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Degeneracy and strategies of LBL Osamu Yasuda Tokyo Metropolitan University NuFACT04 workshop July 28, 2004 at Osaka Univ.
● Discussions on probabilities only w/o statistical and systematic errors ● Discussions in sect. 2 &3 assume JPARC at @ Osc. Max. Based on hep-ph/0405005hep-ph/0405222 Contents 1. Introduction 2. θ13 3. δ 4. Summary scenarios 10 years from now
Notations in this talk: Oscillation Maximum (OM) Notation in this talk normal hierarchy inverted hierarchy
1. Introduction Even if we know andin a long baseline accelerator experiments with approximately monoenergetic neutrino beam, precise determination of θ13, sign(Δm231) and δ is difficult because of the 8-fold parameter degeneracy. ● intrinsic (δ, θ13)degeneracy ● Δm231⇔-Δm231degeneracy ● θ23⇔π/2-θ23 degeneracy
(P=const, δ=const) ( =const, δ=const) (P=const& =const’ off OM ) (P=const& =const’ on OM ) Plots in (sin22θ13, 1/s223) plane The way curves intersect is easy to see hyperbolas (or ellipses) straight lines
●θ23⇔π/2-θ23 degeneracy ●intrinsic (δ, θ13)degeneracy ●Δm231⇔-Δm231degeneracy
2. Determination of θ13 Assumption: and will be measured at JPARC (@OM, 4MW, HK) . Question: Will that be enough to determine |Ue3|? Yes! No! JPARC is almost enough, since (a) there is no intrinsic (δ,θ13)degeneracy, and (b) sign(Δm231)degeneracy is small. Ambiguity due toθ23⇔π/2-θ23 degeneracy is significant.
To resolve θ23 ambiguity, possible ways are: • reactor measurement of θ13 • (B) LBL measurement of (or ) • (C) measurement of The reference values used here are: sin22θ23=0.96, sin22θ13=0.05, δ=π/4, Δm231>0
(A) reactor measurement of θ13 One can resolve θ23 ambiguity at 90%CL. To compete withaccelerator experiments, improvements in the sensitivity is necessary.
One possible way to improve sensitivity of reactor measurements (theorist’s personal speculation) O.Y. LENE3@Niigata, March 20, 2004 If one puts N near detectors and N far detectors with the same σu, then theoretically sensitivity becomes: @90%CL χ2 ⇒ Nχ2 @90%CL σu : the uncorrelated systematic error (～0.005 by optimistic estimate)
δ-w δ+w δ-c δ+c (B) LBL measurement of (or ) Consider 3rd measurement of (or ) in addition to JPARC . The value of δ for each point can be deduced (up to δ⇔π-δ) from ↓(exaggerated figure) correct assumptionwrong assumption on mass hierarchy
Thenfrom the equation for the probability of (or )in the 3rd experiment we can get a unique line (a hyperbola or an ellipse) in (sin22θ13, 1/s223) plane for or . JPARC
● δ⇔π-δ ambiguity Assuming for simplicity P>>C Difference in the gradients is large for Δ=0 or π
● sign(Δm231) ambiguity X-intercepts (a) L: AL～L/1900km → L>2000km is good to identify sgn(Δm231) (b) E: → low energy is advantageous Enhancement of matter effect for π/2<Δ<π In my personal opinion nova should run with lower E!
● θ23 ambiguity Resolution of θ23 ambiguity (a) has to be small (b) has to be large δ is unknown at first, so it is impossible to design to optimize this resolution. It may happen that this ambiguity can be resolved as a byproduct.
The situation doesn’t change much for if Δ≦π/2. JPARC Off-axis NuMI νfactory
(C) measurement of Curves intersect with the JPARC line almost orthogonally. ● θ23 ambiguity may be resolved. ● δ⇔π-δ ambiguity may be resolved. ● sign(Δm231) ambiguity may be resolved . This channel may be interesting to be combined with JPARC in the future.
3. δ Assumption: at JPARC (@OM, 4MW, HK) and will be measured. Question: Will that be enough to determine arg(Ue3)? Answer: In general no. Resolution of sign(Δm231) ambiguity is important.
δ1 δ0 (1) Ambiguity due tosign(Δm231) δ0: by correct assumption =true value δ1: by wrong assumption onsign(Δm231) Difference between δ0 & δ1 turns out to be large. If δ0 =0, then at JPARC = -0.5 (if sin22θ13=0.05) Identification of sign(Δm231) is important.
3σ sensitivity to δ Kobayashi @Nufact02 Assuming Δm231>0 ↑modified from Minakata-Sugiyama (PLB580,216)
Assuming Δm231<0 ↑modified from Minakata-Sugiyama (PLB580,216)
(2) Ambiguity of δ due to θ23 : The Ambiguity due to θ23 is not serious.
Phase I 4.Summary Phase II & or or
It is important ●for determination of θ13 to resolve θ23 ambiguity if . ●for determination of δ to resolve sign(Δm231)ambiguity. If nova runs with lower E, then it will become complementary to JPARC, and only in this case it will play an important role.