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Long Baseline Neutrino Experiments:
长基线中微子实验:

> > >> Long Baseline Neutrino Experiments:
> > >> 长基线中微子实验:
  • Initial studies of neutrino oscillations from atmospheric and solar neutrinos
    来自大气和太阳中微子的中微子振荡初步研究
  • Emphasis of neutrino research now on neutrino beam experiments
    目前中微子研究的重点是中微子束实验
  • Allows the physicist to take control - design experiment with specific goals
    让物理学家掌握控制权--设计具有特定目标的实验
  • In the last few years, long baseline neutrino oscillation experiments have started taking data: K2K, MINOS, CNGS, T2K
    最近几年,长基线中微子振荡实验开始采集数据:K2K、MINOS、CNGS、T2K

    > > >> Basic Idea:   > > >> 基本构思:
  • Intense neutrino beam  强中微子束
  • Two detectors: one close to beam the other hundreds of km away
    两个探测器:一个靠近光束,另一个在数百公里之外
  • Measure ratio of the neutrino energy spectrum in far detector (oscillated) to that in the near detector (unoscillated)
    测量远探测器(振荡)与近探测器(非振荡)中微子能谱的比率
  • Partial cancellation of systematic biases
    部分消除系统偏差

Long Baseline Neutrino Experiments:
长基线中微子实验:

MINOS  米诺斯

> 120 GeV > 120 GeV > 120GeV>120 \mathrm{GeV} protons extracted from the MAIN INJECTOR at Fermilab
> 120 GeV > 120 GeV > 120GeV>120 \mathrm{GeV} 从费米实验室主注入器提取的质子

> 2.5 × 10 13 > 2.5 × 10 13 > 2.5 xx10^(13)>2.5 \times 10^{13} protons per pulse hit target =>\Rightarrow very intense beam -0.3 MW on target
> 2.5 × 10 13 > 2.5 × 10 13 > 2.5 xx10^(13)>2.5 \times 10^{13} 每个脉冲的质子击中目标 =>\Rightarrow 非常强烈的光束 -0.3 兆瓦击中目标

Two detectors:  两个探测器

Long Baseline Neutrino Experiments:
长基线中微子实验:

> > >> Neutrino detection via CC interactions on nucleon:
> > >> 通过核子上的CC相互作用探测中微子:
v μ + N μ + X v μ + N μ + X v_(mu)+N rarrmu^(-)+Xv_{\mu}+N \rightarrow \mu^{-}+X

> > >> The main feature of the MINOS detector is the very good neutrino energy resolution
> > >> MINOS探测器的主要特点是中微子能量分辨率非常高
E v = E μ + E X E v = E μ + E X E_(v)=E_(mu)+E_(X)E_{v}=E_{\mu}+E_{X}
  • Muon energy from range/curvature in B-field
    来自 B 场范围/曲率的μ介子能量
  • Hadronic energy from amount of light observed
    从观测到的光量看强子能量

    > > >> For the MINOS experiment L is fixed and observe oscillations as function of E v E v E_(v)E_{v}
    > > >> 对于 MINOS 实验,L 是固定的,观察振荡与 E v E v E_(v)E_{v} 的函数关系。

    > > >> For | Δ m 32 2 | 2.5 × 10 3 eV 2 Δ m 32 2 2.5 × 10 3 eV 2 |Deltam_(32)^(2)|∼2.5 xx10^(-3)eV^(2)\left|\Delta m_{32}^{2}\right| \sim 2.5 \times 10^{-3} \mathrm{eV}^{2} first oscillation minimum at E v = 1.5 GeV E v = 1.5 GeV E_(v)=1.5GeVE_{v}=1.5 \mathrm{GeV}
    > > >> 对于 | Δ m 32 2 | 2.5 × 10 3 eV 2 Δ m 32 2 2.5 × 10 3 eV 2 |Deltam_(32)^(2)|∼2.5 xx10^(-3)eV^(2)\left|\Delta m_{32}^{2}\right| \sim 2.5 \times 10^{-3} \mathrm{eV}^{2} 第一次振荡最小值,位于 E v = 1.5 GeV E v = 1.5 GeV E_(v)=1.5GeVE_{v}=1.5 \mathrm{GeV}

    > > >> To a very good approximation can use two flavor formula as oscillations corresponding to | Δ m 21 2 | 8 × 10 5 eV 2 Δ m 21 2 8 × 10 5 eV 2 |Deltam_(21)^(2)|∼8xx10^(-5)eV^(2)\left|\Delta m_{21}^{2}\right| \sim 8 \times 10^{-5} \mathrm{eV}^{2} occur at E v = 50 MeV E v = 50 MeV E_(v)=50MeVE_{v}=50 \mathrm{MeV} beam contains very few neutrinos at this energy + well below detection threshold
    > > >> 非常近似地可以使用双味公式,因为与 | Δ m 21 2 | 8 × 10 5 eV 2 Δ m 21 2 8 × 10 5 eV 2 |Deltam_(21)^(2)|∼8xx10^(-5)eV^(2)\left|\Delta m_{21}^{2}\right| \sim 8 \times 10^{-5} \mathrm{eV}^{2} 相对应的振荡发生在 E v = 50 MeV E v = 50 MeV E_(v)=50MeVE_{v}=50 \mathrm{MeV} 波束中,该能量下的中微子数量极少+远低于探测阈值

| Δ m 32 2 | = ( 2.43 ± 0.12 ) × 10 3 eV 2 Δ m 32 2 = ( 2.43 ± 0.12 ) × 10 3 eV 2 |Deltam_(32)^(2)|=(2.43+-0.12)xx10^(-3)eV^(2)\left|\Delta m_{32}^{2}\right|=(2.43 \pm 0.12) \times 10^{-3} \mathrm{eV}^{2}

