Towards absolute neutrino masses Petr Vogel, Caltech NOW 2006, Otranto, September 2006

Are neutrinos Majorana particles? Thanks to the recent triumphs of neutrino physics we know that neutrinos are massive and mixed. However, in order to better delineate the path toward the `New Standard Model’ we would like to know more: Are neutrinos Majorana particles? What is the pattern of neutrino masses? What is the absolute mass scale? Is CP invariance violated in the lepton sector? Is there a relation between all of this and the baryon excess in the Universe?

Neutrino oscillations: 12 (U12), , etc. Summary of methods of neutrino mass determination and (optimistic) sensitivities:: Neutrino oscillations: 12 (U12), , etc. observed ~10-5 eV2 (only mass square differences, independent of Dirac vs. Majorana) Single beta decay: 0.2 eV (independent of Dirac vs. Majorana) <mb>2 = S mi2 |Uei|2 Double beta decay: 0.01 eV (only for Majorana) <mbb> = |S mi |Uei|2 ei| (Majorana phases) Observational cosmology: 0.1 eV (independent of Dirac vs. Majorana) M = S mi

Note that conceptually simple methods of neutrino mass determination, like TOF, are not sensitive enough The time delay, with respect to massless particle, is Dt(E) = 0.514 (m/E)2D, where m is in eV, E in MeV, D in 10 kpc, and Dt in sec. But there are no massless particles emitted by SN at the same time as neutrinos. Alternatively, we might look for a time delay between the charged current signal (i.e. ne) and the neutral current signal (dominated by nx). In addition , one might look for a broadening of the signal, and rearrangement according to the neutrino energy.

<t>signal -<t>reference for several mass values Lower part shows the range of the deduced masses. The dashed lines are 10% and 90% CL. See, Beacom & P.V., Phys.Rev.D58,053010(1998)

The two-body decays, like p+ -> m+ + nm are even simpler conceptually, in the rest frame of the pion mn2 = mp2 + mm2 - 2mpEm , but the sensitivity is only to mn ~ 170 keV with little hope of a substantial improvement.

Relation between <mbb> and other neutrino mass observables as constrained by the oscillation results. Possible interval (unconfirmed) from 0nbb decay blue shading: normal hierarchy, Dm231 > 0. red shading: inverted hierarchy Dm231 < 0 shading:best fit parameters, lines 95% CL errors. Limits of sensitivity in near future

The degenerate mass region will be explored by the next generation of 0nbb experiments and also probed by ways independent on Majorana nature of neutrinos. <mbb> (eV) 0.1 0.01 Planck +SDSS sensitivity Katrin sensitivity

Three regions of <mbb> of interest: i) Degenerate mass region where all mi >> Dm312. There <mbb> > 0.1 eV. T1/2 for 0nbb decay < 1026-27 y in this region. This region will be explored during the next 3-5 years with 0nbb decay experiments using ~100 kg sources . Moreover, most if not all of that mass region will be explored also by study of ordinary b decay and by the `observational cosmology’. These latter techniques are independent of whether neutrinos are Majorana or Dirac particles. ii) Inverted hierarchy region where m3 could be < Dm312. However, quasidenegerate normal hierarchy is also possible for <mbb> ~ 20-100 meV. T1/2 for 0nbb decay is 1027-28 years here, and could be explored with ~ton size experiments. Proposals for such experiments, with timeline ~10 years, exist. iii) Normal mass hierarchy, <mbb> < 20 meV. It would be necessary to use ~100 ton experiments. There are no realistic ideas how to do it.

However, life is not simple However, life is not simple. Even with infinite precision and with two independent mass determinations, we cannot decide which hierarchy is the correct one. We still need a long baseline experiment with matter effects. For example

For a fixed <mbb> there is a continuum of solutions, some with the same Smi and other with different Smi.

