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 searches

Outline of the lectures  Neutrino mass and neutrino properties  Double beta decay: introduction 21 July  Single beta decay: introduction  Overview of the experimental status  The experiments in preparation 22 July  Prospects and conclusions

Neutrino flavor oscillations Premise Flavor eigenstates ≠ Mass eigenstates Weak interaction Propagation Neutrino flavor oscillations what we presently know from neutrino flavor oscillations  oscillations do occur neutrinos are massive

Neutrino mixing and masses  given the three ν mass eigenvalues M 1 , M 2 , M 3 we have TBM mixing 2 ≡ M i approximate measurements of two ∆ M ij 2 – M j 2 (∆ M ij 2 ) < 0.2 2 | ~ (50 meV) 2 |∆ M 23 ∆ M 12 2 ~ (9 meV) 2 Solar Atmospheric elements of the  approximate measurements and/or constraints on U lj ν mixing matrix ν 3 ν 2 ν 1 ν e ν µ ν τ

Summary of our present knowledge Majorana CP c ij =cos θ ij s ij =sin θ ij δ : CP violating phase violating phases N σ solar atmospheric < 0.031 TBM: = 1/3 = 0 = 1/2

…in another form

Neutrino flavor oscillations and mass scale what we do not know from neutrino flavor oscillations:  direct neutrino mass hierarchy inverted  absolute neutrino mass scale degeneracy ? ( M 1 ~ M 2 ~ M 3 )  DIRAC or MAJORANA nature of neutrinos ν ≠ ν ν ≡ ν

Tools for the investigation of the ν mass scale Future Present Tools sensitivity sensitivity (a few year scale) Cosmology (CMB + LSS) 0.5 - 1 eV 0.1 eV Neutrinoless Double Beta Decay 0.5 eV 0.05 eV Single Beta Decay 2.2 eV 0.2 eV Direct determination Laboratory measurements Model dependent

Complementarity of cosmology, single and double β decay Cosmology , single and double β decay measure different combinations of the neutrino mass eigenvalues, constraining the neutrino mass scale In a standard three active neutrino scenario: cosmology 3 Σ ≡ Σ M i simple sum pure kinematical effect i=1 1/2 3 Σ M i beta decay 〈 M β 〉 ≡ incoherent sum 2 |U ei | 2 real neutrino i=1 3 |Σ M i |U ei | 2 e i α | 〈 M ββ 〉 ≡ double beta decay coherent sum i virtual neutrino i=1 Majorana phases

Present bounds The three constrained parameters can be plot as a function of the Σ [eV] 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) 〈 M ββ 〉 [eV] 〈 M β 〉 [eV]

Combined information For simplicity, a two neutrino scenario with degenerate masses ⇒ Majorana phases The two masses are over-constrained S.R. Elliott, J. Engel, J.Phys. G30 (2004) R183 S.R. Elliott, J. Engel, J.Phys. G30 (2004) R183 ∆ m 2 ∆ m 2 solar solar M 2 [meV] M 2 [meV] wrong value right value of the Majorana of the Majorana phase phase M 1 [meV] M 1 [meV]

Combined information: three neutrinos S.R. Elliott, J. Engel, J.Phys. G30 (2004) R183 M 3 M 2 M 1

Neutrino: some basic ingredients Neutrinos and antineutrinos look distinct particles ν e produces electrons when interacting ν e produces positrons when interacting with matter via charge currents with matter via charge currents ν e ν e e+ e- target fermion target fermion Two ways to explain this phenomenology:  ν e and ν e have different lepton numbers: lepton number, like charge, is L( ν e ,e - ) = 1; L( ν e ,e + ) = -1 rigorously conserved ν e is a DIRAC particle → ν e ≠ ν e p p RH LH  ν e and ν e have different helicities: s s ν e ν e H( ν e ) = -1; H( ν e ) = +1 ν e is a MAJORANA particle → ν e ≡ ν e preferred by theorists

