[PPT] - Sterile neutrinos Michele Maltoni Instituto de F sica Te orica PowerPoint Presentation

SLIDE 1

Sterile neutrinos

Michele Maltoni

Instituto de F´ ısica Te´

rica UAM/CSIC

What is ν? Invisibles 2012 and Alexei Smirnov Fest GGI, Firenze, Italy – June 28th, 2012

I. The LSND experiment and four-neutrino models
II. MiniBooNE and models with two sterile neutrinos
III. A word on MiniBooNE data after Neutrino 2012

Summary

SLIDE 2

I. The LSND experiment and four-neutrino models

2

The LSND problem

LSND observed ¯

νe appearance in a ¯ νµ beam (Eν ∼ 30 MeV, L ≃ 35 m);

Karmen did not confirm the claim, but couldn’t fully

exclude it either;

the signal is compatible with ¯

νµ → ¯ νe oscillations

provided that ∆m2 0.1 eV2;

on the other hand, other data give (at 3σ):

∆m2

 ≃ 7.5 ± 0.6 × 10−5 eV2 ,

∆m2



≃ 2.4 ± 0.3 × 10−3 eV2 ;

10

2

10

1

1 10 10 2 10

3

10

2

10

1

1 sin2 2θ ∆m2 (eV2/c4)

Bugey Karmen NOMAD CCFR 90% (Lmax-L < 2.3) 99% (Lmax-L < 4.6)

in order to explain LSND with mass-induced neutrino oscillations one needs at least one

more neutrino mass eigenstate;

WARNING: having enough ∆m2 is not enough. To make sure that the model works,
ne has to check explicitly that all the experiments can be fitted simultaneously.

Michele Maltoni <michele.maltoni@csic.es> M- “W  ν?”, 28/06/2012

SLIDE 3

I. The LSND experiment and four-neutrino models

3

Four neutrino mass models

Approximation: ∆m2

 ≪ ∆m2  ≪ ∆m2  ⇒ 6 different mass schemes: sol atm SBL (a) sol atm SBL (b) sol atm SBL (c) sol atm SBL (d) sol atm SBL (A) sol atm SBL (B)

                 

(3+1) (2+2)

Total: 3 ∆m2, 6 angles, 3 phases. Different set of experimental data partially decouple:

SOL ATM NEV

∆m2

SOL

∆m2

ATM

∆m2

LSND

dµ ηs ηe θSOL θATM θLSND

LSND

ϕ34 ϕ13 ϕ12

Michele Maltoni <michele.maltoni@csic.es> M- “W  ν?”, 28/06/2012

SLIDE 4

I. The LSND experiment and four-neutrino models

4

(2+2): ruled out by solar and atmospheric data

0.2 0.4 0.6 0.8 1 ηs 10 20 30 40 ∆χ

2

3σ

solar (pre SNO salt) solar

solar + K a m L A N D

0.2 0.4 0.6 0.8 1 ηs = ds

χ

2 PG

χ

2 PC

atm + LBL + SBL global solar + K a m L A N D atm + LBL

3σ

0.2 0.4 0.6 0.8 1 ds Restricted atm +

LBL Real

3σ

in (2+2) models, fractions of νs in solar (ηs) and atmos (1 − ds) add to one ⇒ ηs = ds ;
3σ allowed regions ηs ≤ 0.31 (solar) and ds ≥ 0.63 (atmos) do not overlap; superposition
ccurs only above 4.5σ (χ2

 = 19.9);

the χ2 increase from the combination of solar and atmos data is χ2

 = 28.6 (1 dof),

corresponding to a PG = 9 × 10−8 [1].

[1] M. Maltoni, T. Schwetz, M.A. Tortola, J.W.F . Valle, Nucl. Phys. B643 (2002) 321 [hep-ph/0207157]. Michele Maltoni <michele.maltoni@csic.es> M- “W  ν?”, 28/06/2012

SLIDE 5

I. The LSND experiment and four-neutrino models

5

(3+1): tension between LSND and short-baseline data

In (3+1) schemes the SBL appearance probability is

effectively 2ν oscillations:

Pµe = sin2 2θ sin2 ∆m2

41L

4E , sin2 2θ = 4 |Ue4|2 |Uµ4|2 ;

disappearance experiments bound |Ue4|2 and |Uµ4|2;

★

10

3

10

2

10

1

|Ue4|

2

10

2

10

1

10 10

1

10

2

∆m

2 41 [eV 2]

Bugey Chooz

★

10

3

10

2

10

1

|Uµ4|

2

CDHS atmospheric

★

10

4

10

3

10

2

10

1

10 sin

2 2θ = 4 |Ue4| 2 |Uµ4| 2

10

1

10 10

1

∆m

2 41 [eV 2]

9 % C L 99% CL atm + LBL + NEV LSND DAR (90%, 99%)

LSND is in conflict [1]:

− with other appearance experi-

ments (Karmen & Nomad);

− with all disappearance exp’s.

