Oscillations Beyond Three-Neutrino Mixing Carlo Giunti INFN, - - PowerPoint PPT Presentation

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Oscillations Beyond Three-Neutrino Mixing Carlo Giunti INFN, - - PowerPoint PPT Presentation

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Oscillations Beyond Three-Neutrino Mixing Carlo Giunti INFN, Sezione di Torino giunti@to.infn.it Neutrino Unbound: http://www.nu.to.infn.it Neutrino 2016 XXVII International Conference on Neutrino Physics and Astrophysics 4-9 July 2016

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SLIDE 1

Oscillations Beyond Three-Neutrino Mixing Carlo Giunti

INFN, Sezione di Torino giunti@to.infn.it Neutrino Unbound: http://www.nu.to.infn.it Neutrino 2016 XXVII International Conference on Neutrino Physics and Astrophysics 4-9 July 2016 – London, UK

  • C. Giunti − Oscillations Beyond Three-Neutrino Mixing − Neutrino 2016 − 5 July 2016 − 1/37
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SLIDE 2

Oscillations Beyond Three-Neutrino Mixing

◮ Light Sterile Neutrinos. ◮ Non-Unitarity of Mixing Matrix. ◮ Non-Standard Interactions. ◮ Magnetic Moments.

  • C. Giunti − Oscillations Beyond Three-Neutrino Mixing − Neutrino 2016 − 5 July 2016 − 2/37
slide-3
SLIDE 3

Indications of SBL Oscillations Beyond 3ν

  • C. Giunti − Oscillations Beyond Three-Neutrino Mixing − Neutrino 2016 − 5 July 2016 − 3/37
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SLIDE 4

LSND

[PRL 75 (1995) 2650; PRC 54 (1996) 2685; PRL 77 (1996) 3082; PRD 64 (2001) 112007]

¯ νµ → ¯ νe 20 MeV ≤ E ≤ 60 MeV

◮ Well-known source of ¯

νµ µ+ at rest → e+ + νe + ¯ νµ ¯ νe + p → n + e+ Well-known detection process of ¯ νe

◮ But signal not seen by KARMEN at

L ≃ 18 m with the same method

[PRD 65 (2002) 112001]

L ≃ 30 m

≈ 3.8σ excess ∆m2

SBL 0.2 eV2 ≫ ∆m2 ATM ≫ ∆m2 SOL

  • C. Giunti − Oscillations Beyond Three-Neutrino Mixing − Neutrino 2016 − 5 July 2016 − 4/37
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SLIDE 5

Gallium Anomaly

Gallium Radioactive Source Experiments: GALLEX and SAGE νe Sources: e− + 51Cr → 51V + νe e− + 37Ar → 37Cl + νe Test of Solar νe Detection: νe + 71Ga → 71Ge + e− E ≃ 0.75 MeV E ≃ 0.81 MeV

0.7 0.8 0.9 1.0 1.1

R = N exp N cal

Cr1 GALLEX Cr SAGE Cr2 GALLEX Ar SAGE

R = 0.84 ± 0.05

LGALLEX = 1.9 m LSAGE = 0.6 m ≈ 2.9σ deficit ∆m2

SBL 1 eV2 ≫ ∆m2 ATM ≫ ∆m2 SOL

[SAGE, PRC 73 (2006) 045805; PRC 80 (2009) 015807] [Laveder et al, Nucl.Phys.Proc.Suppl. 168 (2007) 344; MPLA 22 (2007) 2499; PRD 78 (2008) 073009; PRC 83 (2011) 065504]

◮ 3He + 71Ga → 71Ge + 3H cross section measurement

[Frekers et al., PLB 706 (2011) 134]

◮ Eth(νe + 71Ga → 71Ge + e−) = 233.5 ± 1.2 keV

[Frekers et al., PLB 722 (2013) 233]

  • C. Giunti − Oscillations Beyond Three-Neutrino Mixing − Neutrino 2016 − 5 July 2016 − 5/37
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SLIDE 6

Reactor Electron Antineutrino Anomaly

[Mention et al, PRD 83 (2011) 073006; updated in White Paper, arXiv:1204.5379]

New reactor ¯ νe fluxes

[Mueller et al, PRC 83 (2011) 054615; Huber, PRC 84 (2011) 024617]

0.6 0.8 1.0 1.2

L [m] R = N exp N cal 10 102 103

R = 0.933 ± 0.021

Bugey−3 Bugey−4 Rovno91 Gosgen ILL Krasno Rovno88 SRP Chooz Palo Verde Double Chooz Daya Bay Nucifer Neutrino−4

≈ 3.2σ deficit ∆m2

SBL 0.5 eV2 ≫ ∆m2 ATM ≫ ∆m2 SOL

  • C. Giunti − Oscillations Beyond Three-Neutrino Mixing − Neutrino 2016 − 5 July 2016 − 6/37
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SLIDE 7

Beyond Three-Neutrino Mixing: Sterile Neutrinos νe νµ ντ

∆m2

SOL

∆m2

ATM

. . . νs2 νs1 ∆m2

SBL

ν4 ν3 ν2 ν1 . . . ν5 m 1 eV2

≃ 2.5 × 10−3 eV2

≃ 7.4 × 10−5 eV2

Terminology: a eV-scale sterile neutrino means: a eV-scale massive neutrino which is mainly sterile

  • C. Giunti − Oscillations Beyond Three-Neutrino Mixing − Neutrino 2016 − 5 July 2016 − 7/37
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SLIDE 8

Four-Neutrino Schemes: 2+2, 3+1 and 1+3

ν1 ν2 ∆m2

SOL

∆m2

SBL

ν4 ν3 ∆m2

ATM

m ∆m2

SBL

∆m2

SOL

ν1 ν2 ν4 ν3 ∆m2

ATM

m ν1 ν2 ν3 ν4 ∆m2

ATM

∆m2

SOL

∆m2

SBL

m ν3 ν2 ν4 ∆m2

ATM

∆m2

SBL

∆m2

SOL

ν1 m ∆m2

SBL

∆m2

ATM

ν1 ν2 ν3 ν4 ∆m2

SOL

m ∆m2

SBL

ν4 ∆m2

SOL

ν1 ν2 ν3 ∆m2

ATM

m

2+2 3+1 1+3

  • C. Giunti − Oscillations Beyond Three-Neutrino Mixing − Neutrino 2016 − 5 July 2016 − 8/37
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SLIDE 9

2+2 Four-Neutrino Schemes

ν1 ν2 ∆m2

SOL

∆m2

SBL

ν4 ν3 ∆m2

ATM

m ∆m2

SBL

∆m2

SOL

ν1 ν2 ν4 ν3 ∆m2

ATM

m ◮ After LSND (1995) 2+2 was preferred to 3+1, because of the 3+1

appearance-disappearance tension

[Okada, Yasuda, IJMPA 12 (1997) 3669; Bilenky, CG, Grimus, EPJC 1 (1998) 247]

