GLoBES: Neutrino Experiment Simulation

• GLoBES Simulations is a comprehensive framework for modeling neutrino oscillation experiments, integrating detailed flux, detector, and statistical analyses.
• It utilizes AEDL-based experiment configurations to precisely control flux propagation, cross sections, energy resolution, and systematic uncertainties.
• Extensions like FaSE-GLoBES and GLoBES-EFT enable exploration of new physics scenarios, including flavour symmetry, sterile neutrinos, and effective field theory models.

GLoBES (General Long Baseline Experiment Simulator) and its extensions such as FaSE-GLoBES, GLoBESfit, and GLoBES-EFT, constitute the leading computational framework for simulating event rates, constructing likelihoods, and performing parameter inference in neutrino oscillation experiments. These tools facilitate detailed modeling of experimental setups, detector systematics, new physics scenarios, and the translation of theoretical models—often from flavour symmetry or effective field theory contexts—into predictions for observable quantities. GLoBES and its wrappers are foundational in the quantitative assessment of future and ongoing experiments in neutrino physics.

1. Core Architecture and Integration

GLoBES is a modular C library designed to handle the entire simulation pipeline for neutrino experiments, from flux propagation to detector response and statistical analysis (Tang et al., 2020). The framework supports user definitions of experiment configurations via AEDL (*.glb) files specifying flux, cross section, energy resolution, backgrounds, efficiency, runtime, fiducial mass, and systematic uncertainties. The main simulation engine computes oscillation probabilities using vacuum and matter-modified Hamiltonians, convolves these with response functions, and evaluates the expected binned event spectra.

Wrappers such as FaSE-GLoBES and GLoBES-EFT extend this architecture by implementing custom probability engines and parameter translation functions. FaSE-GLoBES, for example, allows direct insertion of flavoured mass models, mapping arbitrary parameterizations (up to six free parameters) into the standard oscillation sector ($$\theta_{12}, \theta_{13}, \theta_{23}, \delta, \Delta m_{21}^2, \Delta m_{31}^2$$) while enforcing model-specific priors and restrictions. Model translation can be analytic, mixing matrix-diagonalization, or mass-matrix diagonalization (Tang et al., 2020).

Custom engines are registered via the GLoBES API:

glbRegisterProbabilityEngine(6, FASE_glb_probability_matrix, FASE_glb_set_oscillation_parameters, FASE_glb_get_oscillation_parameters, NULL);

This triggers, for each call, the user’s translation function, which converts model parameters into standard oscillation parameters before standard GLoBES evaluation.

2. Parameter Translation and Priors

Parameter translation functionalities allow the incorporation of new physics and theoretical flavor models directly into simulation workflows. FaSE-GLoBES supports the following schemes (Tang et al., 2020):

• Direct Mapping: Analytic inversion or forward mapping between model and standard parameters, e.g., $\theta_{13} = \arctan(\alpha/\beta)$.
• Mixing-Matrix Diagonalization: User-supplied PMNS matrix $U(\theta_{\text{Model}})$ is diagonalized to extract mixing angles and CP phase via relations like $\tan\theta_{12} = |U_{e2}/U_{e1}|$.
• Mass-Matrix Diagonalization: The neutrino mass matrix $M_\nu(\theta_{\text{Model}})$ is diagonalized so $$U^\dagger M_\nu M_\nu^\dagger U = \mathrm{diag}(m_1^2, m_2^2, m_3^2)$$.

Prior information is encoded with Gaussian routines:

glbRegisterPriorFunction(FASE_prior_OSC, NULL,NULL,NULL);

The prior $\chi^2$ is:

$$\chi^2_\text{prior} = \sum_i \frac{(\theta_i - \theta_i^0)^2}{\sigma_i^2}$$

where $\theta_i^0$ and $\sigma_i$ are set via arrays.

Non-Gaussian priors and region restrictions (e.g., enforcing normal ordering, positive mass parameters) are supported through user-defined callbacks.

3. Simulation Workflows, Experiment Configurations, and Systematics

Defining experiments in GLoBES entails specifying beam spectra, detector characteristics, response matrices, efficiency files, and systematics. Examples include DUNE, T2K, reactor experiments, and solar experiments (Brdar et al., 2017, Collaboration et al., 2021, Fiza et al., 10 Jul 2025, Berryman et al., 2020).

Experiments are instantiated from *.glb files, where one configures appearance/disappearance channels, loading flux, cross-section, migration (smearing), and efficiency files. Signal and background channels are defined, and systematic uncertainties (normalization, energy scale) are incorporated via pull terms.

