Beyond the Standard Model in Okinawa 2016

2  

PROLOGUE: Lessons from the 2015 Nobel Prize in Physics www.nobelprize.org/nobelprizes/physics/laureates/2015/kajita-­‐diploma.html  

“for  the  discovery  of     neutrino  oscilla3ons  ...  

...  which  shows  that     neutrinos  have  mass"   www.nobelprize.org/nobelprizes/physics/laureates/2015/mcdonald-­‐diploma.html  

3  

 It’s  not  always  true  that...   “Yesterday’s  signal     is  today’s  background  and     tomorrow’s  calibra7on”  

                                                               E.g.,  Background  çè  Signal  interplay          in  atmospheric  neutrino  physics:      

202Y:                                 >20YZ:                           >20ZW:   >20WX:  

 Background    to  Nucleon  Decay  Expts  (Kamioka-­‐NDE)        Signal      of  neutrino  oscillaIons    Background    to  high-­‐energy  astrophysical  ν  (IceCube)        Signal    of  Earth  maLer  effects  and  of  ν  mass  hierarchy  ?        Background    to  diffuse  SN  neutrino  signal  (at  low  E)  ?          Signal    of  nonstandard  neutrino  states  or  interacIons?    Background    to  proton  decay  signals?  

...  

Discovery  çè  Precision   From  a  broad-­‐brush     picture  of  neutrinos...  

4  

               ...  to  precision     neutrino  physics  ...  

...  and  back  ...   ...  and  forth  ...   3ν  paradigm  

( νe  , νµ , ντ )

( ν1 , ν2 , ν3 )

with  known   and  unknown   aspects   mass  



+  physics          beyond?  ...     [outline  of  this  talk]  

CKM  à  PMNS  

What we have seen: α à β oscillations in vacuum and matter eàe ( δm2 , θ12 ) µàµ ( Δm2 , θ23 ) eàe ( Δm2 , θ13 )

c

a

eàe ( δm2 , θ12 )

µàµ ( Δm2 , θ23 )

b

e

µàe ( Δm2 , θ13 , θ23 )

f

d

µàτ ( Δm2 , θ23 ) Data from various types of neutrino experiments: (a) solar, (b) long-baseline reactor, (c) atmospheric, (d) long-baseline accelerator, (e) short-baseline reactor, (f,g) long baseline accelerator (and, in part, atmospheric). (a) KamLAND [plot]; (b) Borexino [plot], Homestake, Super-K, SAGE, GALLEX/GNO, SNO; (c) Super-K atmosph. [plot], DeepCore, MACRO, MINOS etc.; (d) T2K (plot), MINOS, K2K; (e) Daya Bay [plot], RENO, Double Chooz; (f) T2K [plot], MINOS, NOvA; (g) OPERA [plot], Super-K atmospheric.

g

5  

...can be interpreted in a simple 3ν theoretical framework eàe ( δm2 , θ12 ) µàµ ( Δm2 , θ23 ) eàe ( Δm2 , θ13 )

c

a

eàe ( δm2 , θ12 )

µàµ ( Δm2 , θ23 )

b

e

µàe ( Δm2 , θ13 , θ23 )

f

d

µàτ ( Δm2 , θ23 ) Known parameters:

δm2 |Δm2| θ12 θ23 θ13  

g

6  

7  

Pontecorvo-Maki-Nakagawa-Sakata (PMNS) matrix

U↵i

2

1 =4 0 0

0 c23 s23

32 0 s23 5 4 c23

c13 0 s13 ei

32 c12 0 s13 e i 5 4 s12 1 0 0 0 c13

Mixing angles θ23, θ13, θ12 : known ✔

s12 c12 0

32 1 0 0 54 0 1 0

0 ei↵/2 0

0 0 ei

/2

[ only if Majorana ]

3 5

CP-violat. phase(s) δ (α, β) : unknown ✗

Mass-squared spectrum (up to absolute scale) “Normal” Hierarchy

2 1

Δm2 δm2

2 1

δm2 Δm2

“Inverted” Hierarchy

[ + contribution in matter ~ GF . E . density ]

δm2, |Δm2|: known ✔

Matter effects (solar ν): ✔

Hierarchy : unknown ✗

Current 3ν picture in one slide (with 1-digit accuracy)

e µ τ

Abs.scale Normal hierarchy… or… Inverted hierarchy

mass2 split

ν3 +Δm2 m2

ν

ν2 ν1

δm2

-Δm2

ν3 We  see:   δm2 ~ 7 x 10-5 eV2 Δm2 ~ 2 x 10-3 eV2 sin2θ12 ~ 0.3 sin2θ23 ~ 0.5 sin2θ13 ~ 0.02

We  expect  to  see:   δ (CP) sign(Δm2) octant(θ23) absolute mass scale Dirac/Majorana nature

8  

9  

Exploring what we see with more digits: global analysis 2016 Analysis includes increasingly rich oscillation data sets:

LBL Acc + Solar + KL LBL Acc + Solar + KL + SBL Reactor LBL Acc + Solar + KL + SBL Reactor + Atmosph. Parameters not shown are marginalized away

C.L.’s refer to Nσ = √ Δχ2 = 1, 2, 3, ...

Results hereafter: from Capozzi, Lisi, Marrone, Montanino, Palazzo, 1601.07777 [includes latest data: DeepCore, SK-IV, T2K, NOvA, SBL reactor, KL + “bump”] To appear in NPB Special Issue on Nobel Prize 2015 and Neutrino Oscillations See also: Forero & al., 1405.7540; Gonzalez-Garcia & al., 1409.5439 / 1512.06856

10  

Single (known) oscillation parameters LBL Acc + Solar + KamLAND + SBL Reactors + Atmos 44

4

4

Current 1σ errors (1/6 of ±3σ range):

Nσ

NH IH 33

3

22

2

3

Note: Δm2 = (Δm231 + Δm232)/2 2

cc + Solar + KL + SBL Reactors + SK Atm 11

1

1

NH IH

00 6.5

0

7

7.5

8

-5

2

8.5 2

8.0

10 eV

2

2.4 -3

2.6

2.8

0

4

3

3

3

8.5 2.0 2.2 2.4 2.6 2.8 0.0 -3 2 2 22

m /10 eV

11

0.5 2

1.0

1.5

/

0.3 2

0.35

sin θ12

0.01

2

1

0

0.02 2

sin θ13

% % % % %

all  <  10%...   Precision Era!