Solar Neutrino Experiments
太阳中微子实验

The Sun is powered by the weak interaction - producing a very large flux of electron neutrinos
太阳由弱相互作用提供能量--产生大量电子中微子流
2 × 10 38 v e s 1 2 × 10 38 v e s 1 2xx10^(38)v_(e)s^(-1)2 \times 10^{38} v_{e} \mathrm{~s}^{-1}
Several different nuclear reactions in the sun =>\Rightarrow complex neutrino energy spectrum
太阳中的几种不同核反应 =>\Rightarrow 复杂的中微子能谱


All experiments saw a deficit of electron neutrinos compared to experimental prediction - the SOLAR NEUTRINO PROBLEM
与实验预测相比,所有实验都发现电子中微子不足--太阳中微子问题
  • e.g. Super Kamiokande  例如:超级卡莫坎德

Solar Neutrinos I: Super Kamiokande
太阳中微子 I:超级 Kamiokande

  • 50000 ton water Čerenkov detector
    50000 吨水Čerenkov 探测器
  • Water viewed by 11146 Photo-multiplier tubes
    11146 光电倍增管观察到的水
  • Deep underground to filter out cosmic rays otherwise difficult to detect rare neutrino interactions
    深入地下过滤宇宙射线,否则难以探测到罕见的中微子相互作用


    > > >> Detect neutrinos by observing Čerenkov radiation from charged particles which travel faster than speed of light in water c / n c / n c//nc / n
    > > >> 通过观察带电粒子在水中以超过光速的速度传播时产生的采伦科夫辐射来探测中微子 c / n c / n c//nc / n .


    > > >> Can distinguish electrons from muons from pattern of light - muons produce clean rings whereas electrons produce more diffuse “fuzzy” rings
    > > >> 可以从光的模式区分电子和μ介子--μ介子产生干净的光环,而电子产生的光环则更分散、更 "模糊"。

    > > >> Sensitive to solar neutrinos with E V > 5 MeV E V > 5 MeV E_(V) > 5MeVE_{V}>5 \mathrm{MeV}
    > > >> 通过 E V > 5 MeV E V > 5 MeV E_(V) > 5MeVE_{V}>5 \mathrm{MeV} 对太阳中微子敏感

    > > >> For lower energies too much background from natural radioactivity ( β β beta\beta-decays)
    > > >> 对于较低能量,天然放射性( β β beta\beta -衰变)产生的背景太强。

    > > >> Hence detect mostly neutrinos from 8 B 8 B e + e + + v e 8 B 8 B e + e + + v e ^(8)B rarr^(8)Be^(**)+e^(+)+v_(e){ }^{8} B \rightarrow{ }^{8} B e^{*}+e^{+}+v_{e}
    > > >> 因此主要探测到来自 8 B 8 B e + e + + v e 8 B 8 B e + e + + v e ^(8)B rarr^(8)Be^(**)+e^(+)+v_(e){ }^{8} B \rightarrow{ }^{8} B e^{*}+e^{+}+v_{e} 的中微子。

Solar Neutrino Experiments
太阳中微子实验

> > >> Detect electron Čerenkov rings from
> > >> 探测电子的切伦科夫环
v e + e v e + e v e + e v e + e v_(e)+e^(-)rarrv_(e)+e^(-)v_{e}+e^{-} \rightarrow v_{e}+e^{-}
> > >> In LAB frame the electron is produced preferentially along the v e v e v_(e)v_{e} direction
> > >> 在 LAB 框架中,电子优先沿 v e v e v_(e)v_{e} 方向产生
Results (The Solar Neutrino “Problem”)
结果(太阳中微子 "问题)
  • Clear signal of neutrinos from the sun
    来自太阳的中微子的清晰信号
  • However too few neutrinos DATA/SSM = 0.45 ± 0.02 = 0.45 ± 0.02 =0.45+-0.02=0.45 \pm 0.02
    然而中微子数量太少 DATA/SSM = 0.45 ± 0.02 = 0.45 ± 0.02 =0.45+-0.02=0.45 \pm 0.02

    SSM = “Standard Solar Model” Prediction
    SSM = "标准太阳模式 "预测

    S.Fukada et al., Phys. Rev. Lett. 86 5651-5655, 2001
    S.Fukada 等人,Phys. Rev. Lett.86 5651-5655, 2001

