neutrino oscillation lunchtalk 1 · 2001. 2. 21. · We know K L ≠ K0, etc. Perhaps ν 1 ≠ ν e...

2/19/01 HEP lunch talk: George Gollin 1

Neutrino mixing

Can νe νµ ντ ?↔ ↔

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

Analogy with mixing

…but the mass eigenstates are what propagate “sensibly” withoutmixing:

0 0K K↔

ud

dn

Λss

Κ0

strong interaction produces a K0

d

W+uπ+

µ+

νµ

weak interaction produces a νµ

We produce flavor eigenstates...

( ) ( ) ( ) ( )2 2

0 0S S L Lim c im cS S L LK K e e K K e eτ τ τ ττ τ−Γ − −Γ −= =h h

( ) ( ) ( ) ( )2 21 2

1 1 2 20 0im c im ce eτ τν τ ν ν τ ν− −= =h h

( ) ( ) 23

3 3 0 im ce τν τ ν −= h


Analogy with mixing0 0K K↔

We know KL ≠ K0, etc. Perhaps ν1 ≠ νe or ν2 ≠ νµ or ν3 ≠ ντ?

Rewrite the production eigenstates as linear combinations ofmass eigenstates:

0

2 20

S

L

K KU

KK×

= ( )

0

2 2 0

S T

L

KKU

K K

∗

×

=

1

2

3

e

Uµ

τ

ν νν νν ν

=

( )1

2

3

eTU µ

τ

ν νν νν ν

∗ =

U is the Maki-Nakagawa-Sakata matrix.


12 12sin ...s θ≡12 12cos ,c θ≡ 0 : violationCPδ ≠

Maki-Nakagawa-Sakata mixing matrix

Parameterize mixing with three angles and one phase:

This form is convenient if only two neutrino species mix.(CP violation requires that all three mix.)

13 13 12 12

23 23 12 12

23 23 13 13

1 0 0 0 0

0 0 1 0 00 0 0 0 1

i

i

c s e c s

U c s s cs c s e c

δ

δ

−

+

= −

− −

e τν ν↔µ τν ν↔ e µν ν↔


d

s

Κ0 Κ0W

s

dW

u,c,t

u,c,t???

Κ0 Κ0 νµ νe

( ) 00 +S LK K K Kτ = = ∼

( ) 2 2

+S S L Lim c im cS LK K e e K e eτ τ τ ττ −Γ − −Γ −= h h

2

~ + ( )S L i mcS L L SK e K e e m m mτ τ τ−Γ −Γ − ∆ ∆ = −h

KL phase rotates (relative to KS phase) ~30° per 10-10 sec.

(maximal mixing!)

Recall: and .0 +S LK K K∼ 0 -S LK K K∼



ν1, ν3 phases rotate relative to ν2 phase if masses are unequal.

( ) 22 231 2

21 1 22 2 23 3im cim c im cU e U e U e ττ τν τ ν ν ν −− −∗ ∗ ∗= + + hh h

( ) 21 1 22 2 23 30 U U Uµν τ ν ν ν ν∗ ∗ ∗= = = + +

d

s

Κ0 Κ0W

s

dW

u,c,t

u,c,t???

Κ0 Κ0 νµ νe

n1 n2 n3m1 = 0.1 eV m2 = 0.3 eV m3 = 0.4 eV

P = 8.73 ´10-34 P = 1. P = 1.1´10-32ne nm nt

q12=10. deg q13=20. deg q23=30. deg

t = 0. sec

Highly 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)

( ) ( ) ( )1 2 30 0.32 0 0.82 0 0.47ν ν ν ν ν ν= − = =

t = 0

( )0 1µν ν =

n1 n2 n3m1 = 0.1 eV m2 = 0.3 eV m3 = 0.4 eV

P = 0.0341 P = 0.961 P = 0.00445ne nm nt

q12=10. deg q13=20. deg q23=30. deg

t = 1.654´10-15 sec

ν1, ν2, ν3 phases have changed: heavier species phase-rotate more rapidly.

t = 1.65×10-15 sec ( ) 1tµν ν ≠

probabilities

2-15 -15 -1531 1 2 dd d

= 8.7 10 sec; 26.1 10 sec; 34.8 10 secd d d

m c ϕϕ ϕτ τ τ

= ° = ° = °h


Mathematica 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)


ν oscillations in a beam with energy Eν ...x = distance from production t = time since production

( ) ( ) 210 im c

i i e τν τ ν −= h

( ) ( )( ) ( )

2

, rest frame: 0,

, rest frame: 0,

all frames (Lorentz scalar) lab frame

i

x x ct c

p p E c mc

p x m cpx E t

µ

µ νµ

µ

ν

τ

τ

≡≡

= −= −

rr

( ) ( ) ( )2 2 2 3 2 ; i ip E c m c E c m c E x ctν ν ν= − ≈ − ≈

( ) ( )2 32 2ii i px E t im c x Eim ce e eν ντ − −−∴ = ≈h hh

( ) ( ) ( )2 3 20 iim c x Ei ix e νν ν −= h


( ) 21 1 22 2 23 30x U U Uµν ν ν ν ν∗ ∗ ∗= = = + +

Relative phases of ν1, ν2, ν3 coefficients change: νµ→ other stuff

2 2221 2 1m m m∆ = − 2 22

31 3 1m m m∆ = −

( ) ( ) ( )2 3 2 321 312 2

21 1 22 2 23 3i m c x E i m c x Ex U U e U eν ν ν ν− ∆ − ∆∗ ∗ ∗+ +h h∼

νµ oscillations in a beam...

