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Neutrino mixing

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2/19/01 HEP lunch talk: George Gollin 1Neutrino mixingCan νe νµ ντ ?↔↔If this happens:•neutrinos have mass•physics beyond the (perturbative) Standard Model participatesOutline:•description/review of mixing phenomenology•possible experimental signatures•short review of existing experimental resultsAnalogy with mixing…but the mass eigenstates are what propagate “sensibly” withoutmixing:00KK↔uddnΛssΚ0strong interaction produces a K0dW+uπ+µ+νµweak interaction produces a νµWe produce flavor eigenstates...( ) ( ) ( ) ( )2 20 0SS LLimc imcSSLLKKeeKKeeττττττ−Γ− −Γ−==hh( ) ( ) ( ) ( )221211220 0imcimceeττντνντν−−==hh( ) ( )23330imceτντν−=h2/19/01 HEP lunch talk: George Gollin 3Analogy with mixing00KK↔We know KL ≠ K0, etc. Perhaps ν1 ≠ νe or ν2 ≠ νµ or ν3 ≠ ντ?Rewrite the production eigenstates as linear combinations ofmass eigenstates:0220SLKKUKK×=( )0220STLKKUKK∗×=123eUµτνννννν=( )123eTUµτνννννν∗=U is the Maki-Nakagawa-Sakata matrix.2/19/01 HEP lunch talk: George Gollin 41212sin...s θ≡1212cos,cθ≡0: violationCPδ≠Maki-Nakagawa-Sakata mixing matrixParameterize mixing with three angles and one phase:This form is convenient if only two neutrino species mix.(CP violation requires that all three mix.)131312122323121223231313100000010000001iicsecsUcsscscsecδδ−+=−−−eτνν↔µτνν↔eµνν↔Analogy with mixing00KK↔dsΚ0Κ0WsdWu,c,tu,c,t???Κ0Κ0νµνe()00+SLKKKKτ == :( )2 2+SS LLimc imcSLKKeeKeeτττττ−Γ− −Γ−=hh2~+ ()S LimcSLLSKeKeemmmττ τ−Γ−Γ −∆∆=−hKL phase rotates (relative to KS phase) ~30° per 10-10 sec.(maximal mixing!)Recall: and .0+SLKKK:0-SLKKK:2/19/01 HEP lunch talk: George Gollin 6Analogy with mixing00KK↔ν1, ν3 phases rotate relative to ν2 phase if masses are unequal.( )222312211222233imcimcimcUeUeUeτττντννν−−−∗∗∗=++hhh()2112222330 UUUµντνννν∗∗∗===++dsΚ0Κ0WsdWu,c,tu,c,t???Κ0Κ0νµνen1n2n3m1= 0.1 eV m2= 0.3 eV m3= 0.4 eVP = 8.73 ´10-34P = 1. P = 1.1´10-32nenmntq12=10. deg q13=20. deg q23=30. degt = 0. secHighly contrived example:m1 = 0.1 eV, m2 = 0.3 eV, m3 = 0.4 eVθ12 = 10°, θ13 = 20°, θ23 = 30°, δ = 0°Radius of circle = |amplitude|; line indicates Arg(amplitude)()()()12300.3200.8200.47νννννν=−==t = 0()01µνν=n1n2n3m1= 0.1 eV m2= 0.3 eV m3= 0.4 eVP = 0.0341 P = 0.961 P = 0.00445nenmntq12=10. deg q13=20. deg q23=30. degt = 1.654´10-15secν1, ν2, ν3 phases have changed: heavier species phase-rotate more rapidly.t = 1.65×10-15 sec( )1tµνν≠probabilities2-15-15-153112ddd = 8.710sec; 26.110sec; 34.810secdddmc ϕϕϕτττ=°=°=°h2/19/01 HEP lunch talk: George Gollin 9Mathematica animation form1 = 0.1 eV, m2 = 0.3 eV, m3 = 0.4 eVθ12 = 10°, θ13 = 20°, θ23 = 30°, δ = 0°(http://web.hep.uiuc.edu/home/g-gollin/neutrinos/amplitudes1.nb)2/19/01 