GLoBES

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GLoBES and its application to neutrino physics - Epiphany 2014 ...

GLoBES

and its application to neutrino physics

Mark Rolinec on behalf of the GLoBES Team

Technische Universität München

Cracow Epiphany Conference on Neutrinos and Dark Matter

5-8 January 2006

GLoBES - M. Rolinec - Cracow Epiphany Conference on Neutrinos and Dark Matter - 5-8 January 2006 – p.1/28


Outline

Part I - GLoBES - General Features

• Features

• Basic Structure

Part II - Experiment description in AEDL

• Features

• AEDL-File Example

Part III - Basics and Applications

• Simulation of event rates

• Calculation of χ 2

• χ 2 -Projections

• Examples of a variety of applications

GLoBES - M. Rolinec - Cracow Epiphany Conference on Neutrinos and Dark Matter - 5-8 January 2006 – p.2/28


Part I

GLoBES - General Features

GLoBES - M. Rolinec - Cracow Epiphany Conference on Neutrinos and Dark Matter - 5-8 January 2006 – p.3/28


GLoBES - Purpose

The General Long Baseline Experiment Simulator

GLoBES is a software package designed for

• Simulation

• Analysis

• Comparison

of neutrino oscillation long baseline experiments

GLoBES - M. Rolinec - Cracow Epiphany Conference on Neutrinos and Dark Matter - 5-8 January 2006 – p.4/28


GLoBES - Availability

GLoBES can be downloaded as tar-ball together with a detailed

manual from

http://www.ph.tum.de/ ∼ globes/

since August 2004.

The software is developed, documented, maintained and

supported by the GLoBES-Team:

• Patrick Huber (UW)

• Joachim Kopp (TUM)

• Manfred Lindner (TUM)

• MR (TUM)

• Walter Winter (IAS)

GLoBES - M. Rolinec - Cracow Epiphany Conference on Neutrinos and Dark Matter - 5-8 January 2006 – p.5/28


GLoBES - Features

• Accurate treatment of systematical errors

• Arbitrary matter density profile & uncertainties

• Arbitrary energy resolution function

• Single and multiple experiment simulation

• Output of oscillation probabilities

• Output of event rates

• Simple χ 2 calculation

• Inclusion of external input

• Projection of χ 2 (minimization)

GLoBES - M. Rolinec - Cracow Epiphany Conference on Neutrinos and Dark Matter - 5-8 January 2006 – p.6/28


GLoBES - Experiments

GLoBES has been used for simulating:

• MINOS, ICARUS and OPERA

• Reactor experiments, Double-CHOOZ, R2D2

• T2K

• NOνA

• SPL CERN-Fréjus

• JHF-HK (T2K upgrade)

• Neutrino factories

• β-beams

• BNL neutrino beam

GLoBES - M. Rolinec - Cracow Epiphany Conference on Neutrinos and Dark Matter - 5-8 January 2006 – p.7/28


GLoBES - Basic Structure

GLoBES

AEDL

Abstract Experiment

Definition Language

Defines Experiments

and modifies them

AEDL−

file(s)

GLoBES User Interface

C−library which loads

AEDL−file(s) and

provides functions to

simulate experiment(s)

Application software to compute

high−level sensitivities, precision etc.

Figure taken from P. Huber, M. Lindner and W. Winter, Comput. Phys. Commun. 167 (2005) 195

GLoBES - M. Rolinec - Cracow Epiphany Conference on Neutrinos and Dark Matter - 5-8 January 2006 – p.8/28


Part II

Experiment Description in

AEDL

GLoBES - M. Rolinec - Cracow Epiphany Conference on Neutrinos and Dark Matter - 5-8 January 2006 – p.9/28


AEDL - Features

The experiment is described within one file: Name.glb

Energy−

Resolution

function

Cross

Section

Initial / final

flavor, polarity

Signal

Background

Channel 1

Channel 2

. . .

. . .

Flux

Channel

Energy

dependent

efficiencies

Rule

Signal + Backgrounds

with systematics

Event rates

∆χ 2

Figures taken from P. Huber, M. Lindner and W. Winter, Comput. Phys. Commun. 167 (2005) 195

• Experiments can contain an arbitrary number of rules

GLoBES can handle any number of experiments

GLoBES - M. Rolinec - Cracow Epiphany Conference on Neutrinos and Dark Matter - 5-8 January 2006 – p.10/28


AEDL-File - Example

Flux and cross sections can be loaded from external files:

flux(#user flux)<

cross(#CC)<

@flux file = "user flux file.dat" @cross file = "XCC.dat"

@time = 5.0 /* years */

>

@power = 4.0 /* MW */

cross(#NC)<

@norm = 1.0

@cross file = "XNC.dat"

>

>

For the case of a neutrino factory GLoBES provides a builtin flux:

flux(#nf flux mu plus)<

@builtin = 1

@parent energy = 50.0 /* GeV */

@stored muons = 5.33e+20

@time = 8.0 /* years */

>

GLoBES - M. Rolinec - Cracow Epiphany Conference on Neutrinos and Dark Matter - 5-8 January 2006 – p.11/28


AEDL-File - Example continued

Basic characteristics of Experiment:

$target mass = 50.0 /* kt */

Mass of Detector (fiducial volume)

$profiletype = 1

$baseline = 3000.0 /* km */

$density = 2.7 /* g cm ˆ -3 */

Baseline and

Density Profile

(average density, PREM or manually defined)

$bins = 20

$emin = 4.0 /* GeV */

$emax = 50.0 /* GeV */

Energy window:

Reconstructed neutrino energy

Analysis level (after energy smearing)

$sampling points = 20

$sampling min = 4.0

$sampling max = 50.0

Energy window:

True neutrino energy

Integral Evaluation (before energy smearing)

GLoBES - M. Rolinec - Cracow Epiphany Conference on Neutrinos and Dark Matter - 5-8 January 2006 – p.12/28


AEDL-File - Example continued

Descripion of energy resolution:

energy(#ERES)<

@type = 1

@sigma e = (alpha,beta,gamma)

>

energy(#manual smearing matrix)<

@energy =

{0,2,0.863,0.182,0.00267}:

{0,3,0.151,0.697,0.151,0.00101}:

...

{16,19,0.00936,0.278,0.483,0.136};

>

Gaussian energy resolution function

with width σ:

σ(E) = α × E + β × √ E + γ

Manual energy smearing:

energy smearing matrix M ij

• number of rows:

$bins

• number of columns:

$sampling points

GLoBES - M. Rolinec - Cracow Epiphany Conference on Neutrinos and Dark Matter - 5-8 January 2006 – p.13/28


AEDL-File - Example

Defining different channels:

channel(#nu mu dissappearance)<

@channel = #user flux : +: m: m: #CC: #ERES

@pre smearing efficiencies = {0.333,0.666,0.999,1.,1., ... ,1.,1.}

>

channel(#nu mu NC bckg)<

@channel = #user flux : +: NOSC m: NOSC m: #NC:

#manual smearing matrix

>

Additional features:

• @post smearing efficiencies

• @pre smearing background

• @post smearing background

GLoBES - M. Rolinec - Cracow Epiphany Conference on Neutrinos and Dark Matter - 5-8 January 2006 – p.14/28


AEDL-File - Example continued

Defining the Rules:

>rule(#Nu Mu DIS)<

@signal = 0.86@#nu mu dissappearance

@signalerror = 0.04 : 0.0001

@background = 0.11@#nu mu NC bckg : 0.11@#nu e NC bckg : 0.05@#BCKG 3

@backgrounderror = 0.05 : 0.0001

@errordim sys on = 2

@errordim sys off = 0

@energy window = 4.0 : 50.0

>

GLoBES - M. Rolinec - Cracow Epiphany Conference on Neutrinos and Dark Matter - 5-8 January 2006 – p.15/28


Part III

GLoBES - Basics and Applications

GLoBES - M. Rolinec - Cracow Epiphany Conference on Neutrinos and Dark Matter - 5-8 January 2006 – p.16/28


GLoBES - Basics

Alays to be done:

glbInit(argv[0]);

Initialize the GLoBES Library

glbClearExperimentList();

Delete earlier loaded AEDL-Files

glbDefineAEDLVariable("Variable",

double value);

Define Variables within the AEDL-File

(has to be set in Name.glb)

glbInitExperiment("Name.glb",

&glb experiment list[0],

&glb num of exps);

Load the experiment described in

Name.glb to the experiment list

(arbitrary number possible)

GLoBES - M. Rolinec - Cracow Epiphany Conference on Neutrinos and Dark Matter - 5-8 January 2006 – p.17/28


GLoBES - Reference Rates

Set the simulated "Data" - Event Rates:

glb params true values = glbAllocParams();

Initialize a parameter vector

glbDefineParams(true values,th12,th13,

th23,delta,sdm,ldm);

Assign parameter values for the

parameter vector true values

(θ 12 , θ 13 , θ 23 , δ, ∆m 2 21 ,∆m2 31 )

glbSetOscillationParameters(true values);

Set true values to be the "True Values"

glbSetRates();

...

glbFreeParams(true values);

Let GLoBES calculate the

reference event rate vector

Free the parameter vector

true values at the end

GLoBES - M. Rolinec - Cracow Epiphany Conference on Neutrinos and Dark Matter - 5-8 January 2006 – p.18/28


GLoBES - χ 2 Calculation

Simple χ 2 including systematics

glb params fit values = glbAllocParams();

Initialize another parameter vector

glbDefineParams(fit values,th12’,th13’,

th23’,delta’,sdm’,ldm’);

glbSwitchSystematics(GLB ALL,

GLB ALL,GLB ON);

Assign parameter values for the

parameter vector fit values

(θ 12 ‘, θ 13 ‘, θ 23 ‘, δ‘,∆m 2 21 ‘,∆m2 31 ‘)

Switch on systematical errors

double chi =

glbChiSys(fit values,GLB ALL,GLB ALL);

Calculate the χ 2 at the parameter

vector fit values

glbFreeParams(fit values);

Free the parameter vector

fit values at the end

GLoBES - M. Rolinec - Cracow Epiphany Conference on Neutrinos and Dark Matter - 5-8 January 2006 – p.19/28


GLoBES - Projection of χ 2

Projection of two-parameter correlations (Here δ - sin 2 2θ 13 )

10 2

Sectionother osc. parameters fixed

3Σ1 d.o.f.

2Σ1 d.o.f.

1Σ1 d.o.f.

20

Projection onto∆ CP axisonly sin 2 2Θ 13

15

sin 2 2Θ13

10 3

Χ 2

10


5


10 4

0 50 100 150 200

∆ CP Degrees

glbChiSys

0


0 50 100 150 200

∆ CP Degrees

glbChiDelta

Figures taken from P. Huber, M. Lindner and W. Winter, Comput. Phys. Commun. 167 (2005) 195

GLoBES - M. Rolinec - Cracow Epiphany Conference on Neutrinos and Dark Matter - 5-8 January 2006 – p.20/28


GLoBES - Projection of χ 2

Including parameter correlations by projection of χ 2

glbDefineParams(in error,d th12,d th13,

d th23,d delta,d sdm,d ldm);

Define the errors on oscillation

parameters (external input)

glbSetDensityParams(in error,

d rho,GLB ALL);

Give the error on the

matter density ρ

glbSetStartingValues(start);

Set center values for defined errors

glbSetInputErrors(in error);

Set all errors as defined before

double chiProj = glbChiTheta(fit values,

minimum,GLB ALL);

Calculate a projection with

respect to sin 2 2θ 13

GLoBES - M. Rolinec - Cracow Epiphany Conference on Neutrinos and Dark Matter - 5-8 January 2006 – p.21/28


GLoBES - Applications I

Atmospheric oscillation parameters ∆m 2 31 and sin2 θ 23

sin 2 θ 23

-precision

0.4

Relative error at 2σ

0.2

0

-0.2

MINOS

NOνA

T2K

CNGS

SK+K2K exluded at 3σ

SK+K2K

T2K

∆m 2 31 -precision 1 2 3 4

CNGS

MINOS

NOνA

SK+K2K current data

-0.4

1 2 3 4

True value of ∆m 2 31 [10-3 eV 2 ]

1 2 3 4

True value of ∆m 2 31 [10-3 eV 2 ]

Figure taken from T. Schwetz, P. Huber, M. Lindner, MR, W. Winter, hep-ph/0412133

GLoBES - M. Rolinec - Cracow Epiphany Conference on Neutrinos and Dark Matter - 5-8 January 2006 – p.23/28


GLoBES - Applications II

Deviation from maximal mixing sin 2 θ 23 = 0.5

5

Conventional Beams

5

JPARCSK

5

NuMI offaxis

10 3 eV 2

True value ofm 31

2

4

3

2

1

10 3 eV 2

True value ofm 31

2

4

3

2

1

10 3 eV 2

True value ofm 31

2

4

3

2

1

0.3 0.4 0.5 0.6 0.7

True value of sin 2 Θ 23

0.3 0.4 0.5 0.6 0.7

True value of sin 2 Θ 23

0.3 0.4 0.5 0.6 0.7

True value of sin 2 Θ 23

5

After ten years

5

JPARCHK

5

NuFactII

10 3 eV 2

True value ofm 31

2

4

3

2

1

10 3 eV 2

True value ofm 31

2

4

3

2

1

10 3 eV 2

True value ofm 31

2

4

3

2

1

0.3 0.4 0.5 0.6 0.7

True value of sin 2 Θ 23

0.3 0.4 0.5 0.6 0.7

True value of sin 2 Θ 23

0.3 0.4 0.5 0.6 0.7

True value of sin 2 Θ 23

Figure taken from S. Antusch, P. Huber, J. Kersten, T. Schwetz, W. Winter, Phys. Rev. D70 (2004) 097302

GLoBES - M. Rolinec - Cracow Epiphany Conference on Neutrinos and Dark Matter - 5-8 January 2006 – p.24/28


GLoBES - Applications III

Sensitivity to sin 2 2θ 13 (true value sin 2 2θ 13 = 0)

150

6

5

right sign

wrong sign

Normal hierarchy

∆CPDegrees

100

50

0

50

sin 2 2Θ13eff sens.

Χ 2

4

3

2

1

0

0 0.01 0.02 0.03

sin 2 2Θ 13 sensitivity limit

6

5

right sign

wrong sign

Inverted hierarchy

final limit

Χ 2 ⩵2.71

100

150

Section, Statistics only

Section, Stat.Syst.

Projection, Bestfit

Projection, Degeneracy

Χ 2

4

3

2

1

final limit

Χ 2 ⩵2.71

0 0.005 0.01 0.015 0.02 0.025

sin 2 2Θ 13

glbChiSys

0

0 0.01 0.02 0.03

sin 2 2Θ 13 sensitivity limit

glbChiTheta

Figures taken from P. Huber, M. Lindner, MR, T. Schwetz and W. Winter, Phys. Rev. D 70 (2004) 073014

GLoBES - M. Rolinec - Cracow Epiphany Conference on Neutrinos and Dark Matter - 5-8 January 2006 – p.25/28


GLoBES - Applications IV

Change AEDL variables within calculations

sin 2 2Θ13 sensitivity limit

10 1

10 2

10 3

10 4

Setup 1Γ⩵200, WC

Systematics

Correlations

Degeneracies

sin 2 2Θ13 sensitivity limit

10 1

10 2

10 3

10 4

Setup 2Γ⩵500, TASD

Systematics

Correlations

Degeneracies

sin 2 2Θ13 sensitivity limit

10 1

10 2

10 3

10 4

Setup 3Γ⩵1000, TASD

Systematics

Correlations

Degeneracies

10 5

0.5 1 1.5 2 2.5 3


10 5

0.5 1 1.5 2 2.5 3


10 5

0.5 1 1.5 2 2.5 3


glbDefineAEDLVariable("baseline",value);

Figure taken from P. Huber, M. Lindner, MR, W. Winter, hep-ph/0506237

GLoBES - M. Rolinec - Cracow Epiphany Conference on Neutrinos and Dark Matter - 5-8 January 2006 – p.26/28


GLoBES - Applications V

Assume large true value sin 2 2θ 13 = 0.1

∆CPDegrees

∆CPDegrees

150

100

50

0

50

100

150

150

100

50

0

50

100

150

JPARCSK: Section

0 0.05 0.1 0.15 0.2

sin 2 2Θ 13

JPARCSK: Projection

0 0.05 0.1 0.15 0.2

sin 2 2Θ 13

0

0

∆CPDegrees

∆CPDegrees

150

100

50

0

50

100

150

150

100

50

0

50

100

150

NuMI: Section

0

0 0.05 0.1 0.15 0.2

sin 2 2Θ 13

NuMI: Projection

0

0 0.05 0.1 0.15 0.2

sin 2 2Θ 13

∆CPDegrees

∆CPDegrees

150

100

50

0

50

100

150

150

100

50

0

50

100

150

ReactorII: Section

0 0.05 0.1 0.15 0.2

sin 2 2Θ 13

ReactorII: Projection

0 0.05 0.1 0.15 0.2

sin 2 2Θ 13

Figure taken from P.Huber, M.Lindner, MR, T.Schwetz, W.Winter, Phys. Rev. D 70 (2004) 073014

∆CPDegrees

∆CPDegrees

150

100

50

0

50

100

150

150

100

50

0

50

100

150

Combined: Section

3.1

0 0.05 0.1 0.15 0.2

sin 2 2Θ 13

Combined: Projection

3.1

0 0.05 0.1 0.15 0.2

sin 2 2Θ 13

GLoBES - M. Rolinec - Cracow Epiphany Conference on Neutrinos and Dark Matter - 5-8 January 2006 – p.27/28


Conclusions

GLoBES is a

• well tested

• powerful

• flexible

software package for the

• Simulation

• Analysis

• Comparison

of neutrino oscillation

experiments

So remember:

www.ph.tum.de/ ∼ globes/

GLoBES - M. Rolinec - Cracow Epiphany Conference on Neutrinos and Dark Matter - 5-8 January 2006 – p.28/28

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