Chart of Elementary Particles
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1 Chart of Elementary Particles
2 Chart of Elementary Particles
3 Better Chart!
4 Better Chart!
5 As of today: Oscillation of 3 massive active neutrinos is clearly the dominant effect: If neutrinos have mass: For 3 Active neutrinos. ' % li = % % & ' 1 % = % c % & s e1 µ1 τ s c e2 µ2 τ Atmospheric, Accel. $ ' 1 " % # & e3 µ3 τ3 $ " " " # 1? ν l = ν Pontecorvo-Maki-Nakagawa-Sakata matrix $ ' c " % e iδ # & s Experimentalist Slide s c $ ' c " % s # & CP Violating Phase Reactor, Accel. Solar,Reactor Majorana CP Phases s c $ ' 1 ".% 1 # & li i (Double β decay only) e iα 2 / 2? e iα 3 / 2+ iδ $ " " " # where c ij = cosθ ij, and s ij = sinθ ij Range defined for Δm 12, Δm 23 For two neutrino oscillation in a vacuum: (a valid approximation in many cases) L P(νµ νe ) = sin 2θ sin ( 127. ) Δm E CP Violating Phase or Majorana Phases: Antimatter/matter asymmetry in Early niverse?
6 As of today: Oscillation of 3 massive active neutrinos is clearly the dominant effect: If neutrinos have mass: For 3 Active neutrinos. ' % li = % % & ' 1 % = % c % & s e1 µ1 τ s c e2 µ2 τ Atmospheric, Accel. $ ' 1 " % # & e3 µ3 τ3 $ " " " # 1? ν l = * ν Pontecorvo-Maki-Nakagawa-Sakata matrix $ ' c " % e iδ # & s Theorist Slide s c $ ' c " % s # & CP Violating Phase Reactor, Accel. Solar,Reactor Majorana CP Phases s c $ ' 1 ".% 1 # & li i (Double β decay only) e iα 2 / 2? e iα 3 / 2+ iδ $ " " " # where c ij = cosθ ij, and s ij = sinθ ij Range defined for Δm 12, Δm 23 For two neutrino oscillation in a vacuum: (a valid approximation in many cases) L P(νµ νe ) = sin 2θ sin ( 127. ) Δm E CP Violating Phase or Majorana Phases: Antimatter/matter asymmetry in Early niverse?
7 Number of Events 14 Sub-GeV e-like cosθ Multi-GeV e-like cosθ Multi-GeV μ-like + PC 1 (LAB + PPO) Surrounded by 9 PMTs Nd-loaded at.1-.3% cosθ.5 1 SNO CC 68% C.L. SNO NC 68% C.L. SNO ES 68% C.L. SK ES 68% C.L ( 1 6 cm -2 s-1) e 2 8 µ %, 95%, 99% C.L % C.L. The SNO+ experiment 78 tonne liquid scintillator 35 NC µ BS5 SSM 6 3 Sub-GeV μ-like 2 Number of Events Number of Events Number of Events Neutrinos Oscillate thus they have mass ( kg of1 natural Nd) cosθ Water shield: flux of atmospheric muon tons PW neutrinos produced by cosmic rays is not up-down symmetric rylon liner solar neutrinos produced as electron neutrinos in the rope Sun are system to hold New detected by SNO as other flavours (νµ, ντ) down the 12 m diameter acrylic vessel ( 16 cm-2 s-1)
8 To be complete we ve also seen the disappearance of reactor antineutrinos due to oscillations at long baselines (~18 km) and short baselines (~1 km) we ve also seen the disappearance of acceleratorproduced beams of ν µ and also their appearance downstream as ν and ν τ We know neutrinos oscillate they can change flavour as they propagate!
9 math on the white board Neutrino Oscillations ν f =! flavour eigenstates and mass eigenstates mix in the lepton sector, like the quarks do i fi ν i different flavour detectable { simplified expressions for two-flavour mixing: ν e = ν 1 cos θ + ν 2 sin θ$ ν µ = ν 1 sin θ + ν 2 cos θ$ P eµ = sin 2 2θ sin Δm 2 L E Δm 2 in [ev 2 ], E in [MeV], L in [m] where
10 Characteristic Oscillation Length Δm 2 L P eµ = sin 2 2θ sin 2 E Δm 2 L osc = π E L osc [m] = π E [MeV] Δm 2 [ev 2 ] calculate a few of these for yourself: KamLAND reactor neutrinos, T2K long baseline GeV neutrinos, Daya Bay reactor neutrinos
11 Typical 2-ν Oscillation Result CHOOZ δm 2 (ev 2 ) E X C L D E D ν e ν x Reactor ν e Disappearance 1-3 analysis A analysis B analysis C 1-4 9% CL Kamiokande (multi-gev) 9% CL Kamiokande (sub+multi-gev) sin 2 (2θ)
12 Schrödinger s Cat Neutrino oscillations is like Schrödinger s Cat TM Hmm wait, I get it! The neutrino wavefunction is simultaneously ν 1 and ν 2 as it propagates!
