Precision measurement of neutrinooscillation parameters @ INO-ICAL

Detector

Daljeet Kaur

Md. Naimuddin, Sanjeev Kumar

University of Delhi, Delhi

UNICOS, 13-15 May 2014, Panjab University, Chandigarh

UNICOS-2014 Precision Measurement

Outline

1 Introduction

2 INO Experiment

3 Neutrino Interaction

4 Analysis Performed

5 Inputs for analysis

6 Results

7 Conclusions

UNICOS-2014 Precision Measurement

Introduction

Neutrinos are chargeless, spin 1/2, very weakly interacting, tinymass particle which comes in three active flavors νe, νµ and ντ

Standard Model of particle physics predicts that the neutrinosare massless but the strong and compelling evidences fromseveral experiments show that neutrinos have masses and theyoscillate.

The phenomenon of flavor changing among the neutrinos iscalled Neutrino Oscillation.

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Neutrino Oscillations

Neutrino Oscillation ⇔ Neutrino are massive and mixed

The relation between flavor and mass eigen state as:

|να〉 =∑

i

U∗αi |νi〉

where α is the flavor (e, µ or τ) and i =1, 2, 3 denotes the neutrinomass eigen state. Uαi’s are the matrix elements of PMNS mixingmatrix U.Probability of flavor change is:

P (να → νβ) = δαβ − 4∑

i>j

ℜ(U∗

αiUβiUαjU∗

βj)sin2[1.27∆m2

ij(L/E)]

+2∑

i>j

ℑ(U∗

αiUβiUαjU∗

βj)sin[2.54∆m2

ij(L/E)]

Where ∆m2

ij = m2

i −m2

j in eV 2, L in Km and E in GeV.

α = β Survival probability, α 6= β Transition probability

requires U 6= 1 and ∆m2

ij 6= 0

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Two flavor Neutrino Oscillation in vacuum

The mixing matrix is:

U =

[

cos θ sin θ− sin θ cos θ

]

=

[

Uα1 Uα2

Uβ1 Uβ2

]

(1)

where θ is the mixing angle.The transition probability is given as :

Pαβ = sin2(2θ)sin2(∆m2L

4E) (2)

where L is the baseline and E is the energy of the neutrino.

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Open Questions : Neutrino Physics

What is the right order of neutrino mass spectrum ?

What is the right octant for mixing angle θ23

What is the value of CP phase delta ?

Precision measurement of neutrino oscillation parameters.

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The INO Experiment

The India-based Neutrino Observatory (INO) is a plannedproposal for studying the properties of atmospheric neutrinosusing a magnetised Iron CALorimeter detector (ICAL).

A large cavern of dimension 170m x 20m x 32m will beconstructed to place the detector under the mountain at Theni(Tamilnadu) in South India.

Precision measurement of atmospheric neutrino oscillationparameters and the determination of neutrino mass hierarchyare the main aims of INO-ICAL experiment.

The ICAL has a special feature to detect the neutrino andanti-neutrino from the bending of the associative leptons andanti-leptons in an applied magnetic field.

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The INO-ICAL Detector

ICAL specifications1. Total Mass : ∼50 ktons2. Dimension : 16m x 16m x 14.5m (for onemodule)3. Target : Iron (5.6 cm thick)4. Active Material : Resistive Plate Chambers(RPCs) of 2m x 2m dimension5. Magnetic field : ∼1.5T

Resistive Plate Chamber(RPC)

Gaseous detector

Two dimensional output

Cheap and Best

Efficiency > 95% at high voltage (∼10kV)

Good spatial (∼3 cm) and timeresolution (∼ 1ns)

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Atmospheric Neutrinos

ICAL is sensitive to atmospheric muon neutrinos (νµ,ν̄µ)

Cosmic ray interactions with theearth atmosphere producesPions.

π+ → µ+νµ µ+ → e+νeν̄µ

π− → µ−ν̄µ µ− → e−ν̄eνµ

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Neutrino Interactions with ICAL detector

Neutrino Interacts weakly via Charge Current(CC) andNeutral Current (NC) process

Atmospheric muon neutrino interact with the ICALdetector and produce associative lepton and hadron shower

For muon neutrino, the energy of neutrino (Eν) will be thesum of muon energy (Eµ) and hadron energy (Ehadron)

To reconstruct the energy and direction of neutrino, energyand direction of muons and hadrons need to bereconstructed precisely

Muon can be identified and reconstructed easily with theirclear tracks and bending inside the detector.

The energy of hadrons can be calibrated as a function ofshower hits.

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Hadron Energy Resolution

M. M. Devi, Daljeet Kaur, Lakshmi S. Mohan et al, Journal of Instrumentation, 2013 JINST 8

P1100

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Muon Energy and Direction Resolutions

Tarak Thakore et.al, 2013 J. High Energy Phys. JHEP05(2013)058

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Analysis Performed

Precise measurement of atmospheric ν oscillationparameters (|∆m2

32|, sin2 θ23) is one of the major goal of

INO-ICAL detector.

For INO-ICAL sensitivity for these parameters, we haveperformed a Monte Carlo based neutrino event simulation.