◮ This is not a perturbation of 3-ν Mixing =

⇒ Large active–sterile

  • scillations for solar or atmospheric neutrinos!
  • C. Giunti − Oscillations Beyond Three-Neutrino Mixing − Neutrino 2016 − 5 July 2016 − 9/37
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SLIDE 10

2+2 Schemes are Strongly Disfavored

0.2 0.4 0.6 0.8 1

ηs

10 20 30 40 50

∆χ

2 99% CL (1 dof)

solar + KamLAND s

  • l

a r s

  • l

a r ( p r e S N O s a l t ) 0.2 0.4 0.6 0.8 1

ηs

χ

2 PG

χ

2 PC

atm + K2K + SBL global solar + KamLAND

Solar: Matter Effects + SNO NC Atmospheric: Matter Effects ηs = |Us1|2 + |Us2|2 = 1 − |Us3|2 + |Us4|2 99% CL: ηs < 0.25 (Solar + KamLAND) ηs > 0.75 (Atmospheric + K2K)

[Maltoni, Schwetz, Tortola, Valle, New J. Phys. 6 (2004) 122]

  • C. Giunti − Oscillations Beyond Three-Neutrino Mixing − Neutrino 2016 − 5 July 2016 − 10/37
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SLIDE 11

3+1 and 1+3 Four-Neutrino Schemes

ν1 ν2 ν3 ν4 ∆m2

ATM

∆m2

SOL

∆m2

SBL

m ν3 ν2 ν4 ∆m2

ATM

∆m2

SBL

∆m2

SOL

ν1 m ∆m2

SBL

∆m2

ATM

ν1 ν2 ν3 ν4 ∆m2

SOL

m ∆m2

SBL

ν4 ∆m2

SOL

ν1 ν2 ν3 ∆m2

ATM

m

3+1 1+3

◮ Perturbation of 3-ν Mixing:

|Ue4|2, |Uµ4|2, |Uτ4|2 ≪ 1 |Us4|2 ≃ 1

◮ 1+3 schemes are disfavored by cosmology (ΛCDM):

3

  • k=1

mk < 0.21 eV (95%, Planck TT + lowP + BAO) [arXiv:1502.01589]

  • C. Giunti − Oscillations Beyond Three-Neutrino Mixing − Neutrino 2016 − 5 July 2016 − 11/37
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SLIDE 12

Effective 3+1 SBL Oscillation Probabilities

Appearance (α = β)

PSBL

(−)

να→

(−)

νβ

≃ sin2 2ϑαβ sin2 ∆m2

41L

4E

  • sin2 2ϑαβ = 4|Uα4|2|Uβ4|2

Disappearance

PSBL

(−)

να→

(−)

να

≃ 1 − sin2 2ϑαα sin2 ∆m2

41L

4E

  • sin2 2ϑαα = 4|Uα4|2

1 − |Uα4|2

U = Ue1 Ue2 Ue3 Ue4 Uµ1 Uµ2 Uµ3 Uµ4 Uτ1 Uτ2 Uτ3 Uτ4 Us1 Us2 Us3 Us4               SBL

◮ 6 mixing angles ◮ 3 Dirac CP phases ◮ 3 Majorana CP phases ◮ CP violation is not observable in SBL

experiments!

◮ Observable in LBL accelerator exp.

sensitive to ∆m2

ATM

[de Gouvea et al, PRD 91 (2015) 053005, PRD 92 (2015) 073012, arXiv:1605.09376; Palazzo et al, PRD 91 (2015) 073017, PLB 757 (2016) 142; Gandhi et al, JHEP 1511 (2015) 039] and solar exp. sensitive to ∆m2

SOL

[Long, Li, CG, PRD 87, 113004 (2013) 113004]

  • C. Giunti − Oscillations Beyond Three-Neutrino Mixing − Neutrino 2016 − 5 July 2016 − 12/37
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SLIDE 13

3+1 Appearance-Disappearance Tension

νe DIS sin2 2ϑee ≃ 4|Ue4|2 νµ DIS sin2 2ϑµµ ≃ 4|Uµ4|2 νµ → νe APP sin2 2ϑeµ = 4|Ue4|2|Uµ4|2 ≃ 1

4 sin2 2ϑee sin2 2ϑµµ

[Okada, Yasuda, IJMPA 12 (1997) 3669; Bilenky, CG, Grimus, EPJC 1 (1998) 247] sin22ϑeµ ∆m41

2 [eV2]

10−4 10−3 10−2 10−1 1 10−1 1 10

+ +

10−4 10−3 10−2 10−1 1 10−1 1 10

3+1 GLO 1σ 2σ 3σ 3σ νe DIS νµ DIS DIS APP

◮ νµ → νe is quadratically suppressed! ◮ Similar constraint in

3+2, 3+3, . . . , 3+Ns

[CG, Zavanin, MPLA 31 (2015) 1650003] Update of [Gariazzo, CG, Laveder, Li, Zavanin, JPG 43 (2016) 033001] with improved treatment of the MiniBooNE background disappearance due to neutrino oscillations according to information from Bill Louis (thanks!)

  • C. Giunti − Oscillations Beyond Three-Neutrino Mixing − Neutrino 2016 − 5 July 2016 − 13/37
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SLIDE 14

Collin, Arguelles, Conrad, Shaevitz

[NPB 908 (2016) 354]

Our Fit

Update of [Gariazzo, CG, Laveder, Li, Zavanin, JPG 43 (2016) 033001]

sin22ϑeµ ∆m41

2 [eV2]

10−4 10−3 10−2 10−1 1 10−2 10−1 1 10 102

+

3+1 GLO 90% CL 99% CL

Best Fit: ∆m2

41 = 1.75 eV2

|Ue4|2 = 0.027 |Uµ4|2 = 0.014 GoF = 57% (χ2

min/NDF = 306.8/312)

GoFnull = 4.4% (χ2/NDF = 359.2/315) ∆χ2/NDF = 52.3/3 (≈ 6.7σ) Best Fit: ∆m2

41 = 1.6 eV2

|Ue4|2 = 0.028 |Uµ4|2 = 0.014 GoF = 6% (χ2

min/NDF = 304.0/268)

GoFnull = 0.04% (χ2/NDF = 355.2/271) ∆χ2/NDF = 51.2/3 (≈ 6.6σ)

  • C. Giunti − Oscillations Beyond Three-Neutrino Mixing − Neutrino 2016 − 5 July 2016 − 14/37
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SLIDE 15

Kopp, Machado, Maltoni, Schwetz

[JHEP 1305 (2013) 050]

Our Fit

Update of [Gariazzo, CG, Laveder, Li, Zavanin, JPG 43 (2016) 033001]

sin22ϑeµ ∆m41

2 [eV2]

10−4 10−3 10−2 10−1 10−1 1 10

APP 90.00% CL APP 99.00% CL APP 99.73% CL DIS 90.00% CL DIS 99.00% CL DIS 99.73% CL

Best Fit: ∆m2

41 = 0.93 eV2

|Ue4|2 = 0.023 |Uµ4|2 = 0.029 GoF = 19% (χ2

min/NDF = 712/680)

