the university of south carolina. columbia carolina...

May 20, 13 A. Bettini. INFN and LSC 1

The University of South Carolina. Columbia�

Carolina International Symposium on Neutrino Physics�20-22 May 2013

A. Bettini Canfranc Underground Laboratory. Spain

G. Galilei Physics Dept. Padua University. Italy INFN

Are neutrinos completely neutral?


Celebrating the 80th birthdays of�

and of


the weak interactions (and neutrino)

Teoria della emissione dei raggi β delle sostanze radioattive, fondata sull'ipotesi che gli elettroni emessi dai nuclei non esistano prima della disintegrazione ma vengano formati, insieme ad un neutrino, in modo analogo alla formazione di un quanto di luce che accompagna un salto quantico di un atomo. Confronto della teoria con l'esperienza.

This article had been rejected by Nature because “too abstract”

Theory of β rays emission of radioactive substances, built on the hypothesis that the electron emitted by the nuclei do not exist before the decay. On the contrary they are created together with a neutrino, similarly to the creation of a light quantum that goes with a quantum jump of an atom. Comparison of theory and experiment


Two giants 4. December. 1930. W. Pauli The “desperate remedy” of a tiny mass “neutron” inside the nuclei “Dear radioactive Ladies and Gentlemen… ……………………… unfortunately I cannot appear in Tübingen since I am indispensable here in Zurich because of a ball on the night of 6-7 December”

1934 Nuovo Cimento 11 1

1932. Chadwick discovers the neutron. Nucleus is made of p and n with similar masses. No electrons in the nucleus.

The discovery of a new fundamental force

English transl. Fred L. Wilson Am. J. Phys. 36 (1968) 1150


How to measure neutrino mass?

The dependence of the form of the energy distribution curve from µ is noticeable especially near the maximum energy E0 of the β rays …… We reach in his way the conclusion that the neutrino mass is equal to zero, or, in any case, small compared to the electron mass.


Completely neutral particles

Completely neutral: antiparticle = particle All “charges” (electric, colour, lepton number, baryon number) = 0 Bosons

can be mass-less: γ or massive: Z0, H, π0, η,….

Fermions must be massive: ν? neutralino?

Definition neutrino = neutral particle produced in β+ decay anti-neutrino = neutral particle produced in β– decay


1935 Phys Rev. 48 512

T1/2 > 1017 yr

Not so bad In fact T1/2 = 1019 – 1021 yr

May 20, 2013 A. Bettini. Padova University and INFN; LSC 8

Two more Giants


1937 Nuovo Cimento 14 171-184

We show that it is possible to achieve complete formal symmetrisation in the electron and positron quantum theory by means of a new quantization process. The meaning of Dirac equations is somewhat modified and it is no more necessary to speak of negative-energy states; nor to assume, for any other type of particles, especially neutral ones, the existence of antiparticles, corresponding to the “holes” of negative energy.

Ettore & Frank go to kinder garden


An unpleasant asymmetry

The new approach allows to “not only to give a symmetric form to the electron-positron theory, but also to build a substantially novel theory for the particles deprived of electric charge (neutrons and hypothetical neutrinos)”

…….it is probably “not yet possible to ask to the experience to decide between this new theory and the simple extension of the Dirac equations to the neutral particles”

Majorana, putting the question of complete neutrality, implicitly introduced the notion of charges different from the electric one (1949 baryon number, 1953 lepton number)


Majorana equation

Dirac equation

E + p ⋅σ( )χ − mϕ = 0

E − p ⋅σ( )ϕ − mχ = 0

E + p ⋅σ( )χ − imaσ 2χ* = 0

E − p ⋅σ( )ϕ − imbσ 2ϕ* = 0

Majorana equation

Φ = iσ 2χM*

Χ = iσ 2ϕM*

iσ 2 =0 1−1 0

Question: is it possible to find a spinor Φ constructed with the components of ϕ only (and hence without further degrees of freedom), which transforms like a χ instead than a ϕ and that can consequently take its place in the Dirac equation? And similarly a spinor X transforming like a ϕ? The answer, found by Majorana, is

