data Concha Gonzalez-Garcia ν Global analysis of · Global analysis of ν data Concha...

Global analysis of ν data Concha Gonzalez-Garcia

GLOBAL ANALYSIS OF NEUTRINO

OSCILLATION DATA

Concha Gonzalez-Garcia

(YITP Stony Brook & ICREA U. Barcelona )

Recent Developments in Neutrino Physics and Astrophysics

Gran Sasso, Sept 2017

http://www.nu-fit.org


GLOBAL ANALYSIS OF NEUTRINO DATA

Concha Gonzalez-Garcia

( YITP Stony Brook & ICREA U. Barcelona )

Determination of 3ν Lepton Flavour Parameters

Matter Potential/Non-standard Neutrino Interactions


Neutrinos in the Standard Model

The SM is a gauge theory based on the symmetry group

SU(3)C × SU(2)L × U(1)Y ⇒ SU(3)C × U(1)EM

With three generation of fermions

(1, 2)− 12

(3, 2) 16

(1, 1)−1 (3, 1) 23(3, 1)− 1

3

(

νee

)

L

(

ui

di

)

LeR ui

R diR(

νµµ

)

L

(

ci

si

)

LµR ciR siR

(

νττ

)

L

(

ti

bi

)

LτR tiR biR

Three and only three

There is no νR


Neutrinos in the Standard Model

The SM is a gauge theory based on the symmetry group

SU(3)C × SU(2)L × U(1)Y ⇒ SU(3)C × U(1)EM

With three generation of fermions

(1, 2)− 12

(3, 2) 16

(1, 1)−1 (3, 1) 23(3, 1)− 1

3

(

νee

)

L

(

ui

di

)

LeR ui

R diR(

νµµ

)

L

(

ci

si

)

LµR ciR siR

(

νττ

)

L

(

ti

bi

)

LτR tiR biR

Three and only three

There is no νR⇒Accidental global symmetry: B × Le × Lµ × Lτ (hence L = Le + Lµ + Lτ )⇒

ν strictly massless


• By 2017 we have observed with high (or good) precision:

∗ Atmospheric νµ & ν̄µ disappear most likely to ντ (SK,MINOS, ICECUBE)

∗ Accel. νµ & ν̄µ disappear at L ∼ 300/800 Km (K2K, T2K, MINOS, NOνA)

∗ Some accelerator νµ appear as νe at L ∼ 300/800 Km ( T2K, MINOS,NOνA)

∗ Solar νe convert to νµ/ντ (Cl, Ga, SK, SNO, Borexino)

∗ Reactor νe disappear at L ∼ 200 Km (KamLAND)

∗ Reactor νe disappear at L ∼ 1 Km (D-Chooz, Daya Bay, Reno)

All this implies that Lα are violated

and There is Physics Beyond SM









All this implies that Lα are violated

and There is Physics Beyond SM

• The starting path:

Precise determination of the low energy parametrization


The New Minimal Standard Model

• Minimal Extension to allow for LFV ⇒ give Mass to the Neutrino

∗ Introduce νR AND impose L conservation ⇒ Dirac ν 6= νc:

L = LSM −MννLνR + h.c.

∗ NOT impose L conservation ⇒ Majorana ν = νc

L = LSM − 12MννLν

CL + h.c.

_ _








CL + h.c.

• The charged current interactions of leptons are not diagonal (same as quarks)

g√2W+

µ

∑

ij

(

U ijLEP ℓi γµ Lνj + U ij

CKM U i γµ LDj)

+ h.c.

j

W+

l_

i

ν

W+

_

i

uj

d








CL + h.c.

• The charged current interactions of leptons are not diagonal (same as quarks)

g√2W+

µ

∑

ij

(

U ijLEP ℓi γµ Lνj + U ij

CKM U i γµ LDj)

+ h.c.

• In general for N = 3 + s massive neutrinos ULEP is 3×N matrix

ULEPU†LEP = I3×3 but in general U †

LEPULEP 6= IN×N

• ULEP: 3 + 3s angles + 2s+ 1 Dirac phases + s+ 2 Majorana phases

Global analysis of ν data Concha Gonzalez-Garciaν Mass Oscillations in Vacuum

• If neutrinos have mass, a weak eigenstate |να〉 produced in lα + N →να + N ′

is a linear combination of the mass eigenstates (|νi〉) : |να〉=n∑

i=1

Uαi |νi〉

• After a distance L it can be detected with flavour β with probability

Pαβ = δαβ − 4n∑

j 6=i

Re[U⋆αiUβiUαjU

⋆βj ]sin

2

(

∆ij

2

)

+ 2∑

j 6=i

Im[U⋆αiUβiUαjU

⋆βj ]sin (∆ij)

∆ij

2 =(Ei−Ej)L

2 = 1.27(m2

i−m2j )

eV2

L/E

Km/GeV

No information on ν mass scale nor Majorana versus Dirac

Global analysis of ν data Concha Gonzalez-Garciaν Mass Oscillations in Vacuum

• If neutrinos have mass, a weak eigenstate |να〉 produced in lα + N →να + N ′

is a linear combination of the mass eigenstates (|νi〉) : |να〉=n∑

i=1

Uαi |νi〉

• After a distance L it can be detected with flavour β with probability

Pαβ = δαβ − 4n∑

j 6=i

Re[U⋆αiUβiUαjU

⋆βj ]sin

2

(

∆ij

2

)

