Stephen Parke Fermilab · 2019-01-24 · - 3 Ben Lee, Mary K Gaillard, Shirley Jackson & Tong...

Stephen Parke IFT - UAM 1/24/2019 # 2

Stephen ParkeFermilab

ν4—

Lessons and prospects from the past, present and

future of \nu_e disappearance experiments

Ben Lee, Mary K Gaillard, Shirley Jackson & Tong Pagnamenta

“can live and work with pride and dignity without regard to such differences as race, religion, sex or national origin. In conflict between technical expediency and human rights, we will stand on the side of human rights.” Wilson 1970

some members of the Fermilab Theory Group 1974:

Interactions:

simple complicated

Propagation:

simplecomplicated

=Uunitary matrix ?

masses ?

W+→ µ+

νµW+→ e+νe

W+→ τ

Neutrino Flavor or Interaction States:

νe νµ ντ

provided L/E 0.5 km/MeV = 500 km/GeV !!!

1 picosecond in Neutrino rest frame !!!

ν1 ν2 ν3

Neutrino Mass EigenStates or Propagation States:

Propagator νj → νk = δjk e−i

21∼ 7.5 × 10

−5eV

∼ ×

|∆m2

31| ≈ |∆m

32| ∼ 2.5 × 10

−3eV

Neutrino Mass EigenStates or Propagation States:

νe = νµ =

ντ =

most νe

ν1 ν2least νe

θ23δ,θ23 δ,θ23

Solar Exp, SNOKamiLANDDaya Bay, RENO, …

SuperK, K2K, T2KMINOS, NOvAICECUBE

UnitaritySK, OperaICECUBE ?

ν1, ν2 Mass Ordering:

ν2 ν1

|∆m221| = |m2

2 − m21| = 7.5 × 10−5

| 21| | 2 − 1| ×

L/E = 15 km/MeV = 15, 000 km/GeV

SNO m2 > m1

–solar mass ordering

νe = νµ =

ντ =

ν3, ν1/ν2 Mass Ordering:–atmospheric mass ordering

|∆m2

31| = |m2

3− m2

1| = 2.5 × 10

−3 eV2

| | | − | ×

L/E = 0.5 km/MeV = 500 km/GeV

νe = νµ =

ντ =

Unknown: NOνA, JUNO, ICECUBE, DUNE, T2HKK....

sin2Θ13

sin2Θ12

sin2Θ23

cos ∆ $

NORMAL

Νe ΝΜ ΝΤ

NeutrinoMassSquared

Fractional Flavor Content varying cos ∆

(msol2

(matm2

! !sinΘ13

sin2Θ13

cos ∆ $

sin2Θ23

sin2Θ12

INVERTED

(msol2

(matm2

! !sinΘ13

|Uαj|2

CPT ⇒ invariant δ ↔ −δ

• Labeling massive neutrinos: |Ue1|2 > |Ue2|

2 > |Ue3|2

sin2θ12 ∼

sin2θ23 ∼

sin2θ13 ∼ 0.02

0 ≤ δ < 2π

|∆m2

31| = |m2

3− m2

1| = 2.5 × 10

−3 eV2

| | | − | ×

L/E = 0.5 km/MeV = 500 km/GeV

|∆m221| = |m2

2 − m21| = 7.5 × 10−5

| 21| | 2 − 1| ×

L/E = 15 km/MeV = 15, 000 km/GeV

Summary:

Unitarity

6 row/column plus 6 triangle conditions

2 row and 1 triangle, independent of ντ

Ross-Lonergan+ SP 1508.05095

∆ij ≡∆m2

kinematic phase:

νe → νe and νe → νe

REACTOR NEUTRINOS:

P (νe → νe) = 1− P13 − P12 with

P13 = 4|Ue3|2(|Ue1|

2 sin2∆31 + |Ue2|2 sin2∆32)

= sin2 2θ13 (cos2θ12 sin

2∆31 + sin2 θ12 sin

2∆32),

P12 = 4|Ue2|2|Ue1|

2 sin2∆21 = sin2 2θ12 cos4θ13 sin

2∆21,

∆ij ≡∆m2

Daya BayRENO

D-ChoozKamLAND

sin22θ13

cos 2θ12 sin22θ13

≈ 0.4 sin22θ13

Reactor θ13 Experiments

@"Yonggwang,"Korea

@"Daya"Bay,"China

Daya'Bay'@"Chooz,"France

Double'Chooz'

entsite

owalso

particul

rvewill

13θ22sin

0 0.05 0.1 0.15 0.2

3.5Rate+SpectrumRate-only

99.7% C.L.95.5% C.L.68.3% C.L.

