Which baseline for neutrino factory could be better for discovering CP violation in neutrino oscillation for standard and non-standard interactions?

0.35 MB·English

by  Arnab Dasgupta

Which baseline for neutrino factory could be better for discovering CP
violation in neutrino oscillation for standard and non-standard interactions?
Arnab Dasgupta,1,∗ Zini Rahman,1,† and Rathin Adhikari1,‡
1
CentreforTheoretical Physics, JamiaMilliaIslamia(Central University), JamiaNagar, New Delhi-110025, INDIA
Considering νe → νµ and ν¯e → ν¯µ oscillations as the signals in neutrino factory we study the
discoveryreach of CP violation in presenceof standard and non-standardinteractions of neutrinos
with matter. For standrad interactions it is found that around 3000 Km baseline the discovery
reach of CP violation is better for neutrino factory. Even this is better than the 130 Km baseline
in superbeam facility but with the conservative choices of neutrino flux and detector specifications
2
as given by GLoBES. However, the precision measurement of CP violating phase δ in neutrino
1
0 factory is found to be good in the baselines ranging from 3000 Km to 4000 Km. In presence of
2 non-standard interactions the discovery reach of CP violation for 3000 Km baseline is better than
t 130 Km superbeam facility in presence of noon-standard interactions εeµ and also for most of the
c
O allowed region of εeτ. However, 130 Km baseline is found to be better for εµµ and εµτ. For other
NSIs-εee ,εττ the3000KmbaselineinneutrinofactoryisbetterforsmallervaluesofNSIswhereas

7 130 Km baseline with superbeam facility is better for larger values of NSIs. Compared to other
1
baselines for neutrino factory the NSI discovery reach is in general better for 3000 Km baseline

] except for εµτ where as for example, 2300 Km baseline for superbeam is found to bebetter.
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∗ [email protected]
† [email protected]
‡ [email protected]
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I. INTRODUCTION
Thepresentexperimentsonneutrinooscillationsconfirmsthatthereismixingbetweendifferentflavoursof
neutrinos(ν ,ν ,ν ). Theprobabilityofneutrinooscillationsdependsonvariousparametersoftheneutrino
e µ τ
mixing matrix-the PMNS matrix [1]. The current experiments tells us about two of the angles θ and θ
23 12
[2]withsomeaccuracy. ThereactorneutrinoexperimentslikeDayaBay[3]andReno[4]providedcompelling
evidences for a relatively large angle θ , with 5.2σ and 4.9σ results respectively. These recent reactor
13
neutrino results indicate θ very close to 8.8◦. The CP violating phase δ is totally unknown. Although the
13
mass squareddifference of the different neutrinos (∆m2 =m2 m2) are known to us but the sign of ∆m2
ij i − j 31
(which is related to mass hierarchy)is still unknown.
In this work we consider long baselines (L > (2000) Km) for neutrinos coming from neutrino factory.
O
However, it is difficult to consider short baseline below 2000 Km for neutrino factory as the first oscillation
peakofoscillationprobabilitywillcorrespondtoenergyoforderMeVforwhichproperneutrinofluxwillnot
beavailable. Weconsidertotallyactivescintillatordetector(TASD)forourstudy. Consideringν ν and
e µ
→
ν¯ ν¯ oscillationsasthe signalswedoacomparativestudyofdiscoveryreachofCP violationfordifferent
e µ
→
long baselines in neutrino factory as well as 130 Km baseline for superbeam in presence of standard and
non-standard interactions. For the oscillation channel considered by us the detection of muon is required.
However, this is supposed to be easier than the detection of electron which is required in superbeam. This
is an advantage in considering ν nu signal in the neutrino factory. There are some studies on the
e µ
→
performance of low enegy neutrino factories in the context of standard [5] and non-standardinteractions [6]
mainly for small θ . We have discussed the prospects of different baselines of neutrino factory considering
13
large θ as obtained from Daya Bay experiment.
13
The paper is organized as follows: In section II we discuss ν ν oscillation probability and how the
e µ
→
δ dependent and independent part varies with the variation of matter density for baselines L > (2000)
O
Km for standard and non-standard interactions. In section III we discuss the experimental set-ups and
the assumptions in doing the numerical simulations using GLoBES. In section IV for standard interactions
we have shown the discovery reach of CP violation and the precision measurement of CP violating phase
δ in different long baselines and also for 130 Km baseline in superbeam. In presence of non-standard
interactions we show the discovery reach of CP violation depending on various NSI true values and also
discuss the discovery reach of NSIs depending on δ true values. In section V we conclude with remarks on
which baselines could be better for discovering CP violation after considering neutrino factory as well as
superbeam for neutrino source.
II. ν →ν OCILLATION PROBABILITIES WITH NSI
e µ
Apart from Standard Model (SM) Lagrangian density we consider the following non-standard fermion-
neutrino interaction in matter defined by the Lagrangian:
M = 2√2G εfP[f¯γ Pf][ν¯ γµLν ] (1)
LNSI − F αβ µ β α
where P (L,R), L = (1−γ5), R = (1+γ5), f = e,u,d and εfP are termed as non-standard interactions
∈ 2 2 αβ
(NSIs) parameterssignifying the deviationfrom SM interactions. Model dependent and independent bound
3
[7–9]areobtainedfortheseNSIparameters. TheseNSIparameterscanbereducedtotheeffectiveparameters
and can be written as:
n
ε = εfP f (2)
αβ αβ n
Xf,P e
where n is the fermion number density and n is the electron number density. As these NSIs modifies the
f e
interactions with matter from the Standard Model interactions the effective mass matrix for the neutrinos
are changed and as such there will be change in the oscillation probability of different flavor of neutrinos.
Although NSIs could be present at the source of neutrinos, during the propagation of neutrinos and also
during detection of neutrinos [10] but as those effects are expected to be smaller at the source and detector
due to their stringent constraints [9], we consider the NSI effect during the propagation of neutrinos only.
In section IV in numerical simulations we shall consider the model independent allowedrange of realvalues
of different NSIs as mentioned in reference [9] for earth like matter.
In vacuum, flavor eigenstates ν may be related to mass eigenstates of neutrinos ν as
α i
ν >= U ν >; i=1,2,3, (3)
α αi i
| |
Xi
where U is PMNS matrix [1] which depends on three mixing angles θ , θ and θ and one CP violating
12 23 13
phase δ. The Hamiltonian due to standard (H ) and non-standard interactions (H ) of neutrinos
SM NSI
interacting with matter during propagation can be written in the flavor basis as:
H =H +H (4)
SM NSI
where
0 0 0 A 0 0
∆m2
HSM = 31 U0 α 0U†+0 0 0, (5)
2E
0 0 1 0 0 0
    
