Is nonstandard interaction a solution to the three ...Is nonstandard interaction a solution to the...

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Is nonstandard interaction a solution to the three neutrino tensions?

Osamu YasudaTokyo Metropolitan University

Based on arXiv:1609.04204 [hep-ph] Shinya Fukasawa, Monojit

Ghosh,OY

Dec. 18 @Miami 2016

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1. Introduction

3. Analysis of T2K, NOvA, solar+KL

with NSI

4. Conclusions

2. New Physics in propagation

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νsolar+KamLAND

(reactor)

⎟⎟⎟⎟

⎠

⎞

⎜⎜⎜⎜

⎝

⎛

⎟⎟⎟⎟

⎠

⎞

⎜⎜⎜⎜

⎝

⎛

τττ

μμμ=

⎟⎟⎟⎟⎟

⎠

⎞

⎜⎜⎜⎜⎜

⎝

⎛

3

2

1

321

321

e3e2e1e

UUUUUUUUU

ννν

ννν

τ

μ

2522112 eV108∆m,

6πθ −×≅≅

Framework of 3 flavor ν

oscillationMixing matrix

All 3 mixing angles have been measured

Functions of mixing angles

θ12

, θ23

, θ13

, and

CP phase

δδ

νatm+K2K,MINOS(accelerators) 2323223 eV102.5|∆m|,

4πθ −×≅≅

20/θ13 π≅DCHOOZ+Daya Bay+Reno

(reactors),

T2K+MINOS+Nova

Both hierarchy patterns are allowed

1. Introduction

Normal Hierarchy

Inverted Hierarchy

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Remaining unknowns are sign(Δm231

),

π/4-θ23

,

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:

νsolar - KamLAND: Δm221NOvA - T2K: θ23T2K vs reactor: θ13

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Tension between Δm221(solar) & Δm221(KamLAND)

Koshio@ NOW2016

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Backhouse@nufact2016

Tension between θ23(T2K) & θ23(nova)

Nova: Maximal mixing excluded at 2.5σ

Quilain@nufact2016

T2K: Compatible with Maximal mixing

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T2K vs reactors results (2015) T2K, PRD91, 072010 (2015)

reactors: 0.0195 < sin2θ13

< 0.023 at 90%CL

Best fit values for θ13

and δ

by T2K alone are

different from those by the combined fit.

T2K, PRD91, 072010 (2015)

If this feature continues in the future, it could be a tension.

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Quilain@nufact2016

T2K: Consistent with the reactor results

T2K vs

reactors results (2016)

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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 (θ23

in NOvA-T2K, θ13

in T2K-reactor).

As a first step, we test the best fit points of the solar-KamLAND

analysis and of the global

analysis.

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να νβ

ffneutral current non-standard interaction

Phenomenological New Physics

considered

in this

talk: 4-fermi Non Standard Interactions:

2. Nonstandard Interaction in propagation

Modification of matter effect

NP

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Biggio

et al., JHEP 0908, 090 (2009) w/o 1-loop arguments

Constraints on εαβ for experiments on Earth

Davidson et al., JHEP 0303:011,2003; Berezhiani, Rossi, PLB535 (‘02) 207; Barranco et al., PRD73 (‘06) 113001; Barranco

et al., arXiv:0711.0698

Constraints are weak

Some model predicts large NSI:Farzan, PLB748 (‘15) 311; Farzan-Shoemaker, JHEP,1607 (‘16)033; Farzan-Heeck, 1607.07616.

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high energy νatm

data implies

at best fit point

at 99%CL

Constraints from high energy νatm

data

95%CL99%CL3σCL

Friedland-Lunardini, PRD72 (‘05) 053009

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Summary of the constraints on εαβ

Furthermore, νatm

data implies|tanβ|=|εeτ/(1+εee)|

<0.8

@2.5σCLFukasawa-OY, arXiv:1503.08056

To a good approximation, we are left with 3 independent variables εee, | εeτ

|, arg(εeτ):

Allowed region in

(εee , | εeτ

|)

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Gonzalez-Garcia, Maltoni, JHEP 1309 (2013) 152

NSI for solar ν: εαβ vs (εD, εN)

f = e, u or d

In solar ν

analysis, Δm312 -> , H -> Heff8

To a good approximation, the oscillation probability is described by 2 mass eigenstates:

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Tension between solar ν

& KamLAND

can be solved by NSI


Best fit value of global fit

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Tension between solar ν

& KamLAND

data comes from little observation of upturn by SK & SNO


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3. Analysis of T2K, NOvA, solar+KL

with NSI

To give a contour plot of χ2

in the (εD, εN)-plane,we need to know the oscillation probability for T2K & NOvA.

We need to know

εαβ

from (εD, εN) which is related by the condition:

Relation between εαβ & (εD, εN)

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This is a special ansatz, but an exact

solution.-> We will use this ansatz

through out this talk.

