Status of neutrino mass-mixing parameters and implications for single and double beta decay searches

Transcription

1 Padova, 24 febbraio 2007 Status of neutrino mass-mixing parameters and implications for single and double beta decay searches 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 1

2 Outline Oscillations vs. absolute mass searches An analysis of the 3ν oscillation constraints Constraints from non-oscillation data A global analysis in the space of the observables Comments about 0ν2β uncertainties Conclusions Mainly based on: hep-ph/ (latest), hep-ph/ , hep-ph/ See references therein for credits to experimental and theoretical works in ν physics 2

3 Oscillations vs. absolute mass searches 3

4 Neutrinos have mass and mix Flavor states Mixing matrix (may include a complex phase) Mass states Indeed, flavor is not a good quantum number during neutrino propagation; in vacuum, it changes ( oscillates ) significantly when: where m i are the neutrino masses and L is the pathlength. This condition may be altered during propagation in matter. In any case: Three neutrinos two independent mass 2 differences 4

5 two different oscillation frequencies observed: Muon flavor non-conservation Electron flavor non-conservation Super-K KamLAND oscillations driven by Δm 2 ~ 2.6 x 10-3 ev 2 oscillations driven by δm 2 ~ 8.0 x 10-5 ev 2 but, in this way, no indication on absolute neutrino mass 5

6 Just for fun : Oscillations of neutrino preprints Δm 2 established (1998) δm 2 established (2002) Next swing? Maybe when absolute mass established 6

7 Absolute neutrino masses: three main probes 1) Beta decay: time-honored search for the absolute mass of the ν e (Fermi 1934) Kurie plot of the tritium β decay Tritium β decay: 3 H 3 He + e + ν e K(T) m ν = m ν = 100 ev T (kev) (Q - m ν ) Q ν e mass estimated from the end points of the Kurie plot But ν e ν 1 (i.e. U e1 1), so what β decay probes is an effective mass, the so-called effective electron neutrino mass, weighted by the ν e mixing with all ν i s: m β 2 = i U ei 2 m i 2 all CP and Majorana phases disappear 7

8 Absolute neutrino masses: three main probes 2) Neutrinoless Double Beta decay (if Majorana) transition N(A, Z) N(A, Z+2) + e - + e - n n m ν ν i p e e p The electroweak part probes the so-called effective Majorana mass 2 m ββ = i U ei m i K. Zuber at SUSSP 2006 CP and Majorana phases enter here 8

9 Absolute neutrino masses: three main probes 3) Precision cosmology (a modern probe) m ν = 0 ev m ν = 1 ev m ν = 7 ev m ν = 4 ev (Ma 1996) 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 sensitive to the sum of the neutrino masses: Σ = m 1 + m 2 + m 3 9

10 Three associated observables: m β, m ββ, Σ that depend on the parameters measured in ν oscillations: 1) β decay a very good approximation, valid if energy smearing prevents observation of separate Kurie plot kinks 2) 0ν2β 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 10

11 Interplay Oscillations fix the mass 2 splittings, and thus induce positive correlations between any pair of the three observables (m β, m ββ, Σ), e.g.: m ββ oscill. allowed Σ i.e., if one observable increases, the other one (typically) must increase to match the mass 2 splitting 11

12 In the absence of new physics (beyond 3ν masses and mixing), determinations of any two observables among (m β, m ββ, Σ) are expected to cross the oscillation band m ββ oscill. allowed oscill. band Interplay/2 This requirement provides either an important consistency check or, if not realized, an indication for new physics (barring expt. mistakes) Σ A careful implementation of oscillation data needed 12

13 An analysis of the 3ν oscillation constraints 13

14 Parameters of 3-neutrino oscillations Mass Spectrum Absolute mass scale unknown Normal Hierarchy Inverted Hierarchy Mixing Angles Solar δm 2 θ 12 θ 13 θ 23 Δm 2 Atmospheric 14

