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Double beta decay, neutrino oscillations and sterile neutrinos. Petr Vogel,

Double beta decay, neutrino oscillations and sterile neutrinos. Petr Vogel, Caltech BSM11, Madison, WI, Oct.15, 2011. Moore’s law of 0nbb decay. This figure, from our 2002 review with Steve Elliott, has not changed since that time.

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Double beta decay, neutrino oscillations and sterile neutrinos. Petr Vogel,

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  1. Double beta decay, neutrino oscillations and sterile neutrinos. Petr Vogel, Caltech BSM11, Madison, WI, Oct.15, 2011

  2. Moore’s law of 0nbb decay This figure, from our 2002 review with Steve Elliott, has not changed since that time. The last entry, from 2001, (Heidelberg-Moscow experiment) is still a record sensitivity, even though by now we should be about an order of magnitude in lifetime better according to this plot. Several experiments of the next generation are ready (or almost), But still, new results are not expected to be available for ~2-3 years. Hence the slope will be probably less steep in the 21st century.

  3. This is worrisome, since it is often claimed that the study of the 0nbb-decay is one of the highest priority issues in particle and nuclear physics APS Joint Study on the Future ofNeutrino Physics (2004) (physics/0411216) We recommend, as a high priority, a phased program of sensitive searches for neutrinoless double beta decay (first on the list of recommendations) The answer to the question whether neutrinos are their own antiparticles is of central importance, not only to our understanding of neutrinos, but also to our understanding of the origin of mass.

  4. Nevertheless, there is considerable experimental activity, in particular many new results on the 2nbb decay. T1/2 (y) M2n(MeV-1) 48Ca (4.3 +2.4-1.1 ±1.4)E19 0.05±0.02 Balysh, PRL77,5186(1996) 76Ge (1.74 ± 0.01+0.18-016)E21 0.13±0.01 Doerr,NIMA513,596(2003) 82Se (9.6 ± 0.3 ± 1.0)E19 0.10±0.01 Arnold,PRL95,182302(2005) 96Zr (2.35 ± 0.14 ± 0.16)E19 0.12±0.01 Argyriades,NPA847,168(2010) 100Mo (7.11 ±0.02 ± 0.54)E18 0.23±0.01 Arnold,PRL95,182302(2005) 116Cd (2.9+0.4-0.3)E19 0.13±0.01 Danevich,PRC68,035501(2003) 128Te* (1.9 ± 0.1 ± 0.3)E24 0.05±0.005 Lin,NPA481,477(1988) 130Te (7.0 ± 0.9 ±1.1)E20 0.033±0.003 Arnold,PRL107,062504(2011) 136Xe (2.1 ± 0.04 ± 0.21)E21 0.019±0.001 Ackerman,arxiv:1108.4193(2011) 150Nd (9.11+0.25-0.22±0.63)E18 0.06±0.003 Argyriades,PRC80,032501R(2009) 238U** (2.2 ± 0.6)E21 0.05±0.01 Turkevich,PRL67,3211(1991) *from geochemical ratio 128Te/130Te; **radiochemical result

  5. If (or when) the 0nbb decay is observed two • problems must be resolved: • What is the mechanism of the decay, • i.e., what kind of virtual particle is (what is n1?) • exchanged between the affected • nucleons (or quarks)? • b) How to relate the observed decay rate • to the fundamental parameters, that is • what is the value of the corresponding • nuclear matrix elements? (how to describe NP above?)

  6. Two basic categories are long-range and short-range contributions to the 0nbb decay. The long-range category involves two pointlike vertices and the exchange of a light Majorana neutrino between them. The standard (plain vanilla) type of that category is when 1/T1/20n = G0n(Q,Z) |M0n|2 |<mbb>|2, <mbb>=|SiUei2 mi| , which represents simple relation between the decay rate and the parameters of the neutrino mass matrix. The short-range category involves only a single pointlike vertex (six fermions, four hadrons and two leptons), i.e. a dimension 9 operator. The relation between the decay rate and neutrino mass is not simple in that case.

  7. It is well known that the amplitude for the light neutrino exchange scales as <m>. On the other hand, if heavy particles of scale are involved the amplitude scales as 1/5 (dimension 9 operator) . The relative size of the heavy (AH) vs. light particle (AL) exchange to the decay amplitude is(a crude estimate, due originaly to Mohapatra) AL ~ GF2 mbb/<q2>, AH ~ GF2 MW4/L5 , where L is the heavy scale and q ~ 100 MeV is the virtual neutrino momentum. For L ~ 1 TeV and mbb ~ 0.1 – 0.5 eV AL/AH ~ 1, hence both mechanisms contribute equally.

