SBND at Sheffield
The Standard Model of particle physics contains three neutrinos, nominally one for each of the three charged leptons e, μ and τ. In the 1990s, experiments at the LEP collider in CERN demonstrated that there were three and only three distinct types of light, weakly-interacting neutrinoAny further weakly-interacting neutrinos would need to have masses above 45 GeV/c2 (so that they could not be produced in Z decays, Z → νν̅) to evade this restriction.
If there are three neutrino species and three distinct mass eigenstates (which, as shown by the results of neutrino oscillation experiments, are not aligned with the flavour eigenstates νe, νμ, ντ), then there are exactly two independent mass differences (or, in neutrino oscillation theory, squared-mass differences): the third one can be expressed as the sum or difference of the other two.
If we know that m22 – m12 = 7.5×10–5 eV2 and |m32 – m12| = 2.52×10–3 eV2, then |m32 – m22| is either the difference of these (if m3 > m2 > m1, "normal ordering") or the sum (if m2 > m1 > m3, "inverted ordering").
However, several neutrino experiments have reported results which could be interpreted as oscillation signals with a squared-mass difference of about 1 eV2, which is certainly not consistent with the experimentally determined values for the known neutrinos.
The longest-standing of these is LSND, which measured an excess of ν̅e events from a ν̅μ source (μ+ decays at rest). Others include MiniBooNE, which observes an excess of low-energy events, and the reactor neutrino experiments, which consistently observe neutrino fluxes about 3% lower than the best available calculations (with the caveat that these calculations are challenging!).
If these results are indeed explained by neutrino oscillations, there must be a fourth species of neutrino, and the LEP results imply that it cannot be produced in Z decays—i.e., it is not weakly interacting ( a so-called sterile neutrino).
On the other hand, analyses of the cosmic microwave background tend to prefer three neutrino species, as shown in the figure. There is also some tension between the neutrino and antineutrino results, which prefer different parameters for the fourth state.
In summary, then, the experimental picture is not as clear as we would wish, and there is no obvious theoretical motivation for a light sterile neutrino. (Right-handed neutrino states, which would be sterile because the weak interaction is inherently left-handed, are theoretically motivated as a natural explanation for the extremely low neutrino masses, but this only works if the right-handed states are very massive.)
Therefore better data are needed to resolve the existing confusion. The Fermilab Short Baseline Neutrino Program is intended to provide the better data, while at the same time acting as a technology development testbed for the DUNE experiment.
It consists of three LAr TPCs at different distances from the Fermilab Booster neutrino beam: ICARUS (imported from Gran Sasso) at 600 m, MicroBooNE at 470 m, and SBND at 110 m. Sheffield's involvement is with SBND.
SBND has a number of physics goals:
- It is the reference (unoscillated beam) detector for the short-baseline neutrino oscillation measurement intended to confirm or refute the existence of a ~1 eV sterile neutrino.
- It is expected to record over a million neutrino interactions per year and should therefore provide accurate cross-section measurements for neutrino interactions on argon. These are critical inputs to the DUNE physics programme.
- The SBND detector and electronics designs are similar to (though not identical to) the DUNE designs, and SBND is therefore an important technology demonstrator for DUNE. This is also, of course, the role played by the ProtoDUNE project at CERN, but, unlike ProtoDUNE, SBND is actually on a neutrino beamline and the events it records will therefore be very similar to DUNE events.
The Sheffield group plays a leading role in SBND. Our hardware responsibilities include:
- design and manufacture of the anode plane assembly (APA) frames that hold the wire readouts inside the cryostat;
- design and manufacture of wire combs, which support the wires and prevent/minimise sag in case of a drop in wire tension;
- contributing to general TPC construction and assembly;
- electronics testing;
- quality control and quality assurance.
In software and physics analysis, we are
- developing liquid argon analysis tools including track and shower reconstruction, particle identification, momentum estimation and liquid argon purity measurements;
- planning to measure neutrino-argon cross sections with the aim of comparing CCQE and/or CC inclusive cross section results with the ANNIE water Cherenkov detector (ANNIE and SBND are in the same beamline and at a very similar baseline so many flux systematics should cancel);
- participating in sterile neutrino searches using the full suite of SBN detectors (SBND, MicroBooNE and ICARUS).
SBND is the near detector of the Fermilab Short Baseline Neutrino Program.