Solar Neutrino Experiments
太阳中微子实验

Solar Neutrinos II: SNO
太阳中微子 II:SNO

Sudbury Neutrino Observatory (SNO) Located in a deep mine in Otario, Canada
萨德伯里中微子天文台(SNO) 位于加拿大奥塔里奥的一个深矿井中
  • 1000 ton heavy water ( D 2 0 ) D 2 0 (D_(2)0)\left(\mathrm{D}_{2} 0\right) Čerenkov detector
    1000吨重水 ( D 2 0 ) D 2 0 (D_(2)0)\left(\mathrm{D}_{2} 0\right) 采伦科夫探测器
  • D 2 O D 2 O D_(2)O\mathrm{D}_{2} \mathrm{O} inside a 12 m diameter acrylic vessel
    D 2 O D 2 O D_(2)O\mathrm{D}_{2} \mathrm{O} 直径为 12 米的丙烯酸容器内
  • Surrounded by 3000 tons of normal water
    被 3000 吨普通水包围
  • Main experimental challenge is the need for very low background from radioactivity
    主要的实验挑战是需要非常低的放射性本底
  • Ultra-pure H 2 O H 2 O H_(2)O\mathrm{H}_{2} \mathrm{O} and D 2 O D 2 O D_(2)O\mathrm{D}_{2} \mathrm{O}
    超纯 H 2 O H 2 O H_(2)O\mathrm{H}_{2} \mathrm{O} D 2 O D 2 O D_(2)O\mathrm{D}_{2} \mathrm{O}
  • Surrounded by 9546 PMTs  周围有 9546 个 PMT

Solar Neutrino Experiments
太阳中微子实验

Detect Čerenkov light from three different reactions:
检测来自三种不同反应的 Čerenkov 光:

CHARGE CURRENT  充电电流

  • Detect Čerenkov light from electron
    探测来自电子的切伦科夫光
  • Only sensitive to v e v e v_(e)v_{e} (thresholds)
    只对 v e v e v_(e)v_{e} (阈值)敏感
  • Gives a measure of v e v e v_(e)v_{e} flux
    测量 v e v e v_(e)v_{e} 流量
CC Rate ϕ ( v e )  CC Rate  ϕ v e " CC Rate "prop phi(v_(e))\text { CC Rate } \propto \phi\left(v_{e}\right)

NEUTRAL CURRENT  中性电流

  • Neutron capture on a deuteron gives 6.25 MeV
    氘核的中子俘获产生 6.25 MeV
  • Detect Čerenkov light from electrons scattered by
    检测由以下物体散射的电子产生的 Čerenkov 光
  • Measures total neutrino flux
    测量中微子总通量
NC Rate ϕ ( v e ) + ϕ ( v μ ) + ϕ ( v τ )  NC Rate  ϕ v e + ϕ v μ + ϕ v τ " NC Rate "prop phi(v_(e))+phi(v_(mu))+phi(v_(tau))\text { NC Rate } \propto \phi\left(v_{e}\right)+\phi\left(v_{\mu}\right)+\phi\left(v_{\tau}\right)

ELASTIC SCATTERING  弹性散射

-Detect Čerenkov light from electron
-探测电子发出的 Čerenkov 光
  • Sensitive to all neutrinos (NC part) - but larger cross section for v e v e v_(e)v_{e}
    对所有中微子敏感(NC 部分)--但 v e v e v_(e)v_{e} 的截面较大

ES Rate ϕ ( v e ) + 0.154 ( ϕ ( v μ ) + ϕ ( v τ ) )  ES Rate  ϕ v e + 0.154 ϕ v μ + ϕ v τ " ES Rate "prop phi(v_(e))+0.154(phi(v_(mu))+phi(v_(tau)))\text { ES Rate } \propto \phi\left(v_{e}\right)+0.154\left(\phi\left(v_{\mu}\right)+\phi\left(v_{\tau}\right)\right)

Solar Neutrino Experiments
太阳中微子实验

Experimentally can determine rates for different interactions from:
通过实验可以确定不同相互作用的速率:
  • angle with respect to sun: electrons from ES point back to sun
    与太阳的夹角:电子从 ES 点返回太阳
  • energy: NC events have lower energy - 6.25 MeV photon from neutron capture
    能量:NC 事件的能量较低 - 中子俘获产生 6.25 MeV 光子
  • radius from center of detector: gives a measure of background from neutrons
    探测器中心半径:用于测量中子的背景值


    > > >> Using different distributions obtain a measure of numbers of events of each type:
    > > >> 使用不同的分布,获得每类事件的数量:
\begin{array}{ll} \cline { 1 - 1 } \text { CC : } 1968 \pm 61 & \propto \phi\left(v_{e}\right) \\ \cline { 1 - 1 } \text { ES: } 264 \pm 26 & \propto \phi\left(v_{e}\right)+0.154\left[\phi\left(v_{\mu}\right)+\phi\left(v_{\tau}\right)\right] \\ \cline { 1 - 2 } \text { NC : } 576 \pm 50 & \propto \phi\left(v_{e}\right)+\phi\left(v_{\mu}\right)+\phi\left(v_{\tau}\right) \end{array}Undefined control sequence \cline
Measure of electron neutrino flux + total flux!
测量电子中微子通量 + 总通量!

Solar Neutrino Experiments
太阳中微子实验

Using known cross sections can convert observed numbers of events into fluxes
利用已知的横截面可以将观测到的事件数转换为通量

The different processes impose different constraints
不同的过程有不同的限制

Where constraints meet gives separate measurements of v e v e v_(e)v_{e} and v μ + v τ v μ + v τ v_(mu)+v_(tau)v_{\mu}+v_{\tau} fluxes
在约束条件相遇时,可分别测量 v e v e v_(e)v_{e} v μ + v τ v μ + v τ v_(mu)+v_(tau)v_{\mu}+v_{\tau} 通量


