1. Helicity of Neutrinos Contents 1. Introduction
ニュートリノのヘリシティ
M. Goldhaber, L. Grodzins and A. W. Sunyar
Brookhaven National Laboratory
Phys. Rev (1958) 1015.
Contents
1. Introduction
2. Principle of experiment
3. Experimental method
4. Result
5. Summary
Shibata Lab.
Akihito Fukuda

2. 1. Introduction History of neutrino Helicity is defined as p σ p σ VA
STP
𝑒 − － ＋
𝑒 + 𝜈
History of neutrino
If we can measure the helicity of neutrino, the type is decided.
1903 Rutherford : Discovery of α-ray , β-ray , γ-ray
1904 Chadwick : Discovery of continuous spectrum of β-ray
Experiment by Goldhaber, Grodzins and Sunyar
1931 Pauli : Neutrino hypothesis 2
Rutherford : Discovery of α-ray , β-ray , γ-ray
1904 Chadwick : Discovery of continuous spectrum of β-ray
1931 Pauli : Propounding of neutrino hypothesis
Fermi : Propounding that β-decay is three-body problem
ℎ=±1
1954 Reines : Detection of neutrino
　　　 𝑃 𝐸 𝑑𝐸= 2𝜋 ℏ 𝛷 𝑓 𝐻 𝛽 𝛷 𝑖 𝑑𝑛 𝑑𝐸
𝐻 𝛽 = 𝐻 𝛽 + 𝐻′ 𝛽
𝐻 𝛽 = 𝑖 𝐶 𝑖 𝜑 † 𝑝 𝑶 𝑖 𝜑 𝑛 𝜑 † 𝑒 𝑶 𝑖 𝜑 𝜈 +ℎ.𝑐.
𝐻′ 𝛽 == 𝑖 𝐶′ 𝑖 𝜑 † 𝑝 𝑶 𝑖 𝜑 𝑛 𝜑 † 𝑒 𝑶 𝑖 𝛾 5 𝜑 𝜈 +ℎ.𝑐.
1956 Yang, Lee : Parity violation in weak interaction
Helicity is defined as p
ℎ=+1 σ
𝑂 𝑖
Scalar
𝐶 𝑆 1
Vector
𝐶 𝑉
𝛾 𝜇
Tensor
𝐶 𝑇
𝛾 𝜇𝜈
Axial vector
𝐶 𝐴
−𝑖𝛾 𝜇 𝛾 5
Pseudo scalar
𝐶 𝑃
𝛾 5
ℎ= 𝝈∙𝒑 𝝈 ∙ 𝒑
Measurement of the helicity of electron
by Frauenfelder p
ℎ=−1 σ
ℎ 𝑒 − =−1
ℎ 𝑒 + =+1
𝛾-Matrix
𝜇=1,2,3,4
𝛾 5 = 𝛾 1 𝛾 2 𝛾 3 𝛾 4
𝛾 𝜇𝜈 =− 𝑖 2 𝛾 𝜇 𝛾 𝜈 − 𝛾 𝜈 𝛾 𝜇
In this experiment, the helicity of neutrino was measured.

3. 2. Principle of experiment
𝜎 𝑒 =+ 1 2
2. Principle of experiment
𝜎 Sm =+1
𝑡 =9.3ℎ
0 −
152m Eu
152m Eu+ e − → 152 Sm +ν *
𝑚 𝑒 =± 1 2 , 𝑚 𝛾 =±1 , 𝑚 𝜈 =± 1 2
3 −
Electron Capture
152 Eu
152 Sm+γ
1 −
𝑚 𝑒 =± 1 2
152m Eu 𝑒
152m Eu 𝑒
839keV
961keV
before
𝜎 𝑒
+ 1 2
− 1 2
after
𝜎 𝛾 −1 +1
𝜎 𝜈
2 +
0 + ν
152 Sm * ν
152 Sm *
152 Sm
𝜎 𝑒 =− 1 2
ℎ 𝜈 =+1
ℎ 𝜈 =−1 γ γ
152 Sm
152 Sm
𝜎 𝛾 =∓1
𝜎 Sm =−1
ℎ 𝛾 =−1 γ
𝜎 𝜈 =± 1 2
ℎ 𝛾 =+1 𝜃
If ℎ 𝛾 =+1, ℎ 𝜈 =+1
If ℎ 𝛾 =−1, ℎ 𝜈 =−1
If we measure the helicity of γ-ray, the helicity of neutrino is determined.
152 Sm ν

4. 3. Experimental method ν
・ 152m Eu , the source, was produced in the Brookhaven reactor.
The helicity of γ-ray is measured by Compton scattering.
・Electromagnet was alternately magnetized in the up or down direction every 3 minutes. 𝛾
Forward γ-rays are selected by resonant scattering.
・9 runs with length from 3 to 9 hours were carried out.
・As a further check, 3 runs were carried out with a shorter magnet with the source on top of the magnet.
I will explain about resonant scattering and measurement of γ-ray helicity with Compton polarimeter.