ε ε ε
ee eµ eτ
HNSI =Aε∗eµ εµµ εµτ (6)
ε∗ ε∗ ε
 eτ µτ ττ 
In equations (5) and (6)
2E√2G n ∆m2
A= F e; α= 21; ∆m2 =m2 m2 (7)
∆m2 ∆m2 ij i − j
31 31
wherem isthemassofthei-thneutrinoandAisconsideredduetotheinteractionofneutrinoswithmatter
i
in SM, G is the Fermi constant and n is the electron number density of matter . ε , ε , ε , ε , ε
F e ee eµ eτ µµ µτ
and ε are considered due to the non-standard interaction (NSIs) of neutrinos with matter. In equation
ττ
(6), (∗ ) denotescomplex conjugation. Inournumericalanalysiswe haveconsideredthe NSIs - ε , ε and
eµ eτ
ε to be real.
µτ
To discuss the variation of δ dependent and independent part in the oscillation probability and for that
whichbaselinecouldbesuitablefordiscoveryreachofCP violationinpresenceofstandardandnon-standrad
4
interactions we present below the oscillation probability P for long baseline (L> 2000 Km). To get
νe→νµ O
theseexpressionsofprobabilitywehavefollowedtheperturbationmethodadoptedinreferences[10–13]. We
shall present the oscillation probability upto order α2 considering small NSI of the order of α. Considering
the the matter effect parameter A in the leading order of perturbation andNSI parametersε of the order
αβ
of α one obtains
α2cos2[θ ]sin2 AL∆m231 sin[2θ ]2
23 4E 12
P = h i
νe→νµ A2
a sin2[θ ]sin2[θ ] ( 1+A)L∆m2 ( 1+A)L∆m2
+ 6 13 23 8Esin2 − 31 ( 1+A)L∆m2 sin − 31
( 1+A)3E (cid:18) (cid:20) 4E (cid:21)− − 31 (cid:20) 2E (cid:21)(cid:19)
−
a sin2[θ ]sin2[θ ] ( 1+A)L∆m2 ( 1+A)L∆m2
+ 1 13 23 8Esin2 − 31 +( 1+A)L∆m2 sin − 31
( 1+A)3E (cid:18)− (cid:20) 4E (cid:21) − 31 (cid:20) 2E (cid:21)(cid:19)
−
( 1+A)L∆m2 sin2[θ ]sin2[θ ]
+sin − 31 13 23 (2E(1+( 6+A)A
(cid:20) 4E (cid:21) ( 1+A)4E −
−
( 1+A)L∆m2 ( 1+A)L∆m2
+ (1+A)2cos[2θ ] sin − 31 +4( 1+A)AL∆m2 cos − 31 sin2[θ ]
13 (cid:20) 4E (cid:21) − 31 (cid:20) 4E (cid:21) 13 (cid:19)
(cid:1)
4a AL∆m2 AL∆m2
+ 2 cos[θ ]sin 31 ( 1+A)cos[θ ]sin 31 (a +αcos[φ ]sin[2θ ])
( 1+A)A2 23 (cid:20) 4E (cid:21)(cid:18) − 23 (cid:20) 4E (cid:21) 2 a2 12
−
L∆m2 ( 1+A)L∆m2
+ 2Acos δ 31 +φ sin − 31 sin[θ ]sin[θ ]
(cid:20) − 4E a2(cid:21) (cid:20) 4E (cid:21) 13 23 (cid:19)
2αsin[θ ]sin[θ ]sin[θ ] ( 1+A)L∆m2 L∆m2
+ 12 13 23 sin − 31 4( 1+A)2Ecos δ 31
( 1+A)3AE (cid:20) 4E (cid:21)(cid:18) − (cid:20) − 4E (cid:21)×
−
AL∆m2 ( 1+A)L∆m2 ( 1+A)L∆m2
cos[θ ]cos[θ ]sin 31 +A ( 1+A)L∆m2 cos − 31 4AEsin − 31
12 23 (cid:20) 4E (cid:21) (cid:18) − 31 (cid:20) 4E (cid:21)− (cid:20) 4E (cid:21)(cid:19)
sin[θ ]sin[θ ]sin[θ ])
12 13 23
×
4a a L∆m2 ( 1+A)L∆m2 AL∆m2
+ 2 3 cos 31 φ +φ sin − 31 sin 31 sin[2θ ]
( 1+A)A (cid:20) 4E − a2 a3(cid:21) (cid:20) 4E (cid:21) (cid:20) 4E (cid:21) 23
−
4a ( 1+A)L∆m2 L∆m2 AL∆m2
+ 3 sin − 31 sin[θ ] ( 1+A)αcos[θ ]cos 31 +φ sin 31 sin[2θ ]
( 1+A)2A (cid:20) 4E (cid:21) 23 (cid:18) − 23 (cid:20) 4E a3(cid:21) (cid:20) 4E (cid:21) 12
−
( 1+A)L∆m2
+ Asin − 31 sin[θ ](a +2cos[δ+φ ]sin[θ ])
(cid:20) 4E (cid:21) 23 3 a3 13 (cid:19)
2a sin2[θ ]sin[2θ ] ( 1+A)L∆m2 ( 1+A)L∆m2
+ 5 13 23 sin − 31 sin − 31 φ
( 1+A)2A (cid:20) 4E (cid:21)(cid:18) (cid:20) 4E − a5(cid:21)
−
( 1+A)L∆m2 (1+A)L∆m2
+ Asin − 31 +φ ( 1+A)sin 31 +φ (8)
(cid:20) 4E a5(cid:21)− − (cid:20) 4E a5(cid:21)(cid:19)
where
a =Aε
1 ee
A ε 2+ ε 2+(ε 2 ε 2)cos2θ 2ε ε cos[φ φ ]sin2θ
eµ eτ eµ eτ 23 eµ eτ eµ eτ 23
a = | | | | | | −| | − | || | −
2 p √2
A ε 2+ ε 2+( ε 2+ ε 2)cos2θ +2ε ε cos[φ φ ]sin2θ
