The Profound The Profound Implications of Implications of - PowerPoint PPT Presentation

The Profound The Profound Implications of Implications of Neutrinoless Double Neutrinoless Double Beta Decay Beta Decay Boris Kayser DNP–JPS Meeting October 13, 2009 1

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

Observation of 0 νββ would be evidence in favor of —  The See-Saw model of the origin of neutrino mass  Leptogenesis as 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 – ) = –L( ν ) = –L( 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 l 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 (tiny) Majorana mass term ∴ 0 νββ A Majorana mass term 12

Does ν = ν ? Does ν = ν ? 13

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 . 14

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 L ν Lc 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 L ν Lc mixing, the neutrino mass eigenstate is — ν i = ν L + ν Lc = “ ν + ν ”. ν i = ν i . 15

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 (tiny) Majorana mass term ∴ 0 νββ ν i = ν i 16

The Nature of The Nature of Majorana Neutrinos Majorana Neutrinos 17

When ν ≠ ν We have 4 mass-degenerate states: ν ν ν ν This collection of 4 states is a Dirac neutrino plus its antineutrino. 18

The SM l ν W interaction, which conserves L, is — Left-handed L SM = � g � + � ( ) L � � � L W � L � � l L W � + l 2 Absorbs right-handed ν When ν ≠ ν makes l – ν ν doesn’t interact 19

When ν = ν We have only 2 mass-degenerate states: ν ν This collection of 2 states is a Majorana neutrino. 20

The SM l ν W interaction is — Left-handed L SM = � g � + � ( ) L � � � L W � L � � l L W � + l 2 Absorbs right-handed ν = ν When ν = ν makes l – ν makes l + ν 21

The See-Saw The See-Saw 22

The See-Saw Mechanism — A Summary — The most popular explanation of why neutrinos are so light. There is both a large RH Majorana mass m R and a much smaller Dirac mass m D ~ m q or l . m R splits the Dirac neutrino. N m N ~ m R – Splitting due to m R Dirac neutrino 2 / m R ν m ν ~ m D – Note that m ν m N ∼ m D2 ∼ m q or l2 . See-Saw Relation See-Saw Relation 23

The See-Saw Mechanism Familiar { ν light neutrino Very } N heavy neutrino Yanagida; Gell-Mann, Ramond, Slansky; Mohapatra, Senjanovic; Minkowski 24

Predictions of the See-Saw  Each ν i = ν i – (Majorana neutrinos)  The light neutrinos have heavy partners N i How heavy?? m 2top m 2top m N ~ ––––– ~ –––––– ~ 10 15 GeV m ν 0.05 eV Near the GUT scale. Coincidence?? 25

Are we Are we de desce scende nded Are we Are we de desce scende nded from the he from the heavy avy from the from the he heavy avy Se See-Saw -Saw partne partne partner Se See-Saw -Saw partner ne neutrinos? utrinos? ne neutrinos? utrinos? 26

The Challenge — A Cosmic Broken Symmetry The universe contains baryons, but essentially no antibaryons. Standard cosmology: Any initial baryon – antibaryon asymmetry would have been erased. How did ? n B = n B n B >> n B 27

Sakharov: requires CP. n B >> n B n B = n B The CP in the quark mixing matrix, seen in B and K decays, leads to much too small a B – B asymmetry. If quark quark CP cannot generate the observed B – B asymmetry, can some scenario involving leptons leptons do it? The candidate scenario: Leptoge ptogene nesis sis , an outgrowth of the Se See-Saw -Saw picture . (Fukugita, Yanagida) 28

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 l or l . CP is expected in these decays. Then, in the early universe, we would have had different rates for the CP-mirror-image decays – + + – N → l + H and N → l + H Standard-Model Higgs This produces a universe with unequal numbers of leptons and antileptons. 29

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 Initial state Final state from N decays There is now a Baryon Asymmetry . 30

Evidence for the See-Saw and for Leptogenesis By confirming the existence of Majorana masses and the Majorana character of neutrinos— 0 νββ — the observation of 0 νββ would be evidence in favor of the Se See-S -Saw , hence of Leptogenesis . Other evidence for Leptogenesis would come ( ( from the observation of CP in neutrino oscillation. 31

— 0 0 νββ — — — νββ A Closer Look A Closer Look 32

We anticipate that 0 νββ is dominated by a diagram with Standard Model vertices: SM vertex e – e – ν i ν i ∑ U ei Mixing matrix U ei i W – W – Nuclear Process Nucl Nucl’ Then — Mass ( ν i ) Amp[0 νββ ] ∝ ∑ m i U ei2 ≡ m ββ 33

Why Amp[0 νββ ] Is ∝ Neutrino Mass e – e – Nucl Nucl’ — manifestly does not conserve L. But the Standard Model (SM) weak interactions do conserve L. Absent any non-SM L-violating interactions, the Δ L = 2 of 0 νββ can only come from Majorana neutrino masses , such as — ν L ( ν ) R m L ( ν Lc ν L + ν L ν Lc ) X m L 34

How Large is m ββ , and What Would We Learn By Measuring It? Talk by Sergue uey P Petc tcov ov this afternoon. 35

Summary Summary A non-zero signal for 0 νββ A non-zero signal for 0 νββ would be a tremendously would be a tremendously important discovery. important discovery. Good luck in finding it! Good luck in finding it! 36