+ 2∑

j 6=i

Im[U⋆αiUβiUαjU

⋆βj ]sin (∆ij)

∆ij

2 =(Ei−Ej)L

2 = 1.27(m2

i−m2j )

eV2

L/E

Km/GeV

No information on ν mass scale nor Majorana versus Dirac

• When osc between 2-ν dominates:Pαα = 1− Posc Disappear

Posc = sin2(2θ) sin2(

1.27∆m2LE

)

Appear

⇒ No info on sign of ∆m2 and θ octant


Matter Effects

• If ν cross matter regions (Sun, Earth...) it interacts coherently

– But Different flavours

have different interactions :

⇒ Effective potential in ν evolution : Ve 6= Vµ,τ ⇒ ∆V ν = −∆V ν̄ =√2GFNe

−i ∂∂x

(

νe

νX

)

=

[

[

−(

Ve − VX − ∆m2

4E cos 2θ ∆m2

4E sin 2θ∆m2

4E sin 2θ ∆m2

4E cos 2θ

)](

νe

νX

)

⇒ Modification of mixing angle and oscillation wavelength (MSW)


Matter Effects

• If ν cross matter regions (Sun, Earth...) it interacts coherently

– But Different flavours

have different interactions :

⇒ Effective potential in ν evolution : Ve 6= Vµ,τ ⇒ ∆V ν = −∆V ν̄ =√2GFNe

−i ∂∂x

(

νe

νX

)

=

[

[

−(

Ve − VX − ∆m2

4E cos 2θ ∆m2

4E sin 2θ∆m2

4E sin 2θ ∆m2

4E cos 2θ

)](

νe

νX

)

⇒ Modification of mixing angle and oscillation wavelength (MSW)

• Mass difference and mixing in matter:

∆m2m =

√

(∆m2 cos 2θ − 2E∆V )2 + (∆m2 sin 2θ)2

sin(2θm) =∆m2 sin(2θ)

∆m2mat

⇒ For solar ν′s in adiabatic regime

Pee = 12[1 + cos(2θm) cos(2θ)]

Dependence on θ octant

⇒ In LBL terrestrial experiments

Dependence on sign of ∆m2

and θ octant









• Confirmed:

SK

MINOS/T2K/NOvA

(km/MeV)eν/E0L

20 30 40 50 60 70 80 90 100

Surv

ival

Pro

babi

lity

0

0.2

0.4

0.6

0.8

1

eνData - BG - Geo Expectation based on osci. parameters

determined by KamLAND

KamLAND

Daya-Bay/RENO/D-Chooz

Vacuum oscillation L/E pattern with 2 frequencies

MSW conversion in Sun

Global analysis of ν data Concha Gonzalez-Garcia3ν Flavour Parameters

• For for 3 ν’s : 3 Mixing angles + 1 Dirac Phase + 2 Majorana Phases

ULEP =

1 0 0

0 c23 s23

0 −s23 c23

c13 0 s13eiδcp

0 1 0

−s13e−iδcp 0 c13

c21 s12 0

−s12 c12 0

0 0 1

eiη1 0 0

0 eiη2 0

0 0 1

• Two Possible Orderings

M

sola

r

sola

r

atm

os

m m 1 3

∆ 2

∆ m

2

m 3

m 2

∆ m

m 1

m 2

NORMAL INVERTED

2

Global analysis of ν data Concha Gonzalez-Garcia3ν Flavour Parameters

• For for 3 ν’s : 3 Mixing angles + 1 Dirac Phase + 2 Majorana Phases

ULEP =

1 0 0

0 c23 s23

0 −s23 c23

c13 0 s13eiδcp

0 1 0

−s13e−iδcp 0 c13

c21 s12 0

−s12 c12 0

0 0 1

eiη1 0 0

0 eiη2 0

0 0 1

• Two Possible Orderings

M

sola

r

sola

r

atm

os

m m 1 3

∆ 2

∆ m

2

m 3

m 2

∆ m

m 1

m 2

NORMAL INVERTED

2

Experiment Dominant Dependence Important Dependence

Solar Experiments → θ12 ∆m221 , θ13

Reactor LBL (KamLAND) →∆m221 θ12 , θ13

Reactor MBL (Daya Bay, Reno, D-Chooz) → θ13 ∆m2atm

Atmospheric Experiments → θ23 ∆m2atm, θ13 ,δcp

Acc LBL νµ Disapp (Minos,T2K,NOvA) →∆m2atm θ23

Acc LBL νe App (Minos,T2K,NOvA) → θ13 δcp , θ23

×

Global analysis of ν data Concha Gonzalez-Garcia3 ν Flavour Parameters: Status Spring 2017

Global 6-parameter fit http://www.nu-fit.orgEsteban, Maltoni, Martinez-Soler, Schwetz, MCG-G ArXiv:1611:01514

★

0.2 0.25 0.3 0.35 0.4

sin2 θ12

6.5

7

7.5

8

8.5∆m

2 21 [1

0-5 e

V2 ]

★

0.015 0.02 0.025 0.03

sin2 θ13

★

0.015

0.02

0.025

0.03

sin2

θ 13

★

0

90

180

270

360

δ CP

0.3 0.4 0.5 0.6 0.7

sin2 θ23

-2.8

-2.6

-2.4

-2.2

★

2.2

2.4

2.6

2.8

∆m2 32

[1

0-3 e

V2 ]

∆m

2 31

★

NuFIT 3.0 (2016)

