Double Beta Decay: Physics, Recollections, and Future Boris Kayser CISNP May 16, 2008 1
Are Neutrinos Majorana Particles? (Does ν = ν?) 2
What Is the Question? For each mass eigenstate ν i, does or ν i = ν i (Majorana neutrinos) ν i ν i (Dirac neutrinos)? Equivalently, do neutrinos have Majorana masses? If they do, then the mass eigenstates are Majorana neutrinos. We note that ν i = ν i means ν i (h) = ν i (h) helicity 3
Majorana Masses Out of, say, a left-handed neutrino field, ν L, and its charge-conjugate, ν Lc, we can build a Majorana mass term m L ν L ν L c (ν) R X ml ν L Majorana masses do not conserve the Lepton Number L defined by L(ν) = L(l ) = L(ν) = L(l + ) = 1. 4
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. Majorana ν masses cannot come from a Yukawa coupling ν R ν L x (Standard-Model Higgs) like that which leads to the quark and charged-lepton masses. Majorana neutrino masses must have a different origin than the masses of quarks and charged leptons. 5
Why Majorana Masses Majorana Neutrinos The objects ν L and ν L c 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 L c 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 c L mixing, the neutrino mass eigenstate is ν i = ν L + ν c L = ν + ν. ν i = ν i. 6
Why Most Theorists Expect Majorana Masses The Standard Model (SM) is defined by the fields it contains, its symmetries (notably gauge invariance), and its renormalizability. Leaving neutrino masses aside, anything allowed by the SM symmetries occurs in nature. Majorana masses are allowed by the SM symmetries. Then quite likely Majorana masses occur in nature too. 7
To Determine Whether Majorana Masses Occur in Nature 8
The Promising Approach Seek Neutrinoless Double Beta Decay [0νββ] e e Nucl Nucl We are looking for a small Majorana neutrino mass. Thus, we will need a lot of parent nuclei (say, one ton of them). 9
Whatever diagrams cause 0νββ, its observation would imply the existence of a Majorana mass term: Schechter and Valle (ν) R e e 0νββ ν L W u d d u W (ν) R ν L : A Majorana mass term 0νββ ν i = ν i 10
We anticipate that 0νββ is dominated by a diagram with Standard Model vertices: SM vertex e e i Nucl ν i ν i U ei U ei W W Nuclear Process Nucl Mixing matrix 11
But there could be other contributions to 0νββ, which at the quark level is the process dd uuee. An example from Supersymmetry: e e u e γ e u d d 12
In SM vertex i Nucl e e ν i ν i U ei U ei W W Nuclear Process Nucl Mixing matrix Mass (ν i ) the ν i is emitted [RH + O{m i /E}LH]. Thus, Amp [ν i contribution] m i Amp[0νββ] m i U ei2 m ββ i 13
Neutrinoless Double Beta Decay and Neutrino Mass A Point of Principle 14
In Down the Garden Path SM vertex i Nucl e e ν i ν i U ei U ei W W Nuclear Process Nucl Mixing matrix Mass (ν i ) the ν i is emitted [RH + O{m i /E}LH]. Thus, Amp [ν i contribution] m i Amp[0νββ] m i U ei2 m ββ i 15
The Trap This makes it look as if 0νββ needs ν mass only because of a helicity mismatch, which a RH current could fix. Suppose we had a parity-conserving world, that treats right-handed and left-handed particles in the same way. Couldn t we then have 0νββ without any ν mass? No! ν mass is still required. 16
Why? 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 ΔL = 2 of 0νββ can only come from Majorana neutrino masses, such as m L ( ν Lc ν L + ν L ν Lc ) (ν) R X m L ν L 17
Assuming Standard Model vertices, 0νββ is e e (ν) X ν R L m L W W Nucl Nuclear Process Nucl The Majorana neutrino mass term plays two roles: 1) Violate L 2) Flip handedness It will be needed for (1) even when not needed for (2). 18
A Parity-Conserving Toy-Model Illustration Suppose there is only one generation. Suppose the W couples to the electron and neutrino via a parity-conserving vector current: "L W = g 2 W # " e $ # % + h.c. = g 2 W # " ( e L $ # % L + e R $ # % ) R + h.c. Suppose the neutrino mass term is also L R invariant: "L M = 1 2 m ( M # c L # L + # c R # ) + m R D# R # L + h.c. We take m M,D real, m M > m D, and neglect the electron mass. 19
