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\mathrm{GeV}$$>120\mathrm{GeV}$> 120GeV>120 \mathrm{GeV} protons extracted from the MAIN INJECTOR at Fermilab
$>120\mathrm{GeV}$$>120\mathrm{GeV}$> 120GeV>120 \mathrm{GeV} 从费米实验室主注入器提取的质子
$>2.5\times {10}^{13}$$>2.5\times {10}^{13}$> 2.5 xx10^(13)>2.5 \times 10^{13} protons per pulse hit target $\Rightarrow$$\Rightarrow$=>\Rightarrow very intense beam -0.3 MW on target
$>2.5\times {10}^{13}$$>2.5\times {10}^{13}$> 2.5 xx10^(13)>2.5 \times 10^{13} 每个脉冲的质子击中目标 $\Rightarrow$$\Rightarrow$=>\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：

$>$$>$>> The main feature of the MINOS detector is the very good neutrino energy resolution
$>$$>$>> MINOS探测器的主要特点是中微子能量分辨率非常高

• 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。
  $>$$>$>> For $\left|\mathrm{\Delta }{m}_{32}^2\right|\sim 2.5\times {10}^{-3}{\mathrm{eV}}^2$$\left|\mathrm{\Delta }{m}_{32}^2\right|\sim 2.5\times {10}^{-3}{\mathrm{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\mathrm{GeV}$$E_v=1.5\mathrm{GeV}$E_(v)=1.5GeVE_{v}=1.5 \mathrm{GeV}
  $>$$>$>> 对于 $\left|\mathrm{\Delta }{m}_{32}^2\right|\sim 2.5\times {10}^{-3}{\mathrm{eV}}^2$$\left|\mathrm{\Delta }{m}_{32}^2\right|\sim 2.5\times {10}^{-3}{\mathrm{eV}}^2$|Deltam_(32)^(2)|∼2.5 xx10^(-3)eV^(2)\left|\Delta m_{32}^{2}\right| \sim 2.5 \times 10^{-3} \mathrm{eV}^{2} 第一次振荡最小值，位于 $E_v=1.5\mathrm{GeV}$$E_v=1.5\mathrm{GeV}$E_(v)=1.5GeVE_{v}=1.5 \mathrm{GeV} 处
  $>$$>$>> To a very good approximation can use two flavor formula as oscillations corresponding to $\left|\mathrm{\Delta }{m}_{21}^2\right|\sim 8\times {10}^{-5}{\mathrm{eV}}^2$$\left|\mathrm{\Delta }{m}_{21}^2\right|\sim 8\times {10}^{-5}{\mathrm{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\mathrm{MeV}$$E_v=50\mathrm{MeV}$E_(v)=50MeVE_{v}=50 \mathrm{MeV} beam contains very few neutrinos at this energy + well below detection threshold
  $>$$>$>> 非常近似地可以使用双味公式，因为与 $\left|\mathrm{\Delta }{m}_{21}^2\right|\sim 8\times {10}^{-5}{\mathrm{eV}}^2$$\left|\mathrm{\Delta }{m}_{21}^2\right|\sim 8\times {10}^{-5}{\mathrm{eV}}^2$|Deltam_(21)^(2)|∼8xx10^(-5)eV^(2)\left|\Delta m_{21}^{2}\right| \sim 8 \times 10^{-5} \mathrm{eV}^{2} 相对应的振荡发生在 $E_v=50\mathrm{MeV}$$E_v=50\mathrm{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
  

  

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

Several different nuclear reactions in the sun $\Rightarrow$$\Rightarrow$=>\Rightarrow complex neutrino energy spectrum
太阳中的几种不同核反应 $\Rightarrow$$\Rightarrow$=>\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"。
  $>$$>$>> Sensitive to solar neutrinos with $E_V>5\mathrm{MeV}$$E_V>5\mathrm{MeV}$E_(V) > 5MeVE_{V}>5 \mathrm{MeV}
  $>$$>$>> 通过 $E_V>5\mathrm{MeV}$$E_V>5\mathrm{MeV}$E_(V) > 5MeVE_{V}>5 \mathrm{MeV} 对太阳中微子敏感
  $>$$>$>> For lower energies too much background from natural radioactivity ( $\beta$$\beta$beta\beta-decays)
  $>$$>$>> 对于较低能量，天然放射性（ $\beta$$\beta$beta\beta -衰变）产生的背景太强。
  $>$$>$>> Hence detect mostly neutrinos from ${}^{8}B\to {}^{8}B{e}^{\ast }+e^{+}+v_e$${}^{8}B\to {}^{8}B{e}^{\ast }+e^{+}+v_e$^(8)B rarr^(8)Be^(**)+e^(+)+v_(e){ }^{8} B \rightarrow{ }^{8} B e^{*}+e^{+}+v_{e}
  $>$$>$>> 因此主要探测到来自 ${}^{8}B\to {}^{8}B{e}^{\ast }+e^{+}+v_e$${}^{8}B\to {}^{8}B{e}^{\ast }+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