SNO Results:  SNO 结果:
ϕ ( v e ) = ( 1.8 ± 0.1 ) × 10 6 cm 2 s 1 ϕ ( v μ ) + ϕ ( v τ ) = ( 3.4 ± 0.6 ) × 10 6 cm 2 s 1 ϕ v e = ( 1.8 ± 0.1 ) × 10 6 cm 2 s 1 ϕ v μ + ϕ v τ = ( 3.4 ± 0.6 ) × 10 6 cm 2 s 1 {:[phi(v_(e))=(1.8+-0.1)xx10^(-6)cm^(-2)s^(-1)],[phi(v_(mu))+phi(v_(tau))=(3.4+-0.6)xx10^(-6)cm^(-2)s^(-1)]:}\begin{gathered} \phi\left(v_{e}\right)=(1.8 \pm 0.1) \times 10^{-6} \mathrm{~cm}^{-2} \mathrm{~s}^{-1} \\ \phi\left(v_{\mu}\right)+\phi\left(v_{\tau}\right)=(3.4 \pm 0.6) \times 10^{-6} \mathrm{~cm}^{-2} \mathrm{~s}^{-1} \end{gathered}
SSM Prediction:  SSM 预测:
ϕ ( v e ) = 5.1 × 10 6 cm 2 s 1 ϕ v e = 5.1 × 10 6 cm 2 s 1 phi(v_(e))=5.1 xx10^(-6)cm^(-2)s^(-1)\phi\left(v_{e}\right)=5.1 \times 10^{-6} \mathrm{~cm}^{-2} \mathrm{~s}^{-1}
  • Clear evidence for a flux of v μ v μ v_(mu)v_{\mu} and/or v τ v τ v_(tau)v_{\tau} from the sun
    来自太阳的 v μ v μ v_(mu)v_{\mu} 和/或 v τ v τ v_(tau)v_{\tau} 通量的明显证据
  • Total neutrino flux is consistent with expectation from SSM
    中微子总通量与 SSM 的预期一致
  • Clear evidence of v e v μ v e v μ v_(e)rarrv_(mu)v_{e} \rightarrow v_{\mu} and/or v e v τ v e v τ v_(e)rarrv_(tau)v_{e} \rightarrow v_{\tau} neutrino transitions
    v e v μ v e v μ v_(e)rarrv_(mu)v_{e} \rightarrow v_{\mu} 和/或 v e v τ v e v τ v_(e)rarrv_(tau)v_{e} \rightarrow v_{\tau} 中微子跃迁的明显证据

Interpretation of Solar Neutrino Data
太阳中微子数据解读

> > >> The interpretation of the solar neutrino data is complicated by MATTER EFFECTS
> > >> 太阳中微子数据的解释因物质效应而变得复杂
  • The quantitative treatment is non-trivial and is not given here
    定量处理并非易事,在此不再赘述。
  • Basic idea is that as a neutrino leaves the sun it crosses a region of high electron density
    基本原理是,当中微子离开太阳时,它会穿过一个电子密度较高的区域
  • The coherent forward scattering process ( v e v e v e v e (v_(e)rarrv_(e):}\left(v_{e} \rightarrow v_{e}\right. for an electron neutrino)
    电子中微子的相干前向散射过程 ( v e v e v e v e (v_(e)rarrv_(e):}\left(v_{e} \rightarrow v_{e}\right. )


    is different to that for a muon or tau neutrino
    与μ介子或头中微子不同

  • It can enhance oscillations - “MSW effect”
    它能增强振荡--"MSW 效应"

    > > >> A combined analysis of all solar neutrino data gives:
    > > >> 对所有太阳中微子数据进行综合分析后得出:
Δ m Solar 2 8 × 10 5 eV 2 , sin 2 2 θ solar 0.85 Δ m Solar  2 8 × 10 5 eV 2 , sin 2 2 θ solar  0.85 Deltam_("Solar ")^(2)~~8xx10^(-5)eV^(2),sin^(2)2theta_("solar ")~~0.85\Delta m_{\text {Solar }}^{2} \approx 8 \times 10^{-5} \mathrm{eV}^{2}, \sin ^{2} 2 \theta_{\text {solar }} \approx 0.85

Atmospheric Neutrino experiment
大气中微子实验

> > >> High energy cosmic rays (up to 10 20 eV 10 20 eV 10^(20)eV10^{20} \mathrm{eV} ) interact in the upper part of the Earth’s atmosphere
> > >> 高能宇宙射线(高达 10 20 eV 10 20 eV 10^(20)eV10^{20} \mathrm{eV} )在地球大气层上部相互作用

> > >> The cosmic rays ( 86 % 86 % ∼86%\sim 86 \% protons, 11% He Nuclei, 1 % 1 % ∼1%\sim 1 \% heavier nuclei, 2% electrons ) mostly interact hadronically giving showers of mesons (mainly pions)
> > >> 宇宙射线( 86 % 86 % ∼86%\sim 86 \% 质子,11% He 核, 1 % 1 % ∼1%\sim 1 \% 更重的原子核,2%电子)大多发生强子相互作用,产生介子群(主要是离子)。