0 0.05 0.1 0.15 0.2

2 χ∆ 2

46 Rate+Spectrum

Rate-only

2χ∆0 2 4 6

RENO 2200 days

(km/MeV)νE/effL

0 0.2 0.4 0.6 0.8

→ eν(

Far Data

Near Data

Prediction from near data

0.065 0.07 0.075 0.08 0.085 0.09 0.095 0.1 0.1050

Entries 0

Mean 0

)13θ(22sin

0.07 0.08 0.09 0.1

2χ∆

2 4 6 8 10

Daya Bay 1958 days

2 4 6 8 10 12

[MeV]promptE2 4 6 8 10 12F

What is ∆m2

0.2 0.4 0.6 0.8 1.0

) = 1− P13

3 curves:NOIO

Approx

L/E (km/MeV)

P13 ≈ sin2 2θ13 sin2∆ee

ee≡ cos2 θ12 ∆m2

31+ sin2 θ12 ∆m2

eeis νe average of ∆m

31and ∆m

Nunokawa, SP, Zukanovich Funchal hep-ph/0503283NPZ=

RENO uses this defn:

| | | | | |

2∆31 + sin2 θ12 sin

2∆32),

∆21 = 0.1

L/E1 km/MeV

minimum

<0.002

cos2 θ12 sin2∆31 + sin2 θ12 sin

2∆32 − sin2∆ee

= 0×∆21 sin 2∆ee + (s212c2

12)∆2

21 cos 2∆ee ±O(∆3

∆31 = ∆ee + s2

12∆21

∆32 = ∆ee − c2

12∆21

Daya Bay Saga:

Invisibles 2015 —> present

DB 1505.03456v1 DB 1505.03456v2 (PRL)

=> SP 1601.07464

How Does Daya Bay Define ∆m2

sin2∆EE ≡ c2

12sin2∆31 + s

12sin2∆32 (1)

⇒ ∆m2

arcsin

(c212sin2∆31 + s2

12sin2∆32)

(arXiv:1310.6732 and 1505.03456v1)

Maladies:

• L/E dependent

• Discontinuous at Osc. Max./Min.

(L/E ≈ 0.5, 1.0, .. km/MeV)

3% jump

• no simple physical meaning !

Why???

RHS (1) never gets exactly to 1,

or back to 0

whereas LHS does !

eg sin2(π2 ) = 1

2 +O(4)

with = s12c12∆21

Daya Bay’s New Defn. ∆m2

(arXiv:1505.03456v2 and 1809.02261)

EE ∆m2

arctan

sin 2∆21

cos 2∆21 + tan2 θ12

= ∆m2

ee(NPZ) L/E 2π/∆m2

31L/E 2π/∆m2

• L/E dependent for > 10 km/MeV

• Jump in JUNO L/E ∼ 1%

• physical meaning ???

Maladies:

∆m221 = 7

KamLAND:

(km/MeV)eν

20 30 40 50 60 70 80 90 100 110

eνData - BG - Geo best-fit oscillationν3-

best-fit oscillationν2-

KamLAND:

| | ≈

Vacuum:

averaged osc

∼ 68% ν1

∼ 30% ν2

∼ 2% ν3

∆m221 = 7.50+0.20

−0.20 × 10−5 eV2,

SuperK

ν? + e→ ν + e

Which type of Neutrino dominates this image ?

Neutrino Energy [MeV]

1−10 1 10

Survival probability for

Solar Neutrinos:

> 90% ν2

| | ≈ |

Vacuum:

averaged osc

∼ 68% ν1

∼ 30% ν2

∼ 2% ν3

pppp 7Be

Be pepep 8B

Borexino

8B SNO/SK

matter effect

Phys. Rev. D94, 052010 (2016)

SK/SNO

day night

∆m221 = 5.1+1.3

−1.0 × 10−5 eV2,

D/N asymmetry + lack of observation of upturn.