Dirac and Majorana neutrinos, neutrinos and antineutrinos Probability to produce a charged lepton

Neutrino: DIRAC or MAJORANA particle? DIRAC and MAJORANA neutrinos m ν ≠ 0 have different behaviors Helicity depends on the reference frame, while Lepton number does not. (1) “gedanken” experiment: High 1 GeV rest proton energy antineutrino proton  1 GeV, 1 eV mass RH antineutrino a positron is produced Interacts with a rest proton via charge currents  The same antineutrino is pursued It is seen as a 1 Gev, by a very energetic proton LH particle by the fast proton will an electron or will a positron be produced ? MAJORANA’s answer: H counts. DIRAC’s answer: L counts.

(2) “gedanken” experiment Let’s put a muon neutrino at rest in the middle of the room with spin down µ − Ceiling If accelerated at relativistic energy upwards , it will produce a negative muon ν µ interacting with the wall If accelerated at relativistic energy downwards , it will s produce  a positive muon interacting with the wall if Majorana  it will never interact if Dirac Floor µ + 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  Photons do not have a mass because they are neutral and do not interact with the Higgs field  Neutrinos do not have a 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 ν R are new fields insensitive to the gauge interactions Destroy RH neutrino – create LH neutrino x ν R ν L Create LH neutrino – destroy RH neutrino 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 x (ν) R ν L Destroy RH antineutrino – create LH antineutrino

Neutrino mass matrix In matrix notation: ν L ν R ν L Provides the Dirac and Majorana mass ν R terms defined before 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 m D must be of the same order of the charged lepton masses (Higgs mechanism) M R can be everywhere (GUT scale) → the condition M R >> m D can naturally explain the small neutrino masses 2 / M R m 1 ~ - m D Eigenvalues: 2 / M R m 2 ~ M R + m D Light Majorana neutrinos ν 1 ~ ν L + ν L c - (m D / M R )( ν R + ν R c ) Eigenvectors: ν 2 ~ ν R + ν R c +(m D / M R )( ν L + ν L c ) 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 Three decay modes are usually discussed: 2 ν Double Beta Decay (A,Z) → (A,Z+2) + 2e - + 2 ν e  allowed by the Standard Model already observed – τ ≥ 10 19 y neutrinoless Double Beta Decay (0 ν -DBD) (A,Z) → (A,Z+2) + 2e -  never observed (except a discussed claim) τ > 10 25 y Double Beta Decay (A,Z) → (A,Z+2) + 2e - + χ  with Majoron (light neutral boson) never observed – τ > 10 22 y 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 0 ν -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 Even-even Weiszaecker’s formula for the binding energy of a nucleus Nuclear mass as a function of Z, with fixed A (even) Odd-odd MASS Odd-odd β X Even-even DBD Q-value Z

How many nuclei in this condition?

Double Beta Decay to excited states Less probable but experimentally interesting

Double Beta Decay and neutrino physics DBD is a second order weak transition very low rates Diagrams for the three processes discussed above: DBD with Majoron emission Standard process A Majoron couples to the two “simultaneous” beta decays exchanged virtual neutrino 0 ν -DBD a virtual neutrino is exchanged between the two electroweak lepton vertices

Neutrino properties and 0 ν -DBD u in pre-oscillations a LH neutrino (L=-1) e - standard particle physics is absorbed at this vertex d (massless neutrinos), ν e the process is forbidden because W - neutrino has not the correct ν e helicity / lepton number W - a RH antineutrino (L=1) to be absorbed is emitted at this vertex at the second vertex d e - u  IF neutrinos are massive DIRAC particles: 0 ν -DBD Helicities can be accommodated thanks to the finite mass, is forbidden BUT Lepton number is rigorously conserved  IF neutrinos are massive MAJORANA particles: 0 ν -DBD Helicities can be accommodated thanks to the finite mass, is allowed AND Lepton number is not relevant