Combined results of the claimed 76Ge 0nbb discovery and the most restrictive observational cosmology constraint. There is a clear conflict in this case. From Fogli et al, hep-ph/0608060

Leaving aside the all important question whether the 0nbb experimental evidence will withstand further scrutiny and whether the cosmological constraint is reliable and model independent, lets discuss various possible scenarios suggested by this test of consistency. Possibility #1: Both neutrino mass determination give a positive and consistent result (the results intersect on the expected `band’ and both suggest a degenerate mass pattern. (Everybody is happy, even though somewhat surprised since the degenerate scenario is a bit unexpected.) Possibility #2: 0nbb will not find a positive evidence (the present claim will be shown to be incorrect) but observational cosmology will give a positive evidence for a degenerate mass scenario, i.e., a situation opposite to the previous slide. (This will also be reluctantly accepted as an evidence that neutrinos are not Majorana but Dirac.)

Possibility #3: The situation on the previous slide is confirmed. The positive evidence stemming from 0nbb decay is confronted with a lack of evidence from observational cosmology. What now? Is there a possible scenario that would accommodate such a possibility? The answer is yes and deserves a more detailed explanation. Actually, this can happen for two reasons: The 0nbb decay is not caused by the exchange of the light Majorana neutrinos, but by some other mechanism. The obvious question then is how can we tell which mechanism is responsible for the 0nbb decay. Even though the 0nbb decay is caused by the exchange of the light Majorana neutrinos the relation between the decay rate and <mbb> is rather different than what we thought, i.e. the nuclear matrix elements we used are incorrect. The obvious question then is how uncertain the nuclear matrix elements really are.

Light or heavy Majorana neutrino. Model extended to include right-handed WR. Mixing extended between the left and right-handed neutrinos. Light Majorana neutrino, only Standard Model weak interactions Supersymmetry with R-parity violation. Many new particles invoked. Light Majorana neutrinos exist also. Heavy Majorana neutrino interacting with WR. Model extended to include right-handed current interactions.

particles of scale are involved the amplitude scales as 1/5. 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. The relative size of the heavy (AH) vs. light particle (AL) exchange to the decay amplitude is (a crude estimate) AL ~ GF2 mbb/<k2>, AH ~ GF2 MW4/L5 , where L is the heavy scale and k ~ 50 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.

AL/AH ~ m5/ <k2> MW4 Thus for m= 0.2 eV, <k2> = 502 MeV2, and AL/AH~ 1 5 ~ 502x1012x804x1036/0.2 eV ~ 5x1059 eV ~ 1012 eV = 1 TeV Clearly, the heavy particle mechanism could compete with the light Majorana neutrino exchange only if the heavy scale  is between about 1 - 5 TeV. Smaller  are already excluded and larger ones will be unobservable due to the fast 5 scale dependence.

In the following I suggest that the Lepton Flavor violation (LFV) involving charged leptons provides a “diagnostic tool” for establishing the mechanism of  decay or Lepton Number Violation (LNV). This assertion is based on “Lepton number violation without supersymmetry” Phys.Rev.D 70 (2004) 075007 V. Cirigliano, A. Kurylov, M.J.Ramsey-Musolf, and P.V. and on “Neutrinoless double beta decay and lepton flavor violation” Phys. Rev. Lett. 93 (2004) 231802 The basic idea is that while the two processes, LFV and LNV are, generally, governed by different mass scales, one can establish (with some ``fine tuning” exceptions) a relation between these scales.

SM extensions with high (GUT) scale LNV, Consider the well studied LFV processes: If then SM extensions with high (GUT) scale LNV, are essentially the only possibility. On the other hand if ~ O(1) >> 10-2 then it is possible that SM extensions with low ( TeV) scale LNV exist.

Nuclear matrix elements A provocative question: Do we know at all how large the matrix elements really are? Or, in other words, why there is so much variation among the published calculated matrix elements? from Bahcall et al hep-ph/0403167 , spread of published values of squared nuclear matrix element for 76Ge This suggests an uncertainty of as much as a factor of 5. Is it really so bad?