Global analysis of ν data Concha Gonzalez-Garcia3 ν Flavour Parameters: Status Spring 2017

Global 6-parameter fit http://www.nu-fit.orgEsteban, Maltoni, Martinez-Soler, Schwetz, MCG-G ArXiv:1611:01514

★

0.2 0.25 0.3 0.35 0.4

sin2 θ12

6.5

7

7.5

8

8.5∆m

2 21 [1

0-5 e

V2 ]

★

0.015 0.02 0.025 0.03

sin2 θ13

★

0.015

0.02

0.025

0.03

sin2

θ 13

★

0

90

180

270

360

δ CP

0.3 0.4 0.5 0.6 0.7

sin2 θ23

-2.8

-2.6

-2.4

-2.2

★

2.2

2.4

2.6

2.8

∆m2 32

[1

0-3 e

V2 ]

∆m

2 31

★

NuFIT 3.0 (2016)

θ23 6= 45

θ23 < 45 ?

N/I

?

δcp

Global analysis of ν data Concha Gonzalez-Garcia3 ν Flavour Parameters: Status Sept 2017

Global 6-parameter fit http://www.nu-fit.orgEsteban, Maltoni, Martinez-Soler, Schwetz, MCG-G effect OF T2K (2017) VERY PRELIMINARY

0.2 0.25 0.3 0.35 0.4

sin2 θ12

0

5

10

15

∆χ2

6.5 7 7.5 8 8.5

∆m221 [10

-5 eV

2]

0.3 0.4 0.5 0.6 0.7

sin2 θ23

0

5

10

15

∆χ2

-2.8 -2.6 -2.4 -2.2

∆m232 [10

-3 eV

2] ∆m

231

2.2 2.4 2.6 2.8

0.015 0.02 0.025 0.03

sin2 θ13

0

5

10

15

∆χ2

0 90 180 270 360δCP

NOIO

NuFIT 3.0 (2016) +T2K(2017) VERY PRELIMINARY

★

0.2 0.25 0.3 0.35 0.4

sin2 θ12

6.5

7

7.5

8

∆m2 21

[10-5

eV

2 ]

★

0.015 0.02 0.025 0.03

sin2 θ13

★

0.015

0.02

0.025

0.03

sin2

θ 13

★

0

90

180

270

360

δ CP

0.3 0.4 0.5 0.6 0.7

sin2 θ23

-2.8

-2.6

-2.4

-2.2

★

2.2

2.4

2.6

2.8

∆m2 32

[1

0-3 e

V2 ]

∆m

2 31

★

NuFIT 3.0 (2016) +T2K (2017) VERY PRELIMINARY


3 ν Analysis: “12” Sector

•∆m213 ≫ E/L⇒ P 3ν

ee = c413P2ν + s413

i ddt

(

νe

νa

)

=

[

∆m221

4E

(

−cos 2θ12 sin 2θ12

sin 2θ12 cos 2θ12

)

±√2GFNe

(

c213 0

0 0

)](

νe

νa

)

Pee ≃

SolarHigh E : c413 sin2 2θ12

Solar Low E : c413(

1− sin2 2θ12/2)

Kam : c413

(

1− sin2 2θ12 sin2 ∆m2

21L4E

)


3 ν Analysis: “12” Sector

•∆m213 ≫ E/L⇒ P 3ν

ee = c413P2ν + s413

i ddt

(

νe

νa

)

=

[

∆m221

4E

(

−cos 2θ12 sin 2θ12

sin 2θ12 cos 2θ12

)

±√2GFNe

(

c213 0

0 0

)](

νe

νa

)

Pee ≃


Solar Low E : c413(

1− sin2 2θ12/2)

Kam : c413

(

1− sin2 2θ12 sin2 ∆m2

21L4E

)

∗ Solar region determined by High E data

∗ Param’s

{

θ12 SNO most sensitivity

∆m221 by KamLAND

With θ13 = 0

★

★

0

5

10

15

20

∆m2 21

[10-5

eV

2 ]

Cl + Ga + BX-lo

★

★

SK (1 + 2 + 3 + 4)

★

★

0.1 0.2 0.3 0.4

sin2θ12

0

5

10

15

20

∆m2 21

[10-5

eV

2 ]

SNO

0.2

0.5

★

★

0.1 0.2 0.3 0.4 0.5

sin2θ12

SK + SNO

[3σ]


3 ν Analysis: “12” Sector and θ13

• For θ13 = 0

sin2 θ12 =

{

0.3 From Solar

0.325 From KLAND

• When θ13 increases

Pee ≃


Solar Low E : c413(

1− sin2 2θ12/2)

Kam : c413

(

1− sin2 2θ12 sin2 ∆m2

21L

4E

)

⇒ KamLAND region shifts left

⇒ Solar slight shifts right (due to High E)


3 ν Analysis: “12” Sector and θ13

• For θ13 ≃ 9◦

⇒ Good match of best fit θ12

⇒ Residual tension on ∆m221

• When θ13 increases

Pee ≃


Solar Low E : c413(

1− sin2 2θ12/2)

Kam : c413

(

1− sin2 2θ12 sin2 ∆m2

21L

4E

)

⇒ KamLAND region shifts left

⇒ Solar slight shifts right (due to High E)

★

0.1 0.2 0.3 0.4 0.5

sin2θ12

0

0.05

0.1

0.15

0.2

sin2 θ 13

[3σ]