• Majorana equations are decoupled, one for ϕ and one for χ spinor (possibly two masses) • If m=0, Dirac equation = Majorana equation • Nature has chosen m≠0, hence differences between the two theories exist

ψ x( ) =

ψ 1

ψ 2

ψ 3

ψ 4

=ϕ

χ

; ϕ =

ϕ1

ϕ2

; χ =

χ1

χ2

The bi-spinor

In the Dirac theory the ϕ and χ components have different transformation properties

May 20, 13 A. Bettini. INFN 12

Majorana bispinor We can write the Majorana bispinor wave function as

ψ D =ϕ

χ

ψ M =

ϕ

iσ 2ϕ *

The charge conjugated Majorana bispinor is

ψ MC = iγ 2ψ M =

0 −iσ 2

iσ 2 0

ϕ

iσ 2ϕ *

=

ϕ

iσ 2ϕ *

=ψ M

Majorana neutrinos are their own antiparticles

Particle and antiparticle have all the “charges” with opposite values ⇒ they are different particles Neutrinos and antineutrinos are possibly distinguished by a unique charge, the lepton number If lepton number is not conserved nothing distinguishes neutrino from antineutrino


1937 Nuovo Cimento 14 323

We show that the symmetry between particles and antiparticles leads to some formal modifications of the Fermi theory of the β radioactivity and that the physical identity between neutrinos and antineutrinos leads directly to Majorana theory.

If neutrinos obey Dirac equation, neutrinos emitted in a β– decay can induce only a β+ process and vice versa If they obey Majorana equation, any neutrino can produce both electrons and positrons Neutrons cannot obey Majorana equation for two reasons 1.  Neutron has a magnetic moment 2.  Neutrons would decay β– into protons and β+ into antiprotons with equal probabilities


1939 Physical Review 56 1184

The Furry proposal can be followed, but unfortunately “the transition probability” is not “much larger”, but rather much smaller In both cases because CC weak current is V-A

The Racah proposal to distinguish between Dirac and Majorana neutrinos cannot be realized in practice

E&F go to elementary school


1946 Report PD-205, Chalk River, Canada.

ν+37Cl→37 Ar* + e−

W. Pauli: “I have done a terrible thing. I have postulated a particle that cannot be detected.”

B. Pontecorvo. Try with

Neutrino or antineutrino?

Use low background proportional counter to detect X ray from Ar* de-excitation

Report was classified. Method might be used to measure neutrinos from a power reactor


1954 Phys. Rev. 97 (1955) 766

νe+37Cl→37 Ar* + e−Neutral particles from a reactor do

not induce Pontecorvo reaction

Neutrino is different from antinutrino

This conclusion, made in the SM, is premature

E&F at university


1956 Science 124 103


1957 JINR Preprint P-95 Recently there came to our attention a paper of Davis (still in press), who investigated the production of 37Ar from 37Cl under bombardment of neutral leptons produced by a powerful reactor. Davis result - a measurable probability of the investigated process (!!!) -if confirmed, definitely indicates that neutrino charge is not strictly conserved

B.M.P. considers an analogy with the system K 0K 0

…neutrino and antineutrino are…. symmetrical and antisymmerical combinations of two truly neutral Majorana particles ν1 and ν2.

ν1 =12ν +ν( )

ν2 =12ν −ν( )

It follows that neutrinos in vacuum can transform themselves in antineutrinos and viceversa....So, a beam of neutral leptons from a reactor which first consists mainly of antineutrinos will change in composition and at a certain distance…will be composed of neutrinos and antineutrinos in equal quantities

The true ones

Concluding that unfortunately, that solar physics is not enough under control


Neutrino mixing

The true ones

1956 Sakata model. Fundamental particles are p, n and Λ

1959 Gamba, Marshak and Okubo baryon-lepton fundamental symmetry (ν, e, µ) - (p, n, Λ )

1960 Maki et al. Nagoya model. “Ur” matter B+ and p = νB+ n = e−B+ Λ = µ−B+

1962 Second neutrino, lepton-baryon symmetry lost Try to recover: Katayama et al. and Maki et al. advanced two hypothesis 1. are not the "true" neutrinos, but linear mixtures, of them

2. only ν2, for not explained reasons, couples to the B+ Maki et al. mentioned also the possibility of “transmutation” between neutrino flavours.

