Neutrino Physics II

Hitoshi Murayama

Taiwan Spring School

March 28, 2002

中性微子物理（二）

村山　斉台湾春期学校

二千二年三月二十八日

3

Outline

• Solar Neutrino Oscillations– Vacuum Oscillation– Matter Effect in the Sun– Matter Effect in the Earth– Seasonal Effect

• Future of Solar Neutrinos– Reactor neutrino– Day/Night Effect– Seasonal Variation

Solar Neutrino Oscillation

5

We don’t get enough

We need survival probabilities of

8B: ~1/3

7Be: <1/3

pp: ~2/3

Can we get three numbers correctly with two parameters?

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Dark Side of Neutrino Oscillation

• Traditional parameterization of neutrino oscillation in terms of (m2, sin22) covers only a half of the parameter space

(de Gouvêa, Friedland, HM)

• Convention: 2 heavier than 1

– Vary from 0˚ to 90˚– sin22 covers 0˚ to 45˚– Light side (0 to 45˚) and Dark Side (45˚ to 90˚ )

ν1 =νecosθ+νμsinθ

ν2 =−νesinθ+νμ cosθ

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Dark Side of Neutrino Oscillation

• To cover the whole parameter space, can’t use (m2, sin22) but (m2, tan2) instead.

(Fogli, Lisi, Montanino; de Gouvêa, Friedland, HM)

• In vacuum, oscillation probability depends only on sin22, i.e., invariant under 90

• Seen as a reflection symmetry on the log scale tan2cot2

• Or use sin2on the linear scale sin2cos2

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Fit to the rates ofsolar neutrino eventsfrom all experiments(Fogli et al)

How do we understand thisplot?

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Vacuum Oscillation

• Ga~1/2, Cl~1/3, water~1/3• One possible explanation is that neutrinos oscillate

in the vaccum just like in atmospheric neutrinos• But oscillation is more prominent for lower

energies while Ga retains the half• The oscillation length needs to be “just right” so

that 8B, 7Be are depleted more than average7Be:

€

m2

4EL ~ n +

12

⎛ ⎝ ⎜

⎞ ⎠ ⎟π ⇒ Δm2 ~ n +

12

⎛ ⎝ ⎜

⎞ ⎠ ⎟1.6 ⋅10−11eV2

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Matter Effect

• CC interaction in the presence of non-relativistic electron

€

L = −GF

2e γμ (1−γ5 )ν eν eγ

μ (1−γ5 )e

= −GF

2e γμ (1−γ5 )eν eγ

μ (1−γ5 )ν e

= − 2GFneν eγ0ν e

• Neutrino Hamiltonian

€

H = common

+Δm2

4E

−cos2θ sin 2θ

sin 2θ cos2θ

⎛

⎝ ⎜

⎞

⎠ ⎟

+ 2GFne1 0

0 0

⎛

⎝ ⎜

⎞

⎠ ⎟

Electron neutrino higher energy in the Sun

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Electron Number Density

Nearly exponentialfor most of the Sun’s interior oscillationprobability can be solved analytically with Whittaker function

€

ne (r) ≈ ne (0)e−r / r0

ne (0) ≈ 100N A /cm3

r0 ≈ Rsun /10 ≈ 7 ⋅104 km

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Propagation of e

• Use “instantaneous” eigenstates + and –

€

e ,Earth ν e ,core = cosθ sinθ( )e−im1

2L /2 p

e−im22L /2 p

⎛

⎝ ⎜ ⎜

⎞

⎠ ⎟ ⎟

a b*

−b a*

⎛

⎝ ⎜

⎞

⎠ ⎟e−iE−t

e−iE+t

⎛

⎝ ⎜

⎞

⎠ ⎟cosθM

sinθM

⎛

⎝ ⎜

⎞

⎠ ⎟

L

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Survival Probability

€

e ,Earth ν e ,core 2

= a cosθe−im12L /2 p − bsinθe−im2

2L /2 p ⎛ ⎝ ⎜ ⎞

⎠ ⎟cosθM e−iE−t

+ b* cosθe−im12L /2 p + a* sinθe−im2

2L /2 p ⎛ ⎝ ⎜ ⎞

⎠ ⎟sinθM e−iE+t

2

= 1− Pc( )cos2 θ + Pc sin2 θ[ ]cos2 θM

+ Pc cos2 θ + 1− Pc( )sin2 θ[ ]sin2 θM

− Pc 1− Pc( ) sin 2θ cosΔm2

2pL + δ

⎛

⎝ ⎜

⎞

⎠ ⎟

€

E+ − E−( )t

~ 2GFne (0)Rsun /10

~ 1000Decoheres uponAveraging overProduction region

€

Pc = b 2

1− Pc = a 2

Hopping probability

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Survival Probability cont.

• Thermal effects E~kT~1keV

• The last term averages out if

• Now we need Pc

€

e ,Earth ν e ,core 2

= 1− Pc( )cos2 θ + Pc sin2 θ[ ]cos2 θM + Pc cos2 θ + 1− Pc( )sin2 θ[ ]sin2 θM

− Pc 1− Pc( ) sin 2θ cosΔm2

2pL + δ

⎛

⎝ ⎜

⎞

⎠ ⎟

€

m2

E≥

10−8 eV2

1MeV

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Level Crossing

• For small angles and <45, e is higher at the core while lower outside, and hence two levels cross

€

Pc =e−γ sin2 θ − e−γ

1− e−γ

γ = 2πr0Δm2

2p=1.05

Δm2

10−9 eV2MeV

p

>>1 Pc0 adiabatic limit1 Pccos2 non-adiabatic limit

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Survival Probability

• “MSW triangle”• 100% lost at the center

of the triangle, possible even for small angles

• Dark side always bigger than 50%

• Scales with energy because of m2/p dependence

No level crossing

Non-adiabatic

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SMA LMA

LOW

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Survival Probability

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Matter Effect in the Earth

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Matter Effect in the Earth

• When neutrino mass eigenstates go through the Earth, some of lost e state may be regenerated