  8. As long as only a limit on the 0nbb decay rate exists, we can constrain all parameters entering the decay amplitudes (light and heavy neutrino masses, strength of the right-handed current, SUSY R-parity violating amplitudes, etc.). However, once the decay rate is convincingly measured, we will need to determine which of the possible mechanism is responsible for the observation. Various particle physics models in which 0nbb-decay of the short-range category might exist. In them LNV violation is associated with low-scale (~TeV) physics, unlike see-saw with LNV at very high scale. As an example, consider the LR symmetric model (Tello et al. (2011). In it the quantity analogous to <mbb> is MNbb= <q2> MWL4/MWR4 x V2Rej / mNj (here MWR is the mass of the right-handed W, and Vrej is the mixing parameter for the heavy right-handed neutrinos of mass mNj)

  9. Usual representation of the relation between <m> and the neutrino mass scale. It shows that the <m> axis can be divided into three distinct regions as indicated. However, it creates the impression (false) that determining <m> would decide between the two competing hierarchies. degenerate inverted normal

  10. Note in passing that less attention has been devoted in the past to the evaluation of the nuclear matrix elements for the case of heavy particle exchange (short-range contribution to 0nbb decay). Proper treatment of the nucleon-nucleon repulsion in that case is obviously crucial; it is traditionally treated crudely using nucleon form factors. Including pion exchange avoids this problem and seems to lead to larger and more consistently evaluated matrix elements. (Vergados 82, Faessler et al. 97, Prezeau et al. 03) 0nbb amplitude is contained in the ppee vertex

  11. Various models of the LNV with ~TeV scale new physics exist. They include, e.g. Left-Right symmetry, R-parity violating SUSY, etc. The common feature of these possibilities, besides LNV, is that they affect also LFV. Observing various manifestations of LFV, m -> e + g, m conversion, or m-> 3e might help to decide which of these models is appropriate if any at all. Thus the relation between LFV and LNV might be used as a diagnostic tool (Cirigliano et al., (2004))

  12. For the analysis of 0nbb decay the knowledge of nuclear matrix elements • is crucial. There is no possibility to evaluate them exactly, approximations • are always necessary. • For the light Majorana neutrino exchange several methods have been used • for the evaluation of M0n. Depending on your disposition, the results are • encouraging or discouraging. Main features are: • Different methods (with very different approximations) give similar • magnitude of M0n. However, differences of a factor ~2 exist. • 2) All methods agree that the M0n should vary slowly (or not at all) • with Z,A of the corresponding nuclei. This would make it possible • to check the observation in one nucleus (say 76Ge) by performing • experiments in another one (say 136Xe or 130Te).

  13. Vogel, 9/2010

  14. Possible existence of light sterile neutrinos: • a) Most models of mn involve sterile neutrinos. • b) Their mass can be large, MGUT for the see-saw type I. • Such heavy nR do not mix with the light n, but are • needed in order to explain the smallness of mn. • The situation is similar for the nR masses of ~TeVscale. • However, a variaty of indications point to the existence • of sterile neutrinos at the ~ eV scale that mix noticeably • with the light neutrinos. If they really exist, their existence would require some additional physics reasons • for their small mass. Nevertheless, it is worthwhile • to consider the experimental indications.

  15. Here is a list of hints for the existence of sterile neutrinos with ~ eV mass scale. These results (2-3 s) are not directly ruled out by other experiments. In addition analysis of the CMB and Large Structures also indicates that additional relativistic fermions existed at the corresponding epochs. Arguments for existence of (now perhaps a bit heavier) sterile neutrinos are also invoked in the explanation of the r-process, supernova kicks or warm dark matter.

  16. <R> = 0.86±0.05 L/En (m/MeV) <R>= 0.937±0.027 Reactor neutrino anomaly (Mention et al., Phys. Rev. D83, 073006(2011).

  17. However, reconciling this with mn~ 1-2 eV is problematic, due to the cosmological mass limit.

  18. Analysis based on P(ne -> ne) = 1 – sin2(2qnew)sin2(Dm2new L/En) Best fit Dm2new = 2.35±0.1 eV2, sin2(2qnew) = 0.165±0.04

  19. Proposals to verify the L/En variation using s strong b decay source and a large liquid scintillator detector.

  20. What the possible existence of such sterile neutrino has to do with the 0nbb decay? Remember that <mbb> = |S Uei2 mi| If we add the 4th neutrino to this sum, it will contribute 0.14 eV using the previous best fit sin2(2qnew) and mnew = (Dm2new)1/2 That would dominate the <mbb> for all but highly degenerate scenario of neutrino masses. This widely used picture would be totally useless

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