What we (would like to) know about the neutrino mass

1. What we (would like to) know about the neutrino mass Venice, April 15, 2008 Gianluigi Fogli Gianluigi Fogli Dipartimento di Fisica dell’Università di Bari & Sezione INFN - Bari Based on work done in collaboration with: E. Lisi, A. Marrone, A. Melchiorri, A. Palazzo, P. Serra, J. Silk, A. Slosar NO-VE 2008, IV International Workshop on “Neutrino Oscillations in Venice”

2. Outline Updating neutrino oscillation parameters Updating non-oscillation observables Interplay of oscillation/non-oscillation bounds Constraining (some) 02 theoretical uncertainties Conclusions

3. 1. Updating neutrino oscillation parameters Based on: GLF, Lisi, Marrone, Melchiorri, Palazzo, Serra, Silk, Slosar Addendum to arXiv:hep-ph/0608060 (in preparation) GLF, Lisi, Palazzo, Rotunno Geo- analysis (in preparation)

4. data provide a better determination of thetwo independent neutrino oscillation frequencies: MINOS 2007 (preliminary) and KamLAND 2008 oscillations driven by m2~ 2.4 x 10-3 eV2 oscillations driven by m2 ~ 7.6 x 10-5 eV2 (Recent solar neutrino results from Borexino 2007 and SK-phase II 2008 do not affect yet the global analysis of neutrino mass/mixing parameters)

5. Visible progress from 2006 (dashed) to 2008 (solid) “Solar” neutrinos “Atmospheric” neutrinos

6. (Addendum tohep-ph/0608060, in preparation) 2008 parameter summary at 2 level (95 % CL) This is what we know.

7. A recent example: slight preference for sin213 ~ 0.01 from the combination of solar+reactor 2008 data (green curve in the figure) Hierarchy (normal or inverted)CP in the  sector13 mixing Concerning What we would like to know Some aspect is currently “hidden” below 1 C.L.

8. Slight disagreement between • Solar data (SNO dominated) • KamLAND data (at 13 = 0) when the two best-fits are compared in the usual plane (m212, tan212) Reason: [figure taken from the official Kamland site (2008)]

9. sin213 = 0 sin213 = 0.03 (figures prepared by A.M. Rotunno for this talk) Disagreement reduced for 13 > 0 … … thanks to the different dependence in SNO and KamLAND from(13, 12).

10. A tiny effect, of course, but with some potential for improvement, once final SNO data and further KamLAND data will be available. Let’s now switch to the

11. 2. Updating non-oscillation observables

12.  decay a very good approximation, valid if energy smearing prevents observation of separate “Kurie plot kinks” 02 decay expression basically exact (as far as no RH currents or new physics interfere with light neutrino exchange) Cosmology leading sensitivity related to the sum of the masses; in the (far) future, maybe some weak sensitivity to mass spectrum hierarchy that depend on the parameters measured in  oscillations: Three absolute mass observables: m, m, 

13. Some updates in the last 1-2 years  decay: None (waiting for KATRIN) • 02 decay: Final results from Klapdor et al. (2006); Revised nuclear matrix elements and uncertainties (2007); Cuoricino results (2008) Cosmology: WMAP 5year data (2008)

14. ν fν = in terms of m Bounds on  for increasingly rich data sets (assuming flat CDM model): Power Spectrum of density fluctuations Cosmology (one year ago) Limits depend on the input data sets: • CMB (WMAP3y + others) • Sloan Digital Sky Survey (SDSS) • Type Ia Supernovae (SN) • Big Bang Nucleosynthesis (BBN) • Large Scale Structure (LSS) • Hubble Space Telescope (HST) • Baryon Acoustic Oscillations (BAO) • Lyman-(Ly-)

15. Constraints from Cosmology standard deviations  (eV) Constraints on  from Cosmology (one year ago) Case 1: most “conservative” (only 1 data set: WMAP 3y) Case 7: most “aggressive” (all available cosmological data) Upper limits range from ~2 to ~0.2 eV at 95% C.L., but no consensus on a specific value yet

16. preliminary Unfortunately the global analysis is not ready: work is in progress. Cosmology today We can only present the preliminary results coming from CMB data aloneafter WMAP 5y  < 1.3 eVat 2 Of course, we expect the limit strengthened in the sub-eV range byLSS + other data [Always adopting the usual caveats about the CDMmodel, its matter-energy content, and the way in which the other data sets are included.] (Addendum to arXiv:hep-ph/0608060, in preparation)

17. Klapdor et al.: MPLA 21, 1547 (2006) Cuoricino, arXiv:0802.3439 [hep-ex] A true dilemma … 02 decay update evidence … or no evidence?