> > >> Neutrinos produced by:
> > >> 中微子产生于:
π + μ + v μ π μ v ¯ μ e + v e v ¯ μ e v ¯ e v μ Flux 1 cm 2 sr 1 s 1 Typical energy: E v 1 GeV π + μ + v μ π μ v ¯ μ e + v e v ¯ μ e v ¯ e v μ  Flux  1 cm 2 sr 1 s 1  Typical energy:  E v 1 GeV {:[qquadpi^(+)rarrmu^(+)v_(mu)quadpi^(-)rarrmu^(-) bar(v)_(mu)],[ longleftrightarrowe^(+)v_(e) bar(v)_(mu)quad↪e^(-) bar(v)_(e)v_(mu)],[" Flux "∼1cm^(-2)sr^(-1)s^(-1)],[" Typical energy: "quadE_(v)∼1GeV]:}\begin{aligned} & \qquad \pi^{+} \rightarrow \mu^{+} v_{\mu} \quad \pi^{-} \rightarrow \mu^{-} \bar{v}_{\mu} \\ & \longleftrightarrow e^{+} v_{e} \bar{v}_{\mu} \quad \hookrightarrow e^{-} \bar{v}_{e} v_{\mu} \\ & \text { Flux } \sim 1 \mathrm{~cm}^{-2} \mathrm{sr}^{-1} \mathrm{~s}^{-1} \\ & \text { Typical energy: } \quad \mathrm{E}_{v} \sim 1 \mathrm{GeV} \end{aligned}
Expect  期望
N ( v μ + v ¯ μ ) N ( v e + v ¯ e ) 2 N v μ + v ¯ μ N v e + v ¯ e 2 (N(v_(mu)+ bar(v)_(mu)))/(N(v_(e)+ bar(v)_(e)))~~2\frac{N\left(v_{\mu}+\bar{v}_{\mu}\right)}{N\left(v_{e}+\bar{v}_{e}\right)} \approx 2
> > >> Observe a lower ratio with deficit of v μ / v μ v μ / v μ v_(mu)//v_(mu)v_{\mu} / v_{\mu} coming from below the horizon, i.e. large
> > >> 观察到来自地平线以下的 v μ / v μ v μ / v μ v_(mu)//v_(mu)v_{\mu} / v_{\mu} 赤字的比率较低,即较大。


distance from production point on other side of the Earth
与地球另一端生产点的距离

Atmospheric Neutrino experiment
大气中微子实验

Super Kamiokande Atmospheric Results
超级 Kamiokande 大气成果

> > >> Typical energy: E v 1 GeV E v 1 GeV E_(v)∼1GeV\mathrm{E}_{v} \sim 1 \mathrm{GeV} (much greater than solar neutrinos - no confusion)
> > >> 典型能量: E v 1 GeV E v 1 GeV E_(v)∼1GeV\mathrm{E}_{v} \sim 1 \mathrm{GeV} (比太阳中微子大得多--不要混淆)

> > >> Identify v e v e v_(e)v_{e} and v μ v μ v_(mu)v_{\mu} interactions from nature of Čerenkov rings
> > >> 从采伦科夫环的性质确定 v e v e v_(e)v_{e} v μ v μ v_(mu)v_{\mu} 相互作用

> > >> Measure rate as a function of angle with respect to local vertical
> > >> 测量速率与当地垂直角度的函数关系

> > >> Neutrinos coming from above travel 20 km
> > >> 来自上方的中微子飞行 20 千米

> > >> Neutrinos coming from below (i.e. other side of the Earth) travel 12800 km
> > >> 来自下方(即地球的另一侧)的中微子飞行 12800 千米

  • Prediction for v e v e v_(e)v_{e} rate agrees with data
    v e v e v_(e)v_{e} 速率的预测与数据一致
  • Strong evidence for disappearance of v μ v μ v_(mu)v_{\mu} for large distances
    v μ v μ v_(mu)v_{\mu} 在远距离消失的有力证据
  • Consistent with v μ v τ v μ v τ v_(mu)rarrv_(tau)v_{\mu} \rightarrow v_{\tau} oscillations
    v μ v τ v μ v τ v_(mu)rarrv_(tau)v_{\mu} \rightarrow v_{\tau} 振荡一致
  • Don’t detect the oscillated v τ v τ v_(tau)v_{\tau} as typically below interaction threshold of 3.5 GeV
    不检测振荡的 v τ v τ v_(tau)v_{\tau} ,因为通常低于 3.5 GeV 的相互作用阈值

Atmospheric Neutrino experiment
大气中微子实验

> > >> Measure muon direction and energy not neutrino direction/energy
> > >> 测量μ介子方向和能量,而不是中微子方向/能量

> > >> Don’t have E/ θ θ theta\theta resolution to see oscillations
> > >> 没有 E/ θ θ theta\theta 分辨率,无法看到振荡

> > >> Oscillations “smeared” out in data
> > >> 数据中的振荡 "模糊 "了

> > >> Compare data to predictions for | Δ m 2 | Δ m 2 |Deltam^(2)|\left|\Delta m^{2}\right|
> > >> 将数据与 | Δ m 2 | Δ m 2 |Deltam^(2)|\left|\Delta m^{2}\right| 的预测进行比较

Data consistent with:  数据符合
| Δ m atmos 2 | 0.0025 eV 2 sin 2 2 θ atmos 1 Δ m atmos 2 0.0025 eV 2 sin 2 2 θ atmos 1 {:[|Deltam_(atmos)^(2)|~~0.0025eV^(2)],[sin^(2)2theta_(atmos)~~1]:}\begin{gathered} \left|\Delta m_{\mathrm{atmos}}^{2}\right| \approx 0.0025 \mathrm{eV}^{2} \\ \sin ^{2} 2 \theta_{\mathrm{atmos}} \approx 1 \end{gathered}

