Degeneracy and Correlation in Neutrino Oscillation Parameters Hisakazu Minakata Tokyo Metropolitan University Hisakazu Minakata Tokyo Metropolitan University

Degeneracy and Correlation in Neutrino Oscillation Parameter

s

Degeneracy and Correlation in Neutrino Oscillation Parameter

s

Hisakazu MinakataTokyo Metropolitan University

Hisakazu MinakataTokyo Metropolitan University

May. 2-6, 2006 SNOW@Stockholm

Degeneracy is common in everyday life


A machinery in my talk

Oscillation probability draw ellipse if plotted in bi-P plane

Role played by CP phase and the matter clearly distinguished

Art work by Adam Para Art work by Adam Para

Two solutions of S232 xTwo solutions of S23

2 x


Cause of the degeneracy; easy to understand

• You can draw two ellipses from a point in P-Pbar space

• Intrinsic degeneracy

• Doubled by the unknown sign of m2

• 4-fold degeneracy


23 octant degeneracy

Pe= sin2213 x s223

Pe= sin2213 x s223

Solar m2 on

Matter effect on

Solar m2 on

Matter effect on

OY Nufact03OY Nufact03

Altogether 8-fold degeneracyAltogether 8-fold degeneracy


Structure of intrinsic & sign-m2 degeneracy in (matter) perturbative regime

• Intrinsic degeneracy;

• sign(m2)- degeneracy arises because P is approx. invariant under:

m2 m2

T2K IIT2K II

MN JHEP01MN JHEP01


Invitation to

degeneracy solving


General comments• Degeneracy occurs because of the lack of

information, e.g., P, Pe and Pe-bar at a particular energy

• Therefore, it can be resolved by adding information easy for theorists

• Practically, however, NOT an easy task to carry out experimentally

• Discussion cannot be purely “theoretical” and has to involve “feasibility of the measurement” you propose, and “practicality of the experiments” No unique

answer !

No unique answer !


Possible alternative strategies toward the resolution

• Conceptually simple• Probably require

multiple detectors/settings

• Inevitable if 3 types of degeneracy tightly couple with each other

• More practical and experimentalists friendly

• Has to show that one can do the job one by one

Everything at once approachEverything at once approach

One by one resolution approachOne by one resolution approach


General comments (continued)

• Lifting sign-m2 degeneracy requires matter effect long baseline => \gsim 1000 km required

• intrinsic degeneracy can be efficiently resolved by spectrum information

• Generally speaking,23 octant degeneracy tends to decouple from others

• many ideas welcome

Exception: m2(ee) - m2() methodException: m2(ee) - m2() method

alternative ways ?alternative ways ?


factory as ultimate degeneracy solver

• By combining at 3 detectors at 130, 730, and 2810 km, it was claimed that neutrino factory can resolve all the 8-fold degeneracy if 13 > 1° (Donini, NuFACT03)

Typical everything at once type Typical everything at once type


Golden + silver NuFact + superbeam

• 1st concrete way that proved to work for resolution of all the degeneracy

• Powerful, work down to 1-2 degree of 13

• Note that Vcb ~ 2 degree • Yet, a bit expensive; • conservatively ~1000 Million Euro/d

egeneracy (rich man’s solution) • Ultimate degeneracy solver, but certainly

not “Mayflower” (unless 13 ~ 1o)

Highly nontrivial!Highly nontrivial!

If NuFACT reached “J-PARC stage” everything changes !If NuFACT reached “J-PARC stage” everything changes !


From “black-box”to the anatomy of degeneracy


Anatomy of degeneracy

• To make real progress, it is important to have a systematic understanding of the nature of degeneracy

• Need concrete framework to analyze the question

• 1st order in matter perturbation theory plus corresponding appropriate experimental setting;

• T2K II or T2KK(Kamioka-Korea) Ishitsuka et al. 05 Ishitsuka et al. 05


Let’s start from the intrinsic degeneracy

• degenerate solution at VOM:

13(2) = 13

(1)

T2K IIT2K II

Spectrum analysis should be powerful !

Spectrum analysis should be powerful !