The neutrino mass eigenstates are the two Majorana particles and [( ) + (" L + " R ) c ] " 2 = 1 2 " L + " R, with mass m 2 = m M + m D, [( ) + (" L # " R ) c ] " 1 = 1 2 " L # " R, with mass. m 1 = m M " m D In terms of them "L W = g 2 W # " & e L $ # 12 % 2L + % ' ( 1L ( ) + e R $ # ( 12 % 2R " % 1R ) ) * + + h.c. 20
Consider now the particle-physics part of 0νββ e e Σ i = 1,2 W ν i W If the electrons both emerge Left-Handed (LH), only the LH leptonic currents contribute. For this final state, one finds that the amplitude, A LL, obeys A LL " m 2 q 2 2 # m + m 1 2 q 2 2 # m $ m 2 + m 1 1 q 2 = 2m M q 2 The amplitude is proportional to the Majorana ν mass m M. 21
Similarly, if both electrons emerge right-handed, the amplitude, A RR, obeys A RR " m 2 q 2 2 # m + m 1 2 q 2 2 # m $ m 2 + m 1 1 q 2 = 2m M q 2 Higher-order (in ν mass) terms: Every term in A LL or A RR must flip both L and the chirality, so it must be proportional to m M Odd md Even Expanding the denominators confirms that every term does have this character. 22
If the electrons emerge with opposite handedness, both the LH and RH currents are involved, and one finds that the amplitude, A LR, obeys $ 1 A LR " iq q 2 2 # m # 1 & 2 q 2 2 % # m 1 $ ' ) * iq m ' 2 2 2 & # m 1 ) ( & ( q 2 ) 2 ) = iq % ( q 2 ( ) 2 4m M m D The amplitude is proportional to the Majorana ν mass m M. 23
Why A LR is also proportional to the Dirac mass m D : BK, Petcov, and Rosen; Enqvist, Maalampi, and Mursula The process is e L e R LH current W (ν) R ν L X m M X ν R m D W RH current Two flips of handedness are needed. 24
Higher-order (in ν mass) terms: Every term in A LR must flip L but not chirality, so it must be proportional to m M Odd md Odd Expanding the denominators (q 2 m i2 ) confirms that every term does have this character. Including the electron mass doesn t make any difference. 25
Summary of this Point of Principle Absent L-nonconserving interactions from beyond the Standard Model, 0νββ0 requires Majorana neutrino mass. This mass is needed to introduce L-nonconservation, even if it is not needed for any other reason. 26
A Recollection Primakoff and Rosen Primakoff and Rosen were pioneers of the whole field of double beta decay. A half-century ago, they contemplated 0 0νββ arising from non-sm, L-nonconserving interactions. Then Majorana neutrino mass is not needed. We have not yet seen any evidence for such interactions, but we do expect Majorana neutrino masses. 27
Assuming the Usual Diagram Dominates 28
How Large is m ββ? How sensitive need an experiment be? Suppose there are only 3 neutrino mass eigenstates. (More might help.) Then the spectrum looks like atm ν 3 sol < ν 2 ν1 Normal hierarchy or ν sol < 2 ν 1 atm ν 3 Inverted hierarchy 29
Takes 1 ton 95% CL m ββ Smallest Takes 100 tons m ββ For Each Hierarchy 30
There is no clear theoretical preference for either hierarchy. Suppose the hierarchy is found, via accelerator neutrino experiments, to be inverted. Then 0νββ searches with sensitivity to m ββ = 0.01 ev have a very good chance to see a signal. If these 0νββ searches establish that m ββ < 0.01 ev, then, barring unlikely cancellations from exotic mechanisms, we can say that neutrinos are Dirac particles: " # ". 31
Heartiest congratulations and thanks to Frank Avignone and Ettore Fiorini for leading the way to the present very exciting point in the quest to find neutrinoless double beta decay. Thanks, with fond memories, to Peter Rosen for pioneering contributions to this field, and for encouraging this very important quest. We eagerly await the results of the 0 0νββ searches with sensitivity at the (0.01 0.05) ev scale. 32