We have performed the analysis using Neutrino energy(Eν = Eµ + Ehadron) and Muon angle (cosθµ) observables.

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Inputs for Analysis

1000 years unoscillated data generated from NUANCEgenerator is used as input which is then scaled for 10 yearsexposure of running ICAL detector.

For the analysis both νµ → νµ and νe → νµ channels areconsidered.

Only Charged-current (CC) events are considered for theanalysis.

To introduce the oscillation effect, Re-weighting algorithmbased on Monte Carlo acceptance/rejection method hasbeen used.

Energy and angular resolutions, Reconstruction and Chargeid efficiencies are used as generated by INO Collaboration.

Energy Binning : 0.8-10.8 GeV with 10 equal bins

cos θ Binning : -1 to 1 with 20 equal bins

Random number smearing is applied both for expected andobserved events.

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Re-weighting Algorithm

For νµ → νµ channel:

1 For an unoscillated νµ event of energy E and zenith angleθz, probabilities Pνµνe , Pνµντ and Pνµνµ are calculated.

2 A uniform random number (r), between 0 and 1 isassociated with every interaction in NUANCE datawithout oscillations.

3 If r < Pνµνe , the event is considered as a νe event.If Pνµνe ≤ r ≤ (Pνµνe + Pνµνµ), the event is considered as aνµ event.

For νe → νµ channel:

1 Atmospheric νe may also change flavor to νµ due tooscillations.

2 We calculate the transition probability (Pνeνµ) for eachevent.

3 a random number (r′), uniformly distributed in [0,1] isassociated with every event.

4 If r′ < (Pνeνµ), we considered the event as a νµ event.Otherwise, we consider it as a νe event.15 / 30 UNICOS-2014

Oscillation parameters

Oscillation parameters True values Marginalisation range

sin2(2θ12) 0.86 Fixedsin2 θ23 0.5 0.4-0.6 (3σ range)sin2 θ13 0.03 0.01 (3σ range )

∆m221(eV

2) 7.6 × 10−5 Fixed∆m2

32(eV2) 2.4 × 10−3 (2.1-2.6) × 10−3 (3σ range)

δCP 0.0 Fixed

Table: Oscillation parameters used for analysis.

Marginalisation over the sin2 θ23 and ∆m232(eV

2) has been donefor the 1D χ2 plots only.

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Theoretical probabilities for neutrinos at L=9700Km.

Energy (GeV)1 2 3 4 5 6 7 8

µµ

P

0

0.2

0.4

0.6

0.8

1 For Neutrinos, L~9700Km

Pmu->mu in Vacuum

Pmu->mu in NH

Pmu->mu in IH

Energy(GeV)1 2 3 4 5 6 7 8

µµ

P

0

0.2

0.4

0.6

0.8

1 For antiNeitrinos, L~9700Km

Pmu->mu in Vacuum

Pmu->mu in NH

Pmu->mu in IH

Figure: Oscillation probabilities P (νµ → νµ) (left) and P (ν̄µ → ν̄µ)(right)in vacuum (Blue), matter for normal hierarchy (Green) andinverted hierarchy (Red)(L∼ 9700 Km.)

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µθCos-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1

Eve

nts

-µ

40

60

80

100

120

140

160

θcos -1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1

Eve

nts

0

20

40

60

80

100

120

140Oscillated

Osc+Eff+Reso

Event comparison for energy bin 1.8-2.8 GeV

Figure: The µ− events for the muon energy range 1.8 - 2.8 GeV inthe absence (Red) and in the presence (Blue) of oscillations (left) andin presence of INO resolutions and efficiencies (Green), for 10 yearsof exposure of ICAL detector.

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χ2 Analysis

Poissonian χ2 (using method of “Pull”)† is defined as:

χ2(νµ) =∑

i,j

(

2(N thi,j(νµ)−Nex

i,j (νµ)) + 2Nexi,j (νµ)(ln

Nexi,j (νµ)

N thi,j(νµ)

)

)

+∑

k

ζ2k

(3)

N thi,j(νµ) = N th′

ij (νµ)

(

1 +∑

k

πkij

)

(4)

Nexij ≡ Observed number of the νµ events in (i = Eν , j = cos θµ) bin

generated using true values of the oscillation parameters.N th′

ij ≡ Theoretically predicted events generated by varying oscillationparameters (without systematic effects)N th

ij ≡ Shifted events spectrum due to different systematicuncertainties.

Above χ2 is minimised as a function of pull variable ζ and theoscillation parameters (∆m2

32, sin2 θ23).

† Atmospheric neutrino oscillations and new physics, Maltoni et.al, arXiv:hep-ph/0404085v1

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We have calculated the χ2(νµ) and χ2(ν̄µ) separately.

