What we (would like to) know about the neutrino mass Venice, April 15, 2008 What we (would like to) know about the neutrino mass 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”

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

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)

MINOS 2007 (preliminary) and KamLAND 2008 data provide a better determination of the two independent neutrino oscillation frequencies: 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)

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

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

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

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

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

Let’s now switch to the 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

2. Updating non-oscillation observables

Three absolute mass observables: m, m,  that depend on the parameters measured in  oscillations:  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

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 5 year data (2008)

Cosmology (one year ago) Power Spectrum of density fluctuations 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-) fν = ν m in terms of Bounds on  for increasingly rich data sets (assuming flat CDM model):

Constraints on  from Cosmology (one year ago) Constraints from Cosmology  (eV) standard deviations 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

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

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

02 decay - evidence 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). 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)

02 decay - no evidence 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) 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.

Let’s now switch to the Comparing What we would like to know the preferred 2 range by Klapdor et al. m[0.16, 0.52] eV the 2 upper limits by Cuoricino m[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 Majorana nature 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

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)

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

 Analysis of established oscillation data is an important ingredient In the absence of new physics (beyond 3 masses and mixing), determinations of any two observables among (m, m, ) are expected to cross the oscillation band m m  oscill. allowed 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

Bands from 2008 osc. data for normal and inverted hierarchy Bands overlap when mass splittings are small with respect to the absolute masses: Degenerate (overlap) Inverted Majorana phase(s) spread Normal

Intermezzo: Dreaming about future precise data below 0.1 eV… e.g., if… 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)

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

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): m = 0  0.12 (< 0.2 at 90% CL) m = 0.30  0.10 (3 evidence) m = 0.35  0.07 (5 discovery) KATRIN discovery potential Let’s now switch to the

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

Benchmarking Nuclear Matrix Elements (NME) 34 Benchmarking Nuclear Matrix Elements (NME) In principle, any nuclear model used to calculate the 02 NME for a given nucleus, should also be able to describe all the other (allowed) weak-interaction processes for that nucleus: 22 decay,  decay, EC, C, and charge-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

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

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

Two conflicting approaches so far 36 Two conflicting approaches so far Rodin, Faessler, Simkovic & Vogel: use 22 decay data to fix gpp Civitarese & Suhonen: use  decay (or EC) to fix gpp Debate between the two groups about which approach is better Both approaches, however, face a severe problem: Difficult to fit both 22 and  decay (EC) data within the same gpp range [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]

Our approach: Strong Quenching We suggest that this discrepancy may be related to unnecessarily restrictive choices for the effective axial coupling (gA) in nuclear matter. 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” BUT: 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: gA = 0.84 “strong quenching”

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

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

Search for the regions allowed in the plane (gpp, gA) 116Cd 100Mo 128Te 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)

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

Some further remarks on 02 NME The unconventional hypothesis gA < 1 must 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. Let’s now switch to the

5. Conclusions

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

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

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