This means that it has two main roles; It should be close enough to the target to observe an unoscillated beam, and therefore provides a reference for neutrino oscillation searches, and it sees the highest flux, and therefore has the highest flux for the measurement of cross sections.
Sheffield is involved in both these strands.
- Cross-section measurements
Cross-section measurements at SBND will be an important input into the DUNE neutrino oscillation measurements. Uncertainties in modelling the neutrino interaction cross sections contribute to the systematic error in neutrino oscillation measurements, and both DUNE and Hyper-Kamiokande are aiming for much lower systematic errors than the current state of the art from T2K.
The interaction used in oscillation searches is charged-current quasi-elastic, CCQE, which is W exchange with no additional particles in the final state (νμ + n → μ– + p or ν̅μ + p → μ+ + n), because the two-body kinematics allow the reconstruction of the neutrino momentum even if the outgoing nucleon is not observed—which in water Cherenkov detectors it usually isn't, because it is below Cherenkov threshold.
In LAr detectors this final state should be better defined, since outgoing protons should leave reconstructable tracks (though neutrons won't); however, the problem of final-state interactions (FSI), where particles from the original neutrino interaction re-interact with other nucleons as they exit the nucleus, is still present—and indeed might be enhanced as argon is a larger nucleus than carbon and oxygen, the typical target nuclei used to date.
An increasingly popular approach to FSI is to define measured cross sections in terms of observed final states (observed CC0π, for example, rather than theoretical CCQE), and leave theorists to figure out the contributions of different primary interactions.
For best results, this requires that the observed final state be accurately identified, with all the final-state hadrons reconstructed. LAr TPCs are particularly well suited to doing this, because they are capable of reconstructing very low-momentum tracks.
The image shows an ArgoNeuT event in which two protons are ejected from the nucleus—a probable "2p2h" interaction in which the incident neutrino interacted with a tightly bound pair of nucleons within the nucleus. Another common source of systematics is the uncertainty in the neutrino flux, which is usually large.
This is one of the main reasons for the use of a near detector (the other being to determine the flavour composition of the beam before oscillation: the neutrino beam produced by directing a proton beam on to a carbon or metal target is not quite a pure νμ or ν̅μ beam, because the proton interactions do not produce only pions (heavier mesons such as kaons, which can decay to final states including νe, are also produced) and because some of the muons produced when the pions decay will themselves decay by μ+ → e+ + νe + ν̅μ (or the equivalent for μ–): the muon mean lifetime is much longer than the pion mean lifetime, but the distribution of individual lifetimes is an exponential).
An interesting feature of the Fermilab setup is that the water Cherenkov experiment ANNIE and the LAr TPC SBND are in the same beam and at very similar distances from the target, so most of the flux systematics should cancel.
This provides a very useful opportunity to directly compare cross-section measurements on argon and water targets. The Sheffield group, which is active on both ANNIE and SBND, plans to do this for CC0π and perhaps CC inclusive (i.e. final state contains a muon and anything else) final states.
- Sterile neutrino searches
Sterile neutrinos are, by definition, neutrinos that do not interact by the weak interaction, and are therefore unobservable (they do interact gravitationally, but this is far too feeble to be useful).
However, they can mix with the active states, extending the 3×3 PMNS matrix to 4×4 or higher. In this case, there must be a fourth neutrino mass eigenstate ν4 (and a fifth state in 3+2 models—one rather feels that if there is one sterile neutrino there ought to be three, to maintain the generational pattern, but of course there is no guarantee that all of them would be light, and as mentioned earlier the seesaw mechanism for neutrino mass generation expects the right-handed neutrino states to be very massive).
If the known flavour eigenstates contain some admixture of ν4, this will produce oscillation signatures in both disappearance and appearance channels.
A disappearance signal for a sterile neutrino in the SBN detector suite would be a reduction in the νμCC (or νμNC) rate in MicroBooNE or ICARUS compared to the rate observed in SBND. In a 3+1 scenario, the survival probability is given by
where the effective mixing angle θμμ is given by sin2 2θμμ = 4|Uμ4|2 (1 – |Uμ4|2) and the second bracket uses experimenters' units ((eV/c2)2 for Δm2, km for L and GeV for E).
We assume all other oscillation probabilities are negligible, since their Δm2 values are very much smaller than the ~1 (eV/c2)2 deduced from sterile neutrino fits.
An appearance signal would be an excess of another flavour, presumably νe (though a liquid argon TPC might even be able to identify ντ). This probability is given be
where in this case the effective mixing angle θμe is given by sin2 2θμe = 4|Uμ4Ue4|2 (the equations in this section come from Kopp et al. 2013).
