Complementarity of T2K/HK with Other Longer Baseline Experiments. F.Suekane. RCνS, Tohoku Univ.

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1 Complementarity of TK/HK with Other Longer Baseline Experiments F.Suekane RCνS, Tohoku Univ. Workshop for Neutrino Programs with Facilities in Japan, WNPFJ 1

2 The purpose of this talk is to motivate to enforce the synergetic activities among the future long baseline (LBL) experiments. The speaker is not a member of LBL experiments. Therefore, an objective view may be provided as a bystander. The discussion is conceptual one and the used parameter values are rough. There might be errors or misunderstandings WNPFJ

3 Flow of this talk * Purpose of this talk * Example of a successful synergy * P(ν µ! ν e ) and A CP with matter effect * Possible synergies * Conclusion WNPFJ 3

4 P(ν µ à ν e ) [Accelerator] An example of successful synergy: The complementarity between Accelerator and Reactor sin θ 13 1 L L 0 1 L L 0 P( ν µ ν e ;Φ 31 = π ) ~ sin θ 3 =1, NH sin θ 3 =1, IH TK Baseline Reactor 1-P = sin θ 13 ( ( )) sinθ 13 ( ) sinδ

5 P(ν µ à ν e ) [Accelerator] An example of successful synergy: The complementarity between Accelerator and Reactor sin θ 13 1 L L 0 1 L L 0 P( ν µ ν e ;Φ 31 = π ) ~ TK sin θ 3 =1, NH sin θ 3 =1, IH TK Baseline Reactor 1-P = sin θ 13 ( ( )) sinθ 13 ( ) sinδ The synergy of Reactor and Accelerator has given us hints of large sinδ & Normal hierarchy,

6 An example of successful synergy: The complementarity between Accelerator and Reactor P 31 ( ν µ ν e ;Φ 31 = π ) ~ sin θ 13 ( ( )) sinθ 13 1 ( L L 0 ) sinδ 1 L L 0 P(ν µ à ν e ) [Accelerator] TK sin θ 3 =1, NH sin θ 3 =1, IH TK Baseline Reactor 1-P=sin θ 13 By the way... The center value is in the unphysical region now. TK: Please shrink the error. Nova: What is your result? Double Chooz will check the DB & RENO results soon with the near detector. " Redundancy is important

7 CCPP AAssyymmmmeettrryy ** DDiiffffeerreennccee bbeettwweeeenn P( ν α ν ) β aanndd P( ν α ν ) β ** EExxppeerriimmeennttaallllyy:: ( ) = P ν µ ν e A 31 = π ~ Δm 1 Δm 31 ( ) P( ν µ ν e ) ( ) + P( ν µ ν e ) P ν µ ν e π sinθ 1 tanθ 3 sinθ 13 sinδ ~ 0.9sinδ Thanks to the all experiments, this coefficients can be calculated now. (synergies!) ** HHoowweevveerr,, tthhee mmaatttteerr eeffffeecctt iinnttrroodduucceess aa ffaakkee AA CCPP WNPFJ 7

8 Matter (MSW) Effect Only ν e and ν e Effective Weak Potential n V W = E e G F ν m 3 m 1 Energy dependent changes the coupling sign depending on ν or ν changes sign depending on the mass hierarchy WNPFJ 8

9 BBaasseelliinnee DDeeppeennddeennccee ooff tthhee MMaatttteerr EEffffeecctt At the oscillation maximum; Φ 31 = Δm 31 L = π 4E ν the weak potential can be expressed by using the baseline L, M.H. V W = E νg F n e m 3 m 1 = ± Reference Baseline: L 0 = πg F L π G F n e = ± L L 0 1 L L[km] 0 L n e dl ν ν ~ ±5, 500km (ρ=3[g/cm 3 ]) V W (=L/L 0 ) TK/HK 95 ±0.055 NOVA 810 ±0.15 LBNF 1,300 ±0.4

10 WWeeaakk PPootteennttiiaall && OOsscciillllaattiioonn PPrroobbaabbiilliittyy Main effect of the weak potential on the oscillaion: sinφ 31 sin ( 1 V W )Φ 31 1 V W At oscillation maximum sin( 1 V W ) π ~ 1 π 8 V W ~ 1 Then, the appearance probability with the matter effect is, ( ) ~ s 3 sin θ 13 P ν µ ν e ;@Φ 31 ± π ( 1 V W ) Δm 1 Δm 31 sinθ 1 sinθ 3 sinθ 13 1 V W ( ) sinδ WNPFJ 10

11 Oscillation probabilities for various cases $ & & & & & % & & & & & '& P ( NH ν µ ν e ;@Φ ) ~ s 3 ( 1 L L ) ( 0 1 L L ) sinδ 0 P ( IH ν µ ν e ;@Φ ) ~ s 3 ( 1+ L L ) ( 0 1+ L L ) sinδ 0 P ( NH ν µ ν e ;@Φ ) ~ s 3 1+ L L 0 ( ) ( 1+ L L ) sinδ 0 P ( IH ν µ ν e ;@Φ ) ~ s 3 ( 1 L L ) ( 0 1 L L ) sinδ WNPFJ 11

12 P(ν µ à ν e ) Baseline Dependence of ν e Appearance Prob P( ν µ ν e ;@Φ 31 ) ~ s 3 ( 1± L L 0 ) ( 1± L L 0 ) sinδ TK/HK MINOS NOVA sinδ=-1, sin θ 3 >0.98 LBNF N.H. uncertainty from θ 3 degeneracy sinδ=-1 sinδ=0 sinδ= I.H L[km] WNPFJ 1

13 P(ν µ à ν e ) sinδ=-1 sinδ=0 sinδ=+1 Baseline Dependence of ν e Appearance Prob P( ν µ ν e ;@Φ 31 ) ~ s 3 ( 1± L L 0 ) ( 1± L L 0 ) sinδ TK/HK MINOS NOVA sinδ=-1, sin θ 3 >0.98 TK ? L[km] LBNF N.H. I.H. TK+NOVA may enforce the hint on M.H. and sinδ or may give us tension WNPFJ 13

14 P(ν µ à ν e ) sinδ=-1 Baseline Dependence of ν e Appearance Prob P( ν µ ν e ;@Φ 31 ) ~ s 3 ( 1 L L 0 ) ( 1 L L 0 ) sinδ TK/HK MINOS NOVA sinδ=-1, sin θ 3 >0.98 sinδ=1 sinδ= TK (3ev.) L[km] LBNF I.H. N.H WNPFJ 14?

