Patrick Huber1, Joachim Kopp2, Manfred Lindner3, Walter Winter4

GLoBESGeneral Long Baseline Experiment Simulator

1 Department of Physics, Virginia Tech, Blacksburg, VA 24062, USA 2 Theoretical Physics Department, Fermilab, PO Box 500, Batavia, IL 60510, USA3 Max–Planck–Institut fur Kernphysik, Postfach 10 39 80, 69029 Heidelberg, Germany 4 Institut fur theoretische Physik und Astrophysik, Universitat Wurzburg, 97074 Wurzburg, Germany

GLoBES is a modular open-source software library for simulating short- and long-baseline neutrino oscillation experiments,and for studying the oscillation phenomenology.

What GLoBES can do:

• Compute 3-flavour oscillation probabilities in matter

• Simulate event spectra for reactor experiments, super-beams, beta beams, neutrino factories, . . .

• Perform sophisticated χ2 analyses

•Adapt to the user’s needs

What GLoBES cannot (yet) do:

•Replace a detector Monte Carlo simulation

• Simulate solar and atmospheric neutrinos

In GLoBES, experiments are described using AEDL, the AbstractExperiment Definition Language. AEDL files specify, for example

• Source types and spectra

•Matter density profiles

• Cross sections

•Detector properties: Efficiencies, resolutions, backgrounds, . . .

• Systematical uncertainties

A channel corresponds to oscillations from one flavour into another:

CrossSection

Flux

Energy−

function

Initial / finalflavor, polarity

Energy

Channel

Event rates

efficienciesdependent

Resolution

A rule consists of the combination of all signal and background chan-nels in an experimental data sample (e.g. νe appearance from νµ → νeoscillations in a superbeam, with contamination from νe→ νe).

Signal

Background

Channel 1

Channel 2

. . .

. . .

RuleSignal + Backgrounds

with systematics

∆χ2

Rule 2Rule 1 Rule 3

Experiment

Σ ∆χ2

. . .

Experiments can contain sev-eral rules, and several exper-iments can be handled si-multaneously.

Experiment definition in GLoBES

The oscillation engine is the heart of the soft-ware. Its main features are

• Full three-flavour treatment

•Arbitrary (non-adiabatic) matter profilesThe PREM (Preliminary Reference EarthModel) matter profile is hard-coded inGLoBES. The user can choose approxima-tions to this profile (e.g. constant density,mantle-core-mantle profile, etc.) or definecompletely new profiles.

•High numerical efficiencyGLoBES uses specifically designed numeri-cal algorithms to ensure an excellent perfor-mance, which is, for the specific problem ofneutrino oscillations, far superior to that of“black box” libraries.

• ExtensibilityThe user has the possibility to modify or com-pletely replace the GLoBES oscillation en-gine, e.g. to include sterile neutrinos, non-standard interactions, and other kinds of“new physics”.

Oscillations

GLoBES uses the χ2 method to extract physical information from thesimulated event spectra. Main features are

• Cuts and projections of the multi-dimensional χ2 manifold (“marginal-ization”)

• Inclusion of systematical uncertainties (fully customizable)

• Inclusion of correlations and degeneracies

• Inclusion of external priors (fully customizable)

• Supports setups with Multiple sources and multiple detectors

• Excellent numerical efficiency

The builtin χ2 functions of GLoBES have the Poissonian form

χ2(~λ,~a) =2∑exp′s

∑rules

∑bins

[N th(~λ,~a)−Nobs + Nobs log

Nobs

N th(~λ,~a)

]

+ χ2prior(

~λ) + χ2pull(~a),

where Nobs and N th are the “observed” and theoretically predicted eventrates, respectively. The vector ~λ contains the oscillation parameters, and~a are the systematical biases. χ2

prior(~λ) and χ2

pull(~a) implement external

input on these parameters. Note that GLoBES allows also for arbitrary,user-defined χ2 functions.

Example: θ13–δCP correlation and intrinsic degeneracy in a ν-fact.

