Q 23 and d can be measured accurately at the same time
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q 23 and d can be measured accurately at the same  time. Hisakazu Minakata PUC -Rio  U. Sao Paulo (with Pilar Coloma & Stephen Parke). n a = U a i n i. All the angles are measured !lepton CP phase d left. T2K-MINOS-DC-DB-RENO. solar+KamLAND. SK-atm+MINOS+T2K.

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Q 23 and d can be measured accurately at the same time

q23 and d can be measured accurately at the same time

Hisakazu Minakata

PUC-Rio  U. SaoPaulo

(with Pilar Coloma & Stephen Parke)


All the angles are measured lepton cp phase d left

na=Uaini

All the angles are measured !lepton CP phase d left

T2K-MINOS-DC-DB-RENO

solar+KamLAND

SK-atm+MINOS+T2K

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New paradigm emerged
New paradigm emerged!

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Parameter determination old paradigm
Parameter determination: old paradigm

Disappearance measurement determines q23 up to the octant

And then, ne and ne-bar appearance measurement determines q13 and dq23 ,q13 and dup to 8-fold parameter degeneracy

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But now q 13 is measured accurately
But now q13 is measured accurately

Daya Bay 2012

RENO 2013

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Q 12 and q 13
q12 and q13

  • sin2q12 = 0.304 +/- 0.013

  • Error of sin2q12 = 4.3%

  • Error of Dm221 = 2.4%

  • Error of sin2q13 (Daya Bay) = 9.6%

  • Error of Dm231 (Daya Bay) ~= 8%

  • Error of Dm231 (MINOS) ~= 4%

KamLAND+solar Mar.2013

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Q 23 is now the least accurately measured angle
q23 is now the least accurately measured angle

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Q 23 mixing angle with the largest error of 10 20 level
q23: mixing angle with the largest error of 10-20% level

Conchaetal. JHEP 2012

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Error of q 23 is and will remain large because
Error of q23is, and will remain large because ..

  • Jacobian effect:

  • Octant degeneracy + exp. uncertainty  merging of clone solution to the true one

HM-Sonoyama-Sugiyama PRD 2004 

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We are in the new paradigm
We are in thenew paradigm !

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It is likely that q 23 is so large that disappearance measurement does not distinguish q 23 octant
It is likely that q23 is so large that disappearance measurement does not distinguish q23 octant

D (sin2q23) ~ 10-20%

D (sin2q13) can go down to 5%

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We need a new setting
We need a new setting !

  • The right framework is then:“given the known value of q13 , determine q23 and d at the same time !”

  • This is merely a new way of thinking, which must be considered before when reactor measurement of q13 was proposed!

HM-S.Parke PRD 2013

Mikaelyan-Sinev 2000,

HM-Sugiyama-Yasuda-Inoue-SuekanePRD 2003

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Appearance first a new way of thinking for q 23 and d
Appearance first: A new way of thinking for q23 and d

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Continuous appearance degeneracy containing q 13 and q 23
Continuous “appearance degeneracy” containing q13and q23

If we consider only appearance measurement continuous degeneracy of q23 and q13

Fixing q23gives “intrinsic q13degeneracy” and vice versa

Disappearance measurement yields generally the 2 bands at

s223 = sin2qeff + s213/2,

s223= cos2qeff+ s213/2, but 2 bands fuse into a single region at near maximal q23

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When q 13 is measured accurately the degeneracy becomes
When q13is measured accurately, the degeneracy becomes

“q23 intrinsic degeneracy”

Looks similar to q13intrinsic degeneracy, but not quite  same size ellipses

More precisely, “q23 intrinsic degeneracy duplicated by the unknown sign of Dm2”

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Nature of the degeneracy again
Nature of the degeneracy again

“Appearance and disappearance q23 degeneracies”

If q23 is far off maximal, accurate measurement of Pem-Pembar determines q23 (including octant) up to intrinsic q23 degeneracy (precision disapp. measurement can solve the degeneracy)

If sin2q23 is near maximal, neither appearance measurement nor disappearance measurement (unless extremely precise) determines q23 ! (appearance and disappearancedegeneracies overlap)

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1 st vacuum oscillation maximum
1st vacuum oscillation maximum

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1 st oscillation maximum
1st Oscillation maximum

Things are much simpler in oscillation maximum

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1 st oscillation maximum continued
1st Oscillation maximum (continued)

Things are much simpler in oscillation maximum

HM-S.Parke PRD 2013

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Breaking the q 23 degeneracy
Breaking the q23 degeneracy

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Breaking q 23 d degeneracy
Breaking q23– d degeneracy

At 1st VOM

Spectrum information must solve the degeneracy!

Off 1st VOM

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Hyper-K: DE= +/- 10%:

LBNE: DE= +/- 20%:


2 nd vacuum oscillation maximum
2nd vacuum oscillation maximum

At 2nd VOM, D=3p/2

DE= +/- 3%:

Movement of clone solution is more prominent at 2nd VOM

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Appearance vs disappearance
Appearance vs. disappearance

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Interplay between appearance and disappearance measurement
Interplay between appearance and disappearance measurement

T2HK

LBNE

P.Coloma, HM, S.Parke, in progress

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Conclusion
Conclusion

  • Given the fact that q13 is measured accurately and the error will be much less in near future, a new strategy for determining q23 and dis called for

  • Correlated simultaneous determination q23 and dby using appearance channels outlined

  • q23 degeneracy and how to break it discussed

  • Near maximalq23, we need to understand interplay between appearance and disappearance measurement

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Simultaneous q 23 d determination
Simultaneous q23– d determination

What you need is to switch q13 q23 everything goes through as in (q13-d) case except for the “same-size ellipses”

For a given set of (P, P-bar) there are 2x2=4 solutions of q23 and d

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