13 Young s Two-Slit Experiment Neutrino oscillations is like the two-slit experiment! If I measure which neutrino mass eigenstate was produced, I will get a single-slit pattern. If I don t measure which mass eigenstate was emitted in the charged-current reaction, both are involved and I will get a two-slit interference pattern. That s neutrino oscillations!
14 Quark Mixing CKM Cabibbo-Kobayashi-Maskawa matrix describes quark flavour mixing we think of this slightly differently than we usually do for leptons from Wikipedia
15 Charged-Current Interactions with Quarks top quarks often decay to bottom quarks, sometimes to strange quarks, very occasionally to down quarks nobody has a problem with this! bottom quarks decay (undergo charged-current interactions that transform them) into charm quarks or sometimes up quarks nobody has a problem with this! Translate into Neutrino Language muons undergo charged-current interactions sometimes into ν 1, sometimes to ν 2, and sometimes to ν 3 if we have a ν 2 state propagating, it can undergo a chargedcurrent interaction that could transform it into an electron, muon (or a tau, if energetic enough) Perfectly analogous!
16 Why Oscillations? If we don t know whether it is a ν 2 state or a ν 1 state that is propagating, we have to consider that it is both, mixed as appropriate for the way the states were produced, coherent if produced that way, and propagating with different phases for the mass eigenstates, interfering with each other. The combination ν 2 state and ν 1 state can undergo a chargedcurrent interaction transforming it into an electron, muon, or tau depending on the coherent superposition of the possibilities for each of the ν 2 state and ν 1 state (which depends on their phases at that instant). It takes some words to say correctly but, if you understand the above, you ve understood neutrino oscillations completely!
17 So, the Next Time Somebody Asks You why do neutrinos oscillate? why don t electrons and muons oscillate? why don t quarks oscillate? or do they? you will be able to answer!
18 Three-Flavour Neutrino Oscillations (in vacuum, plane-wave model) I was going to write this on the white board then, thought I d LaTeX it up for PowerPoint then, decided, let s just cut and paste from Giunti and cite him Giunti
19 Three-Flavour Oscillations, cont d Giunti
20 Neutrinos and Antineutrinos Right-Handed Giunti
21 Neutrinos and Antineutrinos Right-Handed Giunti
22 PMNS Neutrino Mixing Matrix Pontecorvo, Maki, Nakagawa, Sakata ν f = i fi ν i atmospheric reactor/t2k solar plus KamLAND Majorana phases Giunti
23 Being Pedantic How Many Phases? 3 3 unitary matrix (complex-valued) 9 unitarity equations = 9 real parameters or 3 angles and 6 phases if neutrinos are Dirac fermions, all but one phase can be rotated away in the definition of the fields if neutrinos are Majorana fermions, only 3 phases can be absorbed into the definition of the fields PMNS neutrino mixing matrix,, therefore has either: 3 Majorana phases or 1 Dirac phase
24 Being Pedantic Octant Degeneracy what are the possible values of the PMNS matrix elements, αk? construction of the full 3 3 matrix with complex phase is nontrivial the octant can (does) matter oscillation experiments explore sin 2 2θ, resulting in an octant degeneracy in determining αk P eµ = sin 2 2θ sin Δm 2 L E sin 2 2θ [π]
25 Step Back to 2 2 ν e ν µ = cosθ sinθ sinθ cosθ ν 1 ν 2 the 2 2 unitary matrix is trivial if θ is negative (between π and 2π), cosθ stays the same and sinθ sin( θ), so we can map it to the positive angle and the matrix is just the transpose (no effect on oscillations) if θ > π/2, cosθ cos( θ), sinθ stays the same, so we can map it back to the first quadrant and the matrix is just the transpose, multiplied by 1 (no effect)
26 Angles, Octants, Mass Hierarchy if θ > π/4, cosθ sin(π/2 θ) sinθ sinθ cos(π/2 θ) cosθ and then we could map it back to the first octant and it would the same as flipping the mass hierarchy with a relative phase of π = 1 between them No effect on 2-flavour, vacuum oscillations ν e ν µ = sin θ cos θ cos θ sin θ ν 1 ν 2 ν e ν µ = cosθ sinθ sinθ cosθ ν 1 ν 2
27 Conclusions P eµ = sin 2 2θ sin 2 Δm 2 L 4E for 2-neutrino mixing, the first octant is sufficient for describing vacuum oscillations, without loss of generality the second octant is equivalent to flipping the mass hierarchy, which an oscillation experiment in vacuum can t determine in any case i.e. the sign of Δm 2 doesn t matter once we introduce matter effects, the hierarchy does matter and the second octant isn t degenerate with the first you hear all the time that the 2-neutrino approximation is a good one (it is, for what we use it for!); but, we live in a 3- neutrino (or more?!) world and the full treatment does matter when we look at more subtle details
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