Is nonstandard interaction a solution to the three neutrino tensions?

Transcription

1 1/28 Is nonstandard interaction a solution to the three neutrino tensions? Osamu Yasuda Tokyo Metropolitan University Dec Based on arxiv: [hep-ph] Shinya Fukasawa, Monojit Ghosh,OY

2 2/28 1. Introduction 2. New Physics in propagation 3. Analysis of T2K, NOvA, solar+kl with NSI 4. Conclusions

3 1. Introduction Framework of 3 flavor ν oscillation Mixing matrix Functions of mixing angles θ 12, θ 23, θ 13, and CP phase δ e = μ τ μ1 τ1 ν solar +KamLAND (reactor) ν ν ν U U U e1 U U U e2 μ2 τ2 U U U e3 μ3 τ3 θ ν ν ν All 3 mixing angles have been measured π , m ev ν atm +K2K,MINOS(accelerators) π DCHOOZ+Daya Bay+Reno (reactors), T2K+MINOS+Nova θ 23, m ev θ 13 4 π Both hierarchy patterns are allowed Normal Hierarchy Inverted Hierarchy / 20 3/28

4 4/28 Remaining unknowns are sign(δm 2 31 ), π/4-θ 23, δ -> These will be determined in the future experiments In the mean time we have had some possible tensions among the data within the standard oscillation scenario: ν solar -KamLAND: Δm 2 21 NOvA - T2K: θ 23 T2K vs reactor: θ 13

5 5/28 Tension between Δm 2 21 (solar) & Δm 2 21 (KamLAND) Koshio@ NOW2016

6 6/28 Tension between θ 23 (T2K) & θ 23 (nova) T2K: Compatible with Maximal mixing Nova: Maximal mixing excluded at 2.5σ

7 T2K vs reactors results (2015) T2K, PRD91, (2015) Best fit values for θ 13 and δ by T2K alone are different from those by the combined fit. If this feature continues in the future, it could be a tension. T2K, PRD91, (2015) reactors: < sin 2 θ 13 < at 90%CL 7/28

8 T2K vs reactors results (2016) 8/28 T2K: Consistent with the reactor results

9 9/28 Aim of this talk We investigate whether the solution, which explains the tension between solar ν and KamLAND by NSI, improves the other possible tensions (θ 23 in NOvA-T2K, θ 13 in T2K-reactor). As a first step, we test the best fit points of the solar-kamland analysis and of the global analysis.

10 2. Nonstandard Interaction in propagation Phenomenological New Physics considered in this talk: 4-fermi Non Standard Interactions: ν α f neutral current non-standard interaction ν β f Modification of matter effect NP 10/28

11 Constraints on ε αβ for experiments on Earth Davidson et al., JHEP 0303:011,2003; Berezhiani, Rossi, PLB535 ( 02) 207; Barranco et al., PRD73 ( 06) ; Barranco et al., arxiv: Biggio et al., JHEP 0908, 090 (2009) w/o 1-loop arguments Constraints are weak Some model predicts large NSI: Farzan, PLB748 ( 15) 311; Farzan-Shoemaker, JHEP,1607 ( 16)033; Farzan-Heeck, /28

12 12/28 Constraints from high energy ν atm data Friedland-Lunardini, PRD72 ( 05) high energy ν atm data implies 95%CL 99%CL 3σCL at best fit point at 99%CL

13 13/28 Summary of the constraints on ε αβ To a good approximation, we are left with 3 independent variables ε ee, ε eτ, arg(ε eτ ): Furthermore, ν atm data implies tanβ = ε eτ /(1+ε ee ) Fukasawa-OY, arxiv: Allowed region in (ε ee, ε eτ )

14 14/28 NSI for solar ν: ε αβ vs (ε D, ε N ) Gonzalez-Garcia, Maltoni, JHEP 1309 (2013) 152 8In solar ν analysis, Δm312 ->, H -> Heff To a good approximation, the oscillation probability is described by 2 mass eigenstates: f = e, u or d

15 15/28 Tension between solar ν & KamLAND can be solved by NSI Gonzalez-Garcia, Maltoni, JHEP 1309 (2013) 152 Best fit value of global fit

16 Tension between solar ν & KamLAND data comes from little observation of upturn by SK & SNO Gonzalez-Garcia, Maltoni, JHEP 1309 (2013) /28

17 17/28 3. Analysis of T2K, NOvA, solar+kl with NSI Relation between ε αβ & (ε D, ε N ) To give a contour plot of χ 2 in the (ε D, ε N )-plane, we need to know the oscillation probability for T2K & NOvA. We need to know ε αβ from (ε D, ε N ) which is related by the condition:

18 18/28 We take special ansatz for ε αβ which satisfies the relation with (ε D, ε N ) : This is a special ansatz, but an exact solution. -> We will use this ansatz through out this talk.

19 With our ansatz, we are left with only one parameter: δ CP σ: systematic error in overall normalization ξ = 2% (T2K), 5% (NOvA) We fix θ 23 and θ 13 as and turn on NSI Then we check if the fit improves by varying δ CP 19/28

20 20/28 As a constraint for ε eμ <0.15 and ε μτ we introduce a prior: We test 4 sets of (ε D, ε N ): 4 best fit points Best fit value of solar-kl Best fit value of global fit

21 The results: NH with δ=255 o for either f=u or f=d is the best fit. IH does not give a better fit than the standard case. 21/28

22 22/28 The best fit point χ2 std - χ2 NSI =6 δ~255 o ε ττ = 8.95x10-3 ε ee = ε eτ = ε eμ = 9.27x10-4 ε μτ = -6.80x10-3 Goodness of fit (#(extra NSI parameters)=2): Reduced χ 2 = χ 2 /(#(data)-#(parameters)) for our scenario is smaller than for the standard case. if <- This must be satisfied because the standard scenario is expected to give a reasonably good fit.

