Precision measurement of large mixing angles  12 and  23 Hisakazu Minakata Tokyo Metropolitan University

March 9, 2005IFIC, Universitat de Valencia The last year: the oscillatory behavior observed

March 9, 2005IFIC, Universitat de Valencia oscillatory behavior has been seen! KamLAND K2K SK

March 9, 2005IFIC, Universitat de Valencia Neutrino physics has entered into the new era of precision measurement

March 9, 2005IFIC, Universitat de Valencia MNS matrix and mass pattern Neutrino mass hierarchies Left: “normal” Right: “inverted” <= solar Atm.  =>  =U  i i There is the similar structure in quarks

March 9, 2005IFIC, Universitat de Valencia Suppose we have “standard model of flavor mixing” someday … Most likely, it unifies quarks and leptons We may want to test the theory by comparing mixing angles of quark and lepton sectors Then, we recognize that our knowledge of  12 in quark and lepton sectors are not balanced:  (sin 2  C ) = 1.4%  (sin 2   ) ~ 10 % Why don’t we try to measure  12 to a comparable accuracy?

March 9, 2005IFIC, Universitat de Valencia Quark-lepton complementarity?  C +  solar = 45.1 o +/- 2.4 o (1  )    atm < 53.2 o (  CL)    23 q < 2.5 o (  CL)  23 q +  atm = 47.4 o +/- 8.3 o (  CL) => 2  C and 2  solar are complementary => QLC Thanks to all the solar & KamLAND experiments ==> <=Really maximal? HM-Smirnov, Raidal 04

March 9, 2005IFIC, Universitat de Valencia Symmetry for maximal  23 and small  13 ? Some people speculate that nearly maximal  23 and small  13 might be due to a symmetry: Z2, A4, etc. Deviation from maximal  23 and  13 is connected Grimus et al., Ma, Babu et al., Kubo et al. ……

March 9, 2005IFIC, Universitat de Valencia  23 is even worse: present accuracy of determination of mixing angles Maltoni-Schwetz-Tortola-Valle, NJP 04

March 9, 2005IFIC, Universitat de Valencia How to determine these mixing angles accurately? I will concentrate on “tomorrow’s item” based on reactor & accelerator Entirely new possibilities may exist with neutrino factory and/or  beam (?) => interesting question to examine I have supplementary slides if you ask questions on how to measure  13

March 9, 2005IFIC, Universitat de Valencia  12

March 9, 2005IFIC, Universitat de Valencia The best way, so far, to determine  12 SNO CC/NC measurement IS the measurement of sin 2  12 Holanda- Smirnov 02

March 9, 2005IFIC, Universitat de Valencia  12; current status +/-12% error in sin 2  12 (2D)

March 9, 2005IFIC, Universitat de Valencia Newest vs. next- to- newest

March 9, 2005IFIC, Universitat de Valencia Where is the most sensitive place to  12 in the world? The answer: In the solar and/or reactor spectra The answer: In the solar and/or reactor spectra

March 9, 2005IFIC, Universitat de Valencia Low-E solar spectrum measures sin 2 2  12 Nakahata NOON04

March 9, 2005IFIC, Universitat de Valencia

March 9, 2005IFIC, Universitat de Valencia measurement of  12 with reactor HM, Nunokawa, Teves, Zukanovich-Funchal, hep-ph/ SADO = Several-tens of km Antineutrino DetectOr

March 9, 2005IFIC, Universitat de Valencia Where is the right place? Where is the right place for precision measurement of  12 What is the most sensitive part of the probability to variation of  12 ? => First oscillation maximum!

March 9, 2005IFIC, Universitat de Valencia Can you quantify the statement? YES!

March 9, 2005IFIC, Universitat de Valencia KamLAND vs. SADO; verifying the principle Equalize the number of events without oscillation at KL and SADO Common systematic error 4 % Tuning to OM works ! Other 15 reactors included

March 9, 2005IFIC, Universitat de Valencia Systematic error Modest requirement on systematic error of 4% <= 6.5% of KL Feasible if volume error reduced and no spectrum cut at E prompt =2.6 MeV Geo-neutrino “BG” must be taken care of <== KamLAND We take 4%

March 9, 2005IFIC, Universitat de Valencia Geo neutrinos in brief It is expected that about half of terrestrial heat of 40 TW comes from radioactivity in the earth

March 9, 2005IFIC, Universitat de Valencia Optimal baseline distance Without geo- the optimal distance can be as short as ~40km With geo- it is km L < 50 km geo- starts to affect most important part of the spectrum

March 9, 2005IFIC, Universitat de Valencia Definition of  2 We will make comparison with two other definitions of  2 U:Th ratio fixed; Th = 83% of all

March 9, 2005IFIC, Universitat de Valencia Where is the site for  12 experiment? Mt. Komagatake!

