Particle Physics WS 2012/13 ( )

Transcription

1 Particle Physics WS 2012/13 ( ) Stephanie Hansmann-Menzemer Physikalisches Institut, INF 226, 3.101

2 Reminder: No lecture this Friday

3 Neutrino Types and Sources Neutrinos are only detected by their weak IA, thus we define neutrino flavour eigenstates. ν e comes along with e, ν μ comes along with μ, ν τ comes along with τ ν e e ν μ μ W W W ν τ τ (accelerator neutrino) 3

4 History of Neutrino Physics 1926: Problem in β decay: n p + e - For a two body decay of neutron at rest, expect monoenergetic electrons: m n 0 = m p2 + p 2 p + m e2 + p 2 p Observation: continous spectrum 1930: Pauli postulates neutron endpoint of beta spectrum direct measurement of neutrino mass 4

5 History of Neutrino Physics 1932: Fermi theory of β decay: n p ~G F point IA e ν Postulated massless 1956: Discovery of ν e by Cowan and Reines (NP 1985) 5

6 History of Neutrino Physics 1957: Pontecorvo suggests neutrino oscillation 1958: Goldhaber experiment (helicity of neutrinos) 1962: discovery of 2nd neutrino (ν μ ) by Lederman, Steinberger, Schwartz (NP 1988) accelerator neutrinos detected in ν μ + p n + μ - reaction 1970: first discovery of solar neutrinos by Ray Davis (Homestake experiment) solar neutrino problem: defizit of observed neutrinos Discovery of neutrinos from SN 1987 A (Koshiba, NP 2002) 1991: Measurement of Z decay width establish existance of three light neutrinos 1998: Super-Kamiokande measured oscillation of atmospheric neutrinos 2000: Discovery of tau-neutrino 2002: SNO solves solar neutrino problem 2012: Oscillation of neutrinos from nuclear reactor 6

7 Mass Eigenstates & Weak Eigenstates The key to neutrino oscillation is to separate weak eigenstates and mass eigenstates! (This would be a null issue in case of zero neutrino masses as the mass eigenstates would be degenerated) physics beyond SM Start with two neutrino flavours first: flavour eigenstates: ν e, ν μ mass eigenstates: ν 1, ν 2 Wave function of mass eigenstates: ν 1 (t)> = e ip 1 x ie 1 t ν 2 (t)> = e ip 2 x ie 2 t ν e ν μ = cosθ sinθ sinθ cosθ ν 1 ν 2 ν 1 ν 2 = cosθ sinθ sinθ cosθ ν e ν μ 7

8 Time Evolution of Neutrino Flavour Eigenstates at t=0, pure ν e state produced in weak IA ψ(t=0)> = ν e > = cosθ ν 1 > + sinθ v 2 > Suppose neutrino travels along z direction ψ(t)> = cosθ ν 1 >e ip 1 z ie 1 t + sinθ v 2 > e ip 2 z ie 2 t Suppose the neutrino ineracts in a detector at a distance L and at a time T: ψ(l,t)> = cosθ ν 1 >e ip 1 L ie 1 T + sinθ v 2 > e ip 2 L ie 2 T = cosθ (cosθ ν e > - sinθ v μ > )e ip 1 L ie 1 T + sinθ (sinθ ν e > + cosθ v μ > ) e ip 2 L ie 2 T = ν e > (cos 2 ϴ e ip 1 L ie 1 T + sin 2 ϴ e ip 2 L ie 2 T ) + v μ > sinθ cosθ ( e ip 1 L ie 1 T +e ip 2 L ie 2 T ) for (ip 1 L-iE 1 T) = (ip 2 L-iE 2 T) original electron neutrino stays electron neutrino require mass difference between ν 1, ν 2 for mixing Introduce: φ 1 = E 1 T p 1 L ; φ 2 = E 2 T p 2 L ν 1 ν 2 = cosθ sinθ sinθ cosθ ν e ν μ ψ(l,t)> = = ν e > (cos 2 ϴ e iφ 1+ sin 2 ϴ e iφ 2) + v μ > sinθ cosθ ( e iφ 1 +e iφ 2) 8