3-Flavor of Atmospheric Neutrinos
3-大气中微子的味道

The energies of the detected atmospheric neutrinos are of order 1 GeV
探测到的大气中微子的能量约为 1 GeV

The wavelength of oscillations associated with | Δ m 21 2 | = 8 × 10 5 eV 2 Δ m 21 2 = 8 × 10 5 eV 2 |Deltam_(21)^(2)|=8xx10^(-5)eV^(2)\left|\Delta m_{21}^{2}\right|=8 \times 10^{-5} \mathrm{eV}^{2} is
| Δ m 21 2 | = 8 × 10 5 eV 2 Δ m 21 2 = 8 × 10 5 eV 2 |Deltam_(21)^(2)|=8xx10^(-5)eV^(2)\left|\Delta m_{21}^{2}\right|=8 \times 10^{-5} \mathrm{eV}^{2} 相关的振荡波长为
λ 21 = 31000 km λ 21 = 31000 km {:lambda_(21)=31000km:}\begin{aligned} & \lambda_{21}=31000 \mathrm{~km} \end{aligned}
If we neglect the corresponding term in the expression for P ( v μ v τ ) P v μ v τ P(v_(mu)rarrv_(tau))P\left(v_{\mu} \rightarrow v_{\tau}\right) - equation (16)
如果我们忽略 P ( v μ v τ ) P v μ v τ P(v_(mu)rarrv_(tau))P\left(v_{\mu} \rightarrow v_{\tau}\right) 表达式中的相应项 - 公式 (16)
P ( v μ v τ ) 4 U μ 1 U τ 1 U μ 2 U τ 2 sin 2 Δ 21 + 4 U μ 3 2 U τ 3 2 sin 2 Δ 32 = 4 sin 2 θ 23 cos 2 θ 23 cos 4 θ 13 sin 2 Δ 32 = cos 4 θ 13 sin 2 2 θ 23 sin 2 Δ 32 P v μ v τ 4 U μ 1 U τ 1 U μ 2 U τ 2 sin 2 Δ 21 + 4 U μ 3 2 U τ 3 2 sin 2 Δ 32 = 4 sin 2 θ 23 cos 2 θ 23 cos 4 θ 13 sin 2 Δ 32 = cos 4 θ 13 sin 2 2 θ 23 sin 2 Δ 32 {:[P(v_(mu)rarrv_(tau))~~-4U_(mu1)U_(tau1)U_(mu2)U_(tau2)sin^(2)Delta_(21)+4U_(mu3)^(2)U_(tau3)^(2)sin^(2)Delta_(32)],[=4sin^(2)theta_(23)cos^(2)theta_(23)cos^(4)theta_(13)sin^(2)Delta_(32)],[=cos^(4)theta_(13)sin^(2)2theta_(23)sin^(2)Delta_(32)]:}\begin{aligned} P\left(v_{\mu} \rightarrow v_{\tau}\right) & \approx-4 U_{\mu 1} U_{\tau 1} U_{\mu 2} U_{\tau 2} \sin ^{2} \Delta_{21}+4 U_{\mu 3}^{2} U_{\tau 3}^{2} \sin ^{2} \Delta_{32} \\ & =4 \sin ^{2} \theta_{23} \cos ^{2} \theta_{23} \cos ^{4} \theta_{13} \sin ^{2} \Delta_{32} \\ & =\cos ^{4} \theta_{13} \sin ^{2} 2 \theta_{23} \sin ^{2} \Delta_{32} \end{aligned}
The Super-Kamiokande data are consistent with v μ v τ v μ v τ v_(mu)rarrv_(tau)v_{\mu} \rightarrow v_{\tau} which excludes the possibility of cos 4 θ 13 cos 4 θ 13 cos^(4)theta_(13)\cos ^{4} \theta_{13} being small
超级上甘地数据与 v μ v τ v μ v τ v_(mu)rarrv_(tau)v_{\mu} \rightarrow v_{\tau} 一致,这就排除了 cos 4 θ 13 cos 4 θ 13 cos^(4)theta_(13)\cos ^{4} \theta_{13} 偏小的可能性。
  • Hence the CHOOZ limit: sin 2 2 θ 13 < 0.2 sin 2 2 θ 13 < 0.2 sin^(2)2theta_(13) < 0.2\sin ^{2} 2 \theta_{13}<0.2 can be interpreted as sin 2 θ 13 < 0.05 sin 2 θ 13 < 0.05 sin^(2)theta_(13) < 0.05\sin ^{2} \theta_{13}<0.05
    因此,CHOOZ 限制: sin 2 2 θ 13 < 0.2 sin 2 2 θ 13 < 0.2 sin^(2)2theta_(13) < 0.2\sin ^{2} 2 \theta_{13}<0.2 可以解释为 sin 2 θ 13 < 0.05 sin 2 θ 13 < 0.05 sin^(2)theta_(13) < 0.05\sin ^{2} \theta_{13}<0.05
NOTE: the three flavor treatment of atmospheric neutrinos is discussed below. The oscillation parameters in nature conspire in such a manner that the two flavor treatment provides a good approximation of the observable effects of atmospheric neutrino oscillations
注:大气中微子的三味处理方法将在下文讨论。自然界中的振荡参数共同作用,使得两种味道的处理方法可以很好地近似大气中微子振荡的可观测效应