We take special ansatz

for εαβ

which satisfies the relation with (εD, εN) :

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σ: systematic error in overall normalization ξ = 2% (T2K), 5% (NOvA)

We fix θ23

and θ13

as

With our ansatz, we are left with only one parameter: δCP

and turn on NSI Then we check if the fit improves by varying δCP

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As a constraint for |εeμ|<0.15 and |εμτ|<0.15 @90%CL, we introduce a prior:


Best fit value of solar-KLWe test 4 sets of (εD, εN): 4 best fit points

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The results: NH with δ=255o

for either f=u or f=d is the best fit. IH does not give a better fit than the standard case.

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The best fit point

εee

= 0.849

εeτ

= 0.129

εττ

= 8.95x10-3

εeμ

= 9.27x10-4

εμτ

= -6.80x10-3

δ～255o

χ2std

-

χ2NSI

=6

Goodness of fit (#(extra NSI parameters)=2):

Reduced χ2

= χ2/(#(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.

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The allowed region from each data

εN

εD

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However, if we take a close look at each fit, then we find:

T2K: Fit is not improving

NOvA: Fit is slightly improving

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Disappearance (νμ−>νμ) at NOvAGoodness of fit is bad for the standard case: χ2(std)/dof = 42/17 (best fit with θ23 < 45o) -> Std scenario does not fit to Nova data well -> Inclusion of NSI does not improve the fit either

χ2

is almost flat in the (εee, |εeτ|)-

plane

constraint by atmospheric ν (inside of triangle excluded)

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θ23=π/4, Δm2

31=2.5x10-3eV2marginalized over θ23, Δm2

31

A similar result by marginalization over θ23, Δm231

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We studied a class of solution with NSI in propagation, and examined a fit of the best fit points of νsolar+KamLAND to NOvA &T2K.

4. Conclusions (1)

The global best fit point gives the best fit to NOvA +T2K+νsolar+KamLAND at δ=255o. 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 θ23 from the disappearance (νμ−>νμ) NOvA, and the T2K-reactor discrepancy.

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4. Conclusions (2)

Disappearance channel (νμ−>νμ) at NOvAseems to be difficult to explain by NSIas well as by the standard scenario (even with θ23 < 45o).-> It may be explained by other new physics or the systematic errors of NOvA

data may be

optimistically estimated.

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Backup slides

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Relation between

εαβ

& (εD, εN)

For simplicity consider θ13

=0, θ23

= π/4.

If 1+εee

>0 εττ

>0, then λe’

> λτ’

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In the case of λτ’

≠ 0

εττ

satisfies the following relation:

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Relation between

εαβ

& (εD, εN): complicated

For simplicity (only in this

and the next

slides)let’s consider θ13

=0, θ23

= π/4, εττ

=

|εeτ

|2/(1+εee

).

Then the relation is simplified.

For simplicity take f=d; εfD, εfN --> εdD= εD, εdN= εN

νatm

sees only the sumεαβ

= εeαβ

+ 3εuαβ + 3εdαβ

--> 3εdαβ

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In the case of α ≠ 0, the x-intercept shifts:

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First, for simplicity let us look for the solution by perturbation theory in small parameters: |s13|< 0.15, |εeμ

| < 0.15, |εμτ

| < 0.15. Then the

leading terms can be easily solved, i.e., the red parts will drop.

Small terms will drop

Small terms will drop

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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.

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Furthermore, we assume the following:

θ23 =π/4

εμτ is real

the constraint from νatm :the high energy νatm

is

approximately described by vacuum oscillation

Fukasawa-OY, arXiv:1503.08056

=0

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The only extra NSI parameters are εD,

εN There is one free parameter: δcp

Then we can express εαβ

in terms of εD,

εN, θjk

and δ:

← δcp

is important, because the appearance probability of LBL is more sensitive to

δ

than εαβ

(1)

(2)

(3)(1)(2)

(3)

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2γ=arg(εeτ)

Assumption:Appearance probability depends on both δ

& arg(εeτ)

ΔE21=Δm221/2E

ΔE31=Δm231/2E

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Analysis of NOvA & T2K

T2K: 6.6x1020POT with 28 events (appearance) 120 events (disappearance)

NOvA: 6.05x1020POT with 33 events (appearance) 78 events (disappearance)

T2K, PRD91, 072010 (2015)

Vahle

@ ν2016

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Here we consider only the best fit points which were obtained from νsol+KamLAND:



Best fit value of solar-KL

For all the best fit points arg(εD)=arg(εN)=π. ->This gives a strong constraint on arg(εeτ) in our ansatz.

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NB The phase of εeτ

The phase of εeτ

is fixed from the condition (w/o approximation):

-> Unless |εeτ| is small, arg(εeτ) is approximately equal to arg(-εN)=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


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solar ν & KamLAND


Best fit value of solar-KL

We can read off the approximate value of χ2solar+KL

from Gonzalez-Garcia, Maltoni, JHEP 1309 (2013) 152

χ2solar+KL

=0

χ2solar+KL

=0

χ2solar+KL

=0.2

χ2solar+KL

=5.4Standard case (for both f=u & f=d)

χ2solar+KL

=0.3

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The best fit points of νsol+KamLAND

f=u f=d

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The best fit points of the global analysisGonzalez-Garcia, Maltoni, JHEP 1309 (2013) 152

f=df=u

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T2K, PRD91, 072010 (2015)

Is nonstandard interaction a solution to the three ...Is nonstandard interaction a solution to the...

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