0 0.05 0.1

sin2θ13

0

5

10

15

∆χ2

KamLAND

Sol

ar

Sol

ar +

Kam

LAN

D∆m221 = free∆m

221 = 7.5 × 10

-5 eV

2

Global analysis of ν data Concha Gonzalez-Garcia3 ν Analysis: ∆m

221 KamLAND vs SOLAR

For θ13 ≃ 9◦ θ12 OK. But residual tension on ∆m212

❍❍

✵�✁ ✵�✁✂ ✵�✄ ✵�✄✂ ✵�☎

s✆✝✷

q✶✷

✵✁

☎✻

✽✞✵

✞✁✞☎

❉♠✟ ✟✠

✥✡☛✲✺

☞✌✟ ❪

q✶✍ ✎ ✏✑✒✓

✁ ☎ ✻ ✽ ✞✵

✔✕✷

✷✶ ✖✗✘✙✚

✛✜✷

✢

✵✁

☎✻

✽✞✵

✞✁❉✣✟

●✤✦✧

❆●✤✤★✦

❑✩✪✫❆✬✭

◆✮✯✰✱ ✳✴✸ ✹✼✸✾✿❀

Global analysis of ν data Concha Gonzalez-Garcia3 ν Analysis: ∆m

221 KamLAND vs SOLAR

For θ13 ≃ 9◦ θ12 OK. But residual tension on ∆m212

★

★

0.2 0.25 0.3 0.35 0.4

sin2θ12

0

2

4

6

8

10

12

14

∆m2 21

[10−5

eV

2 ]

θ13 = 8.5°

2 4 6 8 10

∆m221 [10

−5 eV

2]

0

2

4

6

8

10

12

∆χ2

GS98 w/o D/NGS98KamLAND

NuFIT 2.1 (2016)

Tension related to: a)“too large” of Day/Night at SK

0.2 0.3 0.4 0.6 1 1.4 2 3 4 6 10 14Eν

0.2

0.3

0.4

0.5

0.6

0.7

< P

ee >

ppBorexino (

7Be)

Borexino (pep)

Super-K

SNO

Borexino (8B)

Best fit (SOLAR only)

Best fit (SOLAR + KamLAND)

b) smaller-than-expected

low-E turn up from MSW

at best global fit

Modified matter potential? More latter . . .


3 ν Analysis: θ23

• Best determined in νµ and ν̄µ disapperance in LBL

Pµµ ≃ 1− (c413sin2 2θ23 + s223 sin

2 2θ13) sin2

(

∆m231L

4E

)

+O(∆m221)

• At osc maximum sin2(

∆m231L

4E

)

= 1⇒ Pµµ ≃ 0 for θ23 ≃ π4

T2K νµ → νµ T2K ν̄µ → ν̄µ NOvA νµ → νµ


3 ν Analysis: θ23

• Best determined in νµ and ν̄µ disapperance in LBL

Pµµ ≃ 1− (c413sin2 2θ23 + s223sin

2 2θ13) sin2

(

∆m231L

4E

)

+O(∆m221)

• Allowed regions by the different experiments:

In making this figure θ13 is constrained by prior from reactor data

Caution: Not the same using θ13 reactor prior than combining with reactor results

(because of ∆m232 in reactors)


∆m223 in LBL vs Reactors

• At LBL determined in νµ and ν̄µ disappearance spectrum

Pµµ ≃ 1− (c413sin2 2θ23 + s223sin

2 2θ13) sin2

(

∆m231L

4E

)

+O(∆m221)

• At MBL Reactors (Daya-Bay, Reno, D-Chooz) determined in ν̄e disapp spectrum

Pee ≃ 1−sin2 2θ13 sin2

(

∆m2eeL

4E

)

−c413 sin2 2θ12 sin

2

(

∆m221L

4E

)

∆m2ee ≃ |∆m2

32| ± c212∆m221 ≃ |∆m2

32| ± 0.05× 10−3 eV2

Nunokawa,Parke,Zukanovich (2005)


∆m223 in LBL vs Reactors: Consistency

• At LBL determined in νµ and ν̄µ disappearance spectrum

• At MBL Reactors (Daya-Bay, Reno, D-Chooz) determined in ν̄e disapp spectrum

LBL νµ disappearance REAC νe disappearance

2

2.2

2.4

2.6

2.8

3

3.2

∆m2 32

[1

0-3 e

V2 ]

∆m

2 31

NOvA

T2K

MINOS

DeepCore

0.3 0.4 0.5 0.6 0.7

sin2θ23

-3.2

-3

-2.8

-2.6

-2.4

-2.2

-2

reactors(no DB)

DayaBay

0.015 0.02 0.025 0.03

sin2θ13

[1σ, 2σ]

Sept (2017) PRELIM

– Consistent values of |∆m232|

– Hint for non-maximal θ23

driven by NOνA and MINOS

– T2K (2017) slight fav θ23 > 45


3 ν Analysis: Reactor Flux anomaly and θ13

• The reactor ν̄e fluxes was recalculated about 6 yrs ago

T.A. Mueller et al.,[arXiv:1101.2663].;P. Huber, [arXiv:1106.0687].