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\pm 0.02$$=0.45\pm 0.02$=0.45+-0.02=0.45 \pm 0.02
  然而中微子数量太少 DATA/SSM $=0.45\pm 0.02$$=0.45\pm 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 $\left({\mathrm{D}}_{2}0\right)$$\left({\mathrm{D}}_{2}0\right)$(D_(2)0)\left(\mathrm{D}_{2} 0\right) Čerenkov detector
  1000吨重水 $\left({\mathrm{D}}_{2}0\right)$$\left({\mathrm{D}}_{2}0\right)$(D_(2)0)\left(\mathrm{D}_{2} 0\right) 采伦科夫探测器
• ${\mathrm{D}}_2\mathrm{O}$${\mathrm{D}}_2\mathrm{O}$D_(2)O\mathrm{D}_{2} \mathrm{O} inside a 12 m diameter acrylic vessel
  ${\mathrm{D}}_2\mathrm{O}$${\mathrm{D}}_2\mathrm{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 ${\mathrm{H}}_2\mathrm{O}$${\mathrm{H}}_2\mathrm{O}$H_(2)O\mathrm{H}_{2} \mathrm{O} and ${\mathrm{D}}_2\mathrm{O}$${\mathrm{D}}_2\mathrm{O}$D_(2)O\mathrm{D}_{2} \mathrm{O}
  超纯 ${\mathrm{H}}_2\mathrm{O}$${\mathrm{H}}_2\mathrm{O}$H_(2)O\mathrm{H}_{2} \mathrm{O} 和 ${\mathrm{D}}_2\mathrm{O}$${\mathrm{D}}_2\mathrm{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

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

ELASTIC SCATTERING  弹性散射

• 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
  

  

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：

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$$v_e$v_(e)v_{e} and $v_{\mu }+v_{\tau }$$v_{\mu }+v_{\tau }$v_(mu)+v_(tau)v_{\mu}+v_{\tau} fluxes
在约束条件相遇时，可分别测量 $v_e$$v_e$v_(e)v_{e} 和 $v_{\mu }+v_{\tau }$$v_{\mu }+v_{\tau }$v_(mu)+v_(tau)v_{\mu}+v_{\tau} 通量

SNO Results:  SNO 结果：

SSM Prediction:  SSM 预测：

• Clear evidence for a flux of $v_{\mu }$$v_{\mu }$v_(mu)v_{\mu} and/or $v_{\tau }$$v_{\tau }$v_(tau)v_{\tau} from the sun
  来自太阳的 $v_{\mu }$$v_{\mu }$v_(mu)v_{\mu} 和/或 $v_{\tau }$$v_{\tau }$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\to v_{\mu }$$v_e\to v_{\mu }$v_(e)rarrv_(mu)v_{e} \rightarrow v_{\mu} and/or $v_e\to v_{\tau }$$v_e\to v_{\tau }$v_(e)rarrv_(tau)v_{e} \rightarrow v_{\tau} neutrino transitions
  $v_e\to v_{\mu }$$v_e\to v_{\mu }$v_(e)rarrv_(mu)v_{e} \rightarrow v_{\mu} 和/或 $v_e\to v_{\tau }$$v_e\to v_{\tau }$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 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\to v_e$$\left(v_e\to v_e\right.$(v_(e)rarrv_(e):}\left(v_{e} \rightarrow v_{e}\right. for an electron neutrino)
  电子中微子的相干前向散射过程 $(v_e\to v_e$$\left(v_e\to v_e\right.$(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：

Atmospheric Neutrino experiment
大气中微子实验

$>$$>$>> Observe a lower ratio with deficit of $v_{\mu }/v_{\mu }$$v_{\mu }/v_{\mu }$v_(mu)//v_(mu)v_{\mu} / v_{\mu} coming from below the horizon, i.e. large
$>$$>$>> 观察到来自地平线以下的 $v_{\mu }/v_{\mu }$$v_{\mu }/v_{\mu }$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