9 Mixing Probabilities ψ(l,t)> = = ν e > (cos 2 ϴ e iφ 1+ sin 2 ϴ e iφ 2) + v μ > sinθ cosθ ( e iφ 1 +e iφ 2) P(ν e ν μ ) = <ν μ Ψ(L,T)> 2 = cos 2 ϴ sin 2 ϴ (-e i φ1 + e iφ 2)(-e +i φ1 + e +iφ 2) = ¼ sin 2 2ϴ (2-2cos(φ 1 -φ 2 )) = sin 2 2ϴ sin 2 ( φ φ 1 2) 2 Warning: the treatement in most text books is dubious. One could assume p 1 = p 2 =p (φ 1 -φ 2 ) = (E 1 -E 2 )T = [(p 2 + m 12 ) 1/2 (p 2 + m 22 ) 1/2 ] L L ~ (c)t = p[(1 + m 2 1 ) 1/2 (1 + m 2 2 ) 1/2 ] L ~ m 1 p 2 p 2 2 m 2 2 φ 1 = E 1 T p 1 L φ 2 = E 2 T p 2 L We have neglected that for the same momentum, different mass eigenstates will propagate at different velocities and be observed at different times. A full derivation requires a wave-packet treatment but gives the same result in the end. 2p L (φ 1 -φ 2 ) = m 2 2 m 1 2 2p L = Δm E L 9

10 Mixing Probabilities 10

11 Neutrino Oscillation P(ν e ν e, t) = 1 sin 2 2ϴ sin 2 ( Δm E L) = 1- sin 2 2ϴ sin 2 ( 1.27Δm 2 [ev 2 ] 21 4E[GeV] L[km]) In natural units P(ν e ν e ) <P(ν e ν μ ) > = sin 2 2ϴ/2 L detector >> L osc fast oscillation P(ν e ν e ) =1 sin2 2ϴ 2 L detector << L osc hardly oscillate before measurement: P(ν e ν e ) =1 sin 2 2ϴ Δm 21 2 L 4E 2 11

12 Sensitivity to Mixing L detector >> L osc fast oscillation P(ν e ν e ) =1 sin2 2ϴ 2 L detector << L osc hardly oscillate before measurement: P(ν e ν e ) =1 sin 2 2ϴ Δm 21 2 L In case of no mixing observed, we can make statements like P(ν e ν e ) > 90% CL 4E 2 P(ν e ν e ) =1 sin2 2ϴ 2 excluded region P(ν e ν e ) = 1 sin 2 2ϴ sin 2 ( Δm 2 21 Δm 2 21 L ~ π/2 4E 4E L) P(ν e ν e ) =1 sin 2 2ϴ Δm 21 2 L 4E 2 12

13 Neutrino Oscillation for Three Flavours Extend to three generations of neutrinos: ν e ν μ ν τ = U e1 U μ1 U τ1 U e2 U μ2 U τ2 U e3 U μ3 U μ3 ν 1 ν 2 ν 3 3x3 unitary matrix U is known as Pontecorvo.Maki-Nakagawa-Sakata matrix (PMNS) Exploiting U U = 1: ν 1 ν 2 ν 3 = U e1 U e2 U e1 U μ1 U μ2 U μ3 U τ1 U τ2 U τ3 ν e ν μ ν τ 13

14 Neutrino Oscillation for Three Flavours ψ(t=0)> = ν e > = U e1 ν 1 > + U e2 v 2 > + U e3 v 3 > ψ(l)> = U e1 ν 1 > e iφ 1+ U e2 v 2 >e iφ 2 + U e3 v 3 > e iφ 3 φ 1 = E 1 T p 1 L φ 2 = E 2 T p 2 L φ 3 = E 3 T p 3 L P(ν e ν μ ) = U e1 U μ1* ν 1 > e iφ 1+ U e2 U μ2 * v 2 > e iφ 2 + U e3 U μ3 * v 3 > e iφ 3 2 U e1 U * μ1 + U e1 U * μ1 + U e1 U * μ1 = 0 (unitarity condition) mixing requires phases to be different Similar computations as for 2 flavour scenario 14

15 Neutrino Oscillation for Three Flavours In case of three flavours: P(ν e ν e ) = 1 4 U e1 2 U e2 2 sin 2 Δ 21 4 U e1 2 U e3 2 sin 2 Δ 31 4 U e2 2 U e3 2 sin 2 Δ 32 Δ 21 = Δm E L mit Δm 21 2 = m 22 -m 1 2 (similar for Δ 31, Δ 32 ) Note: m 3 2 m 1 2 = (m 3 2 m 22 ) + (m 2 2 m 12 ) only 2 independent paramters Compare to case of two flavours: P(ν e ν e ) = 1 sin 2 2ϴ sin 2 ( Δm 12 2 L 4E ) Δm E L 15