23 The allowed region from each data 23/28 ε N ε D

24 However, if we take a close look at each fit, then we find: T2K: Fit is not improving NOvA: Fit is slightly improving 24/28

25 Disappearance (ν μ >ν μ ) at NOvA Goodness of fit is bad for the standard case: χ 2 (std)/dof = 42/17 (best fit with θ 23 <45 o ) -> Std scenario does not fit to Nova data well -> Inclusion of NSI does not improve the fit either χ 2 is almost flat in the (ε ee, ε eτ )- plane constraint by atmospheric ν (inside of triangle excluded) 25/28

26 A similar result by marginalization over θ 23, Δm 2 31 θ 23 =π/4, Δm 2 31 =2.5x10-3 ev 2 marginalized over θ 23, Δm /28

27 4. Conclusions (1) 27/28 We studied a class of solution with NSI in propagation, and examined a fit of the best fit points of ν solar +KamLAND to NOvA &T2K. The global best fit point gives the best fit to NOvA +T2K+ν solar +KamLAND at δ=255 o. A fit to the total data is slightly better for our NSI solution than for the standard case. However this best fit point does not improve the tension with maximal θ 23 from the disappearance (ν μ >ν μ ) NOvA, and the T2Kreactor discrepancy.

28 4. Conclusions (2) 28/28 Disappearance channel (ν μ >ν μ ) at NOvA seems to be difficult to explain by NSI as well as by the standard scenario (even with θ 23 <45 o ). -> It may be explained by other new physics or the systematic errors of NOvA data may be optimistically estimated.

29 Backup slides 29/28

30 30/28 Relation between ε αβ & (ε D, ε N ) For simplicity consider θ 13 =0, θ 23 = π/4. If 1+ε ee >0 ε ττ >0, then λ e > λ τ

31 31/28 In the case of λ τ 0 ε ττ satisfies the following relation:

32 Relation between ε αβ & (ε D, ε N ): complicated For simplicity (only in this and the next slides) let s consider θ 13 =0, θ 23 = π/4, ε ττ = ε eτ 2 /(1+ε ee ). Then the relation is simplified. For simplicity take f=d; ε f D, ε f N --> ε d D= ε D, ε d N= ε N ν atm sees only the sum ε αβ = ε e αβ + 3ε u αβ + 3ε d αβ --> 3ε d αβ 32/28

33 The allowed region in the limit θ 23 = π/4, ε ττ = ε eτ 2 /(1+ε ee ) ν atm data: tanβ Introducing a new variable: one can show ν atm data: tan2β 33/28

34 In the case of α 0, the x-intercept shifts: 34/28

35 35/28 First, for simplicity let us look for the solution by perturbation theory in small parameters: s 13 < 0.15, ε eμ < 0.15, ε μτ < Then the leading terms can be easily solved, i.e., the red parts will drop. Small terms will drop Small terms will drop

36 Next, instead of using perturbation theory in small parameters, let us postulate that (large terms) and (small terms) vanish separately: This is a special ansatz, but an exact solution. -> We will use this ansatz through out this talk. 36/28

37 37/28 Furthermore, we assume the following: θ 23 =π/4 ε μτ is real =0 the constraint from ν atm : the high energy ν atm is approximately described by vacuum oscillation Fukasawa-OY, arxiv:

38 Then we can express ε αβ in terms of ε D, ε N, θ jk and δ: (1) (2) (2) (1) (3) (3) The only extra NSI parameters are ε D, ε N There is one free parameter: δ cp δ cp is important, because the appearance probability of LBL is more sensitive to δ than ε αβ 38/28

39 39/28 Appearance probability depends on both δ & arg(ε eτ ) Assumption: 2γ=arg(ε eτ ) ΔE 21 =Δm 2 21/2E ΔE 31 =Δm 2 31/2E

40 40/28 Analysis of NOvA & T2K NOvA: 6.05x10 20 POT with 33 events (appearance) 78 events (disappearance) T2K: 6.6x10 20 POT with 28 events (appearance) 120 events (disappearance) ν2016 T2K, PRD91, (2015)

41 Here we consider only the best fit points which were obtained from ν sol +KamLAND: Best fit value of solar-kl Gonzalez-Garcia, Maltoni, JHEP 1309 (2013) 152 Best fit value of global fit For all the best fit points arg(ε D )=arg(ε N )=π. ->This gives a strong constraint on arg(ε eτ ) in our ansatz. 41/28

42 NB The phase of ε eτ The phase of ε eτ is fixed from the condition (w/o approximation): -> Unless ε eτ is small, arg(ε eτ ) is approximately equal to arg(-ε N )=0 -> The only phases in appearance probability is δ -> Our ansatz is using only half of the two phases. <- This is due to the result in Gonzalez-Garcia, Maltoni, JHEP 1309 (2013) /28

43 solar ν & KamLAND We can read off the approximate value of χ 2 solar+kl from Gonzalez-Garcia, Maltoni, JHEP 1309 (2013) 152 Best fit value of solar-kl χ 2 solar+kl =0 χ 2 solar+kl =0 Best fit value of global fit χ 2 solar+kl =0.2 χ 2 solar+kl =0.3 Standard case (for both f=u & f=d) χ 2 solar+kl =5.4 43/28

44 44/28 The best fit points of ν sol +KamLAND Gonzalez-Garcia, Maltoni, JHEP 1309 (2013) 152 f=u f=d

45 45/28 The best fit points of the global analysis Gonzalez-Garcia, Maltoni, JHEP 1309 (2013) 152 f=u f=d

46 T2K, PRD91, (2015) 46/28