Eur.Phys.J. A52 (2016) no.4, 87

KamLAND

0.2 0.25 0.3 0.35 0.4

2 21 [

13 = 0.0221

Tension between KamLAND and SNO/SK

Nu-fit

Why do we care about ∆m221 = 7

∼ →

P (νµ → νe)− P (νµ → νe) ≈ π J

where J = sin 2θ12 sin 2θ13 cos θ13 sin 2θ23 sin δ ≈ 0.3 sin δ

where J is Jarlskog Invariant (1986):

At oscillation maximum in vacuum:

CP Violation:

Neutrino mode 1Re candidates

30 40 50 60 70 80 90 100

18T2K Run1-9c Preliminary

0.55, 0.45, 0.50 = 23θ

4/c2 eV

-310× = 2.4432

4/c2 eV

-310× = 2.4113

π = CPδ

/2π = +CPδ

= 0CPδ

/2π = -CPδ

syst err

stat + syst err

bi-event: bi-probability:

KamLAND∆m2

21 = 72 x KamLAND

∆m221 = 7

Can Short Baseline Reactor Neutrinos say anything about

∆m221 = 7

∆ij ≡∆m2

( < 0.01 )

( < 0.1 )

L/E (km/MeV)

0.2 0.4 0.6 0.8 1.0

P (νe → νe) = 1− P13 − P12 with

P13 = 4|Ue3|2(|Ue1|

2 sin2∆31 + |Ue2|2 sin2∆32)

2∆31 + sin2 θ12 sin

2∆32),

P12 = 4|Ue2|2|Ue1|

2 sin2∆21 = sin2 2θ12 cos4θ13 sin

2∆21,

Dependence on Solar Parameters:

0.2 0.4 0.6 0.8 1.0

L/E (km/MeV)

If ∆m221 is 3 times bigger, P12 is 9 times larger !

× KamLAND value

S.H. Seo and SP arXiv:1808.09150

dependence is on sin 2θ12∆m2

(km/MeV)νE/effL

0 0.2 0.4 0.6 0.8

→ eν(

Far Data

Near Data

Prediction from near data

2 4 6 8 10 12

[MeV]promptE2 4 6 8 10 12F

Daya Bay

1 - 10 KamLAND

∆m221 = 7

Simulation S.H. Seo and SP arXiv:1808.09150

L/E ∼ 0.5 km/MeV compared to KamLAND L/E ∼ 50 km/MeV

T2K is at 0.5 km/MeV

14θ22sin

-310 -210 -110 1

Daya Bay 95% C.L.

sDaya Bay 95% CL

)σ1±Daya Bay 95% expected (

Bugey 90% C.L.

1607.01174404 days

Daya BaySterile Neutrino Search | e3| | e4| | e3| 31

1 sin2 2θ14 sin2∆41 sin2 2θ13 sin

2∆31.

× KamLAND value

Reinterpretation !

17,000 20-inch PMTs

25,000 3-inch PMTs

In fact, JUNO will

be the largest

liquid scintillator

(LS) detector so

far in history!

LS Detectors Daya Bay Borexino KamLAND JUNO

Target Mass 20 t x 8 300 t 1 kt 20 kt

Similar in concept

to previous LS

experiments, but

much LARGER

Nominal + B2B (1%) + BG + EL (1%) + NL (1%)

sin2 θ12 0.54% 0.60% 0.62% 0.64% 0.67%

∆m221 0.24% 0.27% 0.29% 0.44% 0.59%

|∆m2ee| 0.27% 0.31% 0.31% 0.35% 0.44%

Table 3-2: Precision of sin2 θ12, ∆m221

and |∆m2ee| from the nominal setup to those including

additional systematic uncertainties. The systematics are added one by one from left to right.

JUNO precision ~2025

of sin2 θ12, ∆m221

and |∆m2ee|

Li, Wang, Xing 1605.00900

Matter Effects in JUNO

Matter Input/Matter Fit Matter Input/Vacuum Fit

Shift 1σ in ∆m2

21and 3σ in θ12

Size of shift unexplained in 1605.00900:

Khan, Nunokawa, SP upcoming 1810.?? or 1811.??