ν1 = νe cosδ +νµ sinδ ν2 = νe cosδ −νµ sinδ

1962 Lipkin et al. notice that the observation of falsifies Sakata model pp→ KL0KS

0

N.B. If it were true neutrino and quark (Cabibbo) mixing angles would have to be equal


Neutrino oscillations 50 years of BSM physics

11 August 1967. R. Davis writes to Fowler “Dear Willy, I do have a preliminary result from our first good run. The sample was taken June 22nd and counting has continued until today. I am now removing the sample and will rerun background. So we do have a result and during the last few weeks I have told a few people that are interested.”.

1963. John Bahcall starts building the Solar Standard Model

Bahcall and Davis at Homestake


Neutrino oscillations 50 years of BSM physics

9 June 1967 (two months before the letter of Davis to Fowler) B. Pontecorvo sends a paper to Zhurnal Eksperim. noi i Teoreticheskoi Fiziki.

From an observational point of view the ideal object is the sun. If the oscillation length is smaller than the radius of the sun effectively producing neutrinos (let us say, one tenth of the solar radius…for the 8B neutrinos)….the only effect on the earth surface must be two times smaller than the total flux

L. Wolfenstein (1978) S. P. Mikheyev, A. Yu. Smirnov (1985) Flavour transition in matter

B.M.P. was almost but not quite right. Boron neutrinos do not change flavour by oscillations but by MSW effect.

Considers νe νe, νµ νµ ,νe νµ assuming eigenstates to be Majorana


1957 Phys. Rev. 105 1413

R. E. Marshak and C. G. Sudarshan. Proceedings of the Padua-Venice Conference on “Mesons and recently discovered particles” 1957 (Società Italiana di Fisica, 1958) Also Feynman and Gell-Mann

The V–A currents


Chirality

€

ψL =12

1− γ5( )ψ, γ5ψL = −ψL

ψR =12

1+γ5( )ψ, γ5ψR = +ψR

Chirality is a property of the 4-component bispinor The states of definite chirality are the eigenstates of γ5 , called L for the eigenvalue –1, R for +1 Neutrino field has negative chirality. Neutrinos and antineutrinos are left

γ5 commutes with the Hamiltonian of free massless Dirac particles (not existing in Nature), γ5 does not commute with the mass term of the Dirac Hamiltonian Chirality is not an observable, we measure helicity instead


Chirality and helicity The fields of definite chirality are

ψ L =12

1− γ 5( )ψ =0 00 1

ϕ

χ

=

0χ

ψ R =

12

1+ γ 5( )ψ =0 10 0

ϕ

χ

=

ϕ

0

If m=0 neutrinos are pure h=– states, antineutrinos pure h=+ states

But m≠0 and E>>m, then neutrinos have a small (m/E) “wrong” helicity component

If Majorana, “neutrino” is the state with h=–1; “antineutrino” is the state with h=+1

Neutrinos = those produced in β+ decays, are created and destroyed by the spinor φ

Antineutrinos = those produced in β+ decays, are created and destroyed by the spinor χ

Both are left

Both have positive (+) and negative (–) helicity components

For E>>m

χ = ν ≈ νL+ +

mEνL−ϕ = ν ≈

mEνL+ +νL

−

May 20, 13 A. Bettini. INFN and LSC

Majorana vs Dirac at relativistic energies m/Eν<10–10

25

The V–A structure of the charged weak currents + smallness of neutrino mass are sufficient to explain experimental observations No need to invoke lepton number conservation No need to have neutrino different from antineutrino