Sun may be brighter in the night

• Day-night asymmetry:

€

ADN =N − D

N + D

7Be

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Day/Night Spectra at SuperK

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• Absence of day/night effect cuts into LMA

€

ADN = 0.066 ± 0.044−0.024+0.026

7Be

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Spectrum Distortion

• Survival probability may be energy-dependent

• Knowing 8B spectrum measured in the laboratory, one can look for spectrum distortion in data

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No spectrum distortion yet at SuperK

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No spectrum distortion yet at SNO

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• Absence of spectrum distortion removes SMA

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Seasonal Effect

• Earth’s orbit is slightly eccentric

• The Earth-Sun distance changes 3.5% from max to min

• 1/r2 law says 7% change in neutrino flux from max (summer) to min (winter)

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So far no seasonal effect in 8B

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Vacuum Oscillation again

€

e ,Earth ν e ,core 2

= 1− Pc( )cos2 θ + Pc sin2 θ[ ]cos2 θM + Pc cos2 θ + 1− Pc( )sin2 θ[ ]sin2 θM

− Pc 1− Pc( ) sin 2θ cosΔm2

2pL + δ

⎛

⎝ ⎜

⎞

⎠ ⎟

→1− sin2 2θ sin2 Δm2

4 p(L − Rsun )

⎛

⎝ ⎜

⎞

⎠ ⎟

€

=2πr0Δm2

2p→ 0

Pc =e−γ sin2 θ − e−γ

1− e−γ→ cos2 θ

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Quasi-Vacuum oscillation

• Vacuum region actually reached slowly as m2 decreased

• Transition region between “MSW” and “vacuum” region: quasi-vacuum

• Both matter effect and oscillatory term need to be kept

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• LOW extends down to VAC, especially in the dark side!

Future of Solar Neutrinos

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More from SNO

• NC/CC

confirmation of neutrino conversion

sterile neutrino?

• Day/night effect LMA

• CC spectrum SMA, VAC

• Seasonal effect VAC

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What Next on Solar Neutrinos?

• We’d like to convincingly verify oscillation with man-made neutrinos

• Hard for low m2

• Need low E, high

• Use neutrinos from nuclear reactors

• To probe LMA, need L~100km, 1kt

Psurv=1−sin2 2θsin2 1.27Δm2c4

eV2GeVEν

Lkm

⎛

⎝ ⎜

⎞

⎠ ⎟

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KAMioka Liquid scintillatorANti-Neutrino Detector

1kt

• KamLAND• Detectors electron

anti-neutrinos from nuclear power plants by inverse beta decay

€

e p → e+n

e+e− → γγ

np → dγ

(2.2MeV, delayed)

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Location, Location, Location

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KamLAND sensitivity on LMA

• First terrestrial expt relevant to solar neutrino problem

• KamLAND will exclude or verify LMA definitively

• Data taking since Nov 2001

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KamLAND first neutrino event

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Measurements at KamLAND

• Can see the dip when m2>210–5eV2

(Pierce, HM)

• Can measure mass & mixing parameters

Data/theory

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If LMA confirmed...

• Dream case for neutrino oscillation physics!

• m2solar within reach of long-baseline expts

• Even CP violation may be probable– neutrino superbeam– muon-storage ring neutrino factory

• If LMA excluded by KamLAND, study of lower energy solar neutrinos crucial

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CP Violation

• Possible only if:– m12

2, s12 large enough (LMA)

– 13 large enough

P(νe→ νμ)−P(νe→ νμ) =16s12c12s13c132 s23c23

sinδsinΔm12

2

4EL

⎛

⎝ ⎜

⎞

⎠ ⎟ sin

Δm132

4EL

⎛

⎝ ⎜

⎞

⎠ ⎟ sin

Δm232

4EL

⎛

⎝ ⎜

⎞

⎠ ⎟

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VAC by seasonal variation

• 7Be neutrino monochromatic

• seasonal effect probes VAC region

(de Gouvêa, Friedland, HM)

• Borexino crucial• Hopefully

KamLAND, too!

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VAC by seasonal variation

• Fit to seasonal variation to measure parameters

Can pep resolve degeneracy?

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LOW by day/night effect

• 7Be neutrino monochromatic

• Day/night effect probes LOW region

• (de Gouvêa, Friedland, HM)

• Borexino crucial• Hopefully

KamLAND, too!

46

LOW by zenith angle dependence

• More information in zenith angle depend. (de Gouvêa, Friedland, HM)

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Flavor Content

• Small difference in recoil spectrum

NC: e– e–

NC+CC: e–e e–e

• Can in principle be used to discriminate flavor of solar neutrinos model-independently

(de Gouvêa, HM)

7BeSMAKamLAND600t*3yrs

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SMA by pp neutrinos

• SMA: Sharp falloff in probability in the pp neutrino region the survival

• Because of the condition for the level crossing

• Measure the falloff m2 measurement

Δm2

2E< 2GFne(0)

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Can pp neutrinos be studied?

• CC+NC (electron recoil)– gaseous He TPC

– HERON: superfluid He (phonon & roton)

– liquid Xe

– GENIUS: Ge

• CC (e capture)– LENS: Yb or In

– MOON: Mo

LENS-Yb

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Conclusions

• Solar neutrino data can be fit well with neutrino oscillation hypothesis

• Definitive signals come from near-future experiments– LMA:KamLAND, day/night at SNO– LOW: day/night at Borexino/KamLAND– VAC: seasonal effect at Borexino/KamLAND– SMA: pp neutrino