eµ eτ eµ eτ 23 eµ eτ eµ eτ 23
a = | | | | −| | | | | || | −
3 p √2
1
a =A ε 2cos22θ cos2φ +(ε ε )2cos2θ sin2θ + ε ((ε ε )cosφ sin4θ
5 µτ 23 µτ µµ ττ 23 23 µτ µµ ττ µτ 23
(cid:18)| | | |−| 2| | | |−| |
5
1/2
+ 2ε sin2φ
µτ µτ
| | (cid:19)
(cid:1)
a =A ε cos2θ + ε sin2θ + ε cosφ sin2θ
6 ττ 23 µµ 23 µτ µτ 23
| | | | | |
(cid:0) ε cosθ sinφ ε sinθ sinφ (cid:1)
φ =tan−1 | eµ| 23 eµ−| eτ| 23 eτ
a2 (cid:20) ε cosθ cosφ ] ε cosφ ]sinθ (cid:21)
eµ 23 eµ eτ eτ 23
| | −| |
ε sinθ sinφ + ε cosθ sinφ
φ =tan−1 | eµ| 23 eµ | eτ| 23 eτ
a3 (cid:20) ε cosθ cosφ + ε cosφ sinθ (cid:21)
eτ 23 eτ eµ eµ 23
| | | |
ε sin[φ ]
φ =tan−1 | µτ| µτ (9)
a5 (cid:20) ε cos2θ cosφ +(ε ε )cosθ sinθ (cid:21)
µτ 23 µτ µµ ττ 23 23
| | | |−| |
For CP violationthere is difference of probabilityin the neutrino oscillationandprobability of antineutrino
oscillation. One can relate the oscillation probabilities for antineutrinos to those probabilities given for
neutrinos above by the following relation:
Pα¯β¯ =Pαβ(δCP →−δCP, A→−A). (10)
In addition, we also have to replace ε with their complex conjugates, in order to deduce the oscillation
αβ
probability for the antineutrino, if one considers non-standard interaction during propagation.
To estimate the order of magnitude of δ dependent and δ independent part in the above two oscillation
probabilityfollowingDayaBayresultweshallconsidersinθ √α. ForonlySMinteractions,(i.eε 0)
13 αβ
∼ →
in above expressions of oscillation probabilities one finds that the δ dependence occurs at order of α3/2.
This order of dependence with δ remains same in the difference of neutrino oscillation probabilities and
antineutrino oscillation probabilities (represented by ∆P later). However, the δ independent part in ∆P
(whichcouldmimic CP violation)isatorderα. Thishappens dueto mattereffectthroughAforSMascan
beseenfromaboveexpressions. Apartfromthisdifferenceintheorderdependencebyα1/2,theparameterA
playsaverycrucialroleindeterminingthevariationofδ dependent(whichvariesas1/A)andδ independent
part(whichvariesas1/(1 A)). Wehaveignoredthevariationoftrigonometricfunctions (whichdependon
−
A)asthe variationis muchslowerforAdue tothe baselinesinthe rangeof2000to 5000Km. Forrelatively
shorter baselines the A value is smaller and the δ dependent part becomes more pronounced. Apparently, it
seems 2000 or 3000 Km baselines will be better than 4000 or 5000 Km baselines. However, it is important
to note that for relatively shorter baselines the first oscillation peak will also correspond to relatively lower
neutrino energy where the neutrino flux may not be that good. It is precisely for this reason that 2000
Km (as found in our numerical simulation) is not that good so far the discovery reach of CP violation is
concerned.
However,when NSIs are also taken into accountone can see that δ dependence in ∆P could occur at the
order of α3/2 through a and a containing terms in (8) for NSIs of the order of α. We have checked that
2 3
for slightly higher NSIs of the order of √α using perturbation method the same δ dependent terms in ∆P
appearswith a and a in the oscillationprobabilityfor longbaseline as givenin (8)andthis slightly higher
2 3
NSI makes these terms at the order of α which could compete with the δ independent part (which could
mimic CP violation)in ∆P for long baseline as that is also at the order of α. So presence of slightly higher