Example configuration table:

Parameter/Class	Typical Value/Comment	Source
Energy resolution (DUNE LAr)	$15-20\%/\sqrt{E}$	(Fiza et al., 10 Jul 2025)
Signal $\nu_e$ efficiency	$$70\%\ (\sim 0.5\,\text{GeV}),\ 90\%~(2-3\,\text{GeV})$$	(Fiza et al., 10 Jul 2025)
Signal normalization error	$2\%$ ($\nu_e$, $\bar{\nu}_e$), $5\%$ ($\nu_\mu$)	(Collaboration et al., 2021)
Background norm error	$5-20\%$	(Collaboration et al., 2021)
Reactor spectrum binning	$0.06/\sqrt{E}$ (energy resolution)	(Berryman et al., 2020)

Systematic uncertainties impact both signal and background, and are handled via covariance matrices and minimization over nuisance parameters in the total $\chi^2$.

4. Statistical Analysis, $\chi^2$ Construction, and Contour Extraction

GLoBES computes the likelihood via a Poisson (or Gaussian) $\chi^2$ function over energy bins and systematics. The general form for each experiment is:

$$\chi^2_e = \min_{\{\varepsilon_i\}} \Bigg[ \sum_{b=1}^{N_{\text{bins}}} \frac{(N^{\text{pred}}_b(\{\theta\},\{\varepsilon_i\}) - N^{\text{obs}}_b)^2}{N^{\text{pred}}_b(\{\theta\},\{\varepsilon_i\})} + \sum_i \Big(\frac{\varepsilon_i}{\sigma_i}\Big)^2 \Bigg]$$

Profiles over nuisance pulls and parameter grids yield $\Delta \chi^2$, allowing extraction of exclusion regions and sensitivity contours (e.g., $1\sigma$ and $3\sigma$). Output typically includes multi-dimensional ASCII files (e.g., $(g, m_\phi, \Delta\chi^2)$ for fuzzy DM (Brdar et al., 2017)) and can be visualized using Python/ROOT.

For sterile neutrino fits using GLoBESfit, grids over $(\sin^2 2\theta_{ee}, \Delta m^2_{41})$ are produced; for each point, the engine computes spectra, rates, and corresponding likelihoods, reflecting global reactor data constraints (Berryman et al., 2020).

5. Incorporation of New Physics Scenarios

GLoBES provides native and plugin-based support for new physics models:

• Flavour Symmetry Models: FaSE-GLoBES translates general flavor model parameters (tri-direct littlest seesaw, modular $S_4$, warped flavor symmetry, TM1 sum rule) into observable mixing angles/masses, enabling exclusion and constraint studies (Tang et al., 2020).
• Sterile Neutrinos: GLoBESfit supports full $3+1$ mixing, custom probability engines, spectral and rate analyses across global reactor datasets (Berryman et al., 2020).
• Effective Field Theory: GLoBES-EFT allows simulation of SMEFT/WEFT scenarios, automatically handling Wilson coefficients, RG running, and matching. Oscillation and cross section modifications are implemented via pseudo-probabilities $\tilde{P}^{S}_{\alpha\beta}(E,L)$ and modified Hamiltonians (Kopp et al., 25 Sep 2025).
• Fuzzy Dark Matter: Custom potential terms are injected into the Hamiltonian for neutrino evolution, with time-averaging of oscillation probabilities performed numerically (Brdar et al., 2017).
• Non-Standard Interactions: Modifications to matter effect terms in the Hamiltonian are supported natively or via plugins (Fiza et al., 10 Jul 2025).

6. Performance and Extensibility

Routine grid scans (e.g., $100 \times 100$) for parameter inference are performant, with run-times $\mathcal{O}$(minutes) for typical Linux setups and no significant overhead versus bare GLoBES (Tang et al., 2020). Diagonalization relies on LAPACK, ensuring numerical stability in physically relevant domains.

Extensions to new models are straightforward: users implement the model-to-standard mapping function, enforce model restrictions, define priors, and instantiate the probability engine. Typical workflows involve (i) defining a “true” parameter point, (ii) computing rates/spectra, (iii) scanning hypothesis space, and (iv) extracting and plotting $\Delta\chi^2$ contours.

7. Impact and Research Applications

GLoBES and its simulation ecosystem are employed extensively in phenomenological studies for long-baseline experiments (e.g., DUNE), reactor neutrino oscillations, global fits to sterile neutrinos, EFT sensitivity analyses, NSI identification, and dark sector searches. The modular architecture supports rapid prototyping and robust statistical analysis, allowing rigorous assessment of model viability under current and future experimental datasets. GLoBES-based simulations underlie sensitivity projections, experiment proposals, and published exclusion or discovery limits across neutrino physics (Tang et al., 2020, Berryman et al., 2020, Brdar et al., 2017, Kopp et al., 25 Sep 2025, Fiza et al., 10 Jul 2025, Collaboration et al., 2021).