Double Beta Decay: A Very Special Experiment Boris Kayser DBD11 - PowerPoint PPT Presentation

Double Beta Decay: A Very Special Experiment Boris Kayser DBD11 November 15, 2011 NASA Hubble Photo 1

Neutrinoless Double Beta Decay [0 νββ ] e – e – Nucl’ Nucl Cannot occur in the Standard Model Observation at any level would imply — Ø Lepton number L is not conserved Ø Neutrinos have Majorana masses — masses with a different origin than the quark and charged lepton masses Ø Neutrinos are their own antiparticles 2

Observation of 0 νββ would make more plausible — Ø The See-Saw model of the origin of neutrino mass Ø Leptogenesis, an outgrowth of the See-Saw, which may be the origin of the baryon-antibaryon asymmetry of the universe 3

What does all What does all this mean? this mean? Why is it Why is it interesting? interesting? 4

Nonconservation of Nonconservation of Lepton Number L Lepton Number L 5

The Lepton Number L is defined by — L( ν ) = L(  – ) = –L( ν ) = –L(  + ) = 1 This is the quantum number that distinguishes antileptons from leptons. It is the leptonic analogue of the Baryon Number B, which distinguishes antibaryons from baryons. 6

0 νββ e – e – Nucl Nucl’ Clearly does not conserve L: Δ L = 2. Non-perturbative Sphaleron processes in the Standard Model (SM) do not conserve L. But Sphaleron processes can only change L by a multiple of 3. 2 is not a multiple of 3. The Δ L = 2 of 0 νββ is outside the SM. 7

Majorana Masses Majorana Masses 8

Out of, say, a left-handed neutrino field, ν L , and its charge-conjugate, ν Lc , we can build a Left-Handed Majorana mass term — ( ν ) R ν L m L ν L ν Lc X m L Majorana masses mix ν and ν , so they do not conserve the Lepton Number L, changing it by Δ L = 2, precisely what is needed for 0 νββ . 9

A Majorana mass for any fermion f causes f f. Quark and charged-lepton Majorana masses are forbidden by electric charge conservation. Neutrino Majorana masses would make the neutrinos very distinctive. SM Higgs Majorana ν masses cannot come from , the ν H SM " L " R analogue of the Higgs coupling that leads to the q and  masses, and the progenitor of a Dirac ν mass term. 10

Possible progenitors of Majorana mass terms: c " L , c " L , c " R H SM H SM " L H I W = 1 " L m R " R No Higgs Not renormalizable This Higgs not in SM Majorana neutrino masses must have a different origin than the masses of quarks and charged leptons. 11

Whatever diagrams cause 0 νββ , its observation would imply the existence of a Majorana mass term: (Schechter and Valle) e – e – ( ν ) R 0 νββ ν L u d d u W W ( ν ) R → ν L : A Majorana mass term 12

Of course, this Majorana mass term is tiny : < 10 –23 eV. (Duerr, Lindner, Merle; Rodejohann) Neutrino oscillation data imply masses > 10 –2 eV . ∴ There must be other sources of neutrino mass. But 0 νββ A Majorana mass term, however tiny. 13

Why Most Theorists Expect Majorana Masses The Standard Model (SM) is defined by the fields it contains, its symmetries (notably weak isospin invariance), and its renormalizability. Leaving neutrino masses aside, anything allowed by the SM symmetries occurs in nature. Right-Handed Majorana mass terms are allowed by the SM symmetries. Then quite likely Majorana masses occur in nature too. 14

Does ν = ν ? Does ν = ν ? 15

What Is the Question? For each mass eigenstate ν i , and given helicty h, does — • ν i (h) = ν i (h) (Majorana neutrinos) or • ν i (h) ≠ ν i (h) (Dirac neutrinos) ? Equivalently, do neutrinos have Majorana masses ? If they do, then the mass eigenstates are Majorana neutrinos . 16

Why Majorana Masses Majorana Neutrinos The objects ν L and ν Lc in m L ν L ν Lc are not the mass eigenstates, but just the neutrinos in terms of which the model is constructed. m L ν L ν Lc induces ν ν mixing. As a result of K 0 K 0 mixing, the neutral K mass eigenstates are — K S,L ≅ (K 0 ± K 0 )/ √ 2 . K S,L = K S,L . As a result of ν ν mixing, the neutrino mass eigenstate is — ν i = ν + ν . ν i = ν i . 17

Whatever diagrams cause 0 νββ , its observation would imply the existence of a Majorana mass term: (Schechter and Valle) e – e – ( ν ) R 0 νββ ν L u d d u W W ( ν ) R → ν L : A Majorana mass term ∴ 0 νββ ν i = ν i 18