2

0

0.25

1.5

2.0

1

00

1

2.4 1.8

5.8

4.7

~ 9

δ/ π

∆m /10 eV 4

3

0.5

2

44

Nσ

-5

2.2 2

δm /10 eV

7.5

0

2

δm2 Δm2 sin2θ12 sin2θ13 sin2θ23

0.03 0.3

0.4

0.5 2

sin θ23

0.6

0.7

11  

Single (unknown) oscillation parameters LBL Acc + Solar + KamLAND + SBL Reactors + Atmos 44

4

4

Nσ

NH IH 33

3

3

22

2

2

11

1

1

00 6.5

0

7

7.5

8

-5

2

8.5

2

2

Nσ

0

2.2

2.4 -3

2

δm /10 eV

2.6

2.8

0

4

33

3

3

22

2

2

11

1

1

0

0.3 2

0.35

sin θ12

0.01

1

1.5

2

NH or IH

δ/ π

∆m /10 eV 4

0.25

0.5

2

44

00

δCP  

θ23 octant

0

0.02 2

sin θ13

0.03 0.3

0.4

0.5 2

sin θ23

0.6

0.7

01

2.2

2.4

2.6

-3

2

2.8

0

0.5

1

1.5

2

LBL+Sol+KL LBL/ Acc + Solar + KL + SBL Reactors

2

m /10 eV

4

NH

θ23

IH

3

octant

N

2

More on single (unknown) parameters:

2

1

0

0.02

sin2

0.03

0.04 0.3 6.5

0.4 7.5 0.5 8.0 0.6 8.5 0.72.0 7.0

sin2-5 23 m /10 eV 2

13

2.2

2.4

2.6

-3

2

2

m /10 eV

2.8 0.0

0.5

1.0

2

1.5

2.0

/

4

Δχ

2

-1.2

(IH-NH)  

3

2

N

cc + Solar + KamLAND LBL Acc + Solar + KL + SBL Reactors 4 2

δCP   2.2

2.4

2.6

N

3 1 2 0

0.25

1

2.8

0 6.5 0

m2/10-3 eV2 4

NH

NH IH

0.30

0.35

IH

0.3

0.4

sin

0.5

0.6

12

sin

23

2.4

2.6

2.2

m /10 / eV

m /10 eV

-5

2

2

-3

0.02

0.03

0.04

2

7.0 0.5 7.51 8.0 1.5 8.5 22.0 2

0.7 0.01

2

2

sin

2.8 0.0 2

0.5

1.0

/

13

1.5

2.0

12  

01

More on single (unknown) parameters:

0 2.4 6.5

2.2

2.6 7

2.8 7.5

08

0.5 8.5

21

1.5 2.2

2 2.4

2.6

-3 m /10 eV m /10 eV m /10 eV2 LBL+Sol+KL LBL/ Acc + Solar -3

2

-5

22

2

2

2.8

0

+ KL

0.5

1

1.5

2

++SBL SBL /Reac Reactors

4

4

NH

θ23

N

octant 2

2

1

1

0 0.02 0.25 0.03

sin2

IH

3

3

N

2

1

13

0

0.04 0.3 0.4 6.5 0.3 0.35 7.0 2

sin

0.5 8.0 0.6 8.5 0.72.0 7.5 0.01 0.02

2 sin2-5 23 m /10 eV 2sin 2

12

13

2.2 0.03 2.40.32.6 0.4 2.8 0.5 0.0 -3

2

m /10 eV

2

0.5 0.6

2

sin

1.0 0.7 1.5

2.0

/

23

4

Δχ2

-1.2

(IH-NH)  

-0.88

3

cc + Solar + KamLAND LBL Acc +LBL SolarAcc + KamLAND + SBL Reactors + Solar + KL + SBL Reactors

2

N

4

1

N

N

δCP   2

0 2.4 6.5

NH IH

3 1

3

2.2

4 2

2 0 1

0.25

0.30

0.35

sin

0.3

0.4

0.5

0.6

12

sin

0.02

0.03

sin

23

0

2.6 7

IH

13

6.5 7.0 7.51 8.0 8.5 22.0 2.2 2.4 2.6 2.8 0.0 0.5 1.0 1.5 2.8 1.5 7.5 0 8 0.5 8.5 2 2.2 2.4 2.6 2 2.8-3 0 2 0.5 1 1.5 2 -5 2 2 4

0.04

2

m2 /10 eV m2/10-3 eVm22/10-5 eV2 m /10 / eV m2/10-3 eV 4

0.7 0.01

2

2

NH

NH IH

/

/

2.0

13  

01

More on single (unknown) parameters:

0 2.4 6.5

2.2

2.6 7

2.8 7.5

08

0.5 8.5

21

1.5 2.2

0 2 2.4 6.5

2.6 7

2.8 7.5

08

0.5 8.5

21

1.5 2.2

2 2.4

2.6

-3 2 2 m2/10-3 eV m22/10-5 eV m2/10 eV +SBL m22/10 eV+ m2/10-3 eV2 LBL+Sol+KL LBL/ Acc + Solar + -5KL SBL /Reac Reactors

4

θ23 3

N

octant 2

4

3

3

2

2

N

4

1

1

0 0.02 0.25 0.03

sin2

14  

1

N

2

1

13

0

sin

0.5

1

1.5

/ +Atmos

2

NH

currently unstable, fragile

IH

0

0.5 8.0 0.6 8.5 0.70.25 7.5 2.0 2.2 2.40.35 2.8 0.01 0.0 0.01 0.02 0.03 0.32.6 0.4 0.5 0.3

2 sin2-5 23 m /10 eV 2sin

-3 sin/1012 m 2 2

2

12

0

1

0.04 0.3 0.4 6.5 0.3 0.35 7.0 2

2.8

13

eV

2

0.5 1.0 0.6 0.02 0.7 1.5

2

sin

23

sin/2

2.0 0.03 0.3

0.4

0.5

sin

13

0.6

2

0.7

23

4

Δχ2

-1.2

(IH-NH)  

-0.88

negligible

+0.98

3

cc + Solar + KamLAND LBL Acc +LBL SolarAcc + KamLAND ++SBL Reactors + Solar + KL + SBL LBL Acc Solar +Reactors KamLAND + SBL Reactors + Atmos

2

N

4

1

2 0 1

4

0.25

0.30

NH IH

IH

0.3

0.4

0.5

0.6

0.7 0.01

2

2

sin

12

intriguing, sin δ ~ -1

2

0.35

1

sin

0.02

0.03

0.04

(or sin δ < 0)

2

sin

23

13

favored

0

2.6 7

6.5 7.0 7.51 8.0 8.50 22.0 2.2 2.4 2.6 2.8 0.0 0.5 1.0 1.5 2.0 2.8 1.5 7.5 0 8 0.5 8.5 2 2.2 6.5 2.4 2.6 2.8-3 08 2 0.5 1.5 2.4 2 7 2 7.5 8.5 21 2.2 2.6 2.8 -5 2 2

m2 /10 eV m2/10-3 eVm22/10-5 eV2 m /10 / eV m2/10-3 eV m2/10-5 eV2 4

NH

NH IH

3

N

N

N

δCP   2

0 2.4 6.5

NH IH

3 1

3

2.2

4 2

4

4

/

2/

-3

2

m /10 eV

0

0.5

1

/

1.5

2

01

1

0 2.2 6.5 2.4

7 2.6 22

-3

2

7.5 2.8

m /10 m /10 eV

More on single (unknown) parameters: NOvA analysis LID à LEM / / Acc eVLBL+Sol+KL m /10 eV m /10 eV+ m /10 eV +SBL +Atmos LBL + Solar + KL SBL /Reac Reactors 08

-5

4

8.5 0.5

21

0 2.4 6.5 2

2.2 1.5

2

2.6 7

-3

2

2.8 7.5

22

08

-5

0.5 8.5

21

1.5 2.2

2

2 2.4

2.6

-3

2

2.8

0

0.5

1

1.5

2

2

4

4

NH 3

N

octant 2

3

3

2

2

N

θ23

N

2

1

1

1

sin2

1

0

0 0.02 0.25 0.03

0.04 0.35 0.3 0.4 6.5 7.0 0.3

sin

0

0.5 8.0 0.6 8.5 0.70.25 7.5 2.0 2.2 2.40.3 2.6 0.42.8 0.01 0.0 0.01 0.02 0.03 0.5 0.3 0.35

2 2 sin -5

2

13

currently unstable, fragile

IH

m /10 23 eV

12

2sin2

-3

22

13

sin/1012 eV m

2

2

sin

23

0.5 1.0 0.6 0.02 0.7 1.5

sin/2

2.0 0.03 0.3

0.4

0.5

sin

13

0.6

2

0.7

23

4

Δχ2

+0.61

(IH-NH)  

+2.2

negligible ?