3-Flavor of Atmospheric Neutrinos
3-大气中微子的味道

> > >> Previously stated that the long-wavelength oscillations due to Δ m 21 2 Δ m 21 2 Deltam_(21)^(2)\Delta m_{21}^{2} have little effect on atmospheric neutrino oscillations because for a the wavelength for a 1 GeV neutrino is approx 30000 km .
> > >> 以前曾指出, Δ m 21 2 Δ m 21 2 Deltam_(21)^(2)\Delta m_{21}^{2} 引起的长波振荡对大气中微子振荡的影响很小,因为 1 GeV 中微子的波长约为 30000 公里。

> > >> However, maximum oscillation probability occurs at λ / 2 λ / 2 lambda//2\lambda / 2
> > >> 然而,最大振荡概率出现在 λ / 2 λ / 2 lambda//2\lambda / 2 处。

> > >> This is not small compared to diameter of Earth and cannot be neglected
> > >> 这与地球直径相比并不小,不可忽视

> > >> As an example, take the oscillation parameters to be
> > >> 例如,将振荡参数设为
θ 12 = 32 ; θ 23 = 45 ; θ 13 = 7.5 θ 12 = 32 ; θ 23 = 45 ; θ 13 = 7.5 theta_(12)=32^(@);theta_(23)=45^(@);theta_(13)=7.5^(@)\theta_{12}=32^{\circ} ; \theta_{23}=45^{\circ} ; \theta_{13}=7.5^{\circ}
> > >> Predict neutrino flux as function of cos θ cos θ cos theta\cos \theta
> > >> 预测中微子通量与 cos θ cos θ cos theta\cos \theta 的函数关系
Consider what happens to muon and electron neutrinos separately
分别考虑μ介子和电子中微子的情况



> Δ m 21 2 > Δ m 21 2 > Deltam_(21)^(2)>\Delta m_{21}^{2} has a big effect at cos θ 1 cos θ 1 cos theta∼-1\cos \theta \sim-1
> Δ m 21 2 > Δ m 21 2 > Deltam_(21)^(2)>\Delta m_{21}^{2} cos θ 1 cos θ 1 cos theta∼-1\cos \theta \sim-1 的影响很大

3-Flavor of Atmospheric Neutrinos
3-大气中微子的味道

> > >> From previous page it is clear that the two neutrino treatment of oscillations of atmospheric muon neutrinos is a very poor approximation
> > >> 从上一页可以看出,对大气μ介子中微子振荡的双中微子处理是一种很差的近似方法

> > >> However, in atmosphere produce two muon neutrinos for every electron neutrino
> > >> 然而,在大气层中,每一个电子中微子会产生两个μ介子中微子

> > >> Need to consider the combined effect of oscillations on a mixed “beam” with both v μ v μ v_(mu)v_{\mu} and v e v e v_(e)v_{e}
> > >> 需要考虑振荡对同时具有 v μ v μ v_(mu)v_{\mu} v e v e v_(e)v_{e} 的混合 "光束 "的综合影响


> > >> At large distances the average muon neutrino flux is still approximately half the initial flux, but onlv because of the oscillations of the original electron neutrinos and the fact that sin 2 2 θ 23 1 sin 2 2 θ 23 1 sin^(2)2theta_(23)∼1\sin ^{2} 2 \theta_{23} \sim 1
> > >> 在较大的距离上,平均μ介子中微子通量仍然大约是初始通量的一半,但由于原始电子中微子的振荡和 sin 2 2 θ 23 1 sin 2 2 θ 23 1 sin^(2)2theta_(23)∼1\sin ^{2} 2 \theta_{23} \sim 1 的事实,μ介子中微子通量仍然是初始通量的一半。

> > >> Because the atmospheric neutrino experiments do not resolve fine structure, the observable effects of oscillations approximated by two flavor formula
> > >> 由于大气中微子实验并不解析精细结构,因此振荡的可观测效应近似于双味公式

Reactor Neutrino Experiments
反应堆中微子实验

> > >> To explain reactor neutrino experiments we need the full three neutrino expression for the electron neutrino survival probability (11) which depends on U e 1 , U e 2 , U e 3 U e 1 , U e 2 , U e 3 U_(e1),U_(e2),U_(e3)U_{e 1}, U_{e 2}, U_{e 3}
> > >> 为了解释反应堆中微子实验,我们需要电子中微子存活概率 (11) 的完整三中微子表达式,它取决于 U e 1 , U e 2 , U e 3 U e 1 , U e 2 , U e 3 U_(e1),U_(e2),U_(e3)U_{e 1}, U_{e 2}, U_{e 3}