18. Claim of 02 decay in 76Ge controversial, but: • Sensitivity to signal, in principle, is no longer disputed. • Final results by Klapdor et al.: MPLA 21, 1547 (2006). 02 decay - evidence In combination with recent nuclear matrix elements and uncertainties from Simkovic et al., arXiv:0710.2055 [nucl-th], these results would provide the 2 preferred range: lower and more conservative than it was adopted ~2 years ago (Addendum to arXiv:hep-ph/0608060, in preparation)

19. Cuoricino has found no 02 decay signal in 130Te. • Recent results in arXiv:0802.3439 [hep-ex]. • Half life in 1024 years: T > 3.1 (90% CL); T > 2.5 (95% CL) 02 decay - no evidence In combination with recent nuclear matrix elements and uncertainties from Simkovic et al., arXiv:0710.2055 [nucl-th], these results would provide the 2 upper limits: where the spread (…) is due to theoretical uncertainties.

20. Comparing • the preferred 2 range by Klapdor et al. m[0.16, 0.52] eV • the 2 upper limits by Cuoricinom[0.23, 0.85] eV we see that Cuoricino is starting to probe the 76Ge 02 claim, but current theory errors (in different isotopes) prevent definite statements. So, concerning the Dirac or Majorananature of neutrinos What we would like to know It is still hidden in the data, with further uncertainties arising from the theory of nuclear structure. [More about the attempt of error reduction later]. Let’s now switch to the

21. 3. Interplay of oscillation/non-oscillation bounds Based on: GLF, Lisi, Marrone, Melchiorri, Palazzo, Serra, Silk, Slosar Addendum to arXiv:hep-ph/0608060 (in preparation)

22. oscill. allowed m  Oscillations fix the mass2 splittings, and thus induce positive correlations between any pair of the three observables(m, m, ), e.g.: Interplay/1 i.e., if one observable increases, the other one (typically) must increase to match the mass2 splitting.

23. m oscill. allowed m  In the absence of new physics(beyond 3 masses and mixing), determinations of any two observables among(m, m, )are expectedtocross the oscillation band Interplay/2  This requirement provides either an important consistency check or, if not realized, an indication for new physics (barring expt. mistakes)  Analysis of established oscillation data is an important ingredient

24. Degenerate (overlap) Inverted Normal Bands overlap when mass splittings are small with respect to the absolute masses: Bands from 2008 osc. datafornormalandinvertedhierarchy Majorana phase(s) spread

25. e.g., if… Intermezzo:Dreaming about future precise data below 0.1 eV… Data = green “dot” in the figure, then … in principle, one might, with some luck: Check the overall consistency between oscill./nonoscill. data … Identify the hierarchy … (inverted, in this case) Probe the Majorana phase(s) … (i.e., reduce vertical spread in m)

26. But no combination if  < 0.45 eV from cosmology (WMAP + other data) … back to real life Relevant example including previous 2008 updates: Constraints from oscillations + WMAP 5y + 02 claim They admitaglobal combination at 2 (thick black wedge in the figure)

27. m = 0  0.12(< 0.2 at 90% CL) m = 0.30  0.10(3 evidence) m = 0.35  0.07 (5 discovery) Assuming the previous combination Each (degenerate) neutrino mass should be found in the 2 range: m1  m2  m3 0.15 - 0.80 eV This range is largely accessible to the KATRIN expt. (except below ~0.2 eV). Possible outcomes within the reach of Katrin might be, e.g., (1 errors): KATRIN discovery potential Let’s now switch to the

28. 33 Based on: Faessler, GLF, Lisi, Rodin, Rotunno, Simkovic arXiv:0711.3996 [nucl-th] 4. Constraining (some) 02 theoretical uncertainties