+2.8

3

cc + Solar + KamLAND LBL Acc +LBL Solar + KamLAND ++SBL Reactors LBL Acc Solar +Reactors KamLAND + SBL Reactors + Atmos Acc + Solar + KL + SBL

N

4

-3

2.6 7 22

0.25

2.8 7.5 -5

sin

0.35

0.3

0.4

0.5

0.6

0.7 0.01

2

12

1

sin

0.02

2m

4

intriguing, sin δ ~ -1

0.03

0.04

sin

23

m2/10 eV /10 / eV m2/10-3 eV m2/10-5 eV2 4

(or sin δ < 0)

2 13

0 0 2.0 2.2 2.4 2.6 2.8 0.0 0.5 1.0 1.5 2.0 6.5 7.0 7.5 8.0 8.5 0 8 0.5 1.5 2 8.5 12 2.2 6.5 2.4 2.62 7.5 2.8-3 0 1.5 2.4 2 2.6 7 8 2 0.5 8.5 21 2.2 2.8 -5 2 2 /

m /10 eVm /10 eV 4

0.30

NH IH

2

2

1

1

0 2.4 6.5

2 0

NH NH IH IH

3

N

δCP  

N

N

2

2

NH IH

3 1

3

2.2

4

4 2

/

2

-3

2

m /10 eV

0

0.5

1

/

1.5

2

favored sin δ ~ +1 ~excluded

16  

Summary of 3ν oscillation parameters, 2016

With  NOvA  LIDàLEM:    

17  

Underlying symmetries? A vast spectrum of possibilities... No organizing principle (“anarchy”) Discrete family simmetries (“geometry”)

linear relations between θ13cosδ and θ12, θ23

Continuous flavor simmetries (“dynamics”)

links between neutrino spectra/angles/phases

Common quark/lepton features (“complementarity”)

links between θ13 and θC

...whose selection will benefit from new data!

18  

Comments on CPV phase From variances to covariances: analysis of a 2D plot LBL Acc + Solar + KL

+ SBL Reactors

2.0

+ Atmos

2.0

2.0

2.0

2.0

2.0

1.5

800

1.4

800

1.4

1.01.2

1.01.2

600

600

1.0

1.0

0.50.8

4000.50.8

4000.50.8

0.6

0.6

0.6

0.4

200

0.0 0.00

0.01

2

θ13 0.04 0.02sin0.03

0.05

2.0 2.0 1.8

1.5

200

0.0 0.00

0.01

2

θ13 0.04 0.02sin0.03

0.05

sin2θ13  

0.4

200

0.0 0.00

0.01

2

θ13 0.04 0.02sin0.03

0.05

1.8 1000 1.6

1.5

1.4 800 1.2

800

Leading appearance amplitude at LBL Acc. ~ sin2θ23 sin2(2θ13)

à uncertainty on θ23 somewhat affects subleading terms

1.0 1.0 0.8 0.6

0.5

0.4 0.2

0.0 0.0 0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.00 0.01 0.02 0.03 0.04 0.05 0.06

sin2θ13

1.01.0 600 0.8

1.01.0 600 0.8

0.6 4000.5 0.4

0.6 4000.5 0.4

0.2 200 0.0 0.0 0.00

0.2 200 0.0 0.0 0.00

0.01

0.02

0.03

0.04

0.05

0.06

0.00 0.01 0.02 0.03 0.04 0.05 0.06

0

0.060

1000

1.5

1.4 800 1.2

1.2

400

2.02.0

1.8 1000 1.6

1.4

600

0.00.2 0.00 0.01 0.02 0.03 0.04 0.05 0.06

0.060

2.02.0

800

Inverted Hierarchy

1.6

0.4

0.00.2 0.00 0.01 0.02 0.03 0.04 0.05 0.06

0.060

1σ 2σ 3σ

1.6

1.0

0.00.2 0.00 0.01 0.02 0.03 0.04 0.05 0.06

δ/ π

1.6 1.4

1.01.2

1000

1.51.8

1.5

1.6

δ/ π

δ/π  

1000 1.8

Normal Hierarchy

1000 1.8

sin2θ13

0.01

0.02

0.03

0.04

600

400

200 0.05

0.06

0.00 0.01 0.02 0.03 0.04 0.05 0.06

0

sin2θ13

Subleading CPV appearance amplitude for ν ~ -sinδ

Subleading CPV appearance amplitude for anti-ν ~ +sinδ

à T2K & NOvA ν signal maximized for sinδ ~ -1 (δ ~ 1.5π) à T2K anti-ν signal minimized for sinδ ~ -1 (δ ~ 1.5π)

0

19  

+ SBL Reactors facts  (sOll  staOsOcally   + Atmos InteresOng   limited)  about  

LBL Acc + Solar + KL

2.0 LBL  accelerator  +  Solar   +  KamLAND  data  set:   2.0 2.0 2.0 1000 1000 1000   1.8 1.8 1.8 1.5 1.5 1.5   1σ 1.6 1.6 1.6 800 800 800 1.4 1.4 1.4 (1)  By  themselves,  these   data  have  almost  23tσσhe   1.01.2 1.01.2 1.2 600 600 same  sin2θ13  best  fi600t  1.0 (~0.02)   as  SBL  reactors   1.0 1.0 1.0 [also  Solar  +  KL  data  a0.8 lone:  “old”  hint  for  θ13>0]   4000.50.8 4000.5 400 0.50.8   0.6 0.6 0.6 0.4 200 0.4 200 (2)  For  such  best  fi200 t,  ν0.4 µàνe  appearance  event   0.00.2 0.00.2 0.00.2 0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.00 0.01 0.02 0.03in   0.04 0.05 0.06 0.00 0.01 0.02 0.03 0.05 0.06   rates   T2K   and   NOvA   are   “large”   à0.04  sinδ   ∼ -1   2 2 2 0.0 0 0.0 0 0.0 θ13 0.04 0.05 0.06 θ13 0.04 0.05 0.06 θ13 0.04 0.05 0.060 0.00 0.01 0.02sin0.03 0.00 0.01 0.02sin0.03 0.00 0.01 0.02sin0.03   2.0 2.02.0 2.02.0 2.0 (3)  Conversely,  anI(ν 1.8 1.8 1.8 µàνe)  appearance  event   1000 1000 1000 1.6 1.6 1.6 à  sinδ  ∼ -1  again!   rate   i n   T 2K   i s   “ small”   1.5 1.5 1.5 1.4 1.4 1.4   800 800 800 1.2 1.2 1.2 (4)  Large  uncertainty   in  sin2θ13  partly  due  to   1.0 1.01.0 1.01.0 1.0 600 6002 600 0.8 0.8 0.8 θ degeneracy  with  sin 23   0.6 0.6 0.6   4000.5 4000.5 400 0.5 0.4 0.4 0.4   0.2 0.2 0.2 200 200 200 Future   T 2K   a nd   N OvA   r esults   a re   g oing   t o   b e   0.0 0.0 0.0 0.0 0.0 0.0 0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.00 0.01 0.02 0.03 0.04 0.05 0.06 interesOng!   (expect   0 0 updates  @  Neutrino’16)   0 sin2θ sin2θ sin2θ