NSIs of order √α present in a and a improves the discovery reach of CP violation for longer baseline. As
2 3
a anda containsNSIs likeε andε it isexpectedthat inpresenceoftheseNSIs the longbaselinecould
2 3 eµ eτ
provide a better discovery reach for CP violation.
6
III. NUMERICAL SIMULATION
In this work we have considered a neutrino factory set-up with four kinds of baselines which are : 2000,
3000, 4000 and 5000 km with 5.5, 7.1, 8.5 and 9 GeV parent muons respectively with 5 1021 number of
×
storedmuons and anti-muons decays per year. The energy of parent muons have been chosenin such a way
that the energy corresponding to the peak of ν flux matches with the neutrino energy correspond to the
e
first oscillation peak of the probability of oscillation ν ν (fixing the probability for Standard Model
e µ
→
interactions only) for different baselines. We have taken a magnetized totally active scintillator detector
of mass 25 kt with threshold energy 1 GeV. In doing the analysis we consider a signal efficiency of 94%
in appearance and 0.1% in disappearance channels. As signal we have taken the ν ν oscilation and
e µ
→
ν¯ ν¯ oscillations. As backgrounds we consider the neutral current events and ν and ν¯ disappearance
e µ µ µ
→
events. The systematic uncertainties of 2.5% and energy calibration error of 0.01% has been considered for
both signal and for the background channels. The Gaussian energy resolution is considered to be 0.1√E .
The numerical simulation has been done by using GLoBES [14]. For the experimental setup of CERN to
Frejusbaselineof130Kmandfor2300Kmforneutrinosandantineutrinoscomingfromsuperbeamwehave
considered the flux and detector specifications as considered in reference [15]. For discovery reach of CP
violationwe havecomparedwith 130Kmbaseline because there the discoveryreachis foundto be better in
comparisonto other baselines. ForNSI discoverywe havecomparedwith2300Kmbaseline asthe discovery
limit is also found to be better in comparisonto other baselines for superbeam.
We consider the true values of the neutrino oscillation parameters as ∆m2 =2.45 10−3 eV2, ∆m2 =
| 31| × 21
7.64 10−5 eV2, θ =9◦, θ =34.2◦ and θ =45◦. Also in calculating the priors we consider an error of
13 12 23
×
3% on θ , 0.005 on sin22θ , 8% on θ , 4% on ∆m2 and 2.5% on ∆m2 . Also we consider an error of
12 13 23 | 31| 21
2% on matter density .
130 km 130 km
103 2000 km 103 2000 km
3000 km 3000 km
4000 km 4000 km
5000 km 5000 km
2 102 2 102
χ χ
∆ ∆
5 σ 5 σ
101 3 σ 101 3 σ
100 100
-180 -90 0 90 180 -180 -90 0 90 180
δ(true) δ(true)
FIG. 1: Discovery reach of CP violation for only SM interactions for different baselines for normal (left panel) and
inverted hierarchy (right panel).
Inthefigure1wehaveshowntheCP violationdiscoveryreachfor2000Km,3000Km,4000Kmand5000
Km baselines for neutrino factory and 130 Km baseline for superbeam. It is found that 3000 Km baseline
7
for neutrino factory gives the better CP violation discovery reach than all other baselines considered for
both the hierarchies of neutrino masses and for normal (inverted) hierarchy this discovery is possible over
the 72 % (79%) of the allowed δ values. However,130 Km baselines for superbeam seems better than other
baselines for neutrino factory as shown above.
180 180
3000 km
2000 km
4000 km
90 5000 km 90
130 km