(factored out .)( )2 31 2im c x Ee− h

( ) ( )2 3 2

2221 21 2121

d 145 per km for in eV , in GeV

d 2m c m

m Ex E E

ϕ ∆ ∆= ≈ ⋅ ° ∆h


Mathematica animation for∆m21

2 = 0.3 eV2 , ∆m312 = 0.6 eV2

θ12 = 5°, θ13 = 10°, θ23 = 15°, δ = 0° (http://web.hep.uiuc.edu/home/g-gollin/neutrinos/amplitudes2.nb)


( ) 12 1 12 20 sin cosx µν ν θ ν θ ν= = = − +

( ) ( )2 321 2

12 1 12 2sin cos i m c x Ex eν θ ν θ ν − ∆= − + h

Two-flavor mixingResults are often analyzed with the simplifying assumption thatonly two of the three ν species mix.

For example: νe νµ ...↔

( ) ( )( )

( ) ( )

2 321

2 321

2

22

12 1 12 2 12 1 12 2

22 212 12

;

cos sin sin cos

cos sin 1

e e

i m c x E

i m c x E

P x x

e

e

µν ν ν ν

θ ν θ ν θ ν θ ν

θ θ

− ∆

− ∆

→ =

= + − +

= −

h

h


Two-flavor mixing

units: ∆m2 in eV2, x in km, E in GeV.

( ) ( ) ( )

( )

( )

( )

2 321

22 212 12

2 32 21

12

2 32 2 21

12

2 2 212 21

; cos sin 1

1sin 2 1 cos

2 2

sin 2 sin4

sin 2 sin 1.27

i m c x EeP x e

m c xE

m c xE

xm

E

µν ν θ θ

θ

θ

θ

− ∆→ = −

∆= −

∆

= ≈ ∆

h

h

h

( ) ( ); 1 ;e e eP x P xµν ν ν ν→ = − →


Mathematica animation for∆m21

2 = 0.3 eV2

θ12 = 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...

( ) ( )2 2 212 21; sin 2 sin 1.27e

LP L m

Eµν ν θ → ≈ ∆

GreenGreen curve is contour of fixedprobability to observe oscillation

A 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...

( ) ( )2 2 212 21; sin 2 sin 1.27e

LP L m

Eµν ν θ → ≈ ∆

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 events

P (limit) determined by experimentcorresponds to smallest sin2(2θ)when 1.27∆m2L/E = π/2.

Even more on those confusing plots...

( ) ( )2 2 212 21; sin 2 sin 1.27e

LP L m

Eµν ν θ → ≈ ∆

Small Small ∆∆mm22:

•uncertainty in L/E corresponds to afraction of an oscillation.

•sin2(1.27∆m2L/E) < 1 since L/E isalways too small

P (limit) determined by experimentcorresponds to larger and largersin2(2θ) as ∆m2L/E shrinks.

(GreenGreen curve is contour of fixedprobability to observe oscillation)


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

νe νµ ντ↔ ↔


Is anything happening?

1. Atmospheric neutrinos

•cosmic ray interactions in the atmosphere produce ν’s throughdecays of π, K, µ.

•expect νµ/ νe ratio for upwards- and downwards-goingneutrinos to be equal if no oscillations.

•expect νµ/ νe ratio for upwards-going neutrinos to shrinkrelative to downwards-going if νµ oscillates into ντ or νsterile butνe doesn’t.

•Super-Kamikande finds νµ(up)/ νµ(down) = 0.52 ± 0.05 butνe(up)/ νe (down) ~ 1.

•suggestive of νµ→ ντ oscillations


2. Solar neutrinos...


... Solar neutrinos...


... Solar neutrinos...

Not enough neutrinos.

MSW mechanism?

(more on this next week)



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)

• in beam

•Look for appearing in liquid scintillator volume

•find 82.8 ± 23.7 excess events

•also see weaker evidence for νµ→ νe

44 10e µν ν −≈ ×

eν

eν


...LSND result

LSND 90%

LSND 95%

BugeyKarmen

BNL E776

LSND has theonly appearanceresult.


Next week

More about the existing results and planned experiments.

neutrino oscillation lunchtalk 1 · 2001. 2. 21. · We know K L ≠ K0, etc. Perhaps ν 1 ≠ ν e...

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