[1] M. Maltoni, T. Schwetz, M.A. Tortola, J.W.F . Valle, Nucl. Phys. B643 (2002) 321 [hep-ph/0207157]. Michele Maltoni <michele.maltoni@csic.es> M- “W  ν?”, 28/06/2012

SLIDE 6

I. The LSND experiment and four-neutrino models

6

The MiniBooNE experiment (≤ 5/2012)

Eν and L very different from LSND (but similar L/Eν)

⇒ can check the oscillation solution of the LSND

problem, not the signal itself;

very peculiar results:

− strong low-energy excess in νe, mild in ¯ νe; − mild mid-energy excess in ¯ νe, but not in νe.

[MB-¯

νe]

[GeV]

ν

Reconstructed E

0.2 0.6 1 1.4 1.8 2.2 2.6 3

Events/(100 MeV)

20 40 60 80 Data Spectrum

e

ν Predicted Uncertainty in Prediction ’s

±

Neutrinos from K ’s

L

Neutrinos from K ’s µ Neutrinos from ’s π Neutrinos from

(GeV)

QE ν

E Events / MeV

0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 0.5 1 1.5 2 2.5 3

Data µ from

e

ν

+

from K

e

ν from K

e

ν misid π γ N → ∆ dirt

ther

Total Background

1.5 3.

[MB-νe] [NuMI-νe]

Michele Maltoni <michele.maltoni@csic.es> M- “W  ν?”, 28/06/2012

SLIDE 7

I. The LSND experiment and four-neutrino models

7

LSND vs MiniBooNE in (3+1)

νe: no signal ⇒ excludes LSND;
¯

νe: signal ⇒ mildly confirms LSND.

) θ (2

2

sin

3

10

2

10

1

10 1 )

4

/c

2

| (eV

2

m ∆ |

2

10

1

10 1 10

2

10

LSND 90% C.L. LSND 99% C.L. ) upper limit θ (2

2

sin y MiniBooNE 90% C.L. MiniBooNE 90% C.L. sensitivity BDT analysis 90% C.L.

[νe] [¯

νe]

Michele Maltoni <michele.maltoni@csic.es> M- “W  ν?”, 28/06/2012

SLIDE 8

I. The LSND experiment and four-neutrino models

8

Status of (3+1) models after MiniBooNE

(3+1) four-neutrino schemes fail because:

− can’t reconcile appearance and disappearance data; − can’t explain the different νe (MB) and ¯ νe (LSND) results; − can’t account for the low-energy νe event excess in MB. ⇒ (3+1) models are ruled out as explanation of SBL data.

)

e µ

θ (2

2

sin )

2

(eV

41 2

m ∆

4

10

3

10

2

10

1

10 1

2

10

1

10 1 10

2

10 (3+1) null SBL 90% CL null SBL 99% CL ) 90% CL ν ) + BNB-MB( ν LSND + BNB-MB( ) 99% CL ν ) + BNB-MB( ν LSND + BNB-MB(

[2]

)

e µ

θ (2

2

sin )

2

(eV

41 2

m ∆

3

10

2

10

1

10

1

10 1 10

2

10

) ν BNB-MB(

90% CL 99% CL

)

e µ

θ (2

2

sin )

2

(eV

41 2

m ∆

3

10

2

10

1

10

1

10 1 10

2

10

) ν BNB-MB(

90% CL 99% CL

)

e µ

θ (2

2

sin )

2

(eV

41 2

m ∆

3

10

2

10

1

10

1

10 1 10

2

10

LSND

90% CL 99% CL

[OLD]

[2]

[2] G. Karagiorgi et al., Phys. Rev. D80 (2009) 073001 [arXiv:0906.1997]. Michele Maltoni <michele.maltoni@csic.es> M- “W  ν?”, 28/06/2012

SLIDE 9

II. MiniBooNE and models with two sterile neutrinos

9

(GeV)

QE ν

E Events / MeV

0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 0.5 1 1.5 2 2.5 3

Data µ from

e

ν

+

from K

e

ν from K

e

ν misid π γ N → ∆ dirt

ther

Total Background

1.5 3.

