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

1Gianluigi Fogli IV International Workshop on “Neutrino Oscillations in Venice”, Venice, April 15,

2008

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

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Venice, April 15, 2008

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

Gianluigi Fogli

NO-VE 2008, IV International Workshop on “Neutrino Oscillations in Venice”


2008

Outline

1. Updating neutrino oscillation parameters

2. Updating non-oscillation observables

3. Interplay of oscillation/non-oscillation bounds

4. Constraining (some) 02 theoretical

uncertainties

5. Conclusions


2008

1. Updating neutrino oscillation parameters

GLF, Lisi, Marrone, Melchiorri, Palazzo, Serra, Silk, SlosarAddendum to arXiv:hep-ph/0608060 (in preparation)

GLF, Lisi, Palazzo, RotunnoGeo- analysis (in preparation)

Based on:


2008

data provide a better determination of the two independent neutrino oscillation frequencies:

oscillations driven bym2 ~ 2.4 x 10-3 eV2

oscillations driven bym2 ~ 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)

MINOS 2007 (preliminary) and KamLAND 2008


2008

Visible progress from 2006 (dashed) to 2008 (solid)

“Solar” neutrinos

“Atmospheric” neutrinos


2008

(Addendum to hep-ph/0608060, in preparation)

2008 parameter summary at 2 level (95 % CL)

This is what we know.


2008

Concerning

Some aspect is currently “hidden” below 1 C.L.

What we would like to know

Hierarchy (normal or inverted)CP in the sector13 mixing

A recent example:

slight preference for

from the combination of solar+reactor 2008 data

(green curve in the figure)

sin213 ~ 0.01


2008

[figure taken from the official Kamland site (2008)]

• Solar data (SNO dominated)

• KamLAND data (at 13 = 0)

when the two best-fits are compared in the usual plane (m2

12, tan212)

Slight disagreement between

Reason:


2008

sin213 = 0 sin213 = 0.03

(figures prepared by A.M. Rotunno for this talk)

… thanks to the different dependence in SNO and KamLAND from (13 , 12).

Disagreement reduced for 13 > 0 …


2008

Let’s now switch to the

but with some potential for improvement, once final SNO data and further KamLAND data will be available.

A tiny effect, of course,


2008

2. Updating non-oscillation observables


2008

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) 02 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


2008

1) decay: None (waiting for KATRIN)

2) 02 decay: Final results from Klapdor et al. (2006); Revised nuclear matrix elements and uncertainties (2007);

Cuoricino results (2008)

3) Cosmology: WMAP 5 year data (2008)

Some updates in the last 1-2 years


2008

Bounds on for increasingly rich data sets (assuming flat CDM model):

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

fν =ν

m

in terms of

Cosmology (one year ago)


2008

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

Constraints from Cosmology

(eV)

stan

dard

devia

tions

Constraints on from Cosmology (one year ago)


2008

(Addendum to arXiv:hep-ph/0608060, in preparation)

preliminary

Unfortunately the global analysis is not ready: work is in progress.

< 1.3 eV at 2

We can only present the preliminary results coming from CMB data alone after WMAP 5y

Of course, we expect the limit strengthened in the sub-eV range by LSS + other data

Cosmology today

[Always adopting the usual caveats about the CDM model, its matter-energy content, and the way in which the other data sets are included.]


2008

evidence …

no evidence?

02 decay update

or

A true dilemma …

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are needed to see this picture.

Klapdor et al.: MPLA 21, 1547 (2006)

Cuoricino, arXiv:0802.3439 [hep-ex]


2008

(Addendum to arXiv:hep-ph/0608060, in preparation)

• Claim of 02 decay in 76Ge controversial, but:• Sensitivity to signal, in principle, is no longer disputed.• Final results by Klapdor et al.: MPLA 21, 1547 (2006).

lower and more conservative than it was adopted ~2 years ago

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:

02 decay - evidence


2008

• Cuoricino has found no 02 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.

02 decay - no evidence


2008

• 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 02 claim, but current theory errors (in different isotopes) prevent definite statements.

So, concerning

What we would like to know

the Dirac or Majorananature of neutrinos

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].


Comparing


2008

3. Interplay of oscillation/non-oscillation bounds

GLF, Lisi, Marrone, Melchiorri, Palazzo, Serra, Silk, SlosarAddendum to arXiv:hep-ph/0608060 (in preparation)

Based on:


2008

m

oscill.

allo

wed

i.e., if one observable increases, the other one (typically) must increase to match the mass2 splitting.