• Both found higher fluxes ∼ 3.5 %

⇒ negative reactor experiments

at short baselines (RSBL) indeed

observed a deficit

0.7

0.8

0.9

1

1.1

1.2

1.3

obse

rved

/ pr

edic

ted

oldnew

Bug

ey 4

RO

VN

O

Bug

ey 3

Goe

sgen

ILL

Kra

snoy

arsk

} } } 235 U

238 U

239 Pu

241 Pu

• For 3ν analysis a consistent approach (T. Schwetz et. al. [arXiv:1103.0734]):

– Fit oscillation parameters and reactor fluxes simultaneously

– Use calculated fluxes (a) or RSBL data (b) as priors

Difference at . 0.3σ level

χ2min,a − χ2

min,b ∼ 7


Leptonic CP Violation

• Leptonic /CP ⇒ Pνα→νβ6= Pν̄α→ν̄β

:

Pνα→νβ− Pν̄α→ν̄β

∝ J with J = Im(Uα1U∗α2Uβ2U

∗β1) = Jmax

LEP,CP sin δCP

JmaxLEP,CP = 1

8c13 sin2 2θ13 sin2 2θ23 sin

2 2θ12


Leptonic CP Violation


:



∗β1) = Jmax

LEP,CP sin δCP

JmaxLEP,CP = 1


2 2θ12

• Maximum Allowed Leptonic CPV:

0.025 0.03 0.035 0.04

JCPmax

= c12 s12 c23 s23 c213 s13

0

5

10

15

∆χ2

NOIO

Sept (2017) PRELIMJmaxLEP,CP = (3.29± 0.07)× 10−2

to compare with

JCKM,CP = (3.04± 0.21)× 10−5

⇒ Leptonic CPV may be largest CPV

in New Minimal SM

if sin δCP not too small


Leptonic CP Phase

• Leptonic CPV Phase: Mainly from νµ → νe in LBL (complicated by matter effects)

Pµe ≃ s223 sin2 2θ13

(

∆31

B∓

)2

sin2(

B∓ L2

)

+ 8 JmaxLEP,CP

∆12

VE

∆31

B∓sin(

VEL2

)

sin(

B∓L2

)

cos(

∆31L2 ± δCP

)

∆ij =∆m2

ij

2E B± = ∆31 ± VE JmaxLEP,CP = 1


2 2θ12

Before T2K (2017)– Best fit δCP ∼ 270◦

– CP conserv at 70% (NO), 97% (IO)

– Driven by “fluctuation” in T2K

⇒ One concluded :

Significance may not grow soon


Leptonic CP Phase:T2K 2017

νe

νe

νe

νµ

νµ

M. Hartz, KeK colloquim, August 2017


Leptonic CP Phase

Including T2K (2017) PRELIMINARY

0 90 180 270 360δCP

0

5

10

15

20

25

30

35

∆χ2

0 90 180 270 360δCP

Rea + MinosRea + NOvARea + T2KRea + LBL-comb

Sept (2017) PRELIM

IO NO

– Best fit at δCP ∼ 240◦

– CP conserv at 95% (NO)

– 15◦–160◦ disfavoured at ∆χ2 > 9

– Sill more than expected sensitiv in T2K

–χ2min,IO − χ2

min,NO ≃ 3

Global analysis of ν data Concha Gonzalez-GarciaLeptonic CP Violation


:



∗β1) = Jmax

LEP,CP sin δCP

• Leptonic CPV Phase: Mainly from νµ → νe in LBL (complicated by matter effects)

Pµe ≃ s223 sin2 2θ13

(

∆31

B∓

)2

sin2(

B∓ L2

)

+ 8 JmaxLEP,CP

∆12

VE

∆31

B∓sin(

VEL2

)

sin(

B∓L2

)

cos(

∆31L2 ± δCP

)

∆ij =∆m2

ij

2E B± = ∆31 ± VE JmaxLEP,CP = 1


2 2θ12

• Leptonic Jarlskog Invariant : Best fit JLEP,CP = −0.030

-0.04 -0.02 0 0.02 0.04

JCP = JCPmax

sinδCP

0

5

10

15

∆χ2

NOIO

Sep (2017) PRELIM


Neutrino Mass Scale

Single β decay : Dirac or Majorana ν mass modify spectrum endpoint

νm

K (T)

QT

m2νe

=∑

m2j |Uej |2 =

NO : m2ℓ +∆m2

21c213s

212 +∆m2

31s213

IO : m2ℓ +∆m2

21c213s

212 −∆m2

31c213

Present bound: mνe≤ 2.2 eV (at 95 % CL)

Katrin (20XX???) Sensitivity to mνe∼ 0.2 eV

ν-less Double-β decay: ⇔ Majorana ν′s

n

p

W

n

p

Wν

e−

e−

If mν only source of ∆L T 0ν1/2 = me

G0ν M2nucl m

2ee

mee = |∑

U2ejmj |

=∣

∣c213c212m1 e

iη1 + c213s212m2 e

iη2 + s213m3 e−iδCP

∣

∣

= f(mℓ, order,maj phases)

Present Bounds: mee < 0.06−0.76 eV

COSMO for Dirac or Majoranamν affect growth of structures

∑

mi=

NO :√

m2ℓ +

√

∆m221 +m2

ℓ +√

∆m231 +m2

ℓ

IO√

m2ℓ +

√

−∆m231 −∆m2

21 −m2ℓ +

√

−∆m231 −m2

ℓ

Global analysis of ν data Concha Gonzalez-GarciaNeutrino Mass Scale: The Cosmo-Lab Connection

Global oscillation analysis

⇒ Correlations mνe, mee and

∑

mν

(Fogli et al (04))

Nufit (95%)

Width due to range in oscillation parameters very narrow

Lower bound on∑

mi depends on ordering

Wide band due to unknown Majorana phases ⇒Possible Det of Maj phases?