15 One-significant-digit summary (may be enough for some purposes) 15

16 But more accurate analyses are often needed (as in other fields of physics) Solar neutrinos (Bari group), 2005 LEP EW Working Group,

17 To make a long story short final results of our global analysis of world neutrino oscillation searches (with solar, atmospheric, accelerator, reactor neutrino beams)*, in terms of, e.g., ±2σ ranges (= 95 % C.L.): *Controversial LSND result (a 4th sterile neutrino?) excluded Determination of sin 2 θ 13 = ν e ν 3 2 is one of the most urgent problems with implications also for CP and hierarchy determination Neutrino oscillations have entered the precision era! 17

18 Impact of MINOS data MINOS not included MINOS included 2σ error on Δm 2 reduced from 24% to 15% no significant impact elsewhere 18

19 Oscillation results: Impact on the (m β, m ββ, Σ) observables We recall that, even in the absence of data on (m β, m ββ, Σ), these parameters are constrained to stay within some bands by previous oscillation results, typically m ββ oscill. allowed Σ 19

20 Considering any pair of observables, we find two bands, for normal and inverted hierarchy. Oscillation results/2 Bands overlap when mass splittings are small with respect to the absolute masses: Normal Inverted Degenerate (overlap) 20

21 Concerning m ββ Oscillation results There is a large intrinsic uncertainty due to the unknown Majorana phases constructive/destructive interference of channels 21

22 Constraints from non-oscillation data 22

23 Dreaming about future precise non-oscillation data In principle, one might: Check overall consistency Identify the hierarchy Probe the Majorana phase(s) 23

24 Back to real life! Info from non-oscillation experiments: 1) β decay: no signal so far. Mainz & Troitsk expts: m β < O(eV) 2) 0ν2β decay, no signal in all experiments, except in the most sensitive one to date (Heidelberg-Moscow). Rather debated claim. Claim accepted: m ββ in sub-ev range (with large uncertainties) Claim rejected: m ββ < O(eV) 3) Cosmology. Upper bounds: Σ < ev/sub-ev range, depending on the adopted data inputs and priors. E.g., Ly-α data crucial to probe sub-ev region deeply (but: systematics?) 24

25 0ν2β Heidelberg-Moscow result 6σ signal claimed by (part of) the experimental collaboration. Still debated. Half-life results can be transformed in bounds on m ββ if nuclear matrix element (and its uncertainty) are known 25

26 Basic relation: 0ν2β Heidelberg-Moscow result/2 Logs to linearize error propagation: We take matrix element(s) and uncertainties from the recent work: Rodin, Faessler, Simkovic & Vogel, NPA 766, 107 (2006). Then, the claim by Klapdor et al. implies (at 95% C.L.): If claim is rejected: Just remove lower bound (accept only upper bound) 26

27 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-α (Ly-α) Bounds on Σ for increasingly rich data sets (assuming flat ΛCDM model): 27

28 Constraints on Σ from Cosmology Case 1: most conservative (only 1 data set: WMAP 3y) Constraints from Cosmology Case 7: most aggressive (all available cosmological data) standard deviations Upper limits range from ~2 to ~0.2 ev at 95% C.L., but no consensus on a specific value yet Σ (ev) 28

29 A global analysis in the space of the observables 29

30 Superposition of all constraints in the space (m β, m ββ, Σ) ν oscillation data β decay 0ν2β decay cosmology Different choices Different possible combinations (and implications) 30

31 I case (most conservative) Restrict cosmo data to WMAP 3y Accept the claim by Klapdor et al. In this case, a global combination is allowed (thick black wedge in the upper part of the figure) Implications (at 95% C.L.): Σ 1.8 ± 0.6 ev m ββ 0.6 ± 0.2 ev m β 0.6 ± 0.2 ev Degenerate spectrum, with m ν 0.6 ± 0.2 ev (2σ) for each neutrino 31