Normal Hierarchy Inverted Hierarchy

Inverted  

δ/ π

2.0

Normal  

δ/ π

2.0

13

13

13

20  

LBL Acc + Solar + KL

+ SBL Reactors

2.0

+ Atmos

2.0

2.0

2.0

2.0

2.0

1.8

1.8

1.5

800

1.4

1.5

1.6

800

1.4

1.01.2

1σ 2σ 3σ

1.6 1.4

1.01.2

1.01.2

600

1.0

1000

1.8

1.5

1.6

δ/ π

1000

600

1.0

Normal Hierarchy

1000

800

600

1.0

4000.50.8

4000.50.8

0.6

0.6

0.6

δ/ π

1.2

1.2

1.2

1.01.0 600 0.8

1.01.0 600 0.8

0.6 4000.5 0.4

0.6 4000.5 0.4

0.2 200 0.0 0.06 0.0 0.00

0.2 200 0.0 0.0 0.00

1.0 1.0 0.8 0.6

0.5

0.4 0.2

0.0 0.0 0.00 0.01 0.02 0.03 0.04 0.05 0.00 0.01 0.02 0.03 0.04 0.05 0.06

sin2θ13

0.01

0.02

0.03

0.04

0.05

0.06

0.00 0.01 0.02 0.03 0.04 0.05 0.06

0

sin2θ13

Inverted Hierarchy

SBL  reactor  data:     400   0.4 200 0.4 200 0.4 200 0.00.2 0.00.2 0.00.2 strong   constraints     0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.00 0.01 0.02 0.03 0.04 0.05 0.06 2 2 2 0.0 0 0.0 0 0.0 2θ0.03 θ13 0.04 0.05 0.06 θ13 0.04 0.05 0.06 θ     0.04 0.05 0.060 0.00 0.01 0.02sin0.03 0.00 0.01 0.02sin0.03 0.00 0.01 on  s0.02 insin 1313 2.0 2.02.0 2.02.0 2.0   1.8 1.8 1.8 1000 1000 improved  bounds     1000 1.6 1.6 1.6 1.5 1.5 1.5 1.4 1.4 1.4 on  sinδ

800 800 800 0.50.8

600

400

200 0.01

0.02

0.03

0.04

0.05

0.06

0.00 0.01 0.02 0.03 0.04 0.05 0.06

0

sin2θ13

0

21  

LBL Acc + Solar + KL

+ SBL Reactors

2.0

+ Atmos

2.0

2.0

2.0

2.0

2.0

1.8

1.8

1.5

800

δ/ π

1.4

1.5

1.6

800

1.4

1.01.2

1000

1.8

1.5

1.6

1.01.2

1.01.2

600

1.0

1.0

1.0

0.50.8

4000.50.8

4000.50.8

0.6

0.6

0.6

0.4

200

0.0 0.00

0.01

2

θ13 0.04 0.02sin0.03

0.05

2.0 2.0 1.8

1.5

200

0.0 0.00

0.01

2

θ13 0.04 0.02sin0.03

0.05

2.02.0

2.02.0

1.8 1000 1.6

1.8 1000 1.6

0.6 4000.5 0.4

0.6 4000.5 0.4

0.2 200 0.0 0.06 0.0 0.00

0.2 200 0.0 0.0 0.00

0.6 0.4 0.2

0.0 0.0 0.00 0.01 0.02 0.03 0.04 0.05 0.00 0.01 0.02 0.03 0.04 0.05 0.06

sin2θ13

0.01

0.02

0.03

0.04

0.05

0.06

0.00 0.01 0.02 0.03 0.04 0.05 0.06

0

2

θ13 0.04 0.02sin0.03

0.05

1.5

1.01.0 600 0.8

0.5

0.01

sin2θ13

0.060

1000

1.01.0 600 0.8

0.8

200

0.0 0.00

1.4 800 1.2

1.0 1.0

400

0.4

1.4 800 1.2

1.2

600

0.00.2 0.00 0.01 0.02 0.03 0.04 0.05 0.06

0.060

1.5

1.4

800

Inverted Hierarchy

1.6

0.4

0.00.2 0.00 0.01 0.02 0.03 0.04 0.05 0.06

0.060

1σ 2σ 3σ

1.6 1.4

600

0.00.2 0.00 0.01 0.02 0.03 0.04 0.05 0.06

δ/ π

1000

Normal Hierarchy

1000

800

600

400

200 0.01

0.02

0.03

0.04

0.05

0.06

0.00 0.01 0.02 0.03 0.04 0.05 0.06

0

sin2θ13

IndicaIons  for  sinδ  <  0  corroborated  by  atmospheric  neutrino  data    

0

22  

NOvA analysis LID à LEM LBL Acc + Solar + KL

+ SBL Reactors 2.0

2.0

2.0

2.0

1.51.8

1.51.8

1.51.8

1.6

1.6

1.6

1.4

1.4

1.4

1.01.2

1.01.2

1.01.2

1.0

1.0

1.0

0.50.8

0.50.8

0.50.8

0.6

0.6

0.6

0.4

0.4

0.00.2 0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.0 0.00

0.01

2

0.02sin0.03 13 0.04

0.05

0.0 0.00

0.01

2

0.02sin0.03 13 0.04

0.05

0.00.2 0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.0 0.00

0.06

2.02.0

1.8

1.8

1.8

1.6

1.6

1.6

1.4

1.4

1.4

1.2

1.2

1.2

1.01.0

1.01.0

0.8

0.8

0.8

0.6

0.6

0.6

0.4

0.4

0.4

0.2

0.2

0.2

1.5

1.0 1.0

0.5

sin2

13

0.0 0.0 0.00

2

0.02sin0.0313 0.04

0.05

1.5

0.5

0.0 0.0 0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.00 0.01 0.02 0.03 0.04 0.05 0.06

0.01

0.5

0.01

0.02

0.03

0.04

0.05

0.06

0.00 0.01 0.02 0.03 0.04 0.05 0.06

sin2

13

0.0 0.0 0.00

0.06

Inverted Hierarchy

2.02.0

1.5

1 2 3

0.4

0.00.2 0.00 0.01 0.02 0.03 0.04 0.05 0.06

0.06

2.0 2.0

/

2.0

Normal Hierarchy

/

2.0

+ Atmos

0.01

0.02

0.03

0.04

0.05

0.06

0.00 0.01 0.02 0.03 0.04 0.05 0.06

sin2

13

Only  in  IH:  slight  tension  between  LBL  accelerator  and  SBL  reactor  data  

23  

Comments on hierarchy No significant hints so far, but we’ll get there via oscillations...