> > >> Substituting these PMNS matrix elements in Equation (11):
> > >> 将这些 PMNS 矩阵元素代入公式 (11):
P ( v e v e ) 1 4 U e 1 2 U e 2 2 sin 2 Δ 21 4 ( 1 U e 3 2 ) U e 3 2 sin 2 Δ 32 = 1 4 ( c 12 c 13 ) 2 ( s 12 c 13 ) 2 sin 2 Δ 21 4 ( 1 s 13 2 ) s 13 2 sin 2 Δ 32 = 1 c 13 4 ( 2 s 12 c 12 ) 2 sin 2 Δ 21 ( 2 c 13 s 13 ) 2 sin 2 Δ 32 = 1 cos 4 θ 13 sin 2 2 θ 12 sin 2 Δ 21 sin 2 2 θ 13 sin 2 Δ 32 P v e v e 1 4 U e 1 2 U e 2 2 sin 2 Δ 21 4 1 U e 3 2 U e 3 2 sin 2 Δ 32 = 1 4 c 12 c 13 2 s 12 c 13 2 sin 2 Δ 21 4 1 s 13 2 s 13 2 sin 2 Δ 32 = 1 c 13 4 2 s 12 c 12 2 sin 2 Δ 21 2 c 13 s 13 2 sin 2 Δ 32 = 1 cos 4 θ 13 sin 2 2 θ 12 sin 2 Δ 21 sin 2 2 θ 13 sin 2 Δ 32 {:[P(v_(e)rarrv_(e))~~1-4U_(e1)^(2)U_(e2)^(2)sin^(2)Delta_(21)-4(1-U_(e3)^(2))U_(e3)^(2)sin^(2)Delta_(32)],[quad=1-4(c_(12)c_(13))^(2)(s_(12)c_(13))^(2)sin^(2)Delta_(21)-4(1-s_(13)^(2))s_(13)^(2)sin^(2)Delta_(32)],[quad=1-c_(13)^(4)(2s_(12)c_(12))^(2)sin^(2)Delta_(21)-(2c_(13)s_(13))^(2)sin^(2)Delta_(32)],[quad=1-cos^(4)theta_(13)sin^(2)2theta_(12)sin^(2)Delta_(21)-sin^(2)2theta_(13)sin^(2)Delta_(32)]:}\begin{aligned} & P\left(v_{e} \rightarrow v_{e}\right) \approx 1-4 U_{e 1}^{2} U_{e 2}^{2} \sin ^{2} \Delta_{21}-4\left(1-U_{e 3}^{2}\right) U_{e 3}^{2} \sin ^{2} \Delta_{32} \\ & \quad=1-4\left(c_{12} c_{13}\right)^{2}\left(s_{12} c_{13}\right)^{2} \sin ^{2} \Delta_{21}-4\left(1-s_{13}^{2}\right) s_{13}^{2} \sin ^{2} \Delta_{32} \\ & \quad=1-c_{13}^{4}\left(2 s_{12} c_{12}\right)^{2} \sin ^{2} \Delta_{21}-\left(2 c_{13} s_{13}\right)^{2} \sin ^{2} \Delta_{32} \\ & \quad=1-\cos ^{4} \theta_{13} \sin ^{2} 2 \theta_{12} \sin ^{2} \Delta_{21}-\sin ^{2} 2 \theta_{13} \sin ^{2} \Delta_{32} \end{aligned}
> > >> Contributions with short wavelength (atmospheric) and long wavelength (solar)
> > >> 短波长(大气)和长波长(太阳)的贡献

For a 1 MeV neutrino
对于 1 MeV 中微子
λ osc ( km ) = 2.47 E ( GeV ) Δ m 2 ( eV 2 ) λ 21 = 30.0 km λ 32 = 0.8 km λ osc ( km ) = 2.47 E ( GeV ) Δ m 2 eV 2 λ 21 = 30.0 km λ 32 = 0.8 km {:[lambda_(osc)(km),=2.47(E(GeV))/(Deltam^(2)(eV^(2)))],[=>lambda_(21),=30.0km],[lambda_(32),=0.8km]:}\begin{array}{cc} \lambda_{\mathrm{osc}}(\mathrm{~km}) & =2.47 \frac{E(\mathrm{GeV})}{\Delta m^{2}\left(\mathrm{eV}^{2}\right)} \\ \Rightarrow \lambda_{21} & =30.0 \mathrm{~km} \\ \lambda_{32} & =0.8 \mathrm{~km} \end{array}

> > >> Amplitude of short wavelength oscillations given by
> > >> 短波长振荡的振幅由以下公式给出
sin 2 2 θ 13 sin 2 2 θ 13 sin^(2)2theta_(13)\sin ^{2} 2 \theta_{13}

Reactor Neutrino Experiments
反应堆中微子实验

> > >> KamLAND(Detector located in same mine as Super Kamiokande)
> > >> 卡姆兰德(与超级卡姆坎德位于同一矿井的探测器)


> 70 GW > 70 GW > 70GW>70 \mathrm{GW} from nuclear power ( 7 % 7 % 7%7 \% of World total) from reactors within 130 130 130-130- 240 km
> 70 GW > 70 GW > 70GW>70 \mathrm{GW} 来自 130 130 130-130- 240 公里范围内反应堆的核电(占世界总量的 7 % 7 % 7%7 \% )。

> > >> Liquid scintillator detector, 1789 PMTs
> > >> 液体闪烁探测器,1789 个 PMT

> > >> Detection via inverse beta decay: v e + p e + + n v e + p e + + n v_(e)+p rarre^(+)+nv_{e}+p \rightarrow e^{+}+n Followed by
> > >> 通过逆β衰变进行探测: v e + p e + + n v e + p e + + n v_(e)+p rarre^(+)+nv_{e}+p \rightarrow e^{+}+n 随后是
e + + e γ + γ prompt n + p d + γ ( 2.2 MeV ) delayed e + + e γ + γ  prompt  n + p d + γ ( 2.2 MeV )  delayed  {:[e^(+)+e^(-)rarr gamma+gammaquad" prompt "],[n+p rarr d+gamma(2.2MeV)" delayed "]:}\begin{gathered} e^{+}+e^{-} \rightarrow \gamma+\gamma \quad \text { prompt } \\ n+p \rightarrow d+\gamma(2.2 \mathrm{MeV}) \text { delayed } \end{gathered}