The interaction of a relatively low-energy neutrino with a nucleus is not a simple matter of W exchange between a neutrino and a quark. As well as the momentum distribution of nucleons within the nucleus and quarks within the nucleon – significant when the energy of your neutrino is typically < 1 GeV, as in T2K – there are also multi-nucleon effects to contend with. The figure shows Feynman graphs from the Nieves et al. model of multi-nucleon interactions (known as MEC or "meson exchange currents").
As a result of such effects, and a lack of good experimental data, the models of neutrino-nucleus interactions used in simulations are not complete descriptions of the physics and frequently do not describe the data very well. This is a critical issue in oscillation analyses because it is necessary to unfold the measured charged lepton energy spectrum back into the neutrino energy spectrum: as multi-nucleon effects can affect the momentum of the outgoing charged lepton, a poor understanding of such effects results in large systematic errors.
The T2K analysis strategy, shown in the flow diagram below, uses both pre-fits to external data and fits to ND280 data to constrain the model for the oscillation fits.
Optimising the physics input to the T2K simulation is the job of the Neutrino Interactions Working Group (NIWG). Sheffield students have maintained an extremely high profile in the NIWG and have played a leading role in tuning models of neutrino-nucleus interactions to external datasets.
Modelling neutrino-nucleus interactions
As with most particle physics experiments, T2K data are analysed with the aid of Monte Carlo programs which simulate the physical processes and track the resulting particles through a mathematical model of the detector. By comparing the simulation with real data, we can investigate the extent to which our theoretical understanding, as embodied in the event generator, is an accurate representation of the real world.
There are several standard event generators for neutrino interactions, and comparison of predictions from different generators is a key component of systematic error studies in neutrino-nucleus interactions. T2K normally uses NEUT, which is Super-Kamiokande's official package and has been refined over many years, but the standard generator for the rest of the neutrino community is GENIE (which is also used by T2K, but usually for cross-checks and systematic error studies). Another useful event generator is NuWro, which is flexible and easy to customise. Finally, the GiBUU generator has a more sophisticated treatment of transporting the reaction products through the nuclear medium, and is therefore an important benchmark for studies of final-state interactions (see below), but is computationally expensive and therefore not used as the standard generator for production simulations.
The principal ingredients of a model of neutrino-nucleus interactions are:
- the nuclear model, describing the initial state of the nucleons within the nucleus;
- the nature of the interaction, whether it be elastic or quasi-elastic scattering off a single nucleon, inelastic scattering off a nucleon (exciting a resonance such as the Δ), coherent scattering off the whole nucleus, or deep inelastic scattering off a constituent quark within the nucleon;
- final-state interactions, where the products of the initial interaction may re-interact with other nucleons before emerging from the nucleus.
In addition, the simulation must take into account nucleon form factors resulting from the fact that nucleons are not fundamental particles, but composite objects consisting of a sea of quarks and gluons occupying a finite spatial extent.
Over the past few years, increasingly sophisticated models of neutrino-nucleus interactions have been developed, making improvements in all these areas. On the right, the Benhar spectral function model of nucleon momentum distribution in the 16O nucleus is compared with the simple relativistic Fermi gas; below, the ingredients of the Nieves model of neutrino-nucleus interactions are shown in the form of contributions to the W self-energy.
All models of neutrino-nucleus interactions have parameters which must be tuned to best describe the data. As shown in the flow-chart above, in T2K this tuning is done using fits to published data from other experiments. This avoids too much circular reasoning—you are not tuning your model to data you will subsequently unfold using the same model—but introduces its own issues: data from different experiments may not agree with each other; published covariance matrices may be incomplete; the data as published may have been subjected to model-dependent corrections for acceptance or selection biases. Nevertheless, it is possible to improve the description of the data very substantially by appropriate tuning of parameters, as shown in the figure on the right.
For more information about this analysis, see Callum Wilkinson's PhD thesis.
The NUISANCE project
The plethora of models, generators and datasets makes the tasks of tuning models to data, comparing data to models, and cross-checking different event generators increasingly complex and time-consuming. The NUISANCE project, led by Sheffield student Patrick Stowell, has been set up to provide a common framework in which all members of the neutrino physics community can undertake these tasks. NUISANCE aims to provide a coherent framework for comparing neutrino generators to external data and tuning model parameters. It currently supports the NEUT, GENIE, NuWro, GiBUU and NUANCE generators, and can provide consistent comparisons between generators, comparisons of any or all supported generators with any dataset that is implemented in the framework, automated parameter tuning using reweight dials, and systematic error studies for cross-section measurements.