The Nature of The Nature of Majorana Neutrinos Majorana Neutrinos 19

SM Interactions Of A Dirac Neutrino We have 4 mass-degenerate states: Conserved L makes  – ν +1 makes  + ν –1 These states, when Ultra ν Rel., do not interact. ( ( The weak interaction ν is Left Handed. 20

SM Interactions Of A Majorana Neutrino We have only 2 mass-degenerate states: makes  – ν makes  + ν The weak interactions violate parity . (They can tell Left from Right .) An incoming left-handed neutral lepton makes  – . An incoming right-handed neutral lepton makes  + . 21

Electromagnetic Electromagnetic Properties Properties 22

Can a Majorana Neutrino Have an Electric Charge Distribution Distribution ? No! – + – + = Anti But for a Majorana neutrino — Anti ( ν ) = ν 23

Dipole Moments ν In the Standard Model, W + γ loop diagrams like —  – ν produce, for a Dirac neutrino of mass m ν , a magnetic dipole moment — µ ν = 3 x 10 –19 (m ν /1eV) µ B (Marciano, Sanda; Lee, Shrock; Fujikawa, Shrock) 24

A Majorana neutrino cannot have a magnetic or electric dipole moment: [ ] [ ] µ µ = – e – e + But for a Majorana neutrino, ν i ν i = Therefore, [ ν i ] [ ν i ] = 0 = µ µ 25

Both Dirac and Majorana neutrinos can have transition dipole moments, leading to — e ν 2 γ ν 1 e One can look for the dipole moments this way. To be visible, they would have to vastly exceed Standard Model predictions. 26

The See-Saw The See-Saw The Most Popular The Most Popular Explanation Of Explanation Of Why Neutrinos Why Neutrinos Are So Light Are So Light 27

Majorana Masses Split Dirac Neutrinos A Majorana mass term splits a Dirac neutrino into two Majorana neutrinos. 2 Majorana neutrino 4 Splitting due to Majorana mass Dirac Majorana neutrino 2 neutrino 28

What Happens In the See-Saw A BIG Majorana mass term splits a Dirac neutrino into two widely-spaced Majorana neutrinos. 2 Majorana N neutrino 4 Splitting due to Majorana mass Dirac D Majorana neutrino ν 2 neutrino 2 m ν m N ≈ m D The See-Saw Relation If m D is a typical fermion mass, m N will be very large. 29

The See-Saw Picture Familiar { ν light neutrino } Very N heavy neutrino Yanagida; Gell-Mann, Ramond, Slansky; Mohapatra, Senjanovic; Minkowski 30

Signature Predictions of the See-Saw Ø Each ν i = ν i (Majorana neutrinos) So look for 0 νβ ! So look for 0 νβ νββ ! νββ Ø The light neutrinos have heavy partners N i 31

Are re w we de descende ded Are re w we de descende ded fro rom t the h heavy fro rom t the h heavy See- See-Sa Saw part part rtner See- See-Sa Saw rtner neutri rinos? neutri rinos? 32

The Challenge — A Cosmic Broken Symmetry The universe contains baryons, but essentially no antibaryons. The Baryon Number of the universe, ( ) B " n B # n B = 3 n q # n q is nonzero. Standard cosmology: Any initial nonzero Baryon Number would have been erased. How did B = 0 B ≠ 0 ? 33

Sakharov: B = 0 B ≠ 0 requires CP. The CP in the quark mixing matrix, seen in B and K decays, leads to much too small a Baryon Number. If quark quark CP cannot generate the observed Baryon Number, can some scenario involving leptons leptons do it? The candidate scenario: Le Leptogenesis , an outgrowth of the Se See-Saw picture . (Fukugita, Yanagida) 34

Leptogenesis — Step 1 The heavy neutrinos N would have been made in the hot Big Bang. The heavy neutrinos N, like the light ones ν , are + Majorana particles. Thus, an N can decay into  or  . CP is expected in these decays. Then, in the early universe, we would have had different rates for the CP-mirror-image decays – + + – N →  + H and N →  + H Standard-Model Higgs This produces a universe with unequal numbers of leptons and antileptons. 35

Leptogenesis — Step 2 The Standard-Model Sphaleron process, which does not conserve Baryon Number B , or Lepton Number L , but does conserve B – L , acts. B f " # 1 3 L i B i = 0 Sphaleron L f " 2 Process L i " 0 3 L i " # 2 B f Final state Initial state from N decays There is now a nonzero Baryon Number . There are baryons, but ∼ no antibaryons. Reasonable parameters give the observed . n B n " 36

What About the Lepton Number ? Big-Bang cosmology: Big-Bang cosmology: The leptons in the universe include electrons and many many neutrinos. # (electrons) = # (protons) < # (protons + neutrons) = 6 × 10 –10 # (photons) (neutrinos) ≈ # (photons) >> # (electrons) # (neutrinos) ≈ # (photons) >> # (electrons) # 37