Gianluigi Fogli XII International Workshop on “Neutrino Telescopes”, Venice, March 8, Based on work done in collaboration with: E. Lisi, A. Marrone, A. Melchiorri, A. Palazzo, P. Serra, J. Silk, A. Slosar Gianluigi Fogli Dipartimento di Fisica dell’Università di Bari & Sezione INFN - Bari Venice, March 8, 2007 Neutrino mass-mixing parameters and implications for single and double beta decay searches Gianluigi Fogli XII International Workshop on “ Neutrino Telescopes ”

Gianluigi Fogli XII International Workshop on “Neutrino Telescopes”, Venice, March 8, Oscillations vs. absolute mass searches An analysis of the 3 oscillation constraints Constraints from non-oscillation data A global analysis in the space of the observables Conclusions Mainly based on: hep-ph/ (latest), hep-ph/ , hep-ph/ See references therein for credits to experimental and theoretical works in physics Outline Based on work done in collaboration with: E. Lisi, A. Marrone, A. Melchiorri, A. Palazzo, P. Serra, J. Silk, A. Slosar

Gianluigi Fogli XII International Workshop on “Neutrino Telescopes”, Venice, March 8, Oscillations vs. absolute mass searches Raffaello - Selfportrait

Gianluigi Fogli XII International Workshop on “Neutrino Telescopes”, Venice, March 8, Super-K oscillations driven by  m 2 ~ 2.6 x eV 2 Muon flavor non-conservation KamLAND oscillations driven by  m 2 ~ 8.0 x eV 2 Electron flavor non-conservation … but, in this way, no indication on absolute neutrino masses As we know, 2 different oscillation frequencies established:

Gianluigi Fogli XII International Workshop on “Neutrino Telescopes”, Venice, March 8, ) Beta decay: time-honored search for the absolute mass of the e (Fermi 1934) Three main probes of absolute neutrino masses But e ≠ 1 (i.e. U e1 ≠ 1), so what  decay probes (in 1st approximation) is an effective mass, the so-called “effective electron neutrino mass”, weighted by the e mixing with all i ’s: m  2 = å i  U ei  2  m i 2 all CP and Majorana phases disappear Tritium  decay: 3 H  3 He + e  + e. e mass estimated from the end points of the Kurie plot

Gianluigi Fogli XII International Workshop on “Neutrino Telescopes”, Venice, March 8, The electroweak part probes the so-called CP and Majorana phases enter here K. Zuber at SUSSP 2006 transition N(A, Z)  N(A, Z+2) + e - + e - n np p ee ee i m  effective Majorana mass m  = å i U ei m i 2 Three main probes of absolute neutrino masses 2) Neutrinoless Double Beta decay (if Majorana)

Gianluigi Fogli XII International Workshop on “Neutrino Telescopes”, Venice, March 8, ) Precision cosmology (a “ modern ” probe) (E..g., Ma 1996) m = 0 eVm = 1 eV m = 7 eVm = 4 eV Neutrinos suppress the growth of fluctuations when they become non relativistic: a neutrino with mass of a fraction of eV would produce a significant suppression in the clustering on small cosmological scales Cosmological data mainly sensitive to the sum of the neutrino masses:   = m 1 + m 2 + m 3 Three main probes of absolute neutrino masses

Gianluigi Fogli XII International Workshop on “Neutrino Telescopes”, Venice, March 8, Three absolute mass observables: m , m ,  that depend on the parameters measured in oscillations: 1)  decay a very good approximation, valid if energy smearing prevents observation of separate “Kurie plot kinks” 2)0 2  decay expression basically exact (as far as no RH currents or new physics interfere with light neutrino exchange) 3)Cosmology leading sensitivity related to the sum of the masses; in the (far) future, maybe some weak sensitivity to mass spectrum hierarchy

Gianluigi Fogli XII International Workshop on “Neutrino Telescopes”, Venice, March 8, m   oscill. allowed i.e., if one observable increases, the other one (typically) must increase to match the mass 2 splitting Oscillations fix the mass 2 splittings, and thus induce positive correlations between any pair of the three observables (m , m ,  ), e.g.: Interplay between oscillation - nonoscillation bounds

Gianluigi Fogli XII International Workshop on “Neutrino Telescopes”, Venice, March 8, m   oscill. allowed 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 This requirement provides either an important consistency check or, if not realized, an indication for new physics (barring expt. mistakes)  m  Interplay/2  Analysis of established oscillation data is an important ingredient

Gianluigi Fogli XII International Workshop on “Neutrino Telescopes”, Venice, March 8, An analysis of the 3 oscillation constraints Marc Chagall - Selfportrait

