Neutrino mixing. Outline: description/review of mixing phenomenology possible experimental signatures short review of existing experimental results

Transcription

1 Neutrino mixing Can ν e ν µ ν τ? If this happens: neutrinos have mass physics beyond the (perturbative) Standard Model participates Outline: description/review of mixing phenomenology possible experimental signatures short review of existing experimental results /19/01 HEP lunch talk: George Gollin 1

2 Analogy with K K 0 0 mixing n We produce flavor eigenstates... u Λ u µ + d π + W + d s s Κ 0 d ν µ strong interaction produces a K 0 weak interaction produces a ν µ but the mass eigenstates are what propagate sensibly without mixing: imc ħ ( τ) = ( 0 ) ( τ) = ( 0) S S L imlc K K e e K K e e Γ τ τ Γ τ τ S S L L ħ imc ( ) ( 0 ) e τ ħ = ( ) = ( 0) 1 imc ν τ ν ν τ ν 1 1 ( ) = ( ) ν τ ν e 3 im cτ ħ e τ ħ

3 Analogy with K K 0 0 mixing We know K L K 0, etc. Perhaps ν 1 ν e or ν ν µ or ν 3 ν τ? Rewrite the production eigenstates as linear combinations of mass eigenstates: 0 K KS = U 0 KL K νe ν1 ν = U ν µ ν τ ν 3 K K S = ( T U ) K K 0 L ν ν 1 e ( T ) ν = U νµ ν 3 ν τ 0 U is the Maki-Nakagawa-Sakata matrix. /19/01 HEP lunch talk: George Gollin 3

4 Maki-Nakagawa-Sakata mixing matrix Parameterize mixing with three angles and one phase: iδ c13 0 s13e c1 s1 0 U = 0 c3 s s1 c1 0 + iδ 0 s3 c 3 s13e 0 c c ν µ ντ νe ν ν τ e νµ cos θ, s sin θ... δ 0: CP violation This form is convenient if only two neutrino species mix. (CP violation requires that all three mix.) /19/01 HEP lunch talk: George Gollin 4

5 Analogy with K K 0 0 mixing Κ 0 Κ 0 ν µ ν e s Κ 0 W W Κ 0 d ( ) u,c,t u,c,t K τ = = K K K d s 0 0 S + L??? (maximal mixing!) ( τ ) S imc S ħ L imc L K = K e e + K e e S Γ τ τ Γ τ τ L ħ ~ K e ΓS τ + K e ΓL τ e i mc τ ħ ( m= m m ) S L L S K L phase rotates (relative to K S phase) ~30 per sec. 0 0 Recall: K K + K and K K - K. S L S L

6 Analogy with K K 0 0 mixing Κ 0 Κ 0 ν µ ν e s d u,c,t Κ 0 W W Κ 0 u,c,t d s??? ( = 0) = µ = U1 1 + U + U3 3 ν τ ν ν ν ν ( ) 1 τ ħ imc ν τ = U ν e + U ν e + U ν e imc τ ħ im cτ ħ ν 1, ν 3 phases rotate relative to ν phase if masses are unequal. /19/01 HEP lunch talk: George Gollin 6

7 Highly contrived example: m 1 = 0.1 ev, m = 0.3 ev, m 3 = 0.4 ev θ 1 = 10, θ 13 = 0, θ 3 = 30, δ = 0 Radius of circle = amplitude ; line indicates Arg(amplitude) t = 0 ( ) ν ν 0 = 1 µ n e n m n t P = P = 1. P = n 1 n n 3 m 1 = 0.1 ev m = 0.3 ev m 3 = 0.4 ev q 1 =10. deg q 13 =0. deg q 3 =30. deg ( ) ( ) ( ) ν ν 0 = 0.3 ν ν 0 = 0.8 ν ν 0 = t = 0. sec

8 dϕ1 mc 1-15 dϕ -15 dϕ3-15 = = sec; = sec; = sec dτ ħ dτ dτ t = sec ν ν ( t ) 1 µ n e n m n t P = P = P = probabilities n 1 n n 3 m 1 = 0.1 ev m = 0.3 ev m 3 = 0.4 ev q 1 =10. deg q 13 =0. deg q 3 =30. deg t = sec ν 1, ν, ν 3 phases have changed: heavier species phaserotate more rapidly.

9 Mathematica animation for m 1 = 0.1 ev, m = 0.3 ev, m 3 = 0.4 ev θ 1 = 10, θ 13 = 0, θ 3 = 30, δ = 0 ( /19/01 HEP lunch talk: George Gollin 9

10 ν oscillations in a beam with energy E ν... x = distance from production t = time since production x xct c µ (, ) rest frame: ( 0, τ ) (, ) rest frame: ( 0, ) p pe c mc µ ν px µ µ = mc i τ = px Et ν all frames (Lorentz scalar) lab frame 3 ( ) ( ) ( ) p= E c mc E c mc E ; x ct ν i ν i ν 3 ( ) ħ ( ħ) i px Et imi c x E i τ ħ ν ν = imc e e e ( ) = ( 0) ν τ ν imc 1 τ i i e ħ ν i ( ) = ν ( ) i 3 i 0 im c x ( E ħ) x e ν /19/01 HEP lunch talk: George Gollin 10

