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Double-Beta Decay and the Search for (Elementary) Majorana Particles

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Double-beta decay and the search for (elementary) Majorana particles Giorgio Gratta Physics Dept. Stanford University Summer Undergraduate Program, Aug Neutrinos - Gratta 1 2020 Summer Undergraduate Program, Aug Neutrinos - Gratta 2 2020 For the first ~50 years since the neutrino was invented by Pauli, its properties could be fairly well described by quoting just 2 papers: Neutrinos really exist! Summer Undergraduate Program, Aug Neutrinos - Gratta 3 2020 Neutrinos are left handed particles Summer Undergraduate Program, Aug Neutrinos - Gratta 4 2020 Helicity is the property that correlates the spin of a particle to its momentum Because of special relativity the helicity of a particle is related to its mass The observer above sees a neutrino passing-by and reports its helicity (the scalar product between spin vector and momentum vector) as negative (left-handed) Summer Undergraduate Program, Aug Neutrinos - Gratta 5 2020 Helicity is the property that correlates the spin of a particle to its momentum Because of special relativity the helicity of a particle is related to its mass Now the observer is cruising in the same direction of the neutrinos, at higher speed. While overtaking the neutrino he will claim that its helicity is positive! Summer Undergraduate Program, Aug Neutrinos - Gratta 6 2020 Helicity is the property that correlates the spin of a particle to its momentum Because of special relativity the helicity of a particle is related to its mass But if the neutrino has zero mass nothing can overtake it Neutrinos with fixed helicity have to be massless So the fixed helicity and the zero mass were encoded in the Standard Model of elementary particles for neutrinos Summer Undergraduate Program, Aug Neutrinos - Gratta 7 2020 Last 20 yrs: the age of ν physics Discovery of ν flavor change - Solar neutrinos (MSW effect) - Reactor neutrinos (vacuum oscillation) - Atmospheric neutrinos (vacuum oscillation) - Accelerator neutrinos (vacuum oscillation) We also found that: • ν masses are non-zero • there are 2.981±0.008 ν (Z lineshape) • 3 ν flavors were active in Big Bang Nucleosynthesis • The Sun emits neutrinos as expected • Supernovae emit neutrinos Summer Undergraduate Program, Aug 2020 Neutrinos - Gratta 8 If mν ≠ 0 neutrinos show a different image depending on our vantage point: ν e • “Weak interaction this is the state of definite flavor: ν µ interactions couple eigenstate” to this state ντ ν m1 this is the state of definite energy: propagation happens • ν “Mass eigenstate” m2 in this state Summer Undergraduate Program, Aug ν Neutrinos m 3 - Gratta 9 2020 ν U U U ν e e1 e2 e3 m1 ν µ = U µ1 U µ 2 U µ 3 ν m2 ντ Uτ1 Uτ 2 Uτ 3 ν m3 A source produces –say- νe always via weak interactions ν e To see what propagates to the − detector I have to project this 1 flavor state onto the mass state ν m = U ν e using the matrix inverse of U Summer Undergraduate Program, Aug Neutrinos - Gratta 10 2020 − − ν (t) = e i(E1t p1L)ν Now each of the νm m1 m1 will evolve in time as −i(E2t− p2L) prescribed by the ν m2 (t) = e ν m2 wave functions −i(E3t− p3L) ν m3 (t) = e ν m3 but note that the periodic term contains the neutrino mass via 2 Ei=mic So at the end of their flight -at the detector- the mix of νm1, νm2, νm3 will not necessarily be the one that makes “exactly” νe ! Summer Undergraduate Program, Aug Neutrinos - Gratta 11 2020 The neutrinos are then detected via weak interactions and so we need to find again the composition in terms of νe , νμ , ντ −i(E jt− p j L) * Formally ν j = ∑∑Ulje U j′l ν j′ j′ l So after some propagation one can “find” a neutrino of a flavor that was not originally present This is a pure quantum-mechanical effect, there is no classical interpretation of it It can ONLY happen if the mass is non-0 Summer Undergraduate Program, Aug Neutrinos - Gratta 12 2020 For 2 flavors this simplifies: θ θ cos sin Only one mixing parameter θ U = − sinθ cosθ 2 2 2 1.3∆m L P(ν →ν µ , L) = sin 2θ sin e E Neutrino oscillations are basically an interferometric technique to measure tiny mass differences. This is the reason for such an exquisite sensitivity! This is a situation analogous to that of beats in acoustics, again a very sensitive technique that allows musicians to accurately tune their instruments. Summer Undergraduate Program, Aug Neutrinos - Gratta 13 2020 The oscillatory nature of the rate of νs of one flavor and, hence, the fact that different flavors really turn into each other is directly shown by some of the experiments ≈Proper time τ L0=180 km Summer Undergraduate Program, Aug Neutrinos - Gratta 14 2020 Our knowledge of the ν mass pattern ~20 eV ~2 eV (PDG 2002) SN1987A from of flight Time From tritium endpoint ~1 eV ~0.3 eV -5 