Global analysis of ν data Concha Gonzalez-GarciaNeutrino Mass Scale: The Cosmo-Lab Connection

Global oscillation analysis

⇒ Correlations mνe, mee and

∑

mν

(Fogli et al (04))

Nufit (95%)

Lower bound on∑

mi depends on ordering

Precision determination/bound of∑

mi can give infor-

mation on ordering ?Hannestad, Schwetz 1606.04691, Simpson etal 1703.03425, Capozzi

etal 1703.04471 . . .

Or much ado about nothing?

Cosmo data will only add to N/I likelihood

when accuracy on Σmν better than 0.02 eV

(to see a 2σ N/I difference between 0.06 and 0.1)

Hannestad, Schwetz 1606.04691


Beyond 3 ν Oscillations?

• Three-flavour oscillation scenario very robust

• Most extensions: VLI, Non-Unitarity, CPT viol, eV sterile neutrinos . . .

Only allowed to be subdominant

• What about non-standard interactions?

Global analysis of ν data Concha Gonzalez-GarciaNon Standard ν Interactions

• Including non-standard neutrino NC interactions with fermion f

LNSI = −2√2GF ε

fPαβ (ν̄αγ

µLνβ)(f̄γµPf) , P = L,R

• In flavour basis ~ν = (νe, νµ, µτ )T the neutrino evolution eq.:

id

dx~ν = Hν~ν with Hν = Hvac +Hmat and H ν̄ = (Hvac −Hmat)

∗

Hmat =√2GFNe(r)

1 0 0

0 0 0

0 0 0

+

√2GFNe(r)

εee εeµ εeτ

ε∗eµ εµµ εµτ

ε∗eτ ε∗µτ εττ

εαβ(r) ≡∑

f=ued

Nf (r)

Ne(r)εfVαβ ⇒ 3ν evolution depends on 6 (vac) + 8 per f (mat)

Global analysis of ν data Concha Gonzalez-GarciaNon Standard ν Interactions

• Including non-standard neutrino NC interactions with fermion f

LNSI = −2√2GF ε

fPαβ (ν̄αγ

µLνβ)(f̄γµPf) , P = L,R

• In flavour basis ~ν = (νe, νµ, µτ )T the neutrino evolution eq.:

id

dx~ν = Hν~ν with Hν = Hvac +Hmat and H ν̄ = (Hvac −Hmat)

∗

Hmat =√2GFNe(r)

1 0 0

0 0 0

0 0 0

+

√2GFNe(r)

εee εeµ εeτ

ε∗eµ εµµ εµτ

ε∗eτ ε∗µτ εττ

εαβ(r) ≡∑

f=ued

Nf (r)

Ne(r)εfVαβ ⇒ 3ν evolution depends on 6 (vac) + 8 per f (mat)

⇒ Parameters degeneracies (some well-known but being rediscovered lately . . . )

In particular CPT ⇒ invariance under simultaneously:

θ12 ↔ π2− θ12 ,

∆m231 → −∆m2

32 ,

δ → π − δ ,

(εee − εµµ) → −(εee − εµµ)− 2 ,

(εττ − εµµ) → −(εττ − εµµ) ,

εαβ → −ε∗αβ (α 6= β) ,


Matter Potential/NSI in ATM and LBL

• Weakest contraints when

2 equal eigenvalues of HmatFriedland, Lunardini,Maltoni 04

• General parametrization for this case

Hmat = QrelUmatDmatU†matQ

†rel

Qrel = diag(

eiα1 , eiα2 , e−iα1−iα2)

,

Umat = R12(ϕ12)R13(ϕ13) ,

Dmat =√2GFNe(r)diag(ε, 0, 0)


Matter Potential/NSI in ATM and LBL

• Weakest contraints when

2 equal eigenvalues of HmatFriedland, Lunardini,Maltoni 04

• General parametrization for this case

Hmat = QrelUmatDmatU†matQ

†rel

Qrel = diag(

eiα1 , eiα2 , e−iα1−iα2)

,

Umat = R12(ϕ12)R13(ϕ13) ,

Dmat =√2GFNe(r)diag(ε, 0, 0)

So

εee − εµµ = ε (cos2 ϕ12 − sin2 ϕ12) cos2 ϕ13 − 1εττ − εµµ = ε (sin2 ϕ13 − sin2 ϕ12 cos2 ϕ13)

εeµ = −ε cosϕ12 sinϕ12 cos2 ϕ13 ei(α1−α2)

εeτ = −ε cosϕ12 cosϕ13 sinϕ13 ei(2α1+α2)

εµτ = ε sinϕ12 cosϕ13 sinϕ13 ei(α1+2α2)

No bound on ε from ATM+LBL

★

-1

-0.5

0

0.5

1

(1 +

ε ee−

ε µµ)

/ ε

★

-1

-0.5

0

0.5

1

(εττ

−ε µµ

) / ε

★

-0.5

-0.25

0

0.25

0.5

ε eµ /

ε

★

-0.5

-0.25

0

0.25

0.5

ε eτ /

ε

★

-100 -10 -1 -0.1 0 0.1 1 10 100ε

-0.5

-0.25

0

0.25

0.5

ε µτ /

ε

Maltoni, MCG-G, Salvado ArXiv:1103.4265

Global analysis of ν data Concha Gonzalez-GarciaMatter Potential/NSI in Solar and KamLAND