MiniBooNE observed a 3.0σ excess at low-E [3];
this excess is incompatible with 2ν oscillations;
therefore, data with EQE

ν

< 475 MeV have not

been used to check LSND.

The MiniBooNE excess

With the analysis cuts set, a signal-blind test of data- MC agreement in the signal region was performed. The full two-neutrino oscillation fit was done in the range 300 < EQE

ν

< 3000 MeV and, with no information on the fit parameters revealed, the sum of predicted background and simulated best-fit signal was compared to data in several variables, returning only the χ2. While agreement was good in most of the comparisons, the Evis spectrum had a χ2 probability of only 1%. This triggered further investigation of the backgrounds, focusing on the lowest energies where νµ-induced backgrounds, some of which are difficult to model, are large. As part of this study, one more piece of information from the signal region was released: unsigned bin-by-bin fractional discrep- ancies in the Evis spectrum. While ambiguous, these re- inforced suspicions about the low-energy region. Though we found no specific problems with the background es- timates, it was found that raising the minimum EQE

ν

f

the fit region to 475 MeV greatly reduced a number of backgrounds with little impact on the fit’s sensitivity to

scillations. We thus performed our oscillation fits in the

energy range 475 < EQE

ν

< 3000 MeV and opened the full data set.

⇒ Omission of low-energy bins in based on the hypothesis of two-flavor oscillations!

Is it possible to do something about these data in more sophisticated models?

[3] A.A. Aguilar-Arevalo et al.[MiniBooNE collab], Phys. Rev. Lett. 98 (2007) 231801 [arXiv:0704.1500]. Michele Maltoni <michele.maltoni@csic.es> M- “W  ν?”, 28/06/2012

SLIDE 10

II. MiniBooNE and models with two sterile neutrinos

10

Explaining the MiniBooNE excess with two sterile neutrinos

With one extra sterile neutrino, m4:

P4ν

µe = 4|Ue4|2|Uµ4|2 sin2 φ41

with

φi j ≡ ∆m2

i jL

4E ;

for large energy P4ν

µe drops as 1E2;

however, the low-energy MB excess is much

sharper (∼ 1E4);

⇒ it is not possible to account for the MB ex-

cess with only one extra sterile neutrino.

300 600 900 1200 1500 Eν [MeV] 0.005 0.01 0.015 0.02 Pµe ∝ 1/E

2

∝ 1/E

4

∝ 1/E

3

On the other hand, with two extra neutrinos, m4 and m5:

P5ν

µe = 4|Ue4|2|Uµ4|2 sin2 φ41 + 4|Ue5|2|Uµ5|2 sin2 φ51 + 8|Ue4Ue5Uµ4Uµ5| sin φ41 sin φ51 cos(φ54 − δ) ;

terms of order 1E2 cancel if δ = π and |Ue4 Uµ4|∆m2

41 = |Ue5 Uµ5|∆m2 51;

⇒ with two extra sterile states it is possible to fit the MB low-energy excess [4].

[4] M. Maltoni, T. Schwetz, Phys. Rev. D76 (2007) 093005 [arXiv:0705.0107]. Michele Maltoni <michele.maltoni@csic.es> M- “W  ν?”, 28/06/2012

SLIDE 11

II. MiniBooNE and models with two sterile neutrinos

11

Reconciling MiniBooNE and LSND in (3+2) models

0.3 0.6 0.9 1.2 1.5 3 Eν

CCQE [GeV]

0.2 0.4 0.6 0.8 1 excess events per MeV MB300 MB475 MB data

475 MeV

0.4 0.6 0.8 1 1.2 1.4 L/Eν [m/MeV] 5 10 15 excess events app data incl. MB best fit LSND only background

Trick: use the CP phase δ = arg(U∗

e4Uµ4Ue5U∗ µ5) to differentiate ν (MB) from ¯

ν (LSND):

P5ν

µe = 4|Ue4|2|Uµ4|2 sin2 φ41 + 4|Ue5|2|Uµ5|2 sin2 φ51 + 8|Ue4Ue5Uµ4Uµ5| sin φ41 sin φ51 cos(φ54 − δ) ;

note that δ = π + ǫ and |Ue4 Uµ4|∆m2

41 ≈ |Ue5 Uµ5|∆m2 51 to suppress MB probability [4].