GoFPG = 0.01% (χ2

PG/NDF = 18.0/2)

Best Fit: ∆m2

41 = 1.6 eV2

|Ue4|2 = 0.028 |Uµ4|2 = 0.014 GoF = 6% (χ2

min/NDF = 304.0/268)

GoFPG = 0.06% (χ2/NDF = 15.0/2)

  • C. Giunti − Oscillations Beyond Three-Neutrino Mixing − Neutrino 2016 − 5 July 2016 − 15/37
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SLIDE 16

MiniBooNE Low-Energy Anomaly

νµ → νe

[PRL 102 (2009) 101802]

LSND signal

¯ νµ → ¯ νe

[PRL 110 (2013) 161801]

LSND signal

◮ Fit of MB Low-Energy Excess requires small ∆m2

41 and large sin2 2ϑeµ, in

contradiction with disappearance data

◮ MB low-energy excess is the main cause of bad APP-DIS GoFPG = 0.06% ◮ Multinucleon effects in neutrino energy reconstruction are not enough to solve

the problem [Martini et al, PRD 85 (2012) 093012; PRD 87 (2013) 013009; PRD 93 (2016) 073008]

◮ Pragmatic Approach: discard the Low-Energy Excess because it is likely not

due to oscillations

[CG, Laveder, Li, Long, PRD 88 (2013) 073008]

◮ MicroBooNE is crucial for checking the MiniBooNE Low-Energy Anomaly and

the consistency of different short-baseline data

  • C. Giunti − Oscillations Beyond Three-Neutrino Mixing − Neutrino 2016 − 5 July 2016 − 16/37
slide-17
SLIDE 17

sin22ϑeµ ∆m41

2 [eV2]

10−4 10−3 10−2 10−1 10−1 1 10

3σ DIS APP−GLO APP−PrGLO

◮ APP-GLO: all MiniBooNE data ◮ APP-PrGLO: only MiniBooNE E > 475 MeV data (Pragmatic)

  • C. Giunti − Oscillations Beyond Three-Neutrino Mixing − Neutrino 2016 − 5 July 2016 − 17/37
slide-18
SLIDE 18

Pragmatic Global 3+1 Fit

Update of [Gariazzo, CG, Laveder, Li, Zavanin, JPG 43 (2016) 033001] (−)

νe →

(−)

νe

sin22ϑee ∆m41

2 [eV2]

10−2 10−1 1 10−1 1 10

+

3+1 PrGLO 1σ 2σ 3σ 3σ νe DIS

(−)

νµ →

(−)

νe

sin22ϑeµ ∆m41

2 [eV2]

10−4 10−3 10−2 10−1 1 10

+ +

3+1 PrGLO 1σ 2σ 3σ 3σ APP DIS

(−)

νµ →

(−)

νµ

sin22ϑµµ ∆m41

2 [eV2]

10−2 10−1 1 10−1 1 10

+

3+1 PrGLO 1σ 2σ 3σ νµ DIS (99.73% CL) IceCube (99% CL) MINOS (95% CL)

GoF = 24% PGoF = 7% No Osc. disfavored at ≈ 6.2σ ∆χ2/NDF = 46.6/3 Not yet included: – IceCube, arXiv:1605.01990 – MINOS Preliminary, arXiv:1605.04544

  • C. Giunti − Oscillations Beyond Three-Neutrino Mixing − Neutrino 2016 − 5 July 2016 − 18/37
slide-19
SLIDE 19

SBL + IceCube

[Collin, Arguelles, Conrad, Shaevitz, arXiv:1607.00011] SBL SBL + IceCube → Red: 90% CL Blue: 99% CL

3+1 ∆m2

41 |Ue4| |Uµ4| |Uτ4| Nbins

χ2

min

χ2

null

∆χ2 (dof) SBL 1.75 0.163 0.117

  • 315

306.81 359.15 52.34 (3) SBL+IC 1.75 0.164 0.119 0.00 524 518.59 568.84 50.26 (4) IC 5.62

  • 0.314
  • 209

207.11 209.69 2.58 (2)

  • C. Giunti − Oscillations Beyond Three-Neutrino Mixing − Neutrino 2016 − 5 July 2016 − 19/37
slide-20
SLIDE 20

The Race for the Light Sterile

(−)

νe →

(−)

νe

sin22ϑee ∆m41

2 [eV2]

10−2 10−1 1 10−1 1 10

+

KATRIN − 2σ

CeSOX (95% CL) BEST (95% CL) IsoDAR@KamLAND (5yr, 3σ) IsoDAR@C−ADS (5yr, 3σ) DANSS (1yr, 95% CL) NEOS (0.5yr, 95% CL) Neutrino−4 (1yr, 95% CL) PROSPECT phase 1 (3yr, 3σ) PROSPECT phase 2 (3yr, 3σ) SoLiD phase 1 (1yr, 95% CL) SoLiD phase 2 (3yr, 3σ) STEREO (1yr, 95% CL)

(−)

νµ →

(−)

νe

sin22ϑeµ ∆m41

2 [eV2]

10−4 10−3 10−2 10−1 1 10

+

3+1 PrGLO 1σ 2σ 3σ SBN (3yr, 3σ) nuPRISM (3σ) JSNS2 (3σ)

(−)

νµ →

(−)

νµ

sin22ϑµµ ∆m41

2 [eV2]

10−2 10−1 1 10−1 1 10

+

3+1 PrGLO 1σ 2σ 3σ SBN (3yr, 3σ) KPipe (3yr, 3σ)

  • C. Giunti − Oscillations Beyond Three-Neutrino Mixing − Neutrino 2016 − 5 July 2016 − 20/37
slide-21
SLIDE 21

Effective 3+2 SBL Oscillation Probabilities

[Sorel, Conrad, Shaevitz, PRD 70 (2004) 073004]

PSBL

(−)

νµ→

(−)

νe

= 4|Ue4|2|Uµ4|2sin2 ∆41 + 4|Ue5|2|Uµ5|2sin2 ∆51 +8|Uµ4Ue4Uµ5Ue5|sin ∆41sin ∆51cos(∆54

(+)

− η) PSBL

(−)

να→

(−)

να

= 1 − 4(1 − |Uα4|2 − |Uα5|2)(|Uα4|2sin2 ∆41 + |Uα5|2sin2 ∆51) −4|Uα4|2|Uα5|2sin2 ∆54 ∆kj = ∆m2

kjL/4E

η = arg[U∗

e4Uµ4Ue5U∗ µ5] ◮ Good: CP violation ◮ Bad: Two massive sterile neutrinos at the eV scale!