March 9, 2005IFIC, Universitat de Valencia We took SADO at Mt. Komagatake SADO_single = detector at km from a NPP at anywhere in the world SADO_multi = detector at ~1000 m below peak of Mt. Komagatake, 54 km from KK For geo- we need to specify the location

March 9, 2005IFIC, Universitat de Valencia Sensitivity for  12 ; SADO_single Whole 40 TW comes from radioactivity U:Th ratio fixed; Th = 83% of all

March 9, 2005IFIC, Universitat de Valencia Sensitivity for  12 ; SADO_multi

March 9, 2005IFIC, Universitat de Valencia Stable against changes of L and  m 2

March 9, 2005IFIC, Universitat de Valencia Does the result depend on statistical treatment?

March 9, 2005IFIC, Universitat de Valencia Yes, I promised to check stability of the results We will make comparison with two other definitions

March 9, 2005IFIC, Universitat de Valencia Dependence on definition of  2

March 9, 2005IFIC, Universitat de Valencia Can you surpass other methods ? YES definitely!

March 9, 2005IFIC, Universitat de Valencia Solar+KL and SADO are good competitors, but.. “SADO” has better sensitivity with long-run because tuning L is powerful 2% (1  ) in sin 2  12 reachable! Bahcall-Pena-Garay <= NOW05 Proc.

March 9, 2005IFIC, Universitat de Valencia Comparing SADO with the present accuracy

March 9, 2005IFIC, Universitat de Valencia Sensitivity; summary and comparison with solar + KamLAND

March 9, 2005IFIC, Universitat de Valencia Implications of precision measurement of  12 Besides the ones for particle physics there are various implications: Observational solar astrophysics dominant error of solar flux determination comes from  12 ! Better determination of geo-neutrino flux in KamLAND and others (to reduce error of reactor background) Neutrino factory measurement of  CPT test ……

March 9, 2005IFIC, Universitat de Valencia  23

March 9, 2005IFIC, Universitat de Valencia Does the same method apply to  23 measurement? YES and NO

March 9, 2005IFIC, Universitat de Valencia Method of tuning to the oscillation maximum for sin 2 2  23 measurement position of the dip -->  m 2 13 depth of the dip --> sin 2 2  23 <= 2 flavor analysis 1% level accuracy expected for sin 2 (2  23 ) (JPARC-SK, LOI)

March 9, 2005IFIC, Universitat de Valencia J-PARC vs. SK 80 yrs: sin 2 (2  23 ) position of the dip -->  m 2 13 depth of the dip --> sin 2 2  23 Kajita, NOON2004 Better then SK 80 yrs !

March 9, 2005IFIC, Universitat de Valencia Sensitivity of s 2 23 is affected by Jacobian and  23 degeneracy  (s 2 23 )  (sin 2 2  23 ) 1st octant assumed

March 9, 2005IFIC, Universitat de Valencia 3 Flavor Effects? + 3 corrections prop. to s 13 2 √(1-sin 2 2  23 )  m 2 solar /  m 2 atm HM, Sonoyama, Sugiyama, hep-ph/

March 9, 2005IFIC, Universitat de Valencia LBL and reactor experiments help but not so much…  e appearance or reactor do indeed help, but not too much -> 2 flavor result

March 9, 2005IFIC, Universitat de Valencia How to improve the accuracy of  23 ?

March 9, 2005IFIC, Universitat de Valencia (1) Resolve 2-3 degeneracy by reactor-LBL experiments Rare chance for resolving (  23  23 ) degeneracy If lucky, one may see CP & mass hierarchy HM-Sugiyama-Yasuda-Inoue-Suekane, hep-ph/

March 9, 2005IFIC, Universitat de Valencia Future atmospheric  may help Not an easy problem for both methods! Concha-Maltoni-Smirnov 04

March 9, 2005IFIC, Universitat de Valencia Deviation from maximal  23 ; already seen? If  23 enhancement of e-like events Explanation of e-excess at low energy? dominant WS, ICRR, Dec.04 Peres-Smirnov 99, 04

March 9, 2005IFIC, Universitat de Valencia Two different results (why?) Concha-Maltoni-Smirnov 04 SK (Subdominant WS, ICRR, Dec.04)

March 9, 2005IFIC, Universitat de Valencia Conclusion 1st oscillation maximum seems to be the best place for precision measurement of large mixing angles (  12,    Dedicated reactor  12 experiment can reach the ultimate sensitivity ~2% in sin 2  12 => balanced accuracies between  C and  12 Implications to: observational solar astrophysics, accurate geo-, CPT test, …. LBL disapp. measurement of   3, though accurate for sin 2 2  23, suffers from “J” and P-degeneracy issues

March 9, 2005IFIC, Universitat de Valencia We have reproduced their results insensitive to systematic errors

March 9, 2005IFIC, Universitat de Valencia How to measure  13 ; There are 2 ways LBL vs. reactor

March 9, 2005IFIC, Universitat de Valencia Reactor measurement of  13 Independent of , matter effect,  23,  12, solar  m 2 => Pure measurement of  13 e disappearance probability

March 9, 2005IFIC, Universitat de Valencia Varying proposals over the globe A European project approved !

March 9, 2005IFIC, Universitat de Valencia LBL measurement of  13 JPARC-SK  13 sensitivity; OA2°, 5 years Very simple form!

March 9, 2005IFIC, Universitat de Valencia Optimal baseline distance Without geo- the optimal distance can be as short as ~40km With geo- it is km  m 2 sensitivity continues to be good until ~200 km