HEP lunch talk: George Gollin 10ν oscillations in a beam with energy Eν ...x = distance from production t = time since production( ) ( )210imciieτντν−=h()()( ) ( )2, rest frame: 0,, rest frame: 0, all frames (Lorentz scalar) lab frameixxctcppEcmcpxmcpxEtµµνµµνττ≡≡=−=−rr( ) ( ) ( )22232; iipEcmcEcmcExctννν=−≈−≈( ) ( )2322iiipxEtimcxEimceeeνντ−−−∴=≈hhh( ) ( )( )2320iimcxEiixeννν−=h2/19/01 HEP lunch talk: George Gollin 11()2112222330xUUUµννννν∗∗∗===++Relative phases of ν1, ν2, ν3 coefficients change: νµ→ other stuff2222121mmm∆=−2223131mmm∆=−( )( ) ( )2323213122211222233imcxEimcxExUUeUeνννν−∆−∆∗∗∗++hh:νµ oscillations in a beam...(factored out .)( )2312imcxEe−h( ) ( )2322221212121d 145 per km for in eV, in GeVd2mcmmExEEϕ ∆∆=≈⋅°∆h2/19/01 HEP lunch talk: George Gollin 12Mathematica animation for∆m212 = 0.3 eV2 , ∆m312 = 0.6 eV2θ12 = 5°, θ13 = 10°, θ23 = 15°, δ = 0° (http://web.hep.uiuc.edu/home/g-gollin/neutrinos/amplitudes2.nb)2/19/01 HEP lunch talk: George Gollin 13()1211220sincosxµννθνθν===−+( )( )23212121122sincosimcxExeνθνθν−∆=−+hTwo-flavor mixingResults are often analyzed with the simplifying assumption thatonly two of the three ν species mix.For example: νe νµ ...↔()( )( )( )( )232123212221211221211222221212;cossinsincoscossin1eeimcxEimcxEPxxeeµννννθνθνθνθνθθ−∆−∆→==+−+=−hh2/19/01 HEP lunch talk: George Gollin 14Two-flavor mixingunits: ∆m2 in eV2, x in km, E in GeV.( )( )( )( )( )( )232122212122322112232221122221221;cossin11sin21cos22sin2sin4sin2sin1.27imcxEePxemcxEmcxExmEµννθθθθθ−∆→=−∆=−∆=≈∆hhh()();1;eeePxPxµνννν→=−→2/19/01 HEP lunch talk: George Gollin 15Mathematica animation for∆m212 = 0.3 eV2θ12 = 15°, θ13 = 0°, θ23 = 0°, δ = 0° (http://web.hep.uiuc.edu/home/g-gollin/neutrinos/amplitudes3.nb)Those confusing plots for two-flavor mixing...( )( )2221221;sin2sin1.27eLPLmEµννθ→≈∆GreenGreen curve is contour of fixedprobability to observe oscillationA search experiment sets a limit (or measures!!) the mixingprobability P, but little else, at the present time.L for an event is uncertain due tolength of π→µ decay/drift region.Large Large ∆∆mm22: uncertainty in L/Ecorresponds to several oscillations.P determined by experiment is anaverage over several oscillations andis insensitive to ∆m2 in this case...More on those confusing plots...( )( )2221221;sin2sin1.27eLPLmEµννθ→≈∆Medium Medium ∆∆mm22:•uncertainty in L/E corresponds to afraction of an oscillation.•1.27∆m2L/E ~ π/2 is possible forsome of the detected eventsP (limit) determined by experimentcorresponds to smallest sin2(2θ)when 1.27∆m2L/E = π/2.Even more on those confusing plots...( )( )2221221;sin2sin1.27eLPLmEµννθ→≈∆Small Small ∆∆mm22:•uncertainty in L/E


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