16 PNMS Matrix Alternative parametrisation: ν ν μ ν τ = U ν 1 ν 2 ν 3 c 12 = cosθ 12, s 12 = sin ϴ 12, etc. U = c 23 s 23 0 s 23 c 23 c 13 s 13 e iδ 1 s 13 e iδ c 13 c 12 s 12 s 12 c 12 1 Complex phase is only non-trivial if ϴ 12, ϴ 23, ϴ 13 are non-zero This requires the three masses of the mass eigenstates to be different! The last missing piece ϴ 13 0 was established in 2012! There is potential CPV in the neutrino sector! 16

17 Neutrino Mass Hierachy 17

18 PNMS Matrix ν e ν μ ν τ = U ν 1 ν 2 ν 3 U = c 23 s 23 0 s 23 c 23 c 13 s 13 e iδ 1 s 13 e iδ c 13 c 12 s 12 s 12 c 12 1 With Δm 12 << Δm 23 ~ Δm 13 and ϴ 13 small For atmospheric and accelerator neutrions (E large, L medium): P(ν μ ν τ ) = 1 sin 2 2ϴ 23 sin 2 ( Δm 2 L 23 ) 4E P(ν e ν e ) ~ 1 Δm 12 2 L E 1 For solar neutrinos and very long baseline neutrinos (L large, E small): (almost like two neutrino system, only one mass difference) P(ν e ν e ) = 1 sin 2 2ϴ 12 sin 2 ( Δm 2 L 12 ) 4E Δm 13 2 L E 1 For short baseline reactor neutrinos (E small, L small): P(ν e ν e ) = 1 sin 2 2ϴ 13 sin 2 ( Δm 2 L 13 ) 4E Δm 12 2 L E 1 18

19 Sensitivity 19

20 No max values Listed, fast mixing is washed out! Sensitivity SBL: Short Base Line; LBL: Long Base Line 20

21 Neutrino Oscillation Experiments: Some Neutrino Experiments Neutrino absolute mass measurements: e.g. Katrin (measurement of endpoint of betas spectrum) 21

22 Atmospheric Neutrinos 22

23 (Super-)Kamiokande treshold: ~ 5 MeV (to produce sufficiently high energetic electrons to produce Cherenkov light, no issue for atmospheric neutrinos, but for solar neutrinos) Advantage: - scattered electron/muons carry direction information - in-situ detection - measurement of neutrino energy 23

24 (Super-)Kamiokande 24

25 Detection of Cherenkov-Light 25

26 ν e ν μ Energy measurement: Thickness of ring is related to travel distance of electron/muon in the detector. This is related to the energy of the electron/muon thus (with some uncertainties) to the original neutrino energy. 26

27 Ratio of Muon to Electron Neutrinos oscillation depend on E, thus split up sample in high and low momentum neutrinos assuming no oscillation in simulation Δm 2 (atmospheric) ~ To few muon neutrinos observed can be explained by oscillation! For atmospheric and accelerator neutrions (E large, L medium): P(ν μ ν τ ) = 1 sin 2 2ϴ 23 sin 2 ( Δm 2 L 23 ) 4E P(ν e ν e ) ~ 1 Δm 12 2 L E 1 27

28 Zenith Angle Dependence of Neutrino Flux Electron neutrion seem to consist mainly of matter eigenstate, which has a significant longer oscillation distance both compared to Distance atmosphere earth and to diameter of the earth. 28

29 Oscillating Pattern of Atmospheric Neutrinos Slide taken from Neutrino 2004 conference 29

30 Solar Neutrinos 5 sources of solar neutrinos: fixed energy from 2 body decay, continious spectrum from multi-body decay measured flux depends strongly on detection treashold 30

31 Homestake Experiment Pioneering experiment, started in 1970: 31

32 Homestake Experiment initially results were ignored maybe a mistake in the measurement method 32

33 Further Solar Neutrino Experiment elastic scattering: direction of electron related to direction of initial neutrino, thus usefull to separate background from neutrinos from the sun. 33

34 Solar Neutrino Problem CC: Charge current IA ES: elastic scattering To establish neutrino mixing, need to measure additionally appearance effects! 34

35 Homestake experiment Nobel Prize in 2002 spokesperson Kamiokande 35

36 SNO Experiment Sudbury Neutrino Observatory: 36

37 SNO Experiment 37

38 φ CC < φ ES < φ NC! appearance of μ/τ neutrinos detected! SNO Experiment 38

39 Neutrino in Matter ν 1 (t)> = e ip 1 x ie 1 t ν 2 (t)> = e ip 2 x ie 2 t 39

40 Neutrino in Matter 40

41 Neutrino in Matter 41

42 Neutrino in Matter n 42