Gianluigi Fogli XII International Workshop on “Neutrino Telescopes”, Venice, March 8, … final results of our global analysis of world neutrino oscillation searches (with solar, atmospheric, accelerator, reactor neutrino beams)*, in terms of, e.g.,  2  ranges (= 95 % C.L.): *Debated LSND result (a 4th sterile neutrino?) excluded here (more info later today by M. Shaevitz) Determination of sin 2  13   e  3  2 is one of the most urgent problems To make a long story short … with implications also for CP and hierarchy determination

Gianluigi Fogli XII International Workshop on “Neutrino Telescopes”, Venice, March 8, no significant impact elsewhere 2  error on  m 2 reduced from 24% to 15% MINOS not included MINOS included (A detail: Impact of MINOS 2006 data)

Gianluigi Fogli XII International Workshop on “Neutrino Telescopes”, Venice, March 8, Inverted Degenerate (overlap) Normal Bands from oscillation data for normal and inverted hierarchy Bands overlap when mass splittings are small with respect to the absolute masses:

Gianluigi Fogli XII International Workshop on “Neutrino Telescopes”, Venice, March 8, Concerning m  Oscillation results There is a large intrinsic uncertainty due to the unknown Majorana phases constructive/destructive interference of channels

Gianluigi Fogli XII International Workshop on “Neutrino Telescopes”, Venice, March 8, Constraints from non-oscillation data Antonio Canova - Selfportrait

Gianluigi Fogli XII International Workshop on “Neutrino Telescopes”, Venice, March 8, 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  ) e.g., if … Dreaming about future precise non-oscillation data … Data = green “ dot ” in the figure, then … in principle, one might, with some luck:

Gianluigi Fogli XII International Workshop on “Neutrino Telescopes”, Venice, March 8, … Back to real life! 1)  decay: no signal so far. Mainz & Troitsk expts: m  < O(eV) 3)Cosmology. Upper bounds:  < eV/sub-eV range, depending on the adopted data inputs and priors. E.g., Ly-  data crucial to probe sub-eV region deeply (but: systematics?) 2)0 2  decay, no signal in all experiments, except in the most sensitive one to date (Heidelberg-Moscow). Rather debated claim. Claim accepted: m  in sub-eV range (with large uncertainties) Claim rejected: m  < O(eV) Info from non-oscillation experiments:

Gianluigi Fogli XII International Workshop on “Neutrino Telescopes”, Venice, March 8,  signal claimed by (part of) the experimental collaboration. Still debated. 0 2  Heidelberg-Moscow result Half-life results can be transformed in bounds on m  if nuclear matrix element (and its uncertainty) are known 

Gianluigi Fogli XII International Workshop on “Neutrino Telescopes”, Venice, March 8, Logs to linearize error propagation: Basic relation: We take matrix element(s) and uncertainties from the recent work: Rodin, Faessler, Simkovic & Vogel, NPA 766, 107 (2006). If claim is rejected: Just remove lower bound (accept only upper bound) Then, the claim by Klapdor et al. implies (at 95% C.L.): 0 2  Heidelberg-Moscow result/2

Gianluigi Fogli XII International Workshop on “Neutrino Telescopes”, Venice, March 8, Bounds on  for increasingly rich data sets (assuming flat  CDM model): Cosmology 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-  ) Power Spectrum of density fluctuations f ν = νν mm in terms of

Gianluigi Fogli XII International Workshop on “Neutrino Telescopes”, Venice, March 8, Case 1: most “ conservative ” (only 1 data set: WMAP 3y) Case 7: most “ aggressive ” (all available cosmological data) Constraints on  from Cosmology Upper limits range from ~2 to ~0.2 eV at 95% C.L., but no consensus on a specific value yet Constraints from Cosmology  (eV) standard deviations

Gianluigi Fogli XII International Workshop on “Neutrino Telescopes”, Venice, March 8, A global analysis in the space of the observables Giorgione - La tempesta

Gianluigi Fogli XII International Workshop on “Neutrino Telescopes”, Venice, March 8, Superposition of all constraints in the space ( m , m ,  ) Different possible combinations (and implications) Different choices oscillation data  decay 0 2  decay cosmology

Gianluigi Fogli XII International Workshop on “Neutrino Telescopes”, Venice, March 8, Degenerate spectrum, with m  0.6  0.2 eV (2  ) for each neutrino Restrict cosmo data to WMAP 3y but accept claim by Klapdor et al. “ Conservative ” case: Implications (at 95% C.L.):   1.8  0.6 eV m   0.6  0.2 eV m   0.6  0.2 eV In this case, a global combination is allowed (thick black wedge in the upper part of the figure)

Gianluigi Fogli XII International Workshop on “Neutrino Telescopes”, Venice, March 8, In this case, a signal should be clearly seen in the (Karlsruhe Tritium Neutrino) beta-decay experiment Expected range for m  would be m  = eV (2  ) KATRIN well within KATRIN sensitivity (~0.3 eV)