δm2   (NH)

+Δm2  

-Δm2  

(IH)

δm2   ... if we can observe interference of oscill. driven by ±Δm2 with oscill. driven by another quantity Q with known sign. Three options:

Q = δm2 (medium-baseline reactors) Q = 2√ 2 GF Ne E (matter effects in accel./atmosph. ν) Q = 2√ 2 GF Nν E (collective effects in supernovae) ... and nonoscillation searches may provide further probes!

24  

Make ± Δm2 interfere with δm2  at medium-baseline reactors Very challenging! [E.g., JUNO, RENO-50] 35

Spectrum/103 [MeV-1]

30

NH IH

25 20 15 10 5 0 0

1

2

3

4

5

6

7

8

9

Evis [MeV]

Will also improve δm2  and θ12 accuracy by O(10)

25  

Once upon a time... all neutrino experiments were limited by stat’s, and systematics could be treated as numbers (normalization, bias ...) Now we have as many as O(106) events collected in SBL reactors, and we expect O(105) events in each of JUNO, ORCA, PINGU expt’s Systematic errors are no longer “numbers” but become “functions”. Dedicated approaches are needed to deal with such uncertainties. [This transition has already taken place in other fields, such as in parton distribution function fits and precision cosmology forecasts.] Unprecedented challenges are awaiting us in neutrino data analyses: We must be prepared to deal with “functions” which ideally should be known in size, shape, correlations and probability distributions, but in practice may also be partly (if not completely!) unknown.

26  

Hard lesson learned from SBL reactor experiments: An unexpected systematic spectral deviation δΦ(E), well beyond supposedly-known shape uncertainties! Daya Bay data Huber + Mueller uncert.

Daya Bay RENO Double Chooz

From S. Jetter (TAU 2014) & J. Cao (TAUP 2015). Ongoing debate on its origin: Nuclear effects?

Now we know its shape, and can correct for it, but residuals do remain:

energy-scale uncertainties flux-shape uncertainties

E à E’(E) Φ (E) à Φ’(E)

(x-axis “stretch”) (y-axis “stretch”)

27  

Impact on JUNO sensitivity to NH/IH discrimination: Current E, Φ uncertainties  

Halved E, Φ uncertainties   5

5

NH true

NH true

osc. + norm.

osc. + norm. 4

4

+ energy scale

+ energy scale (halved) + flux shape (halved)

+ flux shape

3

3

N

N 2

2

1

1

0

0

5

T (y)

10

0

0

5

T (y)

[An example of hierarchy sensitivity study for JUNO, arXiv:1508.01392]

10

Hierarchy: Make ±

Δm2

interfere with GFNeE

 in

atmospheric expts

28  

Observable (lepton) spectra come out from multiple integrations over unobservable (neutrino) kernels PαNH (s2 =0.5)

10

10

1

0.9

0.8

0.7

0.6

0.5

10

1

1

10

1

0.9

0.8

0.7

0.6

0.5

10

1

0.9

0.8

0.7

0.6

0.5

θ/π

Unoscillated kernel

1

NαNH (smeared)

1

10

1

0.9

0.8

0.7

0.6

0.5

10

1

0.9

0.8

0.7

0.6

0.5

θ/π

Oscillation factor

1

1

1

0.9

0.8

0.7

0.6

0.5

1

0.9

0.8

0.7

0.6

0.5

α = electron

E/GeV

1

NαNH (unsmeared)

23

α = muon

E/GeV

Vαeff Φα σαCC

10

1

0.9

0.8

0.7

0.6

0.5

θ/π

Integral (unsmeared)

1

θ/π

Integral (smeared)

Smeared spectra for IH: indistinguishable from NH “by eye” à High stat., low syst.

29  

Observable energy-angle spectra of atmospheric ν-generated µ-like and e-like events will need accurate control of spectral shapes for NH/IH tests Stat + syst (osc+norm)

+ resolution (scale,width)

+ polynomial

+ uncorrelated

10

10

10

5

5

5

5

Normal hierarchy

10

Nσ

0

0

5

10

0

0

5

10

0

0

5

10

0

10

10

10

5

5

5

5

5

10

0

5

10

Inverted hierarchy

10

0

Nσ

0

0

5

Time (y)

10

0

0

5

Time (y)

10

0

0

5

Time (y)

10

0

Time (y)

An example of hierarchy sensitivity study for PINGU, arXiv:1503.01999 Similar remarks apply to the KM3 – ORCA project, or HyperK

3ν paradigm: absolute ν masses and observables (  mβ  ,  mββ  ,  Σ  )      β  decay,  sensiIve  to  the  “effecIve  electron  neutrino  mass”:  

         0νββ  decay:  only  if  Majorana.  “EffecIve  Majorana  mass”:  

       Cosmology:  Dominantly  sensiIve  to  sum  of  neutrino  masses:  

Note 1: These observables may provide handles to distinguish NH/IH. Note 2: Majorana case gives a new source of CPV (unconstrained) Note 2: The three observables are correlated by oscillation dataà

30  

31  

Upper limits on mβ,  mββ,  Σ  (up to some syst.) + osc. constraints 1

m (eV)

0.0

10-1

β  

 :  Mainz+Troitsk

0νββ

 :  GERDA, EXO, KL-Zen, Cuore...

Σ



: CMB+LSS

-0.5

2 2

-2 10-1.0

(NH) (IH)

oscillation constraints

-1.5 -3 10-2.0

10-1

1

-1.4 -1.2 -1.0 -0.8 -0.6 -0.4 -0.2 0.0 0.2 0.4

m (eV)

1

1

100

0.0

0.0

90

-0.5

-0.5

80

-1.0 10-1

70

-1 -1.0 10 -1.5 -2.0

50

-2.0

-2 10-2.5

40

-2.510-2

-3.0

-3.0

-3.5

-3.5

-3 10-4.0

60

-1.5

-1.2 -1.0 -0.8 -0.6 -0.4 -0.2 0.0 0.2 0.4 -1

10

1

(eV)

mββ  spread due to

Majorana CP phase(s): accessible in principle

30 20 10

-4.0 10-3-2.5 -3.0 -3

10

-2.0

-1.5

10-2

-1.0

-0.5

0.0

10-1

m (eV)

1

Major improvements expected in the next decade

32  

Upper limits on mβ,  mββ,  Σ   in ~10 years ? 1

m (eV)

0.0

10-1

β  

 :  KATRIN

0νββ

 :  Upgraded/New expt. (+ NME)

Σ



: Precision Cosmology

-0.5

2 2

-2 10-1.0

(NH) (IH)

oscillation constraints

-1.5 -3 10-2.0

10-1

1

-1.4 -1.2 -1.0 -0.8 -0.6 -0.4 -0.2 0.0 0.2 0.4

m (eV)

1

1

100

0.0

0.0

90

-0.5

-0.5

80

-1.0 10-1

70

-1 -1.0 10 -1.5

-1.5

-2.0

-2.0

-2 10-2.5

50 40

-2.510-2

-3.0

-3.0

-3.5

-3.5

-3 10-4.0

60

-1.2 -1.0 -0.8 -0.6 -0.4 -0.2 0.0 0.2 0.4 -1

10

1

(eV)

30 20 10

-4.0 10-3-2.5 -3.0 -3

10

-2.0

-1.5

10-2

-1.0

-0.5

0.0

10-1

m (eV)

1

Large phase space for discoveries about ν mass and nature.