5 10 15 20 25

L/E (km/MeV)

13 − P12) = 1

5 10 15 20 25

) = 1− P13

L/E (km/MeV)5 10 15 20 25

L/E (km/MeV)

13 − P12) = 1

5 10 15 20 25

L/E (km/MeV)

1−P13−P12

perfect resolution, not 3%/p

E/1 MeV

JUNO and the Mass Ordering:

Px(νe → νe) = 1− cos4 θ13 sin2 2θ12 sin

2∆21

2sin2 2θ13

1− sin2 2θ12 sin2∆21 cosΩ

with Ω = (∆31 +∆32) + arctan(cos 2θ12 tan∆21).

φ(∆21 ± π) = φ(∆21)± 2π sin2 θ12,

0 1 2 3 4 5 6 7

∂ Ω

∂(L/2E)

= cos2 θ12∆m2

31+ sin2 θ12∆m2

where Ω = 2|∆ee| ± φ

| | ±

φ = arctan(cos 2θ12 tan∆21)−∆21 cos 2θ12

2∆21

NO phase advanceIO phase retardation

δ (∆m2

ee) ∼ 0.5%

Parke @ NOW 2008

Ω = 2|∆ee|+ η φ

NO => oO

IO => oO

(NO, oO, IO) given by η=(1, 0, -1)

Neutrino Energy Reconstruction

Nominal Model ± 68% C.L.

Positron Energy Response ModelReconstructed Energy [MeV]

True Positron Energy [MeV]0 1 2 3 4 5 6 7 8 109

Cross-validation

Energy Model + 68.3% C.L.

IBD Positron Energy

0 2 4 6 8 10

Daya Bay

•Energy Resolution to 3% or lower at 1 MeV

•Linearity to sub 1% precision for the

reconstructed neutrino energy

KamLAND# JUNO# RENOB50#

LS##mass# ~1#kt## 20#kt## 18#kt##

Energy#ResoluPon# 6%/# ~3%/# ~3%/#

Light#yield# 250#p.e./MeV# 1200#p.e./MeV# >1000#p.e./MeV#44(

Linearity 1.9% < 0.5% < 0.5% > 4 x

3% 0.3%

RESOLUTION LINEARITY

Other Prospects:

0.001 - 0.01

NEOSPROSPECT

DANSSSTEREO

Nu-4……

Ultra-Short Baseline: 10 m baseline

Matter Effects:

, i ddx = H,

0 ∆m2

0 0 ∆m2

5U † +

a(x) 0 0

a = 2√2GFNeE ≈ 1.52× 10−4

g.cm−3

ν ≡

if ρYe = 1.5 g/cm3 and E = 10 GeV then a ≈ ∆m231

E = 300 MeV then a ≈ ∆m2

Neutrino Propagation in Matter:

ax3 + bx

2 + cx + d = 0

complicated, counter intuitive, …

3 flavor mixing in matter

ax2 + bx + c = 0

simple, intuitive, useful

2 flavor mixing in matter

where H0 is diagonal

and H1 is off-diagonal.

Hamiltonian:

Rewrite as H = H0 + H1

0 ∆m2

0 0 ∆m2

H. Minakata + SP arXiv:1505.01826P. Denton + H. Minakata + SP arXiv:1604.08167

solvable perturbation

Neutrino Evolution in Matter (conti):

D=diagonal OD= off-diagonal

(2E)HOD/∆m2ee = s13c13

+ c13 s12c12

∆m221

∆m2ee

− s13 s12c12

∆m221

∆m2ee

U†23(θ23, δ)H U23(θ23, δ) = HD +HOD

(2E)HD =

13∆m

− s2

12)∆m

13∆m

ee≡ cos2 θ12∆m

31+ sin2 θ12∆m

!!! level crossing !!!

f f e e

cos 2eθ13 = ∆m2ee cos 2θ13a

∆fm2

where a = 2√2GFNeEν and

∆fm2ee = ∆m2

q(cos 2θ13 − a/∆m2

ee)2 + sin2 2θ13

with ∆m2

ee cos

2 θ12∆m2

31+ sin

2 θ12∆m2

cos 2eθ12 = ∆m221 cos 2θ12a

∆fm2

where a 0 ≡ (a+∆m2ee

−∆fm2ee)/2

(the effective matter potential for 1-2 sector.)