[4] M. Maltoni, T. Schwetz, Phys. Rev. D76 (2007) 093005 [arXiv:0705.0107]. Michele Maltoni <michele.maltoni@csic.es> M- “W  ν?”, 28/06/2012

SLIDE 12

II. MiniBooNE and models with two sterile neutrinos

12

Fitting all appearance data in (3+2) models

[2]

data set

|Ue4Uµ4| ∆m2

41

|Ue5Uµ5| ∆m2

51

δ χ2

min/dof

gof appearance (CPC) 0.12 0.18 0.006 2.31 –

95.8/86

22% appearance (CPV) 0.080 0.39 0.029 1.10 1.1π

82.5/85

56% NOTE: data taken from

Ref. [2], which uses old

MB-¯

ν data.

[2] G. Karagiorgi et al., Phys. Rev. D80 (2009) 073001 [arXiv:0906.1997]. Michele Maltoni <michele.maltoni@csic.es> M- “W  ν?”, 28/06/2012

SLIDE 13

II. MiniBooNE and models with two sterile neutrinos

13

The doom of disappearance data

As for (3+1) models, disappearance data imply bounds
n |Uei|2 and |Uµi|2 (i = 4, 5);
these bounds are in conflict with the large values of

|UeiUµi| required by appearance data;

again, a tension between APP and DIS arises:

χ2

 = 17.5 (4 dof) ⇒ PG = 1.5 × 10−3

[no MB];

χ2

 = 17.2 (4 dof) ⇒ PG = 1.8 × 10−3

[MB475];

χ2

 = 25.1 (4 dof) ⇒ PG = 4.8 × 10−5

[MB300];

alternatively, compare LSND and NEV as in (3+1):

χ2

 = 19.6 (5 dof) ⇒ PG = 1.5 × 10−3

[before MB];

χ2

 = 21.2 (5 dof) ⇒ PG = 7.4 × 10−4

[after MB].

⇒ Conclusion: (3+2) models fail exactly as (3+1) [4].

10

3

10

2

10

1

|U

e5 U µ5|

10

3

10

2

10

1

|U

e5 U µ5|

95%, 99% (4 dof) appearance (MB475) disappearance χ

2 PC = 9.3, ∆m 2 41 = 0.87, ∆m 2 51 = 19.9

10

3

10

2

10

1

|U

e4 U µ4|

10

3

10

2

10

1

|U

e5 U µ5|

90%, 99% (4 dof) appearance (MB300) disappearance χ

2 PC = 12.6, ∆m 2 41 = 0.87, ∆m 2 51 = 1.9

[4] M. Maltoni, T. Schwetz, Phys. Rev. D76 (2007) 093005 [arXiv:0705.0107]. Michele Maltoni <michele.maltoni@csic.es> M- “W  ν?”, 28/06/2012

SLIDE 14

II. MiniBooNE and models with two sterile neutrinos

14

The reactor neutrino anomaly

In [6, 7] the reactor ¯

ν fluxes has been reevaluated;

the new calculations result in a small increase of

the flux by about 3.5%;

hence, all reactor short-baseline (RSBL) exp. find-

ing no evidence are actually observing a deficit;

this deficit could be interpreted as being due to

SBL neutrino oscillations;

deficit independent of L ⇒ ∆m2 1 eV2;
impact on previous results:

− 4ν: small (4ν dead anyway); − 5ν: important.

