Degeneracy and strategies of LBL Osamu Yasuda Tokyo Metropolitan University NuFACT04 workshop July 28, 2004 at Osaka Univ.

Contents 1. Introduction 2. θ δ 4. Summary hep-ph/ hep-ph/ Based on ● Discussions on probabilities only w/o statistical and systematic errors ● Discussions in sect. 2 &3 assume JPARC Osc. Max. scenarios 10 years from now

Notation in this talk Notations in this talk: Oscillation Maximum (OM) normal hierarchy inverted hierarchy

1. Introduction ● intrinsic (δ, θ 13 )degeneracy ● Δm 2 31 ⇔ -Δm 2 31 degeneracy ● θ 23 ⇔ π/2-θ 23 degeneracy Even if we know and in a long baseline accelerator experiments with approximately monoenergetic neutrino beam, precise determination of θ 13, sign(Δm 2 31 ) and δ is difficult because of the 8-fold parameter degeneracy.

straight lines hyperbolas (or ellipses) (P=const& =const’ on OM ) (P=const& =const’ off OM ) (P=const, δ=const) ( =const, δ=const) Plots in (sin 2 2θ 13, 1/s 2 23 ) plane The way curves intersect is easy to see

● θ 23 ⇔ π/2-θ 23 degeneracy ● intrinsic (δ, θ 13 ) degeneracy ● Δm 2 31 ⇔ -Δm 2 31 degeneracy

JPARC is almost enough, since (a) there is no intrinsic (δ,θ 13 ) degeneracy, and (b) sign(Δm 2 31 )degeneracy is small. Ambiguity due toθ 23 ⇔ π/2-θ 23 degeneracy is significant. 2. Determination of θ 13 Assumption: and will be measured at JPARC 4MW, HK). Question: Will that be enough to determine |U e3 |? Yes!No!

(A)reactor measurement of θ 13 (B) LBL measurement of (or) (C) measurement of To resolve θ 23 ambiguity, possible ways are: The reference values used here are: sin 2 2θ 23 =0.96, sin 2 2θ 13 =0.05, δ=π/4, Δm 2 31 >0

(A) reactor measurement of θ 13 One can resolve θ 23 ambiguity at 90%CL. To compete with accelerator experiments, improvements in the sensitivity is necessary.

One possible way to improve sensitivity of reactor measurements (theorist’s personal speculation) O.Y. March 20, 2004 If one puts N near detectors and N far detectors with the same σ u, then theoretically sensitivity becomes: σ u : the uncorrelated systematic error ( ～ by optimistic χ 2 ⇒ Nχ 2

Consider 3rd measurement of (or) in addition to JPARC. (B) LBL measurement of (or) δ +w δ -c δ-wδ-w δ +c The value of δ for each point can be deduced (up to δ ⇔ π- δ) from correct assumption wrong assumption on mass hierarchy ↓( exaggerated figure )

we can get a unique line (a hyperbola or an ellipse) in (sin 2 2θ 13, 1/s 2 23 ) plane for or. Then from the equation for the probability of (or) in the 3 rd experiment JPARC

● δ ⇔ π-δ ambiguity Difference in the gradients is large for Δ=0 or π Assuming for simplicity P>>C

● sign(Δm 2 31 ) ambiguity (a) L: AL ～ L/1900km → L>2000km is good to identify sgn(Δm 2 31 ) (b) E: → low energy is advantageous Enhancement of matter effect for π/2<Δ<π X-intercepts In my personal opinion nova should run with lower E!

● θ 23 ambiguity Resolution of θ 23 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. ● θ 23 ambiguity may be resolved. ● δ ⇔ π-δ ambiguity may be resolved. ● sign(Δm 2 31 ) ambiguity may be resolved. This channel may be interesting to be combined with JPARC in the future.

3. δ Assumption: at JPARC 4MW, HK) and will be measured. Question: Will that be enough to determine arg(U e3 )? Answer: In general no. Resolution of sign(Δm 2 31 ) ambiguity is important.

If δ 0 =0, then at JPARC δ0δ0 δ1δ1 δ 0 : by correct assumption =true value δ 1 : by wrong assumption on sign(Δm 2 31 ) Difference between δ 0 & δ 1 turns out to be large. = -0.5 (if sin 2 2θ 13 =0.05) Identification of sign(Δm 2 31 ) is important. (1) Ambiguity due to sign(Δm 2 31 )

3σ sensitivity to δ 2 Assuming Δm 2 31 > 0 ↑modified from Minakata-Sugiyama (PLB580,216)

Assuming Δm 2 31 <0 ↑modified from Minakata-Sugiyama (PLB580,216)

(2) Ambiguity of δ due to θ 23 : The Ambiguity due to θ 23 is not serious.

outside of red or blue lines is almost enough In addition to is necessary to resolve θ 23 ambiguity inside of red or blue lines In addition to LBL w/ L> ～ 1000km is necessary to resolve sign(Δm 2 23 ) ambiguity In addition to (A) is necessary to resolve θ 23 ambiguity (B) LBL w/ L> ～ 1000km is necessary to resolve sign(Δm 2 23 ) ambiguity & or 4.Summary Phase II Phase I

● for determination of θ 13 to resolve θ 23 ambiguity if. ● for determination of δ to resolve sign(Δm 2 31 ) ambiguity. It is important If nova runs with lower E, then it will become complementary to JPARC, and only in this case it will play an important role.