δ (test) 0 δ (test) 0
3000 km
2000 km
4000 km
-90 -90 5000 km
130 km

-180 -180
-180 -90 0 90 180 -180 -90 0 90 180
δ (true) δ (true)
FIG. 2: Precision of measurement of phase δ for only SM interactions for different baselines for normal (left panel)
and inverted hierarchy (right panel).
In figure 2 we have shown at 5 σ confidence level the precision of measurement of phase δ for different
baselines as considered for CP violation discovery reach. From the figures one may find out the precision
(P ) of sensitivity of measurement for any true value of δ using the following expression for it:
δ(true)
δ(test)(max) δ(test)(min)
P = − (11)
δ(true) 2π+δ(test)(max)+δ(test)(min)
where δ(test)(max) and δ(test)(min) are the maximum and minimum δ(test) values respectively corre-
sponding to certain true values. Here also it is found that for most of the δ(true) values the precision of
measurement is found to be better for 3000 Km baselines particularly for normal hierarchy in comparison
to other baselines. As for example for δ (true) =0 the precision for normal(inverted) hierarchy is about 26
% (18%) and for δ (true) =π/4 the precision for normal(inverted) hierarchy is about 9 % (14%). Although
for inverted hierarchy 4000 Km baseline is slightly better.
In figure 3 we have shown at 5σ confidence level the discovery reach of CP violation in presence of NSIs
ǫ , ǫ and ǫ for baselines 3000 Km and 5000 Km baselines for neutrino factory and 130 Km baseline for
ee eµ eτ
superbeam.
In figure 4 we have shown at 5σ confidence level the discovery reach of CP violation in presence of NSIs
ǫ , ǫ and ǫ for baselines 3000Kmand 5000Kmbaselines for neutrino factory and 130Kmbaseline for
µµ µτ ττ
superbeam. In general,it is found that 3000Kmbaseline in neutrino factory is somewhatbetter for smaller
NSI values. However, for higher allowed NSI values 130 Km baseline for superbeam is found to be better
in general. But for ε and ε the CP violation discovery reach is much better for almost all allowed NSI
eµ eτ
values. The possible reason for this significant improvement is discussed in section II in the context of the
8
360 360