May 20, 2013 A. Bettini. Padova University and INFN; LSC 26 26

ββ0ν Decay

Majorana neutrino couples to W exactly as Dirac neutrino The SM violation is in the propagator

νe =Ue1ν1 +Ue2ν2 +Ue3ν3The status created at one vertex has definite flavour, hence is a superposition of mass eigenstates Mass eigenstates do not have definite helicity, are superpositions of Majorana neutrinos and antineutrinos At one vertex the antineutrino component matters, the neutrino component at the other vertex

ν i ≈mi

Eν iL+ +ν iL

−

Mee =| Uei2

i∑ mi |≈ 0.67m1 + 0.30m2e

i2α + 0.03m3ei2 β−δ( )

May 20, 2013 A. Bettini. Padova University and INFN; LSC 27 27

Building LSC programme

76Ge 136Xe 136Xe 130Te

GERDA1/2 EXO200 KL-ZEN CUORE

b (keV–1t–1yr–1) 20/1.2 1.5 8.5 36

ΔE (keV) 4 100 230 5

bkgr/(2ΔE 100 kg yr) 16/1 30 400 36

S(100 meV)/(100 kg yr) 4 60 60 100

Look at the running experiments (GERDA1, EXO200, KL-ZEN) and close to run (GERDA2 in 2014, CUORE in 2015) Exposure = 100 kg (of isotope) yr Mee=100 meV Masses in the table are isotope masses Matrix elements from Tuebingen or Yale Red figures are expected values

Present generation of experiments will reach 100 meV improving BI Monolithic detectors (liquid or gas) have better scalability Self-shielding with the isotope (EXO) is expensive Avoid surfaces near source (KL-ZEN)

28 A. Bettini.

NEXT 100 kg 136Xe high pressure TPC

Simulation

Energy resolution target: FWHM = 1% @ Qββ Exploiting ElectroLuminescence read out

BI target 10–4/(keV kg yr) Exploiting transparency topological signature

29 A. Bettini.

NEXT. Data from prototypes

Energy resolution FWHM = 0.75% @ Qbb measured in prototypes

22Na 511 keV γ

Electron track 600 keV γ source

May 20, 13 A. Bettini.Padova Univ. and INFN and LSC 30

Conclusions

• Is it now “possible to ask to the experience to decide between this new theory and the simple extension of the Dirac equations to the neutral particles”? • Since then enormous progress has been done, both in the theory and in the experiments

• With outstanding contributions of Ettore and Frank • By the 80th anniversary of the Majorana paper, present generation of experiments will be able to answer if Mee> 100 meV • If not, we must reach BI < 10–4 cts/(keV kg yr)

• Stay away from surfaces • Tagging of the final state

• Pulse Shape Analysis • Track images • …………

• Nature might be nice with us, and give her answer by the next anniversary


THANKS


Neutrino mixing now

νeνµντ

=

Ue1 Ue2 Ue3

Uµ1 Uµ2 Uµ3

Uτ1 Uτ 2 Uτ 3

ν1ν2ν3

U =

U11 U12 U13

U21 U22 U23

U31 U32 U33

=0.82 0.55 0.160.44 0.65 0.620.36 0.52 0.77

sin2θ13 = 0.025−0.03+0.03 13%

sin2θ12 = 0.307−0.016+0.018 5.4%

sin2θ23 = 0.398−0.03+0.03 13%

δm2 = 75.4±2.22.6 meV2 2.6%

Δm2 = 2430−90+70 meV2 3.5%


“Majorana mass”

Mee =| Uei2

i∑ mi |≈ 0.67m1 + 0.30m2e

i2α + 0.03m3ei2 β−δ( )

Expected number of events per ton of target per year (proportional to |Mee|2 ) at Mee=100 meV

Ge enrich. (85%)

TeO2 natural

Xe enrich. (85%)

16 10 17

Number of background events in ∆E (FWHM) =4-100 keV must be about 0

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