2 solar~ 7.6·10 eV Cosmology From From 0 -3 2 νββ ~2.4·10 eV if -3 2 ν ~2.4·10 eV is Majorana solar~ 7.6·10-5eV2 But, of course, the oscillation only measures the mass differences, so we still do not know how large neutrino masses really are! Summer Undergraduate Program, Aug Neutrinos - Gratta 15 2020 Some help from Nuclear Physics Double-beta decay: Candidate nuclei with Q>2 MeV a second-order process only detectable if first Candidate Q Abund. order beta decay is (MeV) (%) energetically forbidden 48Ca→48Ti 4.271 0.187 76Ge→76Se 2.040 7.8 82Se→82Kr 2.995 9.2 96Zr→96Mo 3.350 2.8 100Mo→100Ru 3.034 9.6 110Pd→110Cd 2.013 11.8 116Cd→116Sn 2.802 7.5 124Sn→124Te 2.228 5.64 130Te→130Xe 2.533 34.5 136Xe→136Ba 2.479 8.9 150Nd→150Sm 3.367 5.6 Summer Undergraduate Program, Aug Neutrinos - Gratta 16 2020 There are two varieties of ββ decay 2ν mode: a conventional 0ν mode: a hypothetical Theprocess 2ν mode forbidden (that by is not but rare process the Standard Model in nuclear physics relevant for our discussion) was first analyzed by Maria Goeppert-Mayer who calculated lifetimes >1020 years M.Goeppert-Mayer, Phys. Rev. 48 (1935) 512 Summer Undergraduate Program, Aug Neutrinos - Gratta 17 2020 There are two varieties of ββ decay 2ν mode: a conventional 0ν mode: a hypothetical but rare process process forbidden by in nuclear physics the Standard Model 0ν mode: a ν is emitted and reabsorbed by the same process. Particle interaction rules require 1) helicity change 2) particle=antiparticle Summer Undergraduate Program, Aug Neutrinos - Gratta 18 2020 The distinction between particles and antiparticles is clear for charged particles: A positron (anti-electron) carries a positive - charge and cannot be confused with an e ↑ electron (that carries a negative charge) - Electrons (and all other spin ½ particles e ↓ we know) are described by Dirac’s + equation that has for solutions e ↑ 4-component wavefunctions: e+ ↓ Summer Undergraduate Program, Aug Neutrinos - Gratta 19 2020 But the distinction is much less obvious in the case of neutral particles such as neutrinos In fact long time ago Ettore Majorana wrote the possible theory of neutral, spin ½ particles where the particle/antiparticle nature is blurred E.Majorana, Nuovo Cimento 14 (1937) 171 According to this theory neutrinos would be described v ↑ by a Majorana equation with as solutions 2 component wavefunctions: v ↓ Summer Undergraduate Program, Aug Neutrinos - Gratta 20 2020 But the distinction is much less obvious in the case of neutral particles such as neutrinos In fact long time ago Ettore Majorana wrote the possible theory of neutral, spin ½ particles where the particle/antiparticle nature is blurred E.Majorana, Nuovo Cimento 14 (1937) 171 According to this theory neutrinos would be described v ↑ by a Majorana equation with as solutions 2 component wavefunctions: v ↓ Since neutrinos are the only neutral elementary particle this idea can only be tested with them… Are neutrinos their own antiparticles? Summer Undergraduate Program, Aug Neutrinos - Gratta 21 2020 There is a theorem: “0νββ decay always implies new physics” There is no scenario in which observing 0νββ decay would not be a great discovery Majorana neutrinos Lepton number violation Probe new mass mechanism up to the GUT scale Probe key ingredient in generating cosmic baryon asymmetry The process that creates net matter (w/o balancing it with antimatter) Summer Undergraduate Program, Aug Neutrinos - Gratta 22 2020 How to find 0ν double beta decay e- N N’ e- Large amount of Need to find rare nuclear decays a material in a large quantity of material containing nuclei N containing nuclei of species N Summer Undergraduate Program, Aug Neutrinos - Gratta 23 2020 The challenge (1): What is “species N”? Candidate Abund. Most suitable nuclei are Q>2MeV (%) not very common in Nature 48Ca→48Ti 0.187 76 76 Ge→ Se 7.8 Need massive isotopic 82Se→82Kr 9.2 enrichment 96Zr→96Mo 2.8 100Mo→100Ru 9.6 EXO-200 has 200kg of 110Pd→110Cd 11.8 136Xe enriched to 80% 116Cd→116Sn 7.5 from the natural level 124Sn→124Te 5.64 of ~8.8% 130Te→130Xe 34.5 136Xe→136Ba 8.9 150Nd→150Sm 5.6 Summer Undergraduate Program, Aug Neutrinos - Gratta 24 2020 The challenge (2): How much is a “large quantity”? To reach interesting ν mass scales need tons of separated isotopes! Summer Undergraduate Program, Aug Neutrinos - Gratta 25 2020 The challenge (3): How rare is “rare”? Need to be sensitive to half-lives of ~ 1028 years, this is 1018 times the age of the Universe!! detect ~few nuclear decays/year in tons of material Each decay liberates energies of order few MeV Backgrounds are a huge issue - Most standard materials are MANY orders of magnitude too radioactive to be part of the detector!! - Need to locate experiments underground, to suppress the effects of cosmic radiation Summer Undergraduate
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