15 CP asymmetry with the matter effect A CP (@Φ 13 ) = P P P + P ~ π Δm 1 Δm 31 ~ 0.9sinδ CP ± A FK sinθ 1! sinδ CP ± L $ # & t 3 sinθ 13 " L 0 % L[km] V W A FK =(L/L 0 ) TK/HK 95 ±0.055 ±0.11 Nova 810 ±0.15 ±0.30 LBNF 1,300 ±0.4 ±0.48 Error of the sinδ measurement fake CP asymmetry δ ( sinδ CP ) = 3.4 ( δa CP ) + A FK ( δn e n e ) ( ) WNPFJ 15

16 Baseline Dependence of CP asymmetry A CP sinδ=-1 sinδ=0 " A CP ~ 0.9sinδ ± L % $ ' # L 0 & sinδ=+1 TK/HK MINOS NOVA sinδ=-1, sin θ 3 >0.98 LBNF L(km) NH IH

17 Will evaluate the sensitivity by 3σ error of sinδ CP assuming δ CP =0. NOVA + TK σ sinδ ~ WNPFJ 17

18 ±3σ A CP sinδ=-1 A CP ~ 0.9sinδ ± L L 0 TK/HK MINOS NOVA sinδ <±0.5 NOVA + TK ( ) sinδ=-1, sin θ 3 >0.98 LBNF L(km) May be possible to limit δ CP by σ but not 3σ. NH IH

19 HK case δ CP sensitivity PTEP (015) 5, 053C0 3σ sinδ ~ WNPFJ 19

20 A CP ±3σ If sinδ=0 & N.H. and HK measured the expected value. TK/HK MINOS NOVA LBNF sinδ=-1 sinδ=0 sinδ=+1 sinδ=-1, sin θ 3 >0.98 HK case L(km) NH If M.H. is known, sinδ <0.33(3σ) can be obtained. IH

21 HK case sinδ= A CP sinδ=-1 sinδ=+1 TK/HK MINOS NOVA sinδ=-1, sin θ 3 >0.98 LBNF L(km) If M.H. is not known, there are two solutions. sinδ=0 can not be confirmed. " M.H. is necessary. NH IH

22 LBNF case arxive: σ sinδ ~ WNPFJ

23 LBNF case A CP TK/HK MINOS NOVA LBNF sinδ=-1 sinδ=0 sinδ=+1 sin θ 3 > L(km) 3σ NH Unphysical Region IH This case, M.H. is determined to be N.H.

24 LBNF case sinδ= A CP sinδ=-1 sinδ=+1 TK/HK MINOS NOVA sin θ 3 >0.98 LBNF L(km) Then extrapolate to L=0 to obtain sinδ CP. ( ) δ ( sinδ CP ) = 3.4 ( δa CP ) + A FK ( δn e n e ) NH what is the error of the average density?

25 sinδ= A CP sinδ=-1 sinδ=+1 sin θ 3 >0.98 HK+LBNF case Improvement of sinδ accuracy L(km) NH * δsinδ HK =0.1 & δsinδ LB =0.1! δsinδ HK+LB =0.071?? (common error?)

26 HK+LBNF case If δsinδ CP ~0.1" δsinδ CP ~0.1/ by combining with LBNF δ CP sensitivity Need not this proviso WNPFJ 6

27 sinδ= A CP sinδ=-1 sinδ=+1 sin θ 3 >0.98 HK+LBNF case Improvement of sinδ accuracy L(km) * MSW error independent analysis is possible. NH sinδ = 3.4 L HK A LB L LB A HK L LB L HK

28 sinδ= A CP sinδ=-1 sin θ 3 >0.98 HK+LBNF case Strict test of the standard neutrino scheme and MSW effect L(km) This indicates a new physics or failure of the standard MSW

29 Energy dependence of the oscillation # sin( 1 V W )Φ 31 = sin Φ 31 n G e F % $ L & ( ' Constant phase shift (ΔΦ) at given L L[km] V W (L/L 0 ) ΔΦ[rad] TK/HK 95 ±0.055 ±0.11 ±0.086 NOVA 810 ±0.15 ±0.30 ±0.4 LBNF 1300 ±0.4 ±0.48 ±0.38 ( ) ~ 0.9? ΔΦ LB ΔΦ HK = G F n LB e L LB n HK e L HK Strong test of MSW with the same osc. mode. Any merit compared with using Φ 31 from the ν µ disappearance?

30 * Enhance the sensitivity of CPV * Solving θ 3 degeneracy * Improve precision of oscillation parameters. (not only δ CP..) * Search for non standard phenomena: different L and E * Nucleon decay: different channel * Supernova: flavor separated measurements : The last sentence of this report. " A concrete benifit: Proposals will become stronger...

31 Conclusion Be Bosons; 1+1 =4, Rather Incoherence; No Fermions; =, 1-1 = WNPFJ 31