$>$$>$>> Typical energy: ${\mathrm{E}}_v\sim 1\mathrm{GeV}$${\mathrm{E}}_v\sim 1\mathrm{GeV}$E_(v)∼1GeV\mathrm{E}_{v} \sim 1 \mathrm{GeV} (much greater than solar neutrinos - no confusion)
$>$$>$>> 典型能量： ${\mathrm{E}}_v\sim 1\mathrm{GeV}$${\mathrm{E}}_v\sim 1\mathrm{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_{\mu }$$v_{\mu }$v_(mu)v_{\mu} interactions from nature of Čerenkov rings
$>$$>$>> 从采伦科夫环的性质确定 $v_e$$v_e$v_(e)v_{e} 和 $v_{\mu }$$v_{\mu }$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$$v_e$v_(e)v_{e} rate agrees with data
  对 $v_e$$v_e$v_(e)v_{e} 速率的预测与数据一致
• Strong evidence for disappearance of $v_{\mu }$$v_{\mu }$v_(mu)v_{\mu} for large distances
  $v_{\mu }$$v_{\mu }$v_(mu)v_{\mu} 在远距离消失的有力证据
• Consistent with $v_{\mu }\to v_{\tau }$$v_{\mu }\to v_{\tau }$v_(mu)rarrv_(tau)v_{\mu} \rightarrow v_{\tau} oscillations
  与 $v_{\mu }\to v_{\tau }$$v_{\mu }\to v_{\tau }$v_(mu)rarrv_(tau)v_{\mu} \rightarrow v_{\tau} 振荡一致
• Don’t detect the oscillated $v_{\tau }$$v_{\tau }$v_(tau)v_{\tau} as typically below interaction threshold of 3.5 GeV
  不检测振荡的 $v_{\tau }$$v_{\tau }$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
$>$$>$>> Don’t have E/ $\theta$$\theta$theta\theta resolution to see oscillations
$>$$>$>> 没有 E/ $\theta$$\theta$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
$>$$>$>> Compare data to predictions for $\left|\mathrm{\Delta }{m}^2\right|$$\left|\mathrm{\Delta }{m}^2\right|$|Deltam^(2)|\left|\Delta m^{2}\right|
$>$$>$>> 将数据与 $\left|\mathrm{\Delta }{m}^2\right|$$\left|\mathrm{\Delta }{m}^2\right|$|Deltam^(2)|\left|\Delta m^{2}\right| 的预测进行比较

Data consistent with:  数据符合

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 $\left|\mathrm{\Delta }{m}_{21}^2\right|=8\times {10}^{-5}{\mathrm{eV}}^2$$\left|\mathrm{\Delta }{m}_{21}^2\right|=8\times {10}^{-5}{\mathrm{eV}}^2$|Deltam_(21)^(2)|=8xx10^(-5)eV^(2)\left|\Delta m_{21}^{2}\right|=8 \times 10^{-5} \mathrm{eV}^{2} is
与 $\left|\mathrm{\Delta }{m}_{21}^2\right|=8\times {10}^{-5}{\mathrm{eV}}^2$$\left|\mathrm{\Delta }{m}_{21}^2\right|=8\times {10}^{-5}{\mathrm{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

• Hence the CHOOZ limit: ${\sin }^{2}2{\theta }_{13}<0.2$${\sin }^{2}2{\theta }_{13}<0.2$sin^(2)2theta_(13) < 0.2\sin ^{2} 2 \theta_{13}<0.2 can be interpreted as ${\sin }^2{\theta }_{13}<0.05$${\sin }^2{\theta }_{13}<0.05$sin^(2)theta_(13) < 0.05\sin ^{2} \theta_{13}<0.05
  因此，CHOOZ 限制： ${\sin }^{2}2{\theta }_{13}<0.2$${\sin }^{2}2{\theta }_{13}<0.2$sin^(2)2theta_(13) < 0.2\sin ^{2} 2 \theta_{13}<0.2 可以解释为 ${\sin }^2{\theta }_{13}<0.05$${\sin }^2{\theta }_{13}<0.05$sin^(2)theta_(13) < 0.05\sin ^{2} \theta_{13}<0.05