• In |∆m231| → ∞ : Pee = c413Peff + s413

Heffmat =

√2GFNe(r)

(

c213 0

0 0

)

+√2GF

∑

f

Nf (r)

(

−εfD εfNεf∗N εfD

)

εfD = c13s13Re[

eiδCP

(

s23 εfVeµ + c23 ε

fVeτ

)]

−(

1 + s213

)

c23s23Re(

εfVµτ

)

−c2132

(

εfVee − εfVµµ

)

+s223−s213c

223

2

(

εfVττ − εfVµµ

)

εfN = c13(

c23 εfVeµ − s23 ε

fVeτ

)

+s13e−iδCP

[

s223 εfVµτ − c223 ε

fV ∗µτ

+c23s23(


)]

Global analysis of ν data Concha Gonzalez-GarciaMatter Potential/NSI in Solar and KamLAND

• In |∆m231| → ∞ : Pee = c413Peff + s413

Heffmat =

√2GFNe(r)

(

c213 0

0 0

)

+√2GF

∑

f

Nf (r)

(

−εfD εfNεf∗N εfD

)

εfD = c13s13Re[

eiδCP

(

s23 εfVeµ + c23 ε

fVeτ

)]

−(

1 + s213

)

c23s23Re(

εfVµτ

)

−c2132

(

εfVee − εfVµµ

)

+s223−s213c

223

2

(


)

εfN = c13(

c23 εfVeµ − s23 ε

fVeτ

)

+s13e−iδCP

[

s223 εfVµτ − c223 ε

fV ∗µτ

+c23s23(


)]

• LMA-D (θ12 > π4 ) allowed

Miranda etal hep-ph/0406280

★

0.2 0.3 0.4 0.5 0.6 0.7 0.8

sin2θ12

6

6.5

7

7.5

8

8.5

∆m2 21

[10-5

eV

2 ]

f=u

★

-0.8 -0.4 0 0.4 0.8 1.2

εfD

-1

-0.5

0

0.5

1

εf N

f=u

★

0.2 0.3 0.4 0.5 0.6 0.7 0.8

sin2θ12

f=d

★

-0.8 -0.4 0 0.4 0.8 1.2

εfD

f=d

★ATM+LBL [90%, 3σ]

SOLAR+KamLAND [90%, 95%, 99%, 3σ]sin

2θ13=0.023

M.C G-G, M.Maltoni 1307.3092


NSI: Bounds/Degeneracies from/in Oscillation dataM.C G-G, M.Maltoni 1307.3092

– Bounds O(1− 10%)

– Except εq,Vee − εq,Vµµ



– Bounds O(1− 10%)


0.2 0.3 0.4 0.6 1 1.4 2 3 4 6 10 14

Eν

0.2

0.3

0.4

0.5

0.6

0.7

< P

ee >

ppBorexino (

7Be)

Borexino (pep)

Super-K

SNO

Borexino (8B)

sin2θ12 ∆m

221 εf

D εfN

0.310.300.320.310.31

7.407.257.357.457.40

−0.22−0.12−0.14−0.14

−0.30−0.16−0.04−0.04

− −f

−udud

LMA: Improved fit

to Solar+KamLAND



– Bounds O(1− 10%)


Degenerate solution LMA-D (θ12 > 45◦)

Miranda,Tortola, Valle, hep-ph/0406280

Cannot be resolved with osc-experiments

Requires NC scattering experiments

Coloma etal 1701.04828

Requires NSI ∼ GF (light mediators?)

Farzan 1505.06906, and Shoemaker 1512.09147


COHERENT EXPERIMENT

Science 2017 [ArXiv:1708.01294]


NSI: Combination with COHERENT dataColoma, MCGG, Maltoni,Schwetz ArXiv:1708.02899

• COHERENT has detected for first time Coherent νN scattering 1708.01294:

142(1± 0.28(sys)) observed events over a steady bck of 405

136(SM) + 6(1± 0.25(sys) beam-on bck) expected

• In presence of NSI: NNSI(ε) = γ[

fνeQ2

we(ε) + (fνµ+ fν̄µ

)Q2wµ(ε)

]

Q2wα ∝

[

Z(gVp + 2εu,Vαα + εd,Vαα ) +N(gVn + εu,Vαα + 2εd,Vαα )]2

+∑

β 6=α

[

Z(2εu,Vαβ + εd,Vαβ ) +N(εu,Vαβ + 2εd,Vαβ )]2

� ✁✂✄ ✁✂☎ ✁✂✆ ✁✂✝ ✁ ✁✂✝ ✁✂✆ ✁✂☎ ✁✂✄

✁✂✝✁✂�

✁✁✂�

✁✂✝✁✂✞

✁✂✆✁✂✟

✠✡✡☛☞✌

✍ ✎✎✏✑✒

✓✔✕-✖

✓✔✕







fνeQ2


)Q2wµ(ε)

]

Q2wα ∝

[


+∑

β 6=α

[


• Impact on LMA-D: Allowed COHERENT region vs LMA-D required range

�

-� -✁✂✄ -✁✂☎ -✁✂✆ -✁✂✝ ✁ ✁✂✝ ✁✂✆ ✁✂☎ ✁✂✄

-✁✂✝

-✁✂�✁

✁✂�✁✂✝

✁✂✞✁✂✆

✁✂✟

✠✡✡☛☞✌

✍ ✎✎✏✑✒

✓✔✕-✖

✓✔✕







fνeQ2


)Q2wµ(ε)