32 KATRIN In this case, a signal should be clearly seen in the KATRIN (Karlsruhe Tritium Neutrino) beta-decay experiment: From C. Weinheimer talk at NOW

33 CUORICINO And a signal is likely to be seen also in the 130 Te double-beta Cuoricino experiment at Gran Sasso (with more statistics) detail MT = 5.87 (kg 130 Te) x y b = 0.18 ± 0.02 c/kev/kg/y DBD (Jul 2005) Energy [kev] From E. Fiorini talk at NOW

34 II case (most aggressive ) Conversely, assume the aggressive cosmo data set (all 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: Σ < 0.17 ev m ββ < 0.06 ev m β < 0.06 ev (i.e., deep in sub-ev range) Life much harder, especially if mass hierarchy is normal 34

35 Implications/1 Implications for (m β, m ββ, Σ) in extreme and intermediate case Case 1 (cosmo data = WMAP 3y) and case 2 (cosmo data = WMAP 3y + SDSS) can be probed, at least in part, by KATRIN. Other cases (including more constraining cosmological data) are beyond KATRIN sensitivity. 35

36 Corresponding implications for neutrinoless double-beta half-lives in different nuclei (using Faessler et al. matrix elements and errors) Implications/2 Note: Klapdor et al. claim is not compatible with WMAP+X data (where X = any other additional cosmological data set) 36

37 Q.: Can one say that cosmological data rule out Klapdor s claim? A.: NO. Several reasons: A question 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 37

38 e.g., one could allow a non-standard equation of state for dark energy, ruling out a cosmological constant [astro-ph/ ] [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 0ν2β result of Heidelberg-Moscow (+ osc.) leads to < w < at 95% C.L. so excluding a cosmological constant. 38

39 [astro-ph/ ] 33 or one could assume mass-varying neutrinos [astro-ph/ ] Assuming a linear parametrization of the evolution of Σ in terms of the scale factor a (δ being the parameter denoting the time-varying effect) 95% C.L. 68% C.L. Σ = Σ 0 [1 + δ (1 - a)] Σ If the Heidelberg-Moscow result is included together with cosmological data, mass-varying neutrinos are favored at about 3σ. a But other possibilities will certainly be explored in future papers! 39

40 33 Comments about 0ν2β uncertainties 40

41 34 As we have seen, we are still far from an ideal situation where absolute mass observables cross the band allowed by oscillation data: Comments/1 m ββ Σ But let us take a positive attitude, and assume that such a situation will be realized. At this point, it will be even more important to constrain the theoretical uncertainties in neutrinoless double beta decay. This task can be tackled, in principle, with the same logic of the above plot. 41

42 36 Measurements of neutrinoless double beta decay half-lives in different nuclei j and k might be able to discriminate models Comments/2 T 0ν (j) Model A Model B T 0ν (k) provided that different models do not overlap too much and that half-life determinations are precise enough. Needless to say: the more nuclei (j, k, ), the better! 42

43 Within the same specific nuclear model, error reduction can be obtained by exploiting correlations among 0ν and 2ν matrix elements Comments/3 Model A M 0ν (j) Model B approach sistematically used, e.g., in Rodin, Faessler, Simkovic, Vogel M 2ν (j) Further work is worthwhile to make this kind of approach more powerful, using all existing data related to double beta decay (electron capture, single beta decay, charge exchange reactions etc.). 43

44 Conclusions 44

45 Conclusions In the (long) process of cornering the neutrino mass Conclusions/1 38 2β cosmology m ν β oscillations neutrino oscillations currently provide very stable and reliable constraints, which are expected to be followed by progress on non-oscillation searches in the next years 45

46 39 future nightmares, which can t be excluded, might include nonconvergent situations (partly realized now?) Conclusions/2 2β cosmology m? ν β oscillations but we should never forget that such situations might eventually converge if something even more exciting happens: 46

47 Conclusions/3 m ν + new physics! 2β cosmology? β oscillations with the convergence induced by the advent of New Physics! 47