Spectral information IS powerful(almost) resolve intrinsic degeneracy at sin2213=0.01(almost) resolve intrinsic degeneracy at sin2213=0.01

T2K II (from 1000 page Ishitsuka file) T2K II (from 1000 page Ishitsuka file)

SK momentum resolution ~30 MeV at 1 GeVSK momentum resolution ~30 MeV at 1 GeV


Expected Expected signal, BG and signal, BG and

22 and anti-

×Kamioka and Korea

and anti-×

Kamioka and Korea

5 energy bins5 energy bins

syst. Errors:

5% BG (overall) 5% BG (energy dep.) 5% signal efficiency

syst. Errors:

5% BG (overall) 5% BG (energy dep.) 5% signal efficiency

4yrs + 4yrs anti-sin2213=0.1, =/2

4yrs + 4yrs anti-sin2213=0.1, =/2

signalsignal

BGBG

Kajita in NOVE2006Kajita in NOVE2006


Sign-m2 degeneracy• Resolution of sign-m2 degen

eracy requires the matter effect

• Requires baseline ~1000 km• 2nd detector seems required t

o go down to sin2213=.02


T2K(0.54 Mt) vs. T2KK(0.27+0.27 Mt)


It is not quite only the matter effect

• With the same input parameter and Korean detector of 0.54 Mt the sign-m2 degeneracy is NOT completely resolved

2 identical detector method powerful !

2 identical detector method powerful !


Energy dependence far more dynamic in 2nd oscillation maximum


How to solve 23 octant degeneracy

• Detect solar Dm2 term ~c23

2

• Requires baseline ~ earth radius

• well controlled systematic error plus enormous statistics

• Powerful at small 13

• Combining reactor measurement of 13

• Requires great precision in 13 measurement

• Powerful at large 13

• If feasible, “Mossbauer” helps

Strategy: Look for terms which depend on 23 but not through the form s23

2 x sin2213

Strategy: Look for terms which depend on 23 but not through the form s23

2 x sin2213


[email protected]@NNN05Atm ; powerful way for octant degene.Atm ; powerful way for octant degene.


Reactor + accelerator method

• Acc-disappearance => s2

23=0.4 or 0.6• Acc-appearance =

> s223sin2213 = 0.

06• Reactor =>

sin2213 = 0.1

• Solves 23 degeneracy


Region of resolved 23 degeneracy

T2K II (4MW+HK) + phase II type reactorT2K II (4MW+HK) + phase II type reactor

Hiraide et al. (7 samurai) Hiraide et al. (7 samurai)


Decoupling of the degeneracy

• Suppose that you succeed to solve the particular degeneracy, by forgetting about the remaining ones

• It does NOT necessarily mean that the problem is solved

• You have to verify that your treatment of degeneracy A is valid irrespective of the presence of degeneracy B

• One solution: decoupling between the degeneracy


23 and sign-m2 degeneracy decouple

• For example, one can show, to first order in matter effect, the followings:

P(octant) = P(1st octant) - P(2nd) is invariant under the interchange of two sign-m2 degenerate pair

P(hierarchy) = P(m2 +) - P(m2 -) is invariant under the interchange of two 23 octant degenerate pair


Intrinsic degeneracy decouple ?

• Intrinsic degeneracy nearly decouples from the rest

• More importantly, in T2K II setting, it is resolved by spectrum analysis decouple from the game

• Altogether three degeneracies (approximately) decouple with each other in T2K (or T2KK) setting


Correlation rather than

degeneracy

?


Correlation ?• The title of this talk

contains “correlation”. What about that ?

• “correlation” may be incompletely resolved degeneracy

• No continuous degeneracy in Pe

Nufact golden Nufact golden


No significant “correlation” in T2K II

Spectral information importantSpectral information important


Many remaining questions • Does beam help ??

• Does monochromatic beam help ??

• To what extent the lower energy threshold of NuFACT change the sensitivity of resolving degeneracy ?

• What would be a powerful supplementary measurement ?

ISS NuFACT ongoing, report expected in Sep. 06

ISS NuFACT ongoing, report expected in Sep. 06

example: 12 for m2ee - m2

methodexample: 12 for m2ee - m2

method


Conclusion • Nature of the degeneracy well understood

• With T2KK or similar 2 detector settings there appeared a well defined method for lifting intrinsic and sign-m2 degeneracy

• Spectral information solves intrinsic degeneracy and matter effect does sign-m2 degeneracy

• Resolving 23 degeneracy requires solar term or reactor II

• Consistency maintained by “decoupling”


->e appearance probability

Documents

Degeneracy and Correlation in Neutrino Oscillation Parameters Hisakazu Minakata Tokyo Metropolitan University Hisakazu Minakata Tokyo Metropolitan University