Final χ2 is defined as:

χ2ino = χ2(νµ) + χ2(ν̄µ) (5)

Prior on θ13:

χ2 = χ2ino +

(

sin2 θ13(true)− sin2 θ13σsin2 θ13

)2

(6)

For the analysis σsin2 θ13 is taken as 10% of the true value ofsin2 θ13

Finally, we obtain the contour plots assuming∆χ2 = χ2 +m,where values of m are taken as 2.30, 4.61 and 9.21corresponds to 68%, 90% and 99% confidence levels

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Systematic uncertainties

Systematic uncertainties considered the analysis are:1 20% overall flux normalisation uncertainty2 10% cross-section uncertainty3 5% overall statistical uncertainty4 5% uncertainty on the zenith angle dependence of the flux. This

error is calculated by taking 5 % of the mean value of each cos θµbin

5 5% an energy dependent tilt error.

)23θ( 2sin0.4 0.45 0.5 0.55 0.6

)2(e

Vef

f2

m∆

2.2

2.25

2.3

2.35

2.4

2.45

2.5

2.55-310×

Effect of systematics (90% CL)

)23θ( 2sin0.4 0.45 0.5 0.55 0.6

)2(e

Vef

f2

m∆

2.2

2.25

2.3

2.35

2.4

2.45

2.5

2.55-310×

without sysone systwo systhree sysfour sysfive sys

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1D Sensitivity Plots

)2|(eVeff2 m∆|

2 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.9

-310×

2χ

∆

0

2

4

6

8

1012

14

16

18

20

| sensitivityeff2 m∆| With systematics

Without systematics

)23θ(2sin0.2 0.3 0.4 0.5 0.6 0.7

2χ

∆

0

2

4

6

8

1012

14

16

18

20

sensitivity23θ

)23θ(2sin0.2 0.3 0.4 0.5 0.6 0.7

2χ

∆

0

2

4

6

8

1012

14

16

18

20

With systematics

Without systematics

Figure: 1D plot for the sensitivity of |∆m2

eff | at constant sin2 θ23

=0.5 (left) and for the sensitivity of sin2 θ23 as a function of ∆χ2 atconstant ∆m2

31=0.0024eV 2 (right)

This results shows that program is sensitive for θ23 as well as for thesensitivity of ∆m2

31

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Results (Eν, cos θµ) 2D Analysis

)23θ(2sin

0.35 0.4 0.45 0.5 0.55 0.6 0.65

)2

| (e

Ve

ff2

m∆|

2

2.1

2.2

2.3

2.4

2.5

2.6

2.7-310×

)23θ(2sin

0.35 0.4 0.45 0.5 0.55 0.6 0.65

)2

| (e

Ve

ff2

m∆|

2

2.1

2.2

2.3

2.4

2.5

2.6

2.7-310×

NuE(mu+had), Mu_theta, Without systematic errors

68%90%99%

)23θ(2sin

0.35 0.4 0.45 0.5 0.55 0.6 0.65

)2

| (e

Ve

ff2

m∆|

2

2.1

2.2

2.3

2.4

2.5

2.6

2.7-310×

)23θ(2sin

0.35 0.4 0.45 0.5 0.55 0.6 0.65

)2

| (e

Ve

ff2

m∆|

2

2.1

2.2

2.3

2.4

2.5

2.6

2.7-310×

NuE(mu+had), Mu_theta, With systematic errors

68%90%99%

Figure: Contour plots without systematic errors (Left) and withsystematic errors (Right) for 10 years exposure of ICAL

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Precision Measurement

The precision on the oscillation parameters can be defined as:

Precision =Pmax − Pmin

Pmax + Pmin, (7)

where Pmax and Pmin are the maximum and minimum values ofthe concerned oscillation parameters at the given confidencelevel.

Precision without systematic uncertainties

Osc.Parameters 1σ 2σ 3σsin2 θ23 12.7 % 17.40 % 21.08 %|∆m2

eff | 3.29 % 5.11 % 7.63 %

Precision with systematic uncertainties

Osc.Parameters 1σ 2σ 3σsin2 θ23 16.41 % 21.35 % 28.22 %|∆m2

eff | 3.75 % 6.09 % 9.036 %

Table: ICAL precision measurement of oscillation parameters atdifferent confidence levels for 10 year of exposure.

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Conclusions

Neutrino Oscillation gives a first hint for the physicsbeyond Standard Model.

INO-ICAL experiment has been proposed to study theproperties of mysterious neutrinos.

A simulation study has been performed to find theprecision measurement of atmospheric neutrino oscillationparameters using realistics ICAL resolutions.

Final results with Neutrino energy and Muon directionobservables have been shown.

We find that the INO-ICAL can measure sin2 θ23 and|∆m2

32| with 28.22% and 9.036% uncertainties at 3σconfidence level in 10 years of running.

Future Work

To study the mass heirarchy and Octant sensitivity forINO-ICAL detector

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Thank you

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Back Up

Thakore T. et al. 2013 J. High Energy Phys.JHEP05(2013)058.

Atmospheric neutrino oscillations and new physics, Maltoniet.al, arXiv:hep-ph/0404085v1.

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Tilt Error The event spectrum is calculated with the predictedneutrino flux and then with the flux spectrum shifted accordingto:

φδ(E) = φ0(E)(E

E0

)δ = φ0(E)

(

1 + δlnE

E0

)

(8)

where E0 = 2GeV and δ is the 1σ systematic error which wehave taken as 5%.The difference between the predicted event spectrum andshifted event spectrum is then included in to statistical analysis

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