GLoBES

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 


Part I 

GLoBES - General Features 


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 - 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 - 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 - 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 - 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 


Part II 

Experiment Description in 

AEDL 


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 


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 */ 

> 


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) 



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 


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 



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 

> 


Part III 

GLoBES - Basics and Applications 


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 - 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 - 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 - 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 

3Σ 

5 

2Σ 

10 4 

0 50 100 150 200 

∆ CP Degrees 

glbChiSys 

0 

1Σ 

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 - 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 - 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 - 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 


2 

4 

3 

2 

1 

10 3 eV 2 


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 


0.3 0.4 0.5 0.6 0.7 


5 

After ten years 

5 

JPARCHK 

5 

NuFactII 

10 3 eV 2 


2 

4 

3 

2 

1 

10 3 eV 2 


2 

4 

3 

2 

1 

10 3 eV 2 


2 

4 

3 

2 

1 

0.3 0.4 0.5 0.6 0.7 


0.3 0.4 0.5 0.6 0.7 


0.3 0.4 0.5 0.6 0.7 


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


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 - 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 


10 1 

10 2 

10 3 

10 4 

Setup 2Γ⩵500, TASD 

Systematics 

Correlations 

Degeneracies 


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 

LΓ 

10 5 

0.5 1 1.5 2 2.5 3 

LΓ 

10 5 

0.5 1 1.5 2 2.5 3 

LΓ 

glbDefineAEDLVariable("baseline",value); 

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


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 


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

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