4 more parameters: ∆m2

41, |Ue4|2, |Uµ4|2,

  • 3+1

∆m2

51, |Ue5|2, |Uµ5|2, η

[Conrad, Shaevitz et al, PRD 75 (2007) 013011, PRD 80 (2009) 073001, AHEP 2013 (2013) 163897, NPB 908 (2016) 354; Maltoni, Schwetz, et al, PRD 76 (2007) 093005, PRL 107 (2011) 091801, JHEP 1305 (2013) 050; Bandyopadhyay, Choubey, arXiv:0707.2481; Akhmedov, Schwetz, JHEP 1010 (2010) 115; Laveder et al, PRD 84 (2011) 073008, PRD 88 (2013) 073008, JPG 43 (2016) 033001; Donini et al, JHEP 1107 (2011) 105, JHEP 1207 (2012) 161; Archidiacono et al, PRD 86 (2012) 065028, PRD 87 (2013) 125034; Jacques, Krauss, Lunardini, PRD 87 (2013) 083515; Girardi, Meroni, Petcov, JHEP 1311 (2013) 146]

  • C. Giunti − Oscillations Beyond Three-Neutrino Mixing − Neutrino 2016 − 5 July 2016 − 21/37
slide-22
SLIDE 22

3+2 Appearance-Disappearance Tension

Global Fits Our Fit KMMS 3+1 3+2 3+1 3+2 GoF 6% 10% 19% 23% PGoF 0.06% 0.3% 0.01% 0.003%

◮ Our Fit: Update of [Gariazzo, CG, Laveder, Li, Zavanin, JPG 43 (2016) 033001] ◮ KMMS: [Kopp, Machado, Maltoni, Schwetz, JHEP 1305 (2013) 050]

4|U e4|2|U µ4|2 4|U e5|2|U µ5|2

+ +

10−4 10−3 10−2 10−1 10−4 10−3 10−2 10−1

3+2 − 3σ APP DIS

  • C. Giunti − Oscillations Beyond Three-Neutrino Mixing − Neutrino 2016 − 5 July 2016 − 22/37
slide-23
SLIDE 23

3+2 cannot fit MiniBooNE Low-Energy Excess

−0.2 0.0 0.2 0.4 0.6

E [MeV] Excess Events / MeV

200 400 600 800 1000 1200 1400 3000

MiniBooNE − νe Data 3+1 3+2

−0.1 0.0 0.1 0.2 0.3

E [MeV] Excess Events / MeV

200 400 600 800 1000 1200 1400 3000

MiniBooNE − νe Data 3+1 3+2

◮ Note difference between 3+2 νe and ¯

νe histograms due to CP violation

◮ 3+2 can fit slightly better the small ¯

νe excess at about 600 MeV

◮ 3+2 fit of low-energy excess as bad as 3+1 ◮ Claims that 3+2 can fit low-energy excess do not take into account

constraints from other data

◮ Conclusion: with current data 3+2 is not needed

  • C. Giunti − Oscillations Beyond Three-Neutrino Mixing − Neutrino 2016 − 5 July 2016 − 23/37
slide-24
SLIDE 24

Effects of light sterile neutrinos should also be seen in:

◮ β Decay Experiments

[Hannestad et al, JCAP 1102 (2011) 011, PRC 84 (2011) 045503, Formaggio, Barrett, PLB 706 (2011) 68; Esmaili, Peres, PRD 85 (2012) 117301; Gastaldo et al, JHEP 1606 (2016) 061]

◮ Neutrinoless Double-β Decay Experiments

[Rodejohann et al, JHEP 1107 (2011) 091; Li, Liu, PLB 706 (2012) 406; Meroni et al, JHEP 1311 (2013) 146, PRD 90 (2014) 053002; Pascoli et al, PRD 90 (2014) 093005 CG, Zavanin, JHEP 1507 (2015) 171; Guzowski et al, PRD 92 (2015) 012002]

◮ Long-baseline Neutrino Oscillation Experiments

[de Gouvea et al, PRD 91 (2015) 053005, PRD 92 (2015) 073012, arXiv:1605.09376; Palazzo et al, PRD 91 (2015) 073017, PLB 757 (2016) 142, arXiv:1601.05995, arXiv:1603.03759, arXiv:1605.04299; Gandhi et al, JHEP 1511 (2015) 039; Pant et al, arXiv:1509.04096, Choubey, Pramanik, arXiv:1604.04731]

◮ Solar neutrinos

[Dooling et al, PRD 61 (2000) 073011, Gonzalez-Garcia et al, PRD 62 (2000) 013005; Palazzo, PRD 83 (2011) 113013, PRD 85 (2012) 077301; Li et al, PRD 80 (2009) 113007, PRD 87, 113004 (2013), JHEP 1308 (2013) 056; Kopp et al, JHEP 1305 (2013) 050]

◮ Atmospheric neutrinos

[Goswami, PRD 55 (1997) 2931; Bilenky et al, PRD 60 (1999) 073007; Maltoni et al, NPB 643 (2002) 321, PRD 67 (2003) 013011; Choubey, JHEP 0712 (2007) 014; Razzaque, Smirnov, JHEP 1107 (2011) 084, PRD 85 (2012) 093010; Gandhi, Ghoshal, PRD 86 (2012) 037301; Barger et al, PRD 85 (2012) 011302; Esmaili et al, JCAP 1211 (2012) 041, JCAP 1307 (2013) 048, JHEP 1312 (2013) 014; Rajpoot et al, EPJC 74 (2014) 2936; Lindner et al, JHEP 1601 (2016) 124; Behera et al, arXiv:1605.08607]

◮ Supernova neutrinos

[Caldwell, Fuller, Qian, PRD 61 (2000) 123005; Peres, Smirnov, NPB 599 (2001); Sorel, Conrad, PRD 66 (2002) 033009; Tamborra et al, JCAP 1201 (2012) 013; Wu et al, PRD 89 (2014) 061303; Esmaili et al, PRD 90 (2014) 033013]

◮ Cosmic neutrinos

[Cirelli et al, NPB 708 (2005) 215; Donini, Yasuda, arXiv:0806.3029; Barry et al, PRD 83 (2011) 113012]

◮ Indirect dark matter detection [Esmaili, Peres, JCAP 1205 (2012) 002] ◮ Cosmology [see: Wong, ARNPS 61 (2011) 69; Archidiacono et al, AHEP 2013 (2013) 191047]

  • C. Giunti − Oscillations Beyond Three-Neutrino Mixing − Neutrino 2016 − 5 July 2016 − 24/37
slide-25
SLIDE 25

Effective 3+1 LBL Oscillation Probabilities

[de Gouvea et al, PRD 91 (2015) 053005, PRD 92 (2015) 073012, arXiv:1605.09376; Palazzo et al, PRD 91 (2015) 073017, PLB 757 (2016) 142, arXiv:1601.05995, arXiv:1603.03759, arXiv:1605.04299; Gandhi et al, JHEP 1511 (2015) 039]

|Ue3| ≃ sin ϑ13 ≃ 0.15 ∼ ε = ⇒ ε2 ∼ 0.03 |Ue4| ≃ sin ϑ14 ≃ 0.17 ∼ ε |Uµ4| ≃ sin ϑ24 ≃ 0.11 ∼ ε α ≡ ∆m2

