Double beta decay, neutrino oscillations and sterile neutrinos.

Petr Vogel, Caltech

BSM11, Madison, WI, Oct.15, 2011

Moore’s law of decay

This figure, from our 2002 reviewwith Steve Elliott, has not changed since that time.The last entry, from 2001,(Heidelberg-Moscow experiment)is still a record sensitivity, eventhough by now we should be aboutan order of magnitude in lifetimebetter according to this plot.

Several experiments of the nextgeneration are ready (or almost),But still, new results are notexpected to be available for~2-3 years. Hence the slopewill be probably less steep in the 21st century.

APS Joint Study on the Future ofNeutrino Physics (2004)

(physics/0411216)

We recommend, as a high priority, a phased programof sensitive searches for neutrinoless double betadecay (first on the list of recommendations)

The answer to the question whether neutrinos are their own antiparticles is of central importance, notonly to our understanding of neutrinos, but also toour understanding of the origin of mass.

This is worrisome, since it is often claimed that the study of the -decay is one of the highest priority issues in particle and nuclear physics

T1/2 (y) M2(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

Nevertheless, there is considerable experimental activity, in particular manynew results on the decay.

If (or when) the decay is observed twoproblems must be resolved:

a) What is the mechanism of the decay, i.e., what kind of virtual particle is (what is 1?) 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?)

Two basic categories are long-range and short-range contributions to the 0 decay.

The long-range category involves two pointlike verticesand the exchange of a light Majorana neutrino between them. The standard (plain vanilla) type of that category is when

1/T1/20 = G0(Q,Z) |M0|2 |<m>|2, <m=|iUei

2 mi| ,

which represents simple relation between the decay rateand the parameters of the neutrino mass matrix.

The short-range category involves only a single pointlikevertex (six fermions, four hadrons and two leptons),i.e. a dimension 9 operator. The relation between thedecay rate and neutrino mass is not simple in that case.

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 m/<q2>, AH ~ GF

2 MW4/5 ,

where is the heavy scale and q ~ 100 MeV is the virtualneutrino momentum.

For ~ 1 TeV and m ~ 0.1 – 0.5 eV AL/AH ~ 1, hence bothmechanisms contribute equally.

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)

.

As long as only a limit on the 0 decay rate exists,we can constrain all parameters entering the decayamplitudes (light and heavy neutrino masses, strengthof the right-handed current, SUSY R-parity violatingamplitudes, 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 which0-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 <m> isMN

q2> MWL

4/MWR4 x V2

Rej / mNj

(here MWR is the mass of the right-handed W, and Vrej is the mixingparameter for the heavy right-handed neutrinos of mass mNj)

Usual representation of the relation between <m> and the neutrinomass 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.

inverted

normal

degenerate

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

0amplitude is contained in the ee vertex

Various models of the LNV with ~TeV scale new physicsexist. They include, e.g. Left-Right symmetry, R-parityviolating SUSY, etc.

The common feature of these possibilities, besides LNV,is that they affect also LFV. Observing various manifestationsof LFV, -> e + , conversion, or -> 3e might help to decidewhich of these models is appropriate if any at all. Thus the relation between LFV and LNV might be usedas a diagnostic tool (Cirigliano et al., (2004))

For the analysis of decay the knowledge of nuclear matrix elementsis crucial. There is no possibility to evaluate them exactly, approximationsare always necessary.

For the light Majorana neutrino exchange several methods have been usedfor the evaluation of M. Depending on your disposition, the results areencouraging or discouraging. Main features are:1)Different methods (with very different approximations) give similar magnitude of M. However, differences of a factor ~2 exist.2) All methods agree that the Mshould 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).

Vogel, 9/2010

Possible existence of light sterile neutrinos:

a) Most models of m involve sterile neutrinos.b) Their mass can be large, MGUT for the see-saw type I. Such heavy R do not mix with the light , but are needed in order to explain the smallness of m.•The situation is similar for the R 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.

Here is a list of hints for the existence of sterile neutrinos with ~ eV mass scale. These results (2-3 ) are not directly ruled out by other experiments.

In addition analysis of the CMB and Large Structures also indicatesthat 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.

L/E (m/MeV)

Reactor neutrino anomaly (Mention et al., Phys. Rev. D83, 073006(2011). <R>= 0.937±0.027

<R> = 0.86±0.05

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

Analysis based on P(e -> e) = 1 – sin2(2new)sin2(m2new L/E)

Best fit m2new = 2.35±0.1 eV2, sin2(2new) = 0.165±0.04

Proposals to verify the L/E variation using s strong decay source and a largeliquid scintillator detector.

What the possible existence of such sterile neutrino has to do with the decay?Remember that <m> = | Uei

2 mi|If we add the 4th neutrino to this sum,it will contribute 0.14 eV using the previous best fit sin2(2new) and mnew = (m2

new)1/2

That would dominate the <m> for all but highly degeneratescenario of neutrino masses.

This widely used picturewould be totally useless