Документ взят из кэша поисковой машины. Адрес оригинального документа : http://nuclphys.sinp.msu.ru/conf/epp10/Weiler.pdf Дата изменения: Sat Sep 7 16:39:52 2013 Дата индексирования: Fri Feb 28 02:22:24 2014 Кодировка: IBM-866

Cosmic neutrino flavor ratios with broken І- symmetry

Moscow Lomonosov Aug 22-28, 2013

Tom Weiler, Vanderbilt U.


Oscillation phase is = so, = ln =

L m 4E

2

, E 2 E

= 2 N

osc

averages out ! i



L 2 L

L 2 L

+

+



E 2 E

e = 0 |Uej |2 |UjІ |
T 2 2

P P

Іe

= =

j j



~~ =PP
sym



|U j |2 |Uj |
CP

=P



=P

пп

Moscow Lomonosov Aug 22-28, 2013

Tom Weiler, Vanderbilt U.


Some neutrino flavor physics

Fig courtesy Steve King

12 23 13

Quarks (CKM) 13 2 0.2 68

Leptons (PMNS) 35 43 9 unknown

Moscow Lomonosov Aug 22-28, 2013

Tom Weiler, Vanderbilt U.


~ From classical probabilities P ~ P T , get and P P ~
Zeroth Order (TBM) ~ T ~ P )TBM = 1 (P 18 Flavor Evolution Matrix: P
Moscow Lomonosov Aug 22-28, 2013



10 4 4

4 7 7

4 7 7



Tom Weiler, Vanderbilt U.


Wor king forward - guessing injection models, have:

Flavor Mix at Earth, sin
Beam type Conventional (pp,p) Damped Muon Beta Beam(n decay) Prompt
Now we know that sin
13

13

= 0:
Final (output) 1:1:1 4:7:7 5:2:2 14:11:11

Initial (input) 1:2:0 0:1:0 1:0:0 1:1:0
= 0.16

And spacetime foam/virtual black holes democratize neutrino flavors to (1,1,1).
Moscow Lomonosov Aug 22-28, 2013 Tom Weiler, Vanderbilt U.


PeV (300m) decays

Double Bang signature: Learned and Pakvasa (1995)
Moscow Lomonosov Aug 22-28, 2013 Tom Weiler, Vanderbilt U.


More neutrino flavor (astro) physics
[Fu, Ho, TJW, 1209.52382 and PLB (2013)] 10 4 1 ~~ (P P T )TBM = 18 4 7 47


4 7 7




repeated rows => TBM Determinant = 0; ergo, not invertible:
we We ~~ w І = (P P T ) WІ w W

but not



We ~~ WІ = ( P P T ) W

-1

we wІ w

where W and w are the flavor-ratio vectors at injection, and at Earth (after processing), respectively.
e.g., pion chain W=(1,2,0)/3 --> w=(1,1,1)/3; & beta beam W=(1,0,0) --> w=(5,2,2)/9.

Moscow Lomonosov Aug 22-28, 2013

Tom Weiler, Vanderbilt U.


Reducing 3 Flavors to 2 within the TBM paradigm:

(11)

E.g., positivity implies
Moscow Lomonosov Aug 22-28, 2013

2 7



wІ wsh



7 11

Note: IceCube data at low end right now
Tom Weiler, Vanderbilt U.


Some 3-flavor neutrino physics
Constructing inverse propagation matrix, and assuming W = 0 , get, e.g.,

model.

If this relation is violated, then 's are produced at the source!
Moscow Lomonosov Aug 22-28, 2013 Tom Weiler, Vanderbilt U.


Some more neutrino flavor physics
Flavor fractions must sum to one:

we + wІ + w = 1 at Earth

(and We + WІ + W = 1 at source) Restricts 3D space to a tri-symmetric bounded plane, a triangle:
= (square) 2 = 0 (star) = (open circle) Larger symbols = best fit values smaller symbols = ‘2 values TBM value = large solid dot

Moscow Lomonosov Aug 22-28, 2013

Tom Weiler, Vanderbilt U.


and more neutrino flavor physics
Symbolized are three possible values of , and 2-sigma errors on fitted angles.

Moscow Lomonosov Aug 22-28, 2013

Tom Weiler, Vanderbilt U.


Moscow Lomonosov Aug 22-28, 2013

Tom Weiler, Vanderbilt U.


Conclusions:
§ Flavor ratios, like photon polz'n or cosmic ray A, contain valuable information § Propagation of the flavor ratios is easily calculated, and corrects TBM § Due to 13 = 0 the propagation matrix P is (likely) invertible, enabling reconstruction of injection ratios from data. § Presented a general formula for the І /e injection ratio in terms of track-to-shower observable at Earth. § Presented a relation among flavor ratios at Earth that determines whether 's are injected at source. § Flavor ratios are statistical, requiring N >> 1 Events!
Moscow Lomonosov Aug 22-28, 2013 Tom Weiler, Vanderbilt U.