Gianluigi Fogli XII International Workshop on “Neutrino Telescopes”, Venice, March 8, A long way from Fermi ’ s table-top experimental proposal … (, november 2006) KATRIN spectrometer during transportation

Gianluigi Fogli XII International Workshop on “Neutrino Telescopes”, Venice, March 8, E.g., signal might be seen also in Cuoricino, the 130 Te double-beta decay experiment at Gran Sasso (with more statistics and some luck) Energy [keV] detail DBD MT = 5.87 (kg 130 Te) x y b = 0.18  0.02 c/keV/kg/y (Jul 2005) (Fig. from E. Fiorini talk at NOW 2006) Also, 0 2  signal should emerge in other nuclei … Current Cuoricino half-life limit for 130 Te: Range predicted from previous scenario (2  ): T > 2 x y T = 3-19 x y

Gianluigi Fogli XII International Workshop on “Neutrino Telescopes”, Venice, March 8, Conversely, assume ALL cosmo data at face value In this case, a global combination with the claimed double beta signal is not possible Implications (at 95% C.L.) if Klapdor ’ s claim is rejected: Much smaller absolute masses; life much harder, especially if mass hierarchy is normal “ Aggressive ” case  < 0.17 eV m  < 0.06 eV m  < 0.06 eV (i.e., deeply in sub-eV range)

Gianluigi Fogli XII International Workshop on “Neutrino Telescopes”, Venice, March 8, Cases with cosmo data = WMAP 3y or WMAP 3y + SDSS can be probed, at least in part, by KATRIN. Other cases (including more constraining cosmological data) are beyond KATRIN sensitivity. Implications/1 Implications for (m , m ,  ) in “extreme” and “intermediate” case

Gianluigi Fogli XII International Workshop on “Neutrino Telescopes”, Venice, March 8, Corresponding implications for neutrinoless double-beta half-lives in different nuclei (using Faessler et al. matrix elements and errors) Note: Klapdor et al. claim is not compatible with WMAP+X data (where X = any additional cosmo data). Implications/2

Gianluigi Fogli XII International Workshop on “Neutrino Telescopes”, Venice, March 8, Q.: Can one say that “cosmological data” rule out Klapdor’s claim? 1.A laboratory result needs a laboratory - not only an astrophysical - test 2.Claimed signal might be due to new physics (RH currents, SUSY … ) 3.Cosmological constraints are still very much affected by assumptions and by systematics 4.We should never forget that the “ standard ” cosmological model contains mostly unknown sources of gravity (~0.75 dark energy, ~0.20 dark matter), while the known neutrinos are a tiny fraction One can turn the question around, and ask: If we assume that both Klapdor ’ s signal (as due to Majorana neutrinos) and cosmological data are correct, what should one alter in the standard cosmological model to fit the data? Several possible solutions … A question A.: NO. Several reasons:

Gianluigi Fogli XII International Workshop on “Neutrino Telescopes”, Venice, March 8, … e.g., one could allow a “ non-standard ” equation of state for dark energy, ruling out a cosmological constant … [astro-ph/ ] While, up to now, dark energy scenario is consistent with a true cosmological constant, with equation of state w = -1 combining cosmological data with the 0 2  result of Heidelberg-Moscow (+ osc.) leads to < w < at 95% C.L. so excluding a cosmological constant. [astro-ph/ ]

Gianluigi Fogli XII International Workshop on “Neutrino Telescopes”, Venice, March 8, … or one could assume “ mass-varying neutrinos ” … [astro-ph/ ] But other possibilities will certainly be explored in future papers! [astro-ph/ ] Assuming a linear parametrization of the evolution of  in terms of the scale factor a (  being the parameter denoting the time-varying effect)  =  0 [1 +   (1 - a)] If the Heidelberg-Moscow result is included together with cosmological data, mass-varying neutrinos are favored at about 3   a 95% C.L. 68% C.L.

Gianluigi Fogli XII International Workshop on “Neutrino Telescopes”, Venice, March 8, Conclusions Giorgione - Le maraviglie dell ’ arte

Gianluigi Fogli XII International Workshop on “Neutrino Telescopes”, Venice, March 8, m oscillations  22 cosmology In the (long) process of cornering the neutrino mass … … neutrino oscillations currently provide very stable and reliable constraints, … Conclusions/1 Conclusions … which are expected to be followed by progress on non-oscillation searches in the next years …

Gianluigi Fogli XII International Workshop on “Neutrino Telescopes”, Venice, March 8, m oscillations  22 cosmology 39 … future nightmares, which can ’ t be excluded, might include non- convergent situations (partly realized now?) … … but we should never forget that such situations might eventually “ converge ” if something even more exciting happens: Conclusions/2 ?

Gianluigi Fogli XII International Workshop on “Neutrino Telescopes”, Venice, March 8, ? Conclusions/3 oscillations  22 cosmology m + new physics ! … with the “ convergence ” induced by the advent of New Physics !