Notice that sterile neutrino oscillation signals do not come from the beam neutrino "oscillating into a sterile neutrino"—they come from the fact that if there are four flavour eigenstates, there must be four mass eigenstates, and the visible neutrino flavour eigenstates are mixtures of all four (assuming that the relevant matrix elements are not zero).
The key to sterile neutrino searches lies in ensuring that the event rates from the different detectors can be accurately compared.
The SBN programme has the great advantage that all its detectors use the same technology and—given an on-axis geometry—should see essentially the same beam, which makes this problem simpler than it is for T2K, for example.
However (unlike, say, Daya Bay), the detectors are not completely identical: they are different sizes and differ in their construction details.
Therefore, essential inputs to the oscillation analysis such as track reconstruction efficiency, precision of energy determination (necessary because of the energy dependence of the probabilities) and particle misidentification probability will need to be carefully studied in each detector.
Confirming or refuting the current experimental evidence(?) for sterile neutrinos is the main physics goal of the SBN programme.
As yet, with only MicroBooNE operating, this analysis cannot be done—one of the main problems besetting the current experimental evidence is that none of the experiments has a meaningful near detector (the reactor experiments like Daya Bay have near/far pairs that are appropriate for a Δm2 of about 10–3 (eV/c2)2, not 1 (eV/c2)2), so flux and cross-section systematics do not cancel.
The current first priority of the collaboration is to get all three detectors up and running, with good tools for track reconstruction and particle identification, before work can start on the oscillation analysis.
SBND is a liquid argon TPC. Charged particles passing through the liquid argon create ionisation, and an electric field maintained by appropriate voltages on the cathode and anode planes drifts the free electrons to the anode plane assemblies (APAs), where the charge is collected on wires.
Each anode plane assembly consists of three wire planes with the wires running in different directions (y, u and v, where the y wires run vertically and the u and v wires at ±60°—a few representative wires are shown in red, blue and green in the diagram), allowing hits to be reconstructed in two dimensions.
The third dimension is given by the time it took the electrons to drift to the anode planes.
This is determined by comparing the arrival time of the electrons with the photon arrival time: LAr is a scintillator, emitting at 128 nm in the far ultraviolet, so a charged particle produces scintillation light as well as ionisation.
SBND will have photodetectors mounted behind the APAs to detect this emission.
- The APA frames
Sheffield is responsible for the design and manufacture of the APA frames, shown in blue on the diagram. These support the anode wire planes inside the SBND cryostat.
As the wire positions define the x and y coordinates of each point on the particle track, it is essential that the frames are stable, robust and precision engineered so that the readout planes are well calibrated.
The photo shows one APA frame (as you can see by comparing the photo with the schematic diagram, there are four APA frames in all, two on each side). They were manufactured for us in Sheffield by Portobello-RMF Engineering Ltd.
As the wires are under tension to ensure that they remain straight and that there is no risk of wires from one plane touching those from another, the APA frames have to be mechanically strong, and also very flat—no warping or twisting.
The total load on the frame is 250 kg/m (0.5 kg/wire) [yes, that should really be expressed as N/m, but engineers like to work in kg/m...]. Each frame is made of welded steel tubing (more precisely, rectangular hollow section, 100 mm × 150 mm cross-section with 5 mm thick walls) and weighs around 480 kg.
The tolerance on the flatness is ±2 mm on the long side (4 m) and ±1.5 mm on the short side (2.5 m). This is high-precision engineering, but is not quite good enough given that the intended spacing between wire planes is only 3 mm, so the boards that carry the wires will be mounted on "levelling plates" to make the wire planes flat and parallel.
As the frame is inside the LAr cryostat, it is also necessary that the frames can withstand being cooled to LAr temperatures (~85 K) without distorting and without breaking wires.
Cold tests using liquid nitrogen (77 K) have been carried out at the University of Chicago using a single-window prototype frame (i.e. 1/6 of the production frame shown here).
- The wire combs
Each APA frame is about 4 m high by 2.5 m wide. It is important that the wire spacing be maintained as uniform as possible over the entire area of the frame, because the precision of the wire positions determines the resolution of the track position measurement.
In order to improve the constancy of the wire spacing, and to minimise the effect of any reduction in wire tension, the wires run through wire combs mounted on the horizontal bars of the frame for the y wires, and on the vertical bar for the u and v wires.