33  

Upper limits on mβ,  mββ,  Σ   in ~10 years ? 1

m (eV)

0.0

10-1

β  

 :  KATRIN

0νββ

 :  Upgraded/New expt. (+ NME)

Σ



: Precision Cosmology

-0.5

2 2

-2 10-1.0

(NH) (IH)

oscillation constraints

-1.5 -3 10-2.0

10-1

1

-1.4 -1.2 -1.0 -0.8 -0.6 -0.4 -0.2 0.0 0.2 0.4

m (eV)

1

1

100

0.0

0.0

90

-0.5

-0.5

80

-1.0 10-1

70

-1 -1.0 10 -1.5

-1.5

-2.0

-2.0

-2 10-2.5

50 40

-2.510-2

-3.0

-3.0

-3.5

-3.5

-3 10-4.0

60

-1.2 -1.0 -0.8 -0.6 -0.4 -0.2 0.0 0.2 0.4 -1

10

1

(eV)

30 20 10

-4.0 10-3-2.5 -3.0 -3

10

-2.0

-1.5

10-2

-1.0

-0.5

0.0

10-1

m (eV)

1

Cosmology first? Be prepared to Σ>0 (or IH rejection) claims!

34  

Upper limits on mβ,  mββ,  Σ   in ~10 years ? 1

m (eV)

0.0

10-1

β  

 :  KATRIN

0νββ

 :  Upgraded/New expt. (+ NME)

Σ



: Precision Cosmology

-0.5

2 2

-2 10-1.0

(NH) (IH)

oscillation constraints

-1.5 -3 10-2.0

10-1

1

-1.4 -1.2 -1.0 -0.8 -0.6 -0.4 -0.2 0.0 0.2 0.4

m (eV)

1

1

100

0.0

0.0

90

-0.5

-0.5

80

-1.0 10-1

70

-1 -1.0 10 -1.5

-1.5

-2.0

-2.0

-2 10-2.5

50 40

-2.510-2

-3.0

-3.0

-3.5

-3.5

-3 10-4.0

60

-1.2 -1.0 -0.8 -0.6 -0.4 -0.2 0.0 0.2 0.4 -1

10

1

(eV)

30 20 10

-4.0 10-3-2.5 -3.0 -3

10

-2.0

-1.5

10-2

-1.0

-0.5

0.0

10-1

m (eV)

1

[Even now, at face value: with NOvA LEM + cosmology à NH favored]

35  

With “dreamlike” and converging data one could, e.g. 1

m (eV)

Determine  the   mass  scale…  

Check  3ν   consistency  …  

Probe  the   Majorana     phase(s)  …  

m (eV)

IdenIfy  the   hierarchy  …  

0.0

10-1

-0.5

2 2

-2 10-1.0

(NH) (IH)

-1.5 -3 10-2.0

10-1

1

-1.4 -1.2 -1.0 -0.8 -0.6 -0.4 -0.2 0.0 0.2 0.4

1

1

100

0.0

0.0

90

-0.5

-0.5

80

-1.0 10-1

70

-1 -1.0 10 -1.5

-1.5

-2.0

-2.0

-2 10-2.5

50 40

-2.510-2

-3.0

-3.0

-3.5

-3.5

-3 10-4.0

60

-1.2 -1.0 -0.8 -0.6 -0.4 -0.2 0.0 0.2 0.4 -1

10

1

(eV)

30 20 10

-4.0 10-3-2.5 -3.0 -3

10

-2.0

-1.5

10-2

-1.0

-0.5

0.0

10-1

m (eV)

1

36  

But alternative situations might also occur.... 1

?

why the mismatch ?

m (eV)

0.0 -1

10

something wrong ?

-0.5

new

-2 10-1.0

2 (NH) 2 (IH) ? physics

-1.5 -3 10-2.0

10-1

1

-1.4 -1.2 -1.0 -0.8 -0.6 -0.4 -0.2 0.0 0.2 0.4

m (eV)

1

1

100

0.0

0.0

90

-0.5

-0.5

80

-1.0 10-1

70

-1 -1.0 10 -1.5

-1.5

-2.0

-2.0

-2 10-2.5

-3.0

-3.5

-3.5 -1.2 -1.0 -0.8 -0.6 -0.4 -0.2 0.0 0.2 0.4 -1

10

1

(eV)

60 50 40

-2.510-2

-3.0

-3 10-4.0

?

30 20 10

-4.0 10-3-2.5 -3.0 -3

10

-2.0

-1.5

10-2

-1.0

-0.5

0.0

10-1

m (eV)

1

37  

Physics beyond “3 light ν” should always be kept in mind: u

e

e

W

u

u

u

W

e

e

W

u

u

e

e

W

W

u W

ν

N

ν(n)

Standard  

 Heavy  ν    

Kaluza-­‐Klein  

e

e

WR,L

u

WR,L

νL,R RHC  λ,η          λ=RH  had,  η=LH  had  

e

u

u

~ u

e ~ u

~ g

 SUSY  ~ g    

p

e

π

e

 

SUSY

p

π

 SUSY  π    

38  

One scenario is under particular scrutiny: Sterile  ν  states  at  O(1  eV)  scale,  with  small  acIve-­‐sterile  mixing?     Prompted  by  some  “anomalous” results  sIll  under  invesIgaIon:         2 LSND/MiniBooNE   (SBL)?  

Extra  cosmic  radiaIon?  

2. Scenarios

?  

Reactor  anomaly?  

mass  

[Mills]

We take the number of thermally excited sterile neutrinos, Ns , to be an adjustable cosmological fit parameter, while the active neutrinos are assumed to have a fixed abundance corresponding to N = 3.046 so that the total e⇤ective number of neutrinos Neff = 3.046 + Ns . For the neutrino masses, we consider two schematic scenarios. In the first scenario, the ordinary neutrinos are taken to be massless, while the sterile states have a common mass scale ms which is free to vary. We dub this the “3 + Ns ” scenario. The second scenario, the “Ns + 3” scenario, consists of massless sterile states (ms = 0) and active neutrinos that have an adjustable common mass m , i.e., all active species are treated as degenerate in mass.

Gallium  anomaly?  

3. Cosmological analysis Besides the new parameters Ns and ms or m , we consider a cosmological parameter space consisting of the standard “vanilla” CDM parameters: The baryon density ⇥b = ⇥b h2 , cold dark matter density ⇥cdm = ⇥cdm h2 , Hubble parameter H0 , scalar fluctuation amplitude As , scalar spectral index ns , and the optical depth to reionisation . We use either m or ms as a fit parameter, depending on the scenario under consideration, from which we calculate the contribution to the matter density as (i) ⇥ h2 = Ns ms /(93 eV) in the 3 + Ns scheme, and (ii) ⇥ h2 = 3.046 m /(93 eV) in the Ns + 3 case. We use CMB

Figure 1. 2D marginalised 68%-, 95%- and 99%credible regions for the neutrino mass and thermally excited number of degrees of freedom Ns . Top: The 3 + Ns scheme Bottom: The Ns + 3 scheme.

