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Precision measurement of mixing angles and CP. Hisakazu Minakata PUC-Rio. PUC-Rio, where?. Maracana. n a = U a i n i. All the angles are measured !lepton CP phase d left. SK-atm+MINOS+T2K. T2K-MINOS-DC-DB-RENO. solar+KamLAND. q 12.

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Puc rio where
PUC-Rio, where?


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All the angles are measured lepton cp phase d left


All the angles are measured !lepton CP phase d left




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Q 12 has been measured by solar and kamland experiments
q12 has been measured by solar and KamLAND experiments

KamLAND Mar. 2013

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  • sin2q12 = 0.304 +/- 0.013

  • Error of sin2q12 = 4.3%

  • Error of Dm221 = 2.4%

KamLAND Mar.2013

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How to improve q 12
How to improve q12?

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Sado idea proposal july 2004
SADO idea/proposal (July 2004)

  • “SADO” = Several tens of km AntineutrinoDetectOr

  • Basic idea: 1st oscillation minima of Pee is the right place for precision measurement of q12


ArXiv 0407326 PRD(2005)

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Optimal distance estimated as 50 60 km
Optimal distance estimated as 50-60 km

Without geo-nu 40km would be fine

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Sado vs kamland sensitivity
SADO-vsKamLAND sensitivity

SADO 3s sensitivity ~ KamLAND 1s sensitivity

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Solar kamland and sado are good competitors
Solar+KamLANDand SADO are good competitors

2% (1s) in sin2q12 reachable with systematic error of 4%

  • Tuned reactor may have better sensitivity with long-run because tuning L is powerful


Slide at World Physics Summit @Galapagos, June 22-25, 2006

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Quark lepton complementarity
Quark-Lepton Complementarity

QLC is based on observation: q12 + qC = p/4

Bi-maximal mixing from neutrinos

HM-A.Smirnov PRD 2004

Predicted value ofq13in this model agrees well with experiments ! Large q13 natural in QLC

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Impressive to see the real proposals today
Impressive to see the real proposals today!

Daya Bay II

Sin2q12 error:

RENO ~ 1% (K.K.Joo)

Daya Bay II 0.63% claimed! (Yifang Wang), Talk both at ICRR)

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Q 13 reno

  • If added quadrature, sin22q13 = 0.1 +/- 0.018

  • sin2q13 = 0.0257 +/- 0.0048

  • Error of sin2q13 = 19%

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Q 13 daya bay
q13:Daya Bay

  • If added quadrature, sin22q13 = 0.089 +/- 0.011

  • sin2q13 = 0.0228 +/- 0.0029

  • Error of sin2q13 = 13%

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How to improve q 13
How to improve q13?

  • Continued running of reactor experiments

  • Can accelerator measurement supersade reactor q13 accuracy? If yes, when?

  • What is the ultimate error of q13 ?

  • If sin22q13 = 0.1 +/- 0.005 5% error for sin2q13

  • Is 2-3% error achievable for sin2q13 ?

  • Neutrino factory?

  • Reactor + identical 2 detector appears to be practically the best way

Memory of Lev Mikaelyan @ Kurchatov Inst.

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Ultimate error of q 13
Ultimate error of q13?

D(sin2q) / sin2q = (1.6-2.0) (Dq / q)

P. Coloma etal. JHEP12

DayaBay ultimate (syst. only)

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Least accurately measured angle q 23
Least accurately measured angle q23

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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 large because
Error of q23 is large because ..

  • Jacobian effect:

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

HM-Sonoyama-Sugiyama PRD 2004 

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How to measure q 23 accurately
How to measure q23 accurately?

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Use solar term or r a to solve q 23 octant degeneracy
Use solar term or R+A to solve q23 octant degeneracy

Hiraideetal. PRD2006

d=0 assumed

T2K-II + phase II reactor


sin2 2q13

T2KK 2s


> 3s


sin2 2q13


T2KK has better sensitivity

at sin2 2q13 < 0.06~0.07 .

Kajitaetal. PRD2007

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sin2 q23

Use atmospheric neutrino to probe solar n oscillation
Use atmospheric neutrino to probe solar n oscillation

Hyper-K LOI : ArXiv 1109.3262

Barger etal. PRL 2012

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Toward measuring d
Toward measuring d

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How to measure cp
How to measure CP

  • nmsuperbeam appears to be the prime candidate

  • T2KK CP sensitivity ~ T2HK CP sensitivity

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Determination of d in correlation with q 13
Determination of d in correlation with q13?

  • So far CP d measurement has been discussed in a framework of simultaneous d – q13 determination  intrinsic d - q13 degeneracy enriched with unknown mass hierarchy

  • Right framework? NO! Better setting: simultaneous d – q23 determination

People were focused on another cosmos ..

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Why q 23 relevant for cp
Why q23 relevant for CP?

  • In precision era for CP the errors of d will be dominated by uncertainty of s223

  • D sind =

  • D cosd =

Error formula for CP dh = order unity

HM-Parke, ArXiv 1303.6178

For a given set of (P, P-bar) with finite error, a change in s223 can be compensated by adjusting d

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A new method for q 23 and d
A new method for q23 and d

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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

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

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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)

HM-Parke, ArXiv 1303.6178

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Use n e appearance channel
Use ne appearance channel

  • simultaneous d – q23 determination by ne and ne-bar appearance channels

  • q23 intrinsic 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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  • Current status of mixing angle measurement outlined

  • Some ideas seeking for better precision discussed

  • Further improvement appear realistic for q12(new projects) and q13 (continue running), but may not be for q23 at near maximal, because…

  • Fortunately, if you measure d, then you automatically get q23!

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