The Sheffield group is also responsible for the design and construction of these wire combs. The photo shows a prototype wire comb mounted on a test frame. As with the frame itself, a key requirement for the wire combs is that they should not distort or crack when cooled to LAr temperatures.
- Other responsibilities
In addition to manufacturing the APA frames and wire combs, Sheffield is participating in the construction and assembly of the TPC at Fermilab.
We also have responsibilities in quality control and quality assurance, i.e. ensuring that components meet their specifications prior to installation, and electronics testing.
The data from a particle physics experiment are essentially electronic signals. The data required to conduct a physics analysis are physical variables such as particle four-vectors.
There is a great deal of work involved in getting from the raw data to the physics variables, including (but not limited to!) detector calibration, data quality monitoring, track reconstruction and particle identification.
The Sheffield group is heavily involved in developing many of these tools.
- Reconstructing particle properties
Liquid argon detectors provide highly detailed pictures of neutrino interactions, as in this example from ArgoNeuT. However, in order for the experiments to realise the full potential of such detailed event records, it is necessary to ensure that they are accurately reconstructed.
Events may contain tracks created by individual charged particles, for example the red one moving upwards from the first vertex in the picture, and showers produced when photons or electrons create multiple lower-energy electrons and positrons by pair production and bremsstrahlung, as seen in the secondary vertices.
The aim of the reconstruction is to measure the momentum or energy, the direction, and if possible identify the type of particle. This is not a trivial task, because these detectors, unlike most particle physics experiments, do not have a magnetic field to provide a momentum measurement from the resulting curvature of the tracks.
The MicroBooNE collaboration has demonstrated that the momenta of muons can be reconstructed using the properties of multiple Coulomb scattering, i.e. the deviation in the muon trajectory caused by scattering off atomic nuclei.
The theoretical expectation is that this deviation should have a Gaussian distribution with a mean of zero and a width given by the Highland formula
where S2 and ε are parameters (given by MicroBooNE as 11 MeV (with some momentum dependence) and 0.038 respectively), z is the charge of the particle (1 for a muon), ℓ is the distance travelled, and X0 is the radiation length of the medium (i.e. liquid argon).
For any reasonable energy, the muon's speed will be close to c, i.e. β ≈ 1, so this formula can be used to determine momentum by dividing a track into segments, so that a single track produces a distribution of multiple scattering angles whose width can be measured.
Comparing momenta reconstructed using this technique with those derived from the standard method of using the range of the muon (for muon tracks which are "fully contained", i.e. they start and stop within the detector) shows good agreement, but the multiple-scattering method has the advantage that the track need not be fully contained within the detector.
Particle identification in liquid argon detectors is done through measuring the rate of energy deposition, dE/dx. The expected〈dE/dx〉is described by the Bethe formula, though the use of this formula in practice is complicated by the fact that the distribution of dE/dx is far from Gaussian, so there can be large fluctuations in the calculated mean.
Various techniques are employed to deal with this, such as using truncated means or most probable values: these require appropriate modifications to the Bethe formula, but this is a known and well-studied problem. Some typical plots and numerical values for liquid argon can be found on the Brookhaven LAr site.
This work all refers to track reconstruction. Shower reconstruction is a more challenging problem, as showers involve a large number of short tracks that are very close together in three dimensions.
It would be both difficult and time-consuming to reconstruct showers by attempting to reconstruct each individual contributing track, so it is probably necessary to develop a different algorithm which considers the shower as a single entity. This problem has not yet been tackled for SBND.
- Calibration and data quality
LAr TPCs such as SBND require the ionisation electrons to drift for quite large distances before they are collected on the anode plane wires.
Therefore, the electron lifetime—that is, the time for which a free electron will remain free before recombining—is an important property.
As argon is a noble liquid, argon atoms are very disinclined to capture electrons, so the electron lifetime in a real detector is dominated by impurities in the argon. Hence, electron lifetime measurements are a proxy for argon purity.
Sheffield PhD students are currently developing methods for measuring the electron lifetime using cosmic muon tracks. As SBND is not a deep underground detector like Super-Kamiokande or DUNE, the cosmic muon rate is high, so large samples of clean cosmic muon events will be available during SBND running.
As muons are minimum-ionising particles, the number of ionisation electrons they produce per unit track length is expected to be approximately constant, whereas the number of electrons collected at the anode plane is expected to fall exponentially with drift distance (or