]

Q2wα ∝

[


+∑

β 6=α

[


• OSCILLATION + COHERENT ⇒ LMA-D excluded at more than 3.1 (3.6) σ

✵✺

✶✵✶✺

❉�✷ ❖✁✂✄☎✂❖✆✝✞✝✟✠✡

❢☛☞

✲✌ ✲✶ ✵ ✶

❡✍✎✏

✑✑✒ ❡✍✎✏

♠♠

✵✺

✶✵✶✺

❉�✷ ❖✁✂✄☎✂❖✆✝✞✝✟✠✡

✲✵✓✌✺ ✵ ✵✓✌✺

❡✍✎✏

tt✒ ❡✍✎✏

♠♠

✲✵✓✌ ✵ ✵✓✌

❡✍✎✏

✑♠

✲✵✓✺ ✵ ✵✓✺

❡✍✎✏

✑t

✲✵✓✵✺ ✵ ✵✓✵✺

❡✍✎✏

♠t

❢☛✔







fνeQ2


)Q2wµ(ε)

]

Q2wα ∝

[


+∑

β 6=α

[


• OSCILLAT+COHERENT bounds on NSI’s

✵✺

✶✵✶✺

❉�✷ ❖✁✂✰✂❖❈✄☎✄✆✝

❢✞✟

✲✶ ✵ ✶

❡✠✡☛

☞☞

✵✺

✶✵✶✺

❉�✷ ❖✁✂✰✂❖❈✄☎✄✆✝

✲✶ ✵ ✶

❡✠✡☛

♠♠

✲✶ ✵ ✶

❡✠✡☛

tt

❢✞✌

f = u f = d

ǫf,Vee [0.028, 0.60] [0.030, 0.55]

ǫf,Vµµ [−0.088, 0.37] [−0.075, 0.33]

ǫf,Vττ [−0.090, 0.38] [−0.075, 0.33]

ǫf,Veµ [−0.073, 0.044] [−0.07, 0.04]

ǫf,Veτ [−0.15, 0.13] [−0.13, 0.12]

ǫf,Vµτ [−0.01, 0.009] [−0.009, 0.008]


Summary

• 3ν oscillation:

Robust description of all confirmed oscillation data

CP phase: sin δCP < 0 favoured

CP conservation excluded at 2σ CL

Hint for NO emerging but still only ∆χ2 = 3

• Non-standard neutrino NC interactions:

Before august possible degeneracies in ordering and octact determination

New COHERENT results able to exclude LMA-Dark degeneracy

Bounds of OSC+COHERENT at the few % level.


Thank You


Thank You

Happy Birthday!!


Gauge Inv NSI and Lepton Mixing Non-Unitarity

• Take νL mixed with m HEAVY states ULEP = (Kl,3×3 , Kh,3×m) Schechter, Valle (1980)

And ULEPU†LEP = I3×3 but in general U †

LEPULEP 6= I(3+m)×(3+m)

• If m states are heavy (M >> Eν) oscillations measure KL,3×3 (not unitary)

or equivalently Kl ≃ (I + ǫ)U(θij, δ, ηi)


Gauge Inv NSI and Lepton Mixing Non-Unitarity

• Take νL mixed with m HEAVY states ULEP = (Kl,3×3 , Kh,3×m) Schechter, Valle (1980)

And ULEPU†LEP = I3×3 but in general U †

LEPULEP 6= I(3+m)×(3+m)

• If m states are heavy (M >> Eν) oscillations measure KL,3×3 (not unitary)

or equivalently Kl ≃ (I + ǫ)U(θij, δ, ηi)

• But this unitarity violation ⇒Flavour Changing Neutral Currents ≡ NSI’s

Flavour Violation in Charged Lepton Processes

Universality Violation of Charge Current . . .

• Constraints on these processes limit leptonic unitarity violation to

|KlK†l | =

0.9979− 0.9998 < 10−5 < 0.0021

< 10−5 0.9996− 1.0 < 0.0008

< 0.0021 < 0.0008 0.9947− 1.0

Antusch et al ArXiv:1407.6607

or equivalently |ǫαj | ≤ few× 10−3 ⇒Too small to have effect in oscillations Blennow etal 1609.08637

Unless NP is not that heavy (specific models Farzan 1505.06906, and Shoemaker


1512.09147)


3 ν Analysis: Ordering, δCP in ATM

• For θ31 6= 0 ATM sensitivity to

octant θ23 & ordering & δCP

Ne

N0e− 1 ≃ (r̄ c223 − 1)P2ν(∆m2

21, θ12) [∆m221 term]

+(r̄ s223 − 1)P2ν(∆m231, θ13) [θ13 term]

−2r̄ s13s23c23Re(A∗eeAµe) [δCP term]

r̄ ≡ Φ0µ/Φ

0e ≃ 2(subG), 2.6–4.6(multiG)

✵�✁ ✵�✂ ✵�✄ ✵�☎ ✵�✆

s✝✞✷

q✷✟

✵✄

✶✵✶✄

❉✠✡

✵ ✾✵ ✶☛✵ ☞✆✵ ✁☎✵

❞❈✌◆✍✱ ■✍ ✥✎✏ ✑✒✓

◆✍✱ ■✍ ✥✑✒✓

✔✕✖✗✘ ✙✚✛ ✜✢✛✣✤✦


J. Kameda (SK) talk at Nufact 2016

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