y-1]
[ ]
2 2 1 2 / 1 e
m m C T
ββ ν
⋅ =
−
76Ge
The real figure of merit
Basic ideas for direct neutrino mass measurement
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 Mνe < 23 eV However, not better than 1 eV ⇐ uncertainties in time emission spectrum use only: E2 = M2c4 + p2c2 kinematics of processes involving neutrinos in the final state
π+ → µ+ + νµ for Mνµ τ- → m π± + n π0 + vτ for Mντ (A,Z) → (A,Z+1) + e- + νe for Mνe (A,Z) + e-
at→ (A,Z-1) + γ + νe
for Mνe
electron capture with inner bremmsstrahlung
not useful to reach the desired sub-eV sensitivity range, due to the high energy
caveat it is meaningless to attribute a well defined mass to a flavor eigenstate
The nuclear beta decay and the neutrino mass
Fermi theory of weak interaction (1932)
(A,Z) → (A,Z+1) + e- + νe
Q = Mat(A,Z) – Mat(A,Z+1) ≅ Ee + Eν
⇒
(Q – Ee) √ (Q – Ee)2 – Mν
2c4
finite neutrino mass
(Q – Ee)2
dN dp ∝ GF
2 |Mif|2
p2 (Q – Ee)2 F(Z,p) S(p,q) electron momentum distribution dN dE ∝ GF
2 |Mif|2 (Ee+mec2) (Q – Ee)2
F(Z,Ee) S(Ee) [1 + δR(Z,Ee)] electron kinetic energy distribution zero neutrino mass
Spectral effects of a finite neutrino mass
The more relevant part of the spectrum is a range of the order of [Q – Mνc2 , Q] The count fraction laying in this range is ∝ (Mν/Q)3
low Q are preferred
Q
E – Q [eV]
T
Effects of a finite neutrino mass on the Kurie plot
The Kurie plot K(Ee) is a convenient linearization of the beta spectrum
Q
Q–Mνc2 Q
K(E)
zero neutrino mass finite neutrino mass effect of:
K(E) ≡ dN dE GF |Mif|2 (Ee+mec2) F(Z,Ee) S(Ee) [1 + δR(Z,Ee)]
1/2
∝ (Q – Ee)√ (Q – Ee)2 – Mν
2c4
1/2
Q-δE Q
(dN/dE) dE ≅ 2(δE/Q)3
Mass hierarchy
In case of mass hierarchy:
The weight of each sub – Kurie plot will be given by |Uej|2, where
|νe〉 = Σ Uei |νMi 〉
i=1 3
This detailed structure will not be resolved with present and planned experimental sensitivities (~ 0.3 eV)
K(Ee) Ee
Q – M3 Q – M2 Q – M1 Q Ee K(Ee)
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 – Mβ K(Ee) Q Ee
this is the only situation 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
Mβ = (Σ Mi
2 |Uei|2)1/2
Experimental searches based on nuclear beta decay
Requests:
Approximate approach to evaluate sensitivity to neutrino mass σ(Mν): 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
σ(Mν) ≅ 1.6 Q3 ∆E A TM
4
energy resolution total source activity live time
Two complementary experimental approaches
low energy “nuclear” detector
source coincident with detector (calorimetric approach)
electrons operated by proper electric and magnetic fields
source separate from detector (the source is always T)
completely different systematic uncertainties
Beta spectroscopy with magnetic / electrostatic spectrometers
Source Electron analyzer Electron counter T2 high activity high luminosity L∝∆Ω/4π (fraction of transmitted solid angol) high energy resolution two types:
The calorimetric approach to the measurement of the neutrino mass
187Re → 187Os + e- + νe
5/2+ → 1/2– unique first forbidden (computable S(Ee))
Calorimeters measure the entire spectrum at once
Advantages of calorimetry
Drawbacks of calorimetry
The neutrino energy is measured as a “missing energy”
(dN/dE)exp=[(dN/dE)theo+ Aτr(dN/dE)theo⊗ (dN/dE)theo] ⊗ R(E)
generates “background” at the end-point
K(E) Ee (keV) Ee (keV)
pile-up fraction ~ A x τr
Bolometric detectors of particles: basic concepts
Energy absorber
crystal containing Re M ~ 0.25 mg basic parameter: C
Thermal coupling
µ−machined legs basic parameter: G G ≅ 0.02 pW / mK
Thermometer
Si-implanted thermistor basic parameters: R ≅ 1.5 MΩ Τ ≅ 100 mK dR/dT ≅ 50 kΩ/mK
Variable Range Hopping conduction regime exponential increase of R with decreasing T
Heat sink
T ~ 80 mK dilution refrigerator
Advantages over conventional techniques:
Energy resolution ≅ 10 eV