∆fm221 = ∆m2

q(cos 2θ12 − a 0/∆m2

21)2 + cos2(eθ13 − θ13) sin

2 2θ12fq

− e −

∆fm231 = ∆m2

4(∆fm2

ee−∆m2ee) + 1

2(∆fm2

21−∆m221)

DMP 0th order in a nutshell:

Vacuum ⇒ Matter

Pνα!νβ(∆m2

31,∆m221, θ13, θ12, θ23, δ) ⇒ Pνα!νβ

(∆ fm231,∆ fm2

21, eθ13, eθ12, θ23, δ)

(same function just use matter variables)

two 2 flavor

rotatio

∆cm2ee

c c c− −

≈ ∆m2

q(cos 2θ13 − a/∆m2

ee)2 + sin2 2θ13 ,

∆c m

(1−Pa(

|b∆ee|0 π/2 π 3π/2 2π

−E [GeV]

Pa(νe → νe) ≈ 1− sin2 2θ13

∆cm2ee

sin2 b∆ee ,

where b∆ee ≡ ∆cm2eeL/(4E) ,

Denton, SP 1808.09453

νe → νe

New Perturbation Theory for Osc. Probabilities

νµ → νe, L = 1300 (km), δ = 3π/2, NO

0.3 1.0 10E (GeV)

10−14

10−12

10−10

10−8

10−6

10−4

10−2

|∆P|/P

Zeroth First Second

systematic expansion

νµ → νe, L = 1300 (km), δ = 3π/2, NO

0.3 1.0 10E (GeV)

10−13

10−11

10−9

10−7

10−5

10−3

10−1

|∆P|/P

Zeroth First Second

Summary:• Observation of Solar Neutrinos and Reactor Neutrinos have

taught us a great deal the electron row of the PMNS matrix, about U_ei and Delta m^2 ’s.

• the concept of an effective Delta m^2, Delta m^2_ee, is useful for the shape analysis of reactor neutrinos.

• Short baseline reactor experiments can constrain (maybe measure) Delta m^2_21 at twice the KamLAND value.

• the generalization of Delta m^2_ee into matter, is useful for understanding neutrino oscillations in matter for DUNE and T2HK(K)

eeis νe average of ∆m

31and ∆m

∆m2ee

(cos 2θ13 − a/∆m2ee)2 + sin2 2θ13

Ernest Rutherford, emperor of the atomic

domain (Image: Wikipedia Commons)

Ernest Rutherford, master ofsimplicityBy Ashutosh Jogalekar | August 30, 2013 | 6for high-flying theorizing; he once said that

"theorists play games with their symbols while

we discover truths about the universe". And yet

he had an eye for theoretical talent that allowed

him to nurture Niels Bohr, as dyed-in-the-wool a

theoretician and philosopher as you could find.

When asked why he adored Bohr in spite of his

extras

21,eθ13,

eθ12 ∆ fm231,∆

fm221,

Mixings and Masses in Matter:

12, θ23, δ) unchanged

NO: for IO figures see 1604.08167

es12 ≡ sin eθ12, etc

(2E)HOD/∆m2ee = sin(eθ13 − θ13) s12c12

∆m2ee

−es12ec12

−es12 ec12

≈ ×

4× 10−4

for E = 2 GeV and ρ = 3 g.cm−3sin(eθ13 − θ13) ≈ s13c13

∆m2ee

After 2 rotations:

0th Order:

zero in vacuum

νj and νi. Since ∆m221

∆m231

∆m232

[1], the short-

distance (km) reactor νe oscillation is due primarily to the

∆3i terms and naturally leads to the definition of the effec-

tive mass-squared difference sin2 ∆ee cos2 θ12 sin2∆31 +

sin2 θ12 sin2∆32 [11].

The Daya Bay experiment previously determined 2

(arXiv:1310.6732

d 1505.03456v1)071101 (2014).

[8] sin2∆ee ≡ cos2 θ12 sin

2∆31 + sin2

θ12 sin2∆32, where

∆ji ≡ 1.267∆m2

ji(eV2)[L(m)/E(MeV)], and ∆m2

ji is the

difference between the mass-squares of the mass eigenstates νjand νi.

How Does Daya Bay Define ∆m2

Stephen Parke Fermilab · 2019-01-24 · - 3 Ben Lee, Mary K Gaillard, Shirley Jackson & Tong...

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