270 270

e) e) 130 km
u u 3000 km
δ (tr180 3010300 kkmm δ (tr180 5000 km
5000 km
90 90

0 0
-4 -3 -2 -1 0 1 2 3 4 -4 -3 -2 -1 0 1 2 3 4
ε (true) ε (true)
ee ee
360 360

270 270

e) e)
u u
δ (tr180 δ (tr180

130 km 130 km
90 3000 km 90 3000 km
5000 km 5000 km

0 0
-0.3 -0.2 -0.1 0 0.1 0.2 0.3 -0.3 -0.2 -0.1 0 0.1 0.2 0.3
εe µ (true) εe µ (true)
360 360

270 270

e) e)
u u
δ (tr180 δ (tr180

130 km 130 km
90 3000 km 90 3000 km
5000 km 5000 km

0 0
-3 -2 -1 0 1 2 3 -3 -2 -1 0 1 2 3
εe τ (true) εe τ (true)
FIG. 3: Discovery limit of CP violation with NSI for both NH (left panel) and IH (right panel) at 5σ confidence
levels for ǫee, ǫeµ and ǫeτ.
9
360 360

130 km
3000 km
270 270 5000 km

e) e)
u u
δ (tr180 δ (tr180

90 130 km 90
3000 km
5000 km
0 0
-0.3 -0.2 -0.1 0 0.1 0.2 0.3 -0.3 -0.2 -0.1 0 0.1 0.2 0.3
εµ τ (true) εµ τ (true)
360 360

270 270

e) e)
u u
δ (tr180 δ (tr180

130 km 130 km
90 3000 km 90 3000 km
5000 km 5000 km

0 0
-0.6 -0.4 -0.2 0 0.2 0.4 0.6 -0.6 -0.4 -0.2 0 0.2 0.4 0.6
εµ µ (true) εµ µ (true)
360 360

270 270

e) e) 130 km
u 130 km u 3000 km
δ (tr180 35000000 kkmm δ (tr180 5000 km

90 90

0 0
-10 -5 0 5 10 -10 -5 0 5 10
ετ τ (true) ετ τ (true)
FIG. 4: Discovery limit of CP violation with NSI for both NH (left panel) and IH (right panel) at 5σ confidence
levels for ǫµµ, ǫµτ and ǫττ.
10
360 360

2300 km
3000 km
270 5000 km 270
e) e)
u u
δ (tr180 δ (tr180 2300 km
3000 km
5000 km
90 90

0 0
-0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4 -0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4
ε (true) ε (true)
ee ee
360 360

270 270

e) e)
u u
δ (tr180 δ (tr180 23300000 kkmm
5000 km
90 90
2300 km
3000 km
5000 km
0 0
-0.1 -0.05 0 0.05 0.1 -0.1 -0.05 0 0.05 0.1
εe µ (true) εe µ (true)
360 360

270 270

e) e)
u u
δ (tr180 δ (tr180

90 90
2300 km 2300 km
3000 km 3000 km
5000 km 5000 km
0 0
-0.2 -0.15 -0.1 -0.05 0 0.05 0.1 0.15 0.2 -0.2 -0.15 -0.1 -0.05 0 0.05 0.1 0.15 0.2
εe τ (true) εe τ (true)
FIG. 5: Discovery limit of NSIfor both NH(left panel) and IH(right panel) at 5σ confidencelevelsfor ǫee,ǫeµ and
ǫeτ.