5. Resonant scattering of γ-rays
In order to select forward γ-ray, resonant scattering was used.
(共鳴散乱)
𝐸 0
𝐸 0
𝜀 : recoil energy ×
𝜀= 𝐸 𝑀 𝑐 2
𝐸 0 −𝜀
152 Sm
152 Sm
Energy of γ-ray
𝐸 𝛾 = 𝐸 0 − 𝐸 𝑀 𝑐 𝐸 0 𝐸 𝜈 𝑀 𝑐 2 cos 𝜃 γ 𝜃 γ 𝜀
Doppler shift
For resonant scattering ν
152 Sm 𝜃
𝐸 0 = 𝐸 𝛾 −𝜀
𝐸 𝑀 𝑐 2 = 𝐸 0 𝐸 𝜈 𝑀 𝑐 2 cos 𝜃
𝐸 𝛾 ′ : energy of γ-ray that can be spent for excitation of nucleus ν
152 Sm
𝐸 𝜈 cos 𝜃 = 𝐸 0
Condition of resonant scattering

6. Measurement of γ-ray helicity with Compton polarimeter
𝐼 0
・The γ-ray enters into the magnetized iron. Fe 𝑥
・Cross-section of Compton scattering is larger if electron and γ-ray spins are antiparallel. γ
𝐼 0 𝑒𝑥𝑝 −𝜎𝜌𝑥
𝜎 𝑎𝑛𝑡𝑖 > 𝜎 𝑝𝑎𝑟𝑎
・The counting rate varies depending on the direction of the magnetization by Compton scattering.
𝑁 + : counting rate with the magnetic field pointing up
𝛿≡ 𝑁 − − 𝑁 𝑁 − + 𝑁 +
(The spin of electron pointing down)
𝑁 − : counting rate with the magnetic field pointing down
(The spin of electron pointing up)
・If the γ-ray are 100% circularly polarized, we expect an effect of
𝛿=±0.025 with an accuracy of 10%. 𝛿+
𝑁 − ( 𝜎 𝑒 up)> 𝑁 + ( 𝜎 𝑒 down)
𝝈 𝛾 up
𝒉 𝛾 − 𝛿−
𝑁 − 𝜎 𝑒 up < 𝑁 + ( 𝜎 𝑒 down)
𝝈 𝛾 down
𝒉 𝛾 +

7. 4. Result ℎ 𝜈 =−1 ・An effect 𝛿=+0.017±0.003 was observed in channel B.
・In the last 3 runs also a negative helicity was found, the circular polarization being 66±15 %.
・The helicity of γ-ray is negative.
ℎ 𝜈 =−1

8. 5. Summary
𝝈 𝜸
𝝈 𝝂
ℎ 𝜈 =−1
・The helicity of the neutrino was determined by the measurement of γ-ray from the electron capture of 152𝑚 Eu .
・The helicity of neutrinos was necessary to decide the type of the β-interaction.
𝒑 𝜸
𝒑 𝝂
・A combined analysis of circular polarization and resonant scattering of γ-rays measured the helicity of the neutrino.
・To select forward γ-ray, the resonant scattering was used.
・We had γ-ray Compton-scattered, and Circular polarization of γ-ray was measured by the difference of counting rate.
・The helicity of γ-ray was measured by Compton scattering. VA
STP
𝑒 − － ＋
𝑒 + 𝜈
・The helicity of forward γ-ray was negative.
・The resonant-scattered γ-ray was detected.
・It indicates that the helicity of neutrino is negative; ℎ 𝜈 =−1
・That the helicity of γ-ray is negative( ℎ 𝛾 =−1) was found, and that the helicity of neutrinos is negative ( ℎ 𝜈 =−1) was determined.

9. 以下、補足スライド

10. δ and ℎ 𝛾 δ + δ − 𝜇 𝑒 : magnetic moment electric current
𝜇 𝑒 =2 − 𝑒 𝑚 𝜎 𝑒
𝜇 𝑒
𝜎 𝑒
𝝈 𝛾 +
𝑁 + → 𝜎 𝑒 − → anti
𝑁 + =𝐴𝑒𝑥𝑝 𝜎 𝑎𝑛𝑡𝑖 𝜌𝑥
𝑁 − > 𝑁 +
δ +
𝑁 − → 𝜎 𝑒 + → para
𝑁 − =𝐴𝑒𝑥𝑝 𝜎 𝑝𝑎𝑟𝑎 𝜌𝑥
𝒑 𝜸 −
𝝈 𝛾 −
𝑁 + → 𝜎 𝑒 − → para
𝑁 + =𝐴𝑒𝑥𝑝 𝜎 𝑝𝑎𝑟𝑎 𝜌𝑥
𝑁 − < 𝑁 +
δ −
𝒑 𝜸 −
𝑁 − → 𝜎 𝑒 + → anti
𝑁 − =𝐴𝑒𝑥𝑝 𝜎 𝑎𝑛𝑡𝑖 𝜌𝑥 Fe
peripheral electron : 2
density : 7.09× 10 −6 𝑚 3 /𝑚𝑜𝑙 → 0.141𝑚𝑜𝑙/ 𝑐𝑚 3
𝜌=2×0.141×6.02× =1.70× 𝑐𝑚 −3