29. 34 In principle, any nuclear model used to calculate the02NMEfor a given nucleus, should also be able to describe all the other (allowed) weak-interaction processes for that nucleus: Benchmarking Nuclear Matrix Elements (NME) 22 decay, decay,EC,C,andcharge-exchange reaction. The available weak-interactions data could then be used to benchmark the nuclear model parameter space and reduce NME uncertainties. For example,QRPA*calculations involve a particle-particle interaction strength gpp ~ O(1) In principle, a single datum can be used to fix gpp (value  error). *Quasiparticle Random Phase Approximation

30. 36 A lot of measurements available: our Compilation BUT: Data of different quality and not always in agreement with each other.

31. 36 • 22 decay • decay EC To safest data set: lifetimes of 100Mo 116Cd 128Te to the only three nuclei for which all these data are available Unfortunately this choice excludes, at the moment, 76Ge and 130Te, used in the two experiments discussed before. Note: We restrict ourselves

32. 36 Rodin, Faessler, Simkovic & Vogel: use22 decaydata to fixgpp Civitarese & Suhonen: use decay (or EC)to fixgpp Both approaches, however, face a severe problem: Difficult to fit both22 and  decay (EC) data within the samegpprange Two conflicting approaches so far Debate between the two groups about which approach is better [In any case, such experimental constraints cannot reduce those theoretical systematics which are peculiar of 02 decay, such as the so-called “short-range correlation” (SRC) effects]

33. Experimentally, the observed Gamow-Teller strength (~ gA2) in nuclei is weaker than in vacuum: gA < 1.25“quenching” Usually, quenching is implemented by taking gA ≈ 1“standard quenching” Amount and origin of quenching in different nuclei is still debated. Usual practice (gA ≈ 1) should not be considered as a “dogma”, and data-driven departures may well be possible. In our case: BUT: gA = 0.84“strong quenching” We suggest that this discrepancy may be related to unnecessarily restrictive choices for the effective axial coupling (gA) in nuclear matter. Our approach: Strong Quenching

34. 22 QRPA estimates 1 EXPT data 1 Preferred gpp range EC Disjoint gpp ranges [Twofold ambiguity for22 and -] - Problem worse for gA = 1.25 (“bare”) E.g.,116CdwithgA = 1 “standard” quenching Q.: Can gA<1 help? Yes.

35. 22 QRPA estimates 1 EXPT data 1 Preferred gpp range EC Common gpp range, 0.4-0.6 [Ambiguity solved] - gA = 0.84 not much lower than gA = 1 E.g.,116CdwithgA = 0.84 “stronger” quenching If we accept gA < 1, then …

36. The panels show, for each nucleus, the 1 bands for the three processes (22, EC and–) and the corresponding best fit This provides a possible way to reduce the uncertainties in the parameters (gpp, gA), which also affect the 02 NME (Nuclear Matrix Elements) Search for the regions allowed in the plane (gpp, gA) 116Cd 100Mo 128Te

37. Our results (theory in agreement with22,-,andEC data) Previous results (gA=1 fixed, theory in agreement only with 22data) We compare … Implications for the 02 Nuclear Matrix Elements Apparently not very different, but big gain in understanding and controlling errors.

38. The unconventional hypothesis gA < 1must certainly pass further tests. Anyway, we hope that our approach may spark new interest towards a larger research program to benchmark the 02 nuclear models in more nuclei and with more data. This is mandatory to reduce 02 theoretical uncertainties and make the best use of experimental results in terms of m. Some further remarks on 02 NME Let’s now switch to the

39. 5. Conclusions

40. … already a lot about neutrinos, mainly because of the extremely rapid progress in oscillation searches during the last decade 1998-2008 … Going back to the title … We know… but … … concerning what We would like to know… … we needto be patient, in particular to access absolute neutrino masses…

41. 2000 KATRIN, MARE ? 2015 ? 2000 CUORICINO, GERDA … 2015 2030 WMAP ? 2015 2000 :factor of ~10improvement every~15 years “Moore’s law”

42. … but, on a much shorter timescale, let me invite all of you at Indeed, an impressive lot of time … NOW 2008, Conca Specchiulla, Sept. 6-13 (www.ba.infn.it/~now2008) See you there!