q23 and d can be measured accurately at the same time

Hisakazu MinakataPUC-Rio U. Sao Paulo

(with Pilar Coloma & Stephen Parke)

Sep. 17, 2013 WIN2013@Natal

All the angles are measured !lepton CP phase d left

na=Uai ni

solar+KamLANDSK-atm+MINOS+T2K T2K-MINOS-DC-DB-RENO

Sep. 17, 2013 WIN2013@Natal

New paradigm emerged!

WIN2013@Natal

Parameter determination: old paradigm

Sep. 17, 2013

Disappearance measurement determines q23 up to the octant

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

WIN2013@Natal

But now q13 is measured accurately

Sep. 17, 2013

Daya Bay 2012

RENO 2013

WIN2013@Natal

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%Sep. 17, 2013

KamLAND+solar Mar.2013

Sep. 17, 2013 WIN2013@Natal

q23 is now the least accurately measured angle

WIN2013@Natal

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

Sep. 17, 2013Concha etal. JHEP 2012

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Error of q23 is, and will remain large because ..

• Jacobian effect:

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

Sep. 17, 2013

HM-Sonoyama-Sugiyama PRD 2004

Sep. 17, 2013 WIN2013@Natal

We are in the new paradigm

!

WIN2013@Natal

It is likely that q23 is so large that disappearance measurement does not

distinguish q23 octant

Sep. 17, 2013

D (sin2q23) ~ 10-20%

D (sin2q13) can go down to 5%

WIN2013@Natal

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!

Sep. 17, 2013

HM-S.Parke PRD 2013

Mikaelyan-Sinev 2000, HM-Sugiyama-Yasuda-Inoue-Suekane PRD 2003

Sep. 17, 2013 WIN2013@Natal

Appearance first: A new way

of thinking for q23 and

d

WIN2013@Natal

Continuous “appearance degeneracy” containing q13 and q23

Sep. 17, 2013

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

Fixing q23 gives “intrinsic q13 degeneracy” and vice versa

Disappearance measurement yields generally the 2 bands at s2

23 = sin2qeff + s213/2,

s223 = cos2qeff + s2

13/2, but 2 bands fuse into a single region at near maximal q23

WIN2013@Natal

When q13 is measured accurately, the degeneracy becomes

Sep. 17, 2013

“q23 intrinsic degeneracy”

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

Looks similar to q13 intrinsic degeneracy, but not quite same size ellipses

WIN2013@Natal

Nature of the degeneracy again

Sep. 17, 2013

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

“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)

Sep. 17, 2013 WIN2013@Natal

1st vacuum

oscillation maximum

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1st Oscillation maximum

Sep. 17, 2013

Things are much simpler in oscillation maximum

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1st Oscillation maximum (continued)

Sep. 17, 2013

Things are much simpler in oscillation maximum

HM-S.Parke PRD 2013

Sep. 17, 2013 WIN2013@Natal

Breaking the q23

degeneracy

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Breaking q23– d degeneracy

Sep. 17, 2013

At 1st VOM

Spectrum information must solve the degeneracy!

Off 1st VOM

Hyper-K: DE= +/- 10%: LBNE: DE= +/- 20%:

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2nd vacuum oscillation maximum

Sep. 17, 2013

At 2nd VOM, D=3p/2

DE= +/- 3%: Movement of clone solution is more prominent at 2nd VOM

Sep. 17, 2013 WIN2013@Natal

Appearance vs.

disappearance

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Interplay between appearance and disappearance measurement

Sep. 17, 2013

T2HK LBNE

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

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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 d is called for

• Correlated simultaneous determination q23 and d by using appearance channels outlined

• q23 degeneracy and how to break it discussed• Near maximal q23, we need to understand

interplay between appearance and disappearance measurement

Sep. 17, 2013

WIN2013@Natal

Simultaneous q23– d determination

Sep. 17, 2013

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

What you need is to switch q13 q23

everything goes through as in (q13-d) case except for the “same-size ellipses”