21

|∆m2

31| ≃ 7 × 10−5

2.4 × 10−3 ≃ 0.031 ∼ ε2 At order ε3:

[Klop, Palazzo, PRD 91 (2015) 073017]

∆kj ≡ ∆m2

kjL/4E

PLBL

νµ→νe ≃ 4 sin2 ϑ13 sin2 ϑ23 sin2 ∆31

∼ ε2 +2 sin ϑ13 sin 2ϑ12 sin 2ϑ23(α∆31) sin ∆31 cos(∆32 + δ13) ∼ ε3 +4 sin ϑ13sin ϑ14sin ϑ24 sin ϑ23 sin ∆31 sin(∆31 + δ13 − δ14) ∼ ε3

  • C. Giunti − Oscillations Beyond Three-Neutrino Mixing − Neutrino 2016 − 5 July 2016 − 25/37
slide-26
SLIDE 26

CP Violation in T2K and NOνA

[Capozzi, CG, Laveder, Palazzo, in preparation]

68% 90%

  • Rea. 90%

13

θ 2

2

sin

13

θ 2

2

sin π

13

δ π

13

δ

Normal Ordering Inverted Ordering ν 3 ν 4

0.0 0.1 0.2 0.3 0.0 0.1 0.2 0.3 1.0 − 0.5 − 0.0 0.5 1.0 1.0 − 0.5 − 0.0 0.5 1.0 68% 90% 13

θ 2

2

sin

13

θ 2

2

sin π

13

δ π

13

δ

Normal Ordering Inverted Ordering ν 3 ν 4

0.07 0.08 0.09 0.10 0.07 0.08 0.09 0.10 1.0 − 0.5 − 0.0 0.5 1.0 1.0 − 0.5 − 0.0 0.5 1.0

LBL + Reactors Normal Ordering

π

14

δ π

13

δ

1.0 − 0.5 − 0.0 0.5 1.0 1.0 − 0.5 − 0.0 0.5 1.0

π

14

δ π

13

δ

1.0 − 0.5 − 0.0 0.5 1.0 1.0 − 0.5 − 0.0 0.5 1.0

Inverted Ordering Better agreement of LBL & Reactors for δ14 ≈ −π/2

  • C. Giunti − Oscillations Beyond Three-Neutrino Mixing − Neutrino 2016 − 5 July 2016 − 26/37
slide-27
SLIDE 27

New Physics Small (Majorana) Neutrino Masses Neutrino Oscillations Non-Standard Interactions Magnetic Moments Sterile Neutrinos light Non-Unitary Mixing heavy

  • C. Giunti − Oscillations Beyond Three-Neutrino Mixing − Neutrino 2016 − 5 July 2016 − 27/37
slide-28
SLIDE 28

Non-Unitary Mixing

Standard Light Massive Neutrinos ν1, ν3, ν3 Heavy Neutral Leptons (mk 100 GeV) ν4, . . . , νN Ns = N − 3 Heavy Sterile Neutrinos νs1, . . . , νNs

UN×N = Ue1 Ue2 Ue3 · · · UeN Uµ1 Uµ2 Uµ3 · · · UµN Uτ1 Uτ2 Uτ3 · · · UτN . . . . . . . . . ... . . . UsNs 1 UsNs 2 UsNs 3 · · · UsNs N                            

  • U

Effective Low-Energy Mixing of Active Neutrinos (α = e, µ, τ) |να =

3

  • k=1

UN×N

αk

|νk =

3

  • k=1
  • Uαk|νk

Non-Unitary Effective 3 × 3 Mixing Matrix U

  • C. Giunti − Oscillations Beyond Three-Neutrino Mixing − Neutrino 2016 − 5 July 2016 − 28/37
slide-29
SLIDE 29

Global Non-Unitary Fit of Oscillation Data

[Parke, Ross-Lonergan, PRD 93 (2016) 113009]

Assumption: ∆m2

21 = 7.6 × 10−5 eV2

|∆m2

31| = 2.4 × 10−3 eV2

[PDG 2014] See also: [Langacker, London, PRD 38 (1988) 907; Bilenky, CG, PLB 300 (1993) 137; Antusch, Biggio, Fernandez-Martinez, Gavela, Lopez-Pavon, JHEP 0610 (2006) 084; Xing, PLB 718 (2013) 1447; Qian, Zhang, Diwan, Vogel, arXiv:1308.5700]

  • C. Giunti − Oscillations Beyond Three-Neutrino Mixing − Neutrino 2016 − 5 July 2016 − 29/37
slide-30
SLIDE 30

Bounds on Non-Unitarity of the Mixing Matrix

◮ Any matrix can be parameterized as a product of a Hermitian and a

Unitary matrix:

[Fernandez-Martinez, Gavela, Lopez-Pavon, Yasuda, PLB 649 (2007) 427]

  • U = (✶ − η) U

with η = η† U = Standard Unitary 3 × 3 Mixing Matrix

◮ Since massive neutrinos are not observed in flavor neutrinos interactions

  • bservables depend on
  • k
  • Uαk

U†

kα ≈ δαβ − 2ηαβ

for |ηαβ| ≪ 1

◮ From electroweak and LFV measurements:

2|η| ≤   2.5 × 10−3 2.4 × 10−5 2.7 × 10−3 2.4 × 10−5 4.0 × 10−4 1.2 × 10−3 2.7 × 10−3 1.2 × 10−3 5.6 × 10−3   at 2σ

[Fernandez-Martinez, Hernandez-Garcia, Lopez-Pavon, arXiv:1605.08774] See also: [Langacker, London, PRD 38 (1988) 886; Nardi, Roulet, Tommasini, PLB 327 (1994) 319; Antusch, Biggio, Fernandez-Martinez, Gavela, Lopez-Pavon, JHEP 0610 (2006) 084; Rodejohann, PLB 684 (2010) 40; Alonso, Dhen, Gavela, Hambye, JHEP 1301 (2013) 118; Akhmedov, Kartavtsev, Lindner, Michaels, Smirnov, JHEP 1305 (2013) 081; Abada, Das, Teixeira, Vicente, Weiland, JHEP 1302 (2013) 048; Basso, Fischer, van der Bij, Europhys.Lett. 105 (2014) 11001; Abada, Teixeira, Vicente, Weiland, JHEP 1402 (2014) 091; Antusch, Fischer, JHEP 1410 (2014) 094, JHEP 1505 (2015) 053; Abada, De Romeri, Teixeira, JHEP 1602 (2016) 083]

  • C. Giunti − Oscillations Beyond Three-Neutrino Mixing − Neutrino 2016 − 5 July 2016 − 30/37
slide-31
SLIDE 31

Non-Unitarity CP-Violation Ambiguity

◮ Another parameterization:

  • U = T NPU

[Schechter, Valle, PRD 22 (1980) 2227; Xing, PLB 660 (2008) 515; Escrihuela, Forero, Miranda, Tor- tola, Valle PRD 92 (2015) 053009]

T NP =   αee αµe αµµ ατe ατµ αττ   Real: αee, αµµ, αττ Complex: αµe, ατe, ατµ

◮ Pµe = α2 eeα2 µµP3×3 µe

− α2

eeαµµ|αµe|PI µe + α2 ee|αµe|2

zero-distance effect

PI

µe = 2 sin 2θ13 sin θ23 sin ∆31 sin (∆31 + δCP + φ)

+ cos θ13 cos θ23 sin 2θ12 sin 2∆21 sin φ φ = − arg(αµe)

200 400 600 800

L/E (km/GeV)

0.02 0.04 0.06 0.08 0.1

Pµe

Pµe

3x3 with δCP = 0

δCP = 7π/4, φ = 5π/3 δCP = 3π/2, φ = π δCP = 4π/3, φ = 6π/5

Vertical lines indicate the mean value of L/E for NOνA (405), DUNE (433) and T2K (490 km/GeV)

[Miranda, Tortola, Valle, arXiv:1604.05690] See also: [Fernandez-Martinez, Gavela, Lopez-Pavon, Yasuda, PLB 649 (2007) 427; Antusch, Blennow, Fernandez-Martinez, Lopez-Pavon, PRD 80 (2009) 033002; Ge, Pasquini, Tortola, Valle, arXiv:1605.01670]

  • C. Giunti − Oscillations Beyond Three-Neutrino Mixing − Neutrino 2016 − 5 July 2016 − 31/37
slide-32
SLIDE 32

Non-Standard Interactions

◮ Observable non-renormalizable effective NSI of left-handed neutrinos:

Charged-Current-like NSI: (α, β = e, µ, τ) HCC

NSI = 2

√ 2GFVud

  • α,β
  • ℓαLγρνβL

εudL

αβ uLγρdL + εudR αβ uRγρdR

  • + H.c.

+2 √ 2GF

  • α,β

(ναLγρνβL)

  • γ=δ
  • εγδL

αβ ℓγLγρℓδL + εγδR αβ ℓγRγρℓδR

  • Neutral-Current-like or Matter NSI:

(εfP

αβ = εfP∗ βα )

HNC

NSI = 2

√ 2GF

  • α,β

(ναLγρνβL)

  • f =e,u,d
  • εfL

αβfLγρfL + εfR αβfRγρfR

  • ◮ Bounds from non-oscillation data:

[Davidson, Pena-Garay, Rius, Santamaria, JHEP 0303 (2003) 011; Biggio, Blennow, Fernandez-Martinez, JHEP 0908 (2009) 090; Forero, Guzzo, PRD 84 (2011) 013002; Khan, PRD 93 (2016) 093019]

◮ Reviews: [Ohlsson, RPP 76 (2013) 044201;

Miranda, Nunokawa, NJP 17 (2015) 095002]

  • C. Giunti − Oscillations Beyond Three-Neutrino Mixing − Neutrino 2016 − 5 July 2016 − 32/37
slide-33
SLIDE 33

Neutrino flavor evolution equation in matter with NSI:

(∆kj = ∆m2

kj/2E)

i d dx   νe νµ ντ   =  U   ∆21 ∆31   U† +

  • f =e,u,d

Vf   δef + εf

ee

εf

eµ

εf

eτ

εf ∗

eµ

εf

µµ

εf

µτ

εf ∗

eτ

εf ∗

µτ

εf

ττ

      νe νµ ντ  

unpolarized matter: εf

αβ = εfL αβ + εfR αβ

vector couplings Global Analysis of Neutrino Oscillation Data

[Gonzalez-Garcia, Maltoni, JHEP 1309 (2013) 152; Gonzalez-Garcia, Maltoni, Schwetz, NPB 908 (2016) 199]

★ 0.2 0.3 0.4 0.5 0.6 0.7 0.8 sin

2 θ12

6 6.5 7 7.5 8 8.5 ∆m

2 21 [10

  • 5 eV

2]

★ 0.01 0.02 0.03 0.04 sin

2 θ13

0.3 0.4 0.5 0.6 0.7 sin

2 θ23

  • 3
  • 2.5
  • 2

★ 2 2.5 3 ∆m

2 31 [10

  • 3 eV

2]

★

f=u

★ w/o Solar & KamLAND [90%, 3σ] All data [90%, 95%, 99%, 3σ] All data, no NSI [90%, 95%, 99%, 3σ] w/o NSI in Atmospheric sector [90%, 3σ] 5 10 15 20 ∆χ

2

f=u

  • 2
  • 1

1 ε

f ee − ε f µµ

5 10 15 20 ∆χ

2

  • 0.25

0.25 ε

f ττ − ε f µµ

  • 0.2

0.2 ε

f eµ

  • 0.5

0.5 ε

f eτ

  • 0.05

0.05 ε

f µτ

f=d LMA LMA-D

◮

“Dark-Side” LMA-D with ϑ12 > 45◦ and large NSI. [Miranda, Tortola, Valle, JHEP 0610 (2006) 008]

◮

NSI have small effects on the determination of the other mixing parameters.

  • C. Giunti − Oscillations Beyond Three-Neutrino Mixing − Neutrino 2016 − 5 July 2016 − 33/37
slide-34
SLIDE 34

Electromagnetic Interactions

◮ Effective Hamiltonian:

H(ν)

em (x) = j(ν) µ (x)Aµ(x) =

  • k,j=1

νk(x)Λkj

µ νj(x)Aµ(x)

◮ Effective electromagnetic vertex:

νi(pi) Λ γ(q) νf (pf ) νf (pf )|j(ν)

µ (0)|νi(pi) = uf (pf )Λfi µ(q)ui(pi)

q = pi − pf

◮ Vertex function:

Λµ(q) =

  • γµ − qµ/

q/q2 ❢Q(q2) + ❢A(q2)q2γ5

  • − iσµνqν

❢M(q2) + i❢E(q2)γ5

  • form factors:

Lorentz-invariant charge anapole magnetic electric q2 = 0 = ⇒ q ❛ µ ε

◮ Hermitian form factor matrices

= ⇒ µ = µ† ε = ε† q = q† ❛ = ❛†

◮ Majorana neutrinos

= ⇒ µ = −µT ε = −εT q = −qT ❛ = ❛T no diagonal charges and electric and magnetic moments

  • C. Giunti − Oscillations Beyond Three-Neutrino Mixing − Neutrino 2016 − 5 July 2016 − 34/37
slide-35
SLIDE 35

◮ Extended Standard Model with right-handed neutrinos and ∆L = 0:

µD

kk ≃ 3.2 × 10−19µB

mk eV

  • εD

kk = 0

µD

kj

iεD

kj

  • ≃ −3.9 × 10−23µB

mk ± mj eV

ℓ=e,µ,τ

U∗

ℓkUℓj

mℓ mτ 2

  • ff-diagonal moments are GIM-suppressed

[Fujikawa, Shrock, PRL 45 (1980) 963; Pal, Wolfenstein, PRD 25 (1982) 766; Shrock, NPB 206 (1982) 359; Dvornikov, Studenikin, PRD 69 (2004) 073001, JETP 99 (2004) 254]