10-4 10-3 10-2

sin2 2Θ13

0

50

100

150

200

∆C

P@D

egre

esD

Correlation between sin2 2Θ13 and ∆CP

1Σ2Σ3Σ

GLoBES 2007

10-4 10-3 10-2

sin2 2Θ13

0

5

10

15

20

Χ2

Projection onto sin2 2Θ13-axis

1Σ

2Σ

3Σ

GLoBES 2007

χ2 analysis

The AEDL file: A simple neutrino factory

$version="3.0.0"

nuflux(#mu plus)<

@builtin = 1

@parent energy = 50

@stored muons = 10.66e+20

@time = 4

>

$target mass = 50

$bins = 20

$emin = 4

$emax = 50

$profiletype = 1

$baseline = 3000

energy(#ERES)< /*E res.*/

@type = 1

@sigma e = {0.15, 0, 0}>

cross(#CC)< /* Cross sections */

@cross file = "XCC.dat"

>

channel(#nu mu app)<

@channel = #mu plus:+:e:m:#CC:#ERES

>

channel(#nu mu bar disapp)<

@channel = #mu plus:-:m:m:#CC:#ERES

>

rule(#Nu Mu Appearance)<

@signal = 0.45@#nu mu app

@signalerror = 0.025 : 0.0001

@background = 5e-6@#nu mu bar disapp

@backgrounderror = 0.2 : 0.0001

@sys on function = "chiSpectrumTilt"

@sys off function = "chiNoSysSpectrum"

>

Application code snippet: Project χ2 onto θ13 axis

/* Define priors for θ12 and ∆m221 */

glbDefineParams(input errors, theta12*0.1, 0, 0, 0, sdm*0.1, 0);

glbSetDensityParams(input errors, 0.05, GLB ALL);

glbSetCentralValues(true values);

glbSetInputErrors(input errors);

/* Loop over log(sin2 2θ13) */

double theta13, x;

for (x=-4; x < -2.0+0.001; x+=2.0/50)

{theta13 = asin(sqrt(pow(10,x)))/2;

/* Choose starting value for δCP marginalization */

glbSetOscParams(test values, 200.0/2*(x+4)*M PI/180, GLB DELTA CP);

/* Compute χ2 and marginalize over all parameters except θ13 */

chi2 = glbChiTheta13(test values, NULL, GLB ALL);

}

GLoBES example

GLoBES website:

www.mpi-hd.mpg.de/∼globes/• Software download

•Many predefined AEDL files

•Extensive documentation

•Examples and tutorials

GLoBES publications:

CPC 167, 195 (2005), hep-ph/0407333CPC 177, 432 (2007), hep-ph/0701187

Contact the authors:

globes@mpi-hd.mpg.de

Fermilab

Evolution of sin2 2θ13 disc. reach

2005 2010 2015 2020 2025 2030Year

10-5

10-4

10-3

10-2

10-1

100

sin2

2Θ13

disc

over

yre

achH3ΣL

CHOOZ+Solar excluded

Branching pointConv. beams

Superbeams+Reactor exps

Superbeam upgrades

Ν-factories

MINOSCNGSD-CHOOZT2KNOîAReactor-IINOîA+FPD2ndGenPDExpNuFact

δCP sensitivity of different exp’s

10−5 10−4 10−3 10−2 10−1

True value of sin22θ13

0

0.2

0.4

0.6

0.8

1

CP

SPLT2HKWBBNFBB

GLoBES 2006

Frac

tion

ofδ

Impact of systematical errorsin a reactor experiment

101 102 103 104 105

Integrated Luminosity in Far Detector @GW×t×yearsD

0.002

0.005

0.01

0.02

0.05

0.1

sin2

2Θ13

sens

itivi

tyat

90%

C.L

.

Statistical Limit

5ye

ars

DC

10ye

ars

DC

5ye

ars

DC+

5ye

ars

TC

Σcorr = 2.8%Σuncorr = 0.6%Σcal = 0.5%

Σshape = 2.0%

Σbin-to-bin = 0.5%

Σbin-to-bin = 2.0%

GLoBES 2006

Sensitivity of ν-fact to standardand non-standard physics

10-5 10-4 10-3 10-2 10-1

10-5 10-4 10-3 10-2 10-1

sin2 2Θ13

H5ΣL

NH for ∆CPtrue = 3Π�2

H5ΣL

CPV for ∆CPtrue = 3Π�2

H5ΣL

sin2 2Θ13

H5ΣL

NH for ∆CPtrue = 3Π�2

H5ΣL

CPV for ∆CPtrue = 3Π�2

H5ΣL

ÈΕeem È H3ΣL

ÈΕeΤm È H3ΣL

ÈΕΜΤm È H3ΣL

ÈΕΤΤm È H3ΣL

ÈΕΑΒmÈ

sin2 2Θ13

GLoBES 2008

better

5 GeV

25 GeV

50 GeV

Improvement bySilver* � 4000 km

sin2

2Θ13

reac

hno

NSI

sin2

2Θ13

reac

hfi

tinc

ludi

ngΕ eΤm

ÈΕΑΒ

mÈre

ach

Recent GLoBES results