In contrast, Rodin et al, nucl-th/0503063 suggest that the uncertainty is much less, perhaps only ~ 30% (within QRPA and its generalizations, naturally). So, who is right? Slowly and smoothly decreasing (except 96Zr) with A

1/T1/2 = G(E,Z) (MGT2n)2 Nuclear matrix elements for the 2n decay deduced from measured halflives. Note the pronounced shell dependence. 1/T1/2 = G(E,Z) (MGT2n)2 easily calculable phase space factor

What are the causes for the spread of the QRPA calculated values of M0n? M0n = <f|O|i> There are two sources of spread: Differences in the way |i> and |f> are obtained, often related to the difference in which the effective hamiltonian is chosen. In particular, the choice of the effective neutron-proton coupling constant gpp. Differences in the way the operator O is handled. In particular whether the correction for the short range nucleon-nucleon repulsion is made and how.

In QRPA the 0n matrix element depends on the number of s.p. states included. However, that dependence is drastically reduced if we adjust the coupling strength gpp accordingly (from the 2n decay here). Calculation by F.Simkovic

Comparison of M0n of Rodin et al. (RQRPA) and the shell model results reported by A. Poves at NDM06 Nucleus RQRPA Poves Poves/1.3 ratio 76Ge 2.3-2.4 2.35 1.80 1.3 82Se 1.9-2.1 2.26 1.74 1.3 96Zr 0.3-0.4 100Mo 1.1-1.2 116Cd 1.2-1.4 130Te 1.3 2.13 1.64 0.8 136Xe 0.6-1.0 1.77 1.36 0.6 Note that the SM calculations include the reduction caused by the s.r.c. but not by the induced currents (about 30% reduction). Also note that the previous (tentative and preliminary) results as privately communicated by F. Nowacki in 2004 included a rather small values for 100Mo and 96Zr, similar to the ‘hole’ for 96Zr in QRPA. It remains to be seen whether this feature persists.

Summary and/or Conclusions Study of 0nbb decay entered a new era. No longer is the aim just to push the sensitivity higher and the background lower, but to explore specific regions of the <mbb> values. In agreement with the `phased’ program the plan is to explore the `degenerate’ region (0.1-1 eV) first, with ~100 kg sources, and prepare the study of `inverted hierarchy’ (0.01-0.1eV) region with ~ ton sources that should follow later. In this context it is important to keep in mind the questions I discussed: Relation of <mbb> and the absolute mass (rather clear already, becoming less uncertain with better oscillation results). Mechanism of the decay (exploring LFV, models of LNV, running of LHC to explore the ~TeV mass particles). Nuclear matrix elements (exploring better, and agreeing on, the reasons for the spread of calculated values, and deciding on the optimum way of performing the calculations, while pursuing vigorously also the application of the shell model).

Illustration I: RPV SUSY [R = (-1)3(B-L) + 2s ] Spares: Illustration I: RPV SUSY [R = (-1)3(B-L) + 2s ]

Illustration II: Left-Right Symmetric Model Spares: Illustration II: Left-Right Symmetric Model SU(2)L  SU(2)R  U(1)B-L  SU(2)L  U(1)Y  U(1)EM 

Two-nucleon probability distribution, with and without correlations, Spares: Two-nucleon probability distribution, with and without correlations, MC with realistic interaction. O. Benhar - private communication no s.r.c. = nuclear matter, saturation density = nuclear matter, half of the saturation density

P(r) dr based on a semirealistic, exactly Spares: The integrand of M0n, M0n = P(r) dr based on a semirealistic, exactly solvable model, see J. Engel and P.V., PRC69,034304 (2004). There is essentially no effect of short range on the broken “pairs part” One can see that the partial cancellation between the two parts enhances the effect of short range correction. Without short range correction With short range correction P(r) Pairing part Broken pairs part r (fm)