0.7 0.8 0.9 1 1.1 1.2 1.3

bserved / predicted
ld

new

Bugey 4 ROVNO Bugey 3 Goesgen ILL Krasnoyarsk

} } }

235U 238U 239Pu 241Pu

[5]

VSBL

sin2(2θnew) ∆mnew

2

(eV2)

2 3 4 5 6 7 8 2 3 4 5 6 7 8 2 3 4 5 6 7 8 2 4 6 8 2 4 6 8 2 4 6 8 2 4 6 8

2 dof ∆χ2 contours

10

−3

10

−2

10

−1

10 10

−2

10

−1

10 10

1

10

2

∆χ2

1 dof ∆χ2 profile

5 10 ∆χ2

1 dof ∆χ2 profile

5 10 90.00 % 95.00 % 99.00 %

[8]

[5] T. Schwetz, M. Tortola, J.W.F . Valle, New J. Phys. 13 (2011) 063004 [arXiv:1103.0734]. [6] T.A. Mueller et al., Phys. Rev. C83 (2011) 054615 [arXiv:1101.2663]. [7] P . Huber, Phys. Rev. C 84 (2011) 024617 [arXiv:1106.0687]. [8] G. Mention et al., Phys. Rev. D83 (2011) 073006 [arXiv:1101.2755]. Michele Maltoni <michele.maltoni@csic.es> M- “W  ν?”, 28/06/2012

SLIDE 15

II. MiniBooNE and models with two sterile neutrinos

15

Can the reactor neutrino anomaly save the day?

As expected, the new reactor fluxes

lead to a clear preference for |Ue4|2 0;

however, the upper bound on |Ue4|2 is

not dramatically reduced;

morever, the bound on |Uµ4|2 from at-

mospheric data is now independently confirmed by MINOS;

all together, there is no reason to ex-

pect an impressive weakening of the disappearance bound.

[9] T. Schwetz, talk at Neutrino Conference, Ky-

to, Japan, June 3-9, 2012.

Old reactor fluxes

★

10

3

10

2

10

1

|Ue4|

2

10

2

10

1

10 10

1

10

2

∆m

2 41 [eV 2]

Bugey Chooz

★

10

3

10

2

10

1

|Uµ4|

2

CDHS atmospheric

New reactor fluxes & MINOS

★

10

3

10

2

10

1

|Ue4|

2

0.1 1 10 ∆m

2 [eV 2]

90, 95, 99% CL (2 dof)

SBL react rates only rates + Bugey3 spectr.

[9]

Michele Maltoni <michele.maltoni@csic.es> M- “W  ν?”, 28/06/2012

SLIDE 16

II. MiniBooNE and models with two sterile neutrinos

16

Impact of the new reactor fluxes

(3+1)models: χ2

/dof = 24.2/2 → 21.5/2 for LSND + MB(¯

ν) vs NEV (∆χ2

 = 2.7);

(3+2) models:

       χ2

/dof = 25.1/5 → 19.9/5 for LSND + MB(¯

ν) vs NEV (∆χ2

 = 5.2);

χ2

/dof = 19.4/4 → 14.7/4 for APP vs DIS (∆χ2  = 4.7).

10

4

10

3

10

2

10

1

sin

22θSBL

10

1

10 10

1

∆m

2 41 [eV 2]

99% CL (2 dof)

LSND + MBν − MBν KARMEN NOMAD disappearance

90, 99% CL

[10]

100 120 140 160 χ

2

(3+1) (3+2) global SBL data 0.1 1 10 ∆m

2 41 [eV 2]

50 55 60 65 χ

2

SBL reactor data (3+1) (3+2)

[10] J. Kopp, M. Maltoni and T. Schwetz, Phys. Rev. Lett. 107 (2011) 091801 [arXiv:1103.4570]. Michele Maltoni <michele.maltoni@csic.es> M- “W  ν?”, 28/06/2012

SLIDE 17

II. MiniBooNE and models with two sterile neutrinos

17

Status of (3+2) models with the new reactor fluxes

(3+2) models experience substantial improvement, but tension with disappearance data

remains considerably strong: PG=0.53%;

situation becomes more critical if the MiniBooNE low-E excess is included, since larger

mixing angles are required;

(1+3+1) works slightly better, but has stronger problems with cosmology since the sum
f neutrino masses ( mν) is larger.