11 ( x = 0) = µ = U1 1 + U + U3 3 ν ν ν ν ν ( ) ν µ oscillations in a beam... ( ħ) ( ħ) i m c x E i m cx E ν x U ν U ν e U ν e 1 1 m = m m m = m m 3 1 im c x e ( E ħ ) (factored out.) 3 dϕ1 m1c m1 = ( 145 per km ) for m1 in ( ev ), E in GeV dx Eħ E Relative phases of ν 1, ν, ν 3 coefficients change: ν µ other stuff /19/01 HEP lunch talk: George Gollin 11

12 Mathematica animation for m 1 = 0.3 ev, m 31 = 0.6 ev θ 1 = 5, θ 13 = 10, θ 3 = 15, δ = 0 ( /19/01 HEP lunch talk: George Gollin 1

13 Two-flavor mixing Results are often analyzed with the simplifying assumption that only two of the three ν species mix. For example: ν e ν µ... ( x = 0) = µ = sin cos 1 ν ν θ ν θ ν ( x) ν = sinθ ν + cosθ ν ( ν ν ; ) = ν ν ( ) P x x µ e e e 3 1 i m cx ( Eħ) 3 1 ( Eħ) = cosθν + sinθ ν sinθν + cosθ ν i m c x e ( θ θ ) = cos sin 1 e 1 1 i m c x 3 1 ( Eħ) /19/01 HEP lunch talk: George Gollin 13

14 ( ν ) µ νe ( θ1 θ1 ) Two-flavor mixing P ; x = cos sin 1 e i m c x ( Eħ) /19/01 HEP lunch talk: George Gollin m1cx = sin ( θ1 ) 1 cos Eħ 3 m1cx = sin ( θ 1 ) sin 4Eħ x sin ( θ 1) sin 1.7 m1 E units: m in ev, x in km, E in GeV. ( ν ν ; ) = 1 ( ν ν ; ) P x P x e e µ e

15 Mathematica animation for m 1 = 0.3 ev θ 1 = 15, θ 13 = 0, θ 3 = 0, δ = 0 ( /19/01 HEP lunch talk: George Gollin 15

16 Those confusing plots for two-flavor mixing... ( ν ) µ νe ( θ ) P ; L sin 1 sin 1.7 m1 E A search experiment sets a limit (or measures!!) the mixing probability P, but little else, at the present time. Green curve is contour of fixed probability to observe oscillation L for an event is uncertain due to length of π µ decay/drift region. Large Dm : uncertainty in L/E corresponds to several oscillations. P determined by experiment is an average over several oscillations and is insensitive to m in this case... L

17 More on those confusing plots... ( ν ) µ νe ( θ ) P ; L sin 1 sin 1.7 m1 E Medium m : uncertainty in L/E corresponds to a fraction of an oscillation. 1.7 m L/E ~ π/ is possible for some of the detected events P (limit) determined by experiment corresponds to smallest sin (θ) when 1.7 m L/E = π/. L

18 Even more on those confusing plots... ( ν ) µ νe ( θ ) P ; L sin 1 sin 1.7 m1 E Small m : uncertainty in L/E corresponds to a fraction of an oscillation. sin (1.7 m L/E) < 1 since L/E is always too small P (limit) determined by experiment corresponds to larger and larger sin (θ) as m L/E shrinks. (Green Green curve is contour of fixed probability to observe oscillation) L

19 What could be happening? Nothing Two- or three-flavor oscillations Oscillations into sterile neutrinos (ν s just disappear ) Neutrinos decay (into what??) Matter-enhanced (Mikheyev-Smirnov-Wolfenstein mechanism) oscillations Extra dimensions Something else ν e ν µ ν τ /19/01 HEP lunch talk: George Gollin 19

20 1. Atmospheric neutrinos Is anything happening? cosmic ray interactions in the atmosphere produce ν s through decays of π, K, µ. expect ν µ / ν e ratio for upwards- and downwards-going neutrinos to be equal if no oscillations. expect ν µ / ν e ratio for upwards-going neutrinos to shrink relative to downwards-going if ν µ oscillates into ν τ or ν sterile but ν e doesn t. Super-Kamikande finds ν µ (up)/ ν µ (down) = 0.5 ± 0.05 but ν e (up)/ ν e (down) ~ 1. suggestive of ν µ ν τ oscillations /19/01 HEP lunch talk: George Gollin 0

21 . Solar neutrinos... Is anything happening?

22 ... Solar neutrinos... Is anything happening?

23 ... Solar neutrinos... Is anything happening? Not enough neutrinos. MSW mechanism? (more on this next week)

24 Is anything happening? 3. LSND result 1 ma beam of 800 MeV (kinetic) energy protons produces π +, µ + which decay in flight (most π -, µ - captured in shielding) 4 ν ν 4 10 in beam e µ Look for ν e appearing in liquid scintillator volume find 8.8 ± 3.7 excess ν e events also see weaker evidence for ν µ ν e /19/01 HEP lunch talk: George Gollin 4

25 Is anything happening?...lsnd result BNL E776 Karmen Bugey LSND has the only appearance result. LSND 90% LSND 95%

26 Next week More about the existing results and planned experiments. /19/01 HEP lunch talk: George Gollin 6