Oscillations fix the mass2 splittings, and thus induce positive correlations between any pair of the three observables (m, m, ), e.g.:

Interplay/1


2008

m

oscill.

allo

wed

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


2008

Bands from 2008 osc. data for normal and inverted hierarchy

Invert

ed

Deg

en

era

te (

overl

ap

)N

orm

al

Bands overlap when mass splittings are small with respect to the absolute masses:

Majoranaphase(s)spread


2008

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…

Intermezzo: Dreaming about future precise data below 0.1 eV…

Data = green “dot” in the figure, then …

in principle, one might, with some luck:


2008

Relevant example including previous 2008 updates:

Constraints from

They admit a global combination at 2

(thick black wedge in the figure)

oscillations + WMAP 5y + 02 claim

… back to real life

But no combination if

from cosmology (WMAP + other data)

< 0.45 eV


2008

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):

Assuming the previous combination

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



2008

33

4. Constraining (some) 02 theoretical uncertainties

Based on:

Faessler, GLF, Lisi, Rodin, Rotunno, SimkovicarXiv:0711.3996 [nucl-th]


2008

34

In principle, any nuclear model used to calculate the 02 NME for a given nucleus, should also be able to describe all the other (allowed) weak-interaction processes for that nucleus:

*Quasiparticle Random Phase Approximation

22 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).

Benchmarking Nuclear Matrix Elements (NME)


2008

36

BUT: Data of different quality and not always in agreement with each other.

A lot of measurements available: ourCompilation


2008

36

To safest data set: lifetimes of 22 decay decay EC

to the only three nuclei for which all these data are available

100Mo 116Cd 128Te

We restrict ourselves

Note: Unfortunately this choice excludes, at the moment, 76Ge and 130Te, used in the two experiments discussed before.


2008

36

Debate between the two groups about which approach is better

Rodin, Faessler, Simkovic & Vogel:use 22 decay data to fix gpp

Civitarese & Suhonen:use decay (or EC) to fix gpp

[In any case, such experimental constraints cannot reduce those theoretical systematics which are peculiar of 02 decay, such as the so-called “short-range correlation” (SRC) effects]

Two conflicting approaches so far

Both approaches, however, face a severe problem:

Difficult to fit both 22 and decay (EC) data within the same gpp range


2008

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”

Our approach: Strong Quenching


2008

E.g., 116Cd with gA = 1

QRPA estimates 1

EXPT data 1

Preferred gpp range

22

EC

-

Disjoint gpp ranges

[Twofold ambiguity for 22 and -]

Problem worse for gA = 1.25 (“bare”)

Q.: Can gA<1 help?

“standard” quenching

Yes.


2008

22

EC

-

Common gpp range, 0.4-0.6

[Ambiguity solved]

gA = 0.84 not much lower than gA = 1

E.g., 116Cd with gA = 0.84

“stronger” quenching

QRPA estimates 1

EXPT data 1

Preferred gpp range

If we accept gA < 1, then …


2008

Search for the regions allowed in the plane (gpp, gA)

116Cd

100Mo 128Te

This provides a possible way to reduce the uncertainties in the

parameters (gpp, gA), which also affect the 02 NME (Nuclear Matrix

Elements)

The panels show, for each nucleus, the 1 bands for the three

processes (22, EC and –) and the corresponding best fit


2008

Apparently not very different, but big gain in understanding and controlling errors.

Implications for the 02 Nuclear Matrix ElementsWe compare …

Our results (theory in agreementwith 22, -, and EC data)

Previous results (gA=1 fixed, theory in agreement only with 22 data)


2008

Some further remarks on 02 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 02 nuclear models in more nuclei and with more data.

This is mandatory to reduce 02 theoretical uncertainties and make the best use of experimental results in terms of m.



2008

5. Conclusions


2008

… concerning what

We would like to know …

… we need to be patient, in particular to access absolute neutrino masses…

already a lot about neutrinos, mainly because of the extremely rapid progress in oscillation searches during the last decade 1998-2008 …

…

We know …

but …

Going back to the title …


2008

“Moore’s law”

: factor of ~10 improvement every ~15 years

2000

2015

2000

2015

2030

2015 2000

?

?

KATRIN, MARE ?

CUORICINO,GERDA …

WMAP


2008

See you there!





… 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)

Indeed, an impressive lot of time …

Documents

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