0.3 0.6 0.9 1.2 1.5 3

Eν

CCQE [GeV]

0.2 0.4 0.6 0.8 1

excess events

MiniBooNE (neutrinos) LSND 0.3 0.6 0.9 1.2 1.5 3

Eν

CCQE [GeV]

0.1 0.2 0.3 MiniBooNE (anti-neutrinos)

0.1 0.2 0.3 0.4 PLSND [%]

★ ★

0.1 1 10 ∆m

2 41

0.1 1 10 ∆m

2 51

90%, 95%, 99%, 99.73% CL (2 dof)

3+2 1+3+1

[10]

[10] J. Kopp, M. Maltoni and T. Schwetz, Phys. Rev. Lett. 107 (2011) 091801 [arXiv:1103.4570]. Michele Maltoni <michele.maltoni@csic.es> M- “W  ν?”, 28/06/2012

SLIDE 18

III. A word on MiniBooNE data after Neutrino 2012

18

MiniBooNE: neutrino data

No new data, but improved analysis. Full details: [→ Steve Brice’s talk];
is ν signal compatible with 2ν oscillations?

      

2007: Posc ≃ 1% ⇒ no it isn’t [3]; 2012: Posc ≃ 6% ⇒ maybe it is [11];

do MB ν data rule out LSND ¯

ν signal in (3+1)? 2007: yes [3]; 2012: not really [11].

) θ (2

2

sin

3

10

2

10

1

10 1 )

4

/c

2

| (eV

2

m ∆ |

2

10

1

10 1 10

2

10

LSND 90% C.L. LSND 99% C.L. ) upper limit θ (2

2

sin y MiniBooNE 90% C.L. MiniBooNE 90% C.L. sensitivity BDT analysis 90% C.L.

[Eν ≥ 475 MeV]

→

[Eν ≥ 475 MeV]

[11]

r

[Eν ≥ 200 MeV]

[3] A.A. Aguilar-Arevalo et al.[MiniBooNE collab], Phys. Rev. Lett. 98 (2007) 231801 [arXiv:0704.1500]. [11] C. Polly, talk at Neutrino Conference, Kyoto, Japan, June 3-9, 2012. Michele Maltoni <michele.maltoni@csic.es> M- “W  ν?”, 28/06/2012

SLIDE 19

III. A word on MiniBooNE data after Neutrino 2012

19

MiniBooNE: antineutrino data

New data presented at Neutrino 2012, statistics doubled [11];
compatibility with ν data:

      

low-energy excess increased ⇒ better agreement; mid-energy excess reduced ⇒ better agreement;

is ¯

ν signal compatible with 2ν oscillations? Posc = 67% ⇒ definitely yes [11];

is MB-¯

ν signal compatible with LSND? Yes, irrespective of the energy threshold.

⇒

[E¯

ν ≥ 475 MeV]

[11]

r

[E¯

ν ≥ 200 MeV]

[11] C. Polly, talk at Neutrino Conference, Kyoto, Japan, June 3-9, 2012. Michele Maltoni <michele.maltoni@csic.es> M- “W  ν?”, 28/06/2012

SLIDE 20

III. A word on MiniBooNE data after Neutrino 2012

20

MiniBooNE: global ν + ¯

ν appearance analysis in (3+1)

MiniBooNE ν and ¯

ν no longer in open disagreement with LSND within (3+1) models;

however, dramatic change in interpretation not linked to dramatic change in data;
problems still there (Posc ≃ 6.7% [11]) ⇒ no great change expected in our conclusions.

[11]

[11] C. Polly, talk at Neutrino Conference, Kyoto, Japan, June 3-9, 2012. Michele Maltoni <michele.maltoni@csic.es> M- “W  ν?”, 28/06/2012

SLIDE 21

Summary

21

A few experiments exhibit deviations from the “standard” 3ν scenario:

− LSND observed an excess of ¯ νe events in a ¯ νµ beam; − MiniBooNE mildly “confirm” this excess:       

in both ¯

ν mode and ν mode at low-E;

nly in ¯

ν mode at mid-E; − new fission ¯ ν fluxes suggests that all SBL reactor experiments are observing a deficit;

however, these “hints” for sterile neutrinos are not in agreement among them:

− MiniBooNE asymmetry in ν/¯ ν requires CP violation, hence at least two sterile ν’s; − (3+2) models reconcile APP data, but DIS ones still show strong tension; − attempts to include the low-E excess in the game further increase such tension; − new reactor fluxes reduce tension with DIS data only marginally;

efforts to produce an updated global analysis are presently under way [12];

⇒ we are still quite far from the solution of the LSND puzzle!

[12] J. Kopp, P . Machado, M. Maltoni, T.Schwetz, work in progress. Michele Maltoni <michele.maltoni@csic.es> M- “W  ν?”, 28/06/2012