◮ Extended Standard Model with Majorana neutrinos (|∆L| = 2):

µM

kj ≃ −7.8 × 10−23µBi (mk + mj)

  • ℓ=e,µ,τ

Im [U∗

ℓkUℓj] m2 ℓ

m2

W

εM

kj ≃ 7.8 × 10−23µBi (mk − mj)

  • ℓ=e,µ,τ

Re [U∗

ℓkUℓj] m2 ℓ

m2

W

[Shrock, NPB 206 (1982) 359]

GIM-suppressed, but additional model-dependent contributions of the scalar sector can enhance the Majorana transition dipole moments [Pal, Wolfenstein, PRD 25 (1982) 766; Barr,

Freire, Zee, PRL 65 (1990) 2626; Pal, PRD 44 (1991) 2261]

  • C. Giunti − Oscillations Beyond Three-Neutrino Mixing − Neutrino 2016 − 5 July 2016 − 35/37
slide-36
SLIDE 36

Method Experiment Limit CL Reference Reactor ¯ νe-e− Krasnoyarsk µνe < 2.4 × 10−10 µB 90% Vidyakin et al. (1992) Rovno µνe < 1.9 × 10−10 µB 95% Derbin et al. (1993) MUNU µνe < 9 × 10−11 µB 90% Daraktchieva et al. (2005) TEXONO µνe < 7.4 × 10−11 µB 90% Wong et al. (2007) GEMMA µνe < 2.9 × 10−11 µB 90% Beda et al. (2012) Accelerator νe-e− LAMPF µνe < 1.1 × 10−9 µB 90% Allen et al. (1993) Accelerator (νµ, ¯ νµ)-e− BNL-E734 µνµ < 8.5 × 10−10 µB 90% Ahrens et al. (1990) LAMPF µνµ < 7.4 × 10−10 µB 90% Allen et al. (1993) LSND µνµ < 6.8 × 10−10 µB 90% Auerbach et al. (2001) Accelerator (ντ, ¯ ντ)-e− DONUT µντ < 3.9 × 10−7 µB 90% Schwienhorst et al. (2001) Solar νe-e− Super-Kamiokande µS(Eν 5 MeV) < 1.1 × 10−10 µB 90% Liu et al. (2004) Borexino µS(Eν 1 MeV) < 5.4 × 10−11 µB 90% Arpesella et al. (2008)

[CG, Studenikin, RMP 87 (2015) 531]

◮ Gap of about 8 orders of magnitude between the experimental limits and

the 10−19 µB prediction of the minimal Standard Model extensions.

◮ µν ≫ 10−19 µB discovery ⇐

⇒ non-minimal new physics beyond the Standard Model.

◮ Neutrino spin-flavor precession in a magnetic field

[Lim, Marciano, PRD 37 (1988) 1368; Akhmedov, PLB 213 (1988) 64]

  • C. Giunti − Oscillations Beyond Three-Neutrino Mixing − Neutrino 2016 − 5 July 2016 − 36/37
slide-37
SLIDE 37

Conclusions

◮ Exciting indications of light sterile neutrinos at the eV scale:

◮ LSND ¯

νµ → ¯ νe signal.

◮ Reactor ¯

νe disappearance.

◮ Gallium νe disappearance.

◮ Vigorous experimental program to check conclusively in a few years:

◮ νe and ¯

νe disappearance with reactors and radioactive sources.

◮ νµ → νe transitions with accelerator neutrinos. ◮ νµ disappearance with accelerator neutrinos.

◮ Neutrinos provide a Window to the New Physics beyond the Standard

Model through:

◮ Small (Majorana) Masses. ◮ Sterile Neutrinos. ◮ Non-Unitarity of Mixing Matrix. ◮ Non-Standard Interactions. ◮ Electromagnetic Interactions. ◮ . . .

  • C. Giunti − Oscillations Beyond Three-Neutrino Mixing − Neutrino 2016 − 5 July 2016 − 37/37
slide-38
SLIDE 38

Backup Slides

  • C. Giunti − Oscillations Beyond Three-Neutrino Mixing − Neutrino 2016 − 5 July 2016 − 38/37
slide-39
SLIDE 39

Reactor Rates

sin22ϑee ∆m41

2 [eV2]

+

10−3 10−2 10−1 1 10−2 10−1 1 10 102

Reactor Rates − 99% CL Bugey−3 (1995) Bugey−4 (1994) + Rovno (1991) Gosgen (1986) + ILL (1995) Krasnoyarsk (1994) Rovno (1988) SRP (1996) Nucifer (2016) Neutrino−4 (2016) Chooz (1999) + Palo Verde (2001) Double Chooz (2014) Daya Bay (2014)

Combined 90% CL 95% CL 99% CL

No Oscillations χ2/NDF = 34.9/30 GoF = 25% Oscillations χ2

min/NDF = 18.1/28

GoF = 92% Best Fit ∆m2

41 = 0.47 eV2

sin2 2ϑee = 0.14

  • C. Giunti − Oscillations Beyond Three-Neutrino Mixing − Neutrino 2016 − 5 July 2016 − 39/37
slide-40
SLIDE 40

0.6 0.8 1.0 1.2

L [m] Pνe→νe

1 10 102 103

DC DB DB R E ≈ 4MeV ∆m41

2 = 0.47eV2, sin22ϑee = 0.14

Bugey−4 Rovno91 Bugey−3 Gosgen ILL Krasno Rovno88 SRP Nucifer Neutrino−4

sin2 2ϑee = 4|Ue4|2 1 − |Ue4|2 = sin2 2ϑ14 PSBL

(−)

νe→

(−)

νe

≃ 1 − sin2 2ϑ14 sin2 ∆m2

41L

4E

  • PLBL

(−)

νe→

(−)

νe

≃ 1 − 1 2 sin2 2ϑ14 − cos4 ϑ14 sin2 2ϑ13 sin2 ∆m2

31L

4E

  • C. Giunti − Oscillations Beyond Three-Neutrino Mixing − Neutrino 2016 − 5 July 2016 − 40/37
slide-41
SLIDE 41

Reactor Rates + Bugey-3 Spectrum

sin22ϑee ∆m41

2 [eV2]

+

10−3 10−2 10−1 1 10−2 10−1 1 10 102

99% CL Reactor Rates Bugey−3 Spectrum Combined 90% CL 95% CL 99% CL

No Oscillations χ2/NDF = 50.3/54 GoF = 62% Oscillations χ2

min/NDF = 39.4/52

GoF = 90% Best Fit ∆m2

41 = 2.7 eV2

sin2 2ϑee = 0.14 We use the Bugey-3 40 m / 15 m spectral ratio, which is independent from the 5 MeV bump!

  • C. Giunti − Oscillations Beyond Three-Neutrino Mixing − Neutrino 2016 − 5 July 2016 − 41/37
slide-42
SLIDE 42

0.6 0.8 1.0 1.2

L [m] Pνe→νe

1 10 102 103

DC DB DB R E ≈ 4MeV ∆m41

2 = 0.47eV2, sin22ϑee = 0.14

∆m41

2 = 2.7eV2, sin22ϑee = 0.14

Bugey−4 Rovno91 Bugey−3 Gosgen ILL Krasno Rovno88 SRP Nucifer Neutrino−4

1 2 3 4 5 6 0.11 0.12 0.13 0.14 0.15 0.16

Ee+ [MeV] R

Bugey−3 Spectral Ratio: 40 m / 15 m ∆m41

2 = 0.47eV2, sin22ϑee = 0.14

∆m41

2 = 2.7eV2, sin22ϑee = 0.14

  • C. Giunti − Oscillations Beyond Three-Neutrino Mixing − Neutrino 2016 − 5 July 2016 − 42/37
slide-43
SLIDE 43

Global νe and ¯ νe Disappearance

sin22ϑee ∆m41

2 [eV2]

+

10−2 10−1 1 10−1 1 10 102

νe & νe DIS 90% CL 95% CL 99% CL 99% CL Rea Gal νeC Sun T2K

sin22ϑee ∆m41

2 [eV2]

+

10−2 10−1 1 10−1 1 10 102

νe & νe DIS + β 90% CL 95% CL 99% CL 99% CL νe & νe DIS β decay

KARMEN + LSND νe + 12C → 12Ng.s. + e− [Conrad, Shaevitz, PRD 85 (2012) 013017] [CG, Laveder, PLB 706 (2011) 200] solar νe + KamLAND ¯ νe + ϑ13 [CG, Li, PRD 80 (2009) 113007] [Palazzo, PRD 83 (2011) 113013; PRD 85 (2012) 077301] [CG, Laveder, Li, Liu, Long, PRD 86 (2012) 113014] T2K Near Detector νe disappearance [T2K, PRD 91 (2015) 051102] Mainz + Troitsk Tritium β decay [Mainz, EPJC 73 (2013) 2323] [Troitsk, JETPL 97 (2013) 67; JPG 41 (2014) 015001]

No Osc. excluded at 2.9σ (∆χ2/NDF = 11.4/2)

7 cm Losc

41

E [MeV] 6 m (2σ)

  • C. Giunti − Oscillations Beyond Three-Neutrino Mixing − Neutrino 2016 − 5 July 2016 − 43/37
slide-44
SLIDE 44

The Race for νe and ¯ νe Disappearance

sin22ϑee ∆m41

2 [eV2]

10−2 10−1 1 10−1 1 10 102

+

KATRIN − 2σ

νe & νe DIS + β 90% CL 95% CL 99% CL CeSOX shape (95% CL) CeSOX rate (95% CL) CeSOX rate+shape (95% CL) BEST (95% CL) IsoDAR@KamLAND (5yr, 3σ)

sin22ϑee ∆m41

2 [eV2]

10−2 10−1 1 10−1 1 10 102

+

KATRIN − 2σ

νe & νe DIS + β 90% CL 95% CL 99% CL STEREO (1yr, 95% CL) SoLiD phase 1 (1yr, 95% CL) SoLiD phase 2 (3yr, 3σ) Neutrino−4 (1yr, 95% CL) PROSPECT phase 1 (3yr, 3σ) PROSPECT phase 2 (3yr, 3σ) DANSS (1yr, 95% CL) NEOS (0.5yr, 95% CL)

CeSOX (Gran Sasso, Italy) 144Ce → ¯ νe

BOREXINO: L ≃ 5-12m [Vivier@TAUP2015]

BEST (Baksan, Russia) 51Cr → νe L ≃ 5-12m [PRD 93 (2016) 073002] IsoDAR@KamLAND (Kamioka, Japan)

8Li → ¯

νe L ≃ 16m [arXiv:1511.05130] KATRIN (Karlsruhe, Germany) 3H → ¯ νe Mass Measurement [Mertens@TAUP2015] STEREO (ILL, France) L ≃ 8-12m [arXiv:1602.00568] SoLid (SCK-CEN, Belgium) L ≃ 5-8m [arXiv:1510.07835] Neutrino-4 (RIAR, Russia) L ≃ 6-11m [JETP 121 (2015) 578] PROSPECT (ORNL, USA) L ≃ 7-12m [arXiv:1512.02202] DANSS (Kalinin, Russia) L ≃ 10-12m [arXiv:1606.02896] NEOS (Hanbit, Korea) L ≃ 25m [Oh@WIN2015]

  • C. Giunti − Oscillations Beyond Three-Neutrino Mixing − Neutrino 2016 − 5 July 2016 − 44/37
slide-45
SLIDE 45

¯ νµ → ¯ νe and νµ → νe Appearance

sin22ϑeµ ∆m41

2 [eV2]

+

10−3 10−2 10−1 1 10−2 10−1 1 10 102

99% CL LSND MiniBooNE KARMEN NOMAD BNL−E776 ICARUS OPERA νµ → νe 90% CL 95% CL 99% CL

  • C. Giunti − Oscillations Beyond Three-Neutrino Mixing − Neutrino 2016 − 5 July 2016 − 45/37
slide-46
SLIDE 46

Origin of Appearance Signal

Without LSND Without MiniBooNE

sin22ϑeµ ∆m41

2 [eV2]

10−4 10−3 10−2 10−1 10−1 1 10

+ +

10−4 10−3 10−2 10−1 10−1 1 10

3+1 − GLO−noLSND 1σ 2σ 3σ 3σ DIS APP

sin22ϑeµ ∆m41

2 [eV2]

10−4 10−3 10−2 10−1 10−1 1 10

+ +

10−4 10−3 10−2 10−1 10−1 1 10

3+1 − GLO−noMB 1σ 2σ 3σ 3σ DIS APP

Best Fit: ∆m2

41 = 1.6 eV2

|Ue4|2 = 0.022 |Uµ4|2 = 0.0080 GoF = 13% (χ2

min/NDF = 289.7/264)

GoFPG = 0.5% (χ2/NDF = 10.7/2) GoFnull = 7% (χ2/NDF = 302.7/267) ∆χ2/NDF = 13.0/3 (≈ 2.8σ) Best Fit: ∆m2

41 = 1.6 eV2

|Ue4|2 = 0.028 |Uµ4|2 = 0.014 GoF = 16% (χ2

min/NDF = 251.2/230)

GoFPG = 5% (χ2/NDF = 6.2/2) GoFnull = 0.2% (χ2/NDF = 299.2/233) ∆χ2/NDF = 48.1/3 (≈ 6.4σ)

  • C. Giunti − Oscillations Beyond Three-Neutrino Mixing − Neutrino 2016 − 5 July 2016 − 46/37