3ν  paradigm  

Sterile  neutrinos:  Appearance  vs  Disappearance...  [from  GiunI+  2015]  

...  precision  physics  and  (possible)  discoveries...  

39  

EPILOGUE: Bridging two fundamental research programs

1. Test Higgs sector

2. Find ν masses

 coupling  to  Higgs    à  

 1  +  2        Where  are  the  ν’s  on  this  plot?    Why  are  they  so  light?    

ν?

             <  1  eV  

parOcle  mass  à  

41  

 coupling  to  Higgs    à  

Options:

ν

Dirac:  neutrinos  “talk”     very  weakly  to  the     Higgs  boson,  y  <  10-­‐12   for  unknown  reasons...  

Ÿ  

             <  1  eV  

parOcle  mass  à  

42  

 coupling  to  Higgs    à  

Options:

« ... Vuolsi così colà dove si puote! ciò che si vuole, e più non dimandare »! !

«... It is so willed there where is power to do! That which is willed; and ask no further question »# !

«... 人欲(のぞ)みし事叶う時にはそこそこを欲むものなり よってそれ以上尋ぬるなかれ » !

(Dante, Inferno)!

ν

Ÿ  

             <  1  eV  

parOcle  mass  à  

43  

Options:

 coupling  to  Higgs    à  

ν

Ÿ   Ÿ   Ÿ   Ÿ  

             <  1  eV  

Majorana:  neutrinos  talk     “normally”  to  the  Higgs,     but  also  to  other  (much)     higher  scale(s)  M  -­‐-­‐>   suppression  yMH/M     (see-­‐saw)   parOcle  mass  à  

44  

New mass states could then emerge at (different) new scales ...

 coupling  to  Higgs    à  

ν

Ÿ   Ÿ   Ÿ   Ÿ  

GUT                         TeV      

       

      GeV       keV    

               

  eV                <  1  eV  

    parOcle  mass  à  

45  

... and contribute to a rich phenomenology, e.g.,

 coupling  to  Higgs    à  

ν

Ÿ   Ÿ   Ÿ   Ÿ  

GUT                         TeV    

 [proton  decay]    [leptogenesis]    [LHC]    [heavy  neutral  leptons]  

  GeV       keV    

 [SHiP]    [low-­‐scale  see-­‐saw]    [DM]    [direct  mass  searches]  

  eV                <  1  eV  

 [oscillaIons]     parOcle  mass  à  

46  

 coupling  to  Higgs    à  

Let us remain open-minded: while looking at precision 3ν physics, new broad-brush pictures may emerge!

Ÿ   Ÿ   Ÿ   Ÿ  

?   Ÿ  

Ÿ   parOcle  mass  à  

Ÿ  

Ÿ  

Ÿ  

47  

Thank you for your attention

Backup  

LBL Acc + Solar + KL

+ SBL Reactors

0.06

0.06

0.06 0.05 1200

0.06 0.05 1200

0.05 1000 0.04

0.05 1000 0.04

0.04

0.04 800 0.03

0.04 800 0.03

0.03

0.03 600 0.02

0.03 600 0.02

0.02

400 0.02

400 0.02

0.01

200 0.01

200 0.01

0.06

0.05

sin2θ13

0.04 0.03 0.02

0.01

0.01

0.00 0.3 0.00 0.2

0.4 0.3

0.5

0.4

0.6

2 sin 0.5θ23 0.6

0.7 0.7

0.8 0

0.00 0.2

0.4 0.3

0.5

0.4

0.6

sin0.52θ23 0.6

0.7

0.8 0

0.05 0.05

0.05 1200 0.05

0.05 1200 0.05

0.04 0.04

1000 0.04 0.04

1000 0.04 0.04

0.03 0.03

800 0.03 0.03

800 0.03 0.03

0.02 0.02

600 0.02 0.02

600 0.02 0.02

0.01 0.01

400 0.01 0.01

400 0.01 0.01

0.4

0.4

0.5

0.5

0.6

sin2θ23

0.6

0.7

200 0.00 0.8 0.00 0.2

0.7

0.3

0.3

0

0.4

0.4

0.5

0.6

0.5

sin2θ23

0.7

0.6

0.8

0.7

200 0.00 0.00 0.2

400

200

0.4 0.3

0.5 0.4

0.6

2 sin 0.5 θ230.6

0.7 0.7

0.8 0

1200

1000

800

600

400

200 0.3

0.3

0

800

Inverted Hierarchy

0.06 0.06

1000

600

0.00 0.2

0.06 0.06

0.3

1σ 2σ 3σ

0.00 0.3

0.7

0.06 0.06

0.00 0.00 0.2 0.3

1200

0.01

0.00 0.3

Normal Hierarchy

0.06

0.05

sin2θ13

+ Atmos

0.4

0.4

0.5

0.6

0.5

sin2θ23

0.7

0.6

0.8

0.7 0

LBL Acc + Solar + KL

+ SBL Reactors

2.8

+ Atmos

2.8

2.8

2.8

2.8

∆m2/10 -3 eV2

2.62.7

250

250 2.6

2.6

2.42.5

2002.42.5

2002.42.5

2.4

150

150

2.22.3

50

0.4 0.3

0.5

0.4

0.6

2 sin 0.5θ23 0.6

0.7 0.7

2.0 0.2

50

0.4 0.3

0.5

0.4

0.6

sin0.52θ23 0.6

0.7 0.7

0.8 0

2.0 0.2

2.82.8

2.7

2.7 300 2.62.6

2.7 300 2.62.6

250 2.5

250 2.5

200 2.42.4

200 2.42.4

2.3 150

2.3 150

2.22.2 100 2.1

2.22.2 100 2.1

2.4 2.4 2.3 2.2 2.2 2.1 2.0 2.0 0.2 0.3

0.3

0.4

0.4

0.5

0.5 2

0.6

sin θ23

0.6

0.7

0.8

0.7

50 2.0 2.0 0.2

0.3

0.3

0

0.4

0.4

0.5

0.6

0.5

2

sin θ23

0.7

0.6

0.8

0.7

0.3

0.5 0.4

0.6

2 sin 0.5 θ230.6

0.7 0.7

0.8 0

300

250

200

150

50 2.0 2.0 0.2

100

50 0.3

0.3

0

50

0.4

Inverted Hierarchy

2.82.8

2.5

100

2.02.1 0.3

2.8 2.8

2.6 2.6

150

2.2

2.02.1 0.3

0.8 0

2.4

100

2.2

2.02.1 0.3

200

2.22.3

100

2.2

2.0 0.2

2.4

300

250

2.6

2.22.3

∆m2/10 -3 eV2

300

2.62.7

Normal Hierarchy

300

2.62.7

1σ 2σ 3σ

2.8

0.4

0.4

0.5

0.6

0.5

2

sin θ23

0.7

0.6

0.8

0.7 0

LBL Acc + Solar + KL

+ SBL Reactors

2.0

+ Atmos

2.0

2.0

2.0

2.0

2.0

1.51.8

250

1.51.8

1.6

1.6

1.6

δ/ π

200

1.4

1.01.2

1.01.2

150

150

150

1.0

1.0

1.0

0.50.8 0.6

1000.50.8 0.6

1000.50.8 0.6

0.4

50

0.00.2 0.3 0.0 0.2

0.4 0.3

0.5 2

θ23 0.4sin 0.5

0.6 0.6

0.7

0.4

0.8 0

0.0 0.2

0.4 0.3

0.5 2

θ23 0.4sin 0.5

0.6 0.6

0.8 0

2.02.0

0.0 0.2

1.8

1.6

250 1.6

1.5

1.4

1.4

1.2

200 1.2

1.01.0 150 0.8

1.01.0 150 0.8

0.6 1000.5 0.4

0.6 1000.5 0.4

0.2 50 0.0 0.0 0.2

0.2 50 0.0 0.0 0.2

0.6 0.4 0.2 0.0 0.0 0.2 0.3

0.3

0.4

0.4

0.5

0.5 2

sin θ23

0.6

0.6

0.7

0.8

0.7

0.3

0.3

0

0.6

θ23 0.6 0.4 sin0.5

0.7 0.7

0.8 0

250

200 1.2

0.5

2

1.5

1.4

0.8

0.3

0.5

Inverted Hierarchy

1.8 250 1.6

1.0 1.0

0.4

2.02.0

1.8

1.5

50

0.00.2 0.3

0.7 0.7

100

0.4

50

0.00.2 0.3

0.7

2.0 2.0

δ/ π

200 1.4

1.01.2

250

1.51.8

200 1.4

Normal Hierarchy

250

0.4

0.4

0.5

0.6

0.5 2

sin θ23

0.7

0.6

0.8

0.7

200

150

1σ 2σ 3σ

50 0.3

0.3

0

100

0.4

0.4

0.5

0.6

0.5 2

sin θ23

0.7

0.6

0.8

0.7 0

0.06 0.06

1σ 2σ 0.04 0.04

Solar + KL

sin2θ13

3σ

1σ 0.02 0.02

2σ

All data

3σ

8.5

8.5

8.0

8.0

7.5

7.5

7.0

7.0

-5

δm2/10 eV2

0.00 0.00

6.5

0.25

0.30

sin2θ12

0.35

6.5

0.00

0.02

0.04

sin2θ13

0.06

Energy-scale and flux-shape errors with constrained “size” but unconstrained “shape” can bring the JUNO sensitivity below 3σ 5 NH true osc. + norm.

+ energy scale

1.02

+ flux shape

1.02

1.02

1.01

1.01

1.01

E’/E 1.00

1.00

1.00

0.99

0.99

0.99

osc. + norm.

NH true

4

+ energy scale + flux shape

3 0.98

’/

2

3

4

5

6

7

8

9

0.98

2

3

4

5

6

7

8

9

0.98

1.2

1.2

1.2

1.1

1.1

1.1

1.0

1.0

1.0

0.9

0.9

0.9

0.8

2

3

4

5

6

7

E (MeV)

8

9

0.8

2

3

4

5

6

7

E (MeV)

8

9

0.8

2

3

4

5

6

7

8

9

N 2

2

3

4

5

6

7

E (MeV)

8

9

1

0

0

5

T (y) (Note abscissa prop. to √T)

10

Roughly need halving their size to bring JUNO above 3σ in ~5 years [similar results for the case of true IH, see 1508.01391]

5 NH true osc. + norm.

+ energy scale (halved)

1.02

+ flux shape (halved)

1.02

1.02

1.01

1.01

1.01

E’/E 1.00

1.00

1.00

0.99

0.99

0.99

osc. + norm.

NH true

0.98

’/

2

3

4

5

6

7

8

9

0.98

2

3

4

5

6

7

8

9

0.98

1.2

1.2

1.2

1.1

1.1

1.1

1.0

1.0

1.0

0.9

0.9

0.9

0.8

2

3

4

5

6

7

E (MeV)

8

9

0.8

2

3

4

5

6

7

E (MeV)

8

9

0.8

4

+ energy scale (halved) + flux shape (halved)

3 2

3

4

5

6

7

8

9

N 2

2

3

4

5

6

7

8

9

1

E (MeV)

0

0

5

T (y)

10

doubled (3%)

default (1.5%)

halved (0.75%)

+ polynomial (doubled) + uncorrelated (doubled) + uncorrelated Stat + syst (osc+norm) + resolution (scale,width)+ polynomial +(halved) + uncorrelated +polynomial polynomial (doubled) +(halved) uncorrelated (doubled)

10

5

5

5

10

Nσ

Nσ 5

0

0 50

0

0

0

5

10

0

10

10

5

5

5

0

0

0 10

Time (y)

10

0

0

5

10

0

10

Time (y) Time (y)

Stat + syst (osc+norm)

5

5

5

5

0

0

0

5

10 5

0

0 510

0

010 0 0

10

10

10

10

5

5

5

5

5

10 5

Nσ 5

5 0

0

10

Nσ

0 50

0

5

5

10

Nσ 5

10

5

0

5

0 10

0

0

0

0

5

10 5

0

0 510

0

Time (y) TimeTime (y) (y)

Time (y)

+ resolution (scale,width)

10 5

010 0 0

5

10 5

10 5

10

10

5

5

5

5

Normal hierarchy

10

Nσ

0

0

5

10

0

0

5

10

0

0

5

10

0

10

10

10

5

5

5

5

5

10

5

10

Inverted hierarchy

10

0

Nσ

0

0

5

Time (y)

10

0

0

5

Time (y)

10

0

0

5

Time (y)

10

0

0

Time (y)

5

0

0

5

10

0

10

10

5

5

0

0

5

Time (y)

+ uncorrelated

10

5

0

5

10

5

10

Nσ

10

sin2θ23 in [0.45, 0.55] + polynomial

10

Nσ

10

Time (y) Time Time (y) (y)

10

Inverted hierarchy

10

10

10

Nσ 5

5 0

10

Inverted hierarchy

Nσ

10

10

Inverted hierarchy

10

10

+ uncorrelated (halved)

Normal hierarchy

10

Normal hierarchy

Nσ

10

Normal hierarchy

10

+ polynomial (halved)

10

0

0

Time (y)

PINGU itself can better constrain θ23, but with strong bias if hierarchy is unknown (so θ23 and hierarchy must be determined at the same time) NH true

IH true

0.70

0.70

(d)

0.65

0.65

0.60

0.60

0.55

0.55

0.50

0.50

0.45

0.45

0.40

0.40

0.35

0.35

0.30 0.40

0.45

0.50

0.55

0.60

0.70

0.30 0.40

0.50

0.55

0.60

0.45

0.50

0.55

0.60

(c)

0.65

0.65

0.60

0.60

0.55

0.55

0.50

0.50

0.45

0.45

0.40

0.40

0.35

0.35

0.45

0.50

sin2θtrue 23

0.55

0.60

0.30 0.40

IH test

sin2θfit 23

0.45

0.70

(b)

0.30 0.40

Best fit 1σ 2σ 3σ

NH test

sin2θfit 23

(a)

sin2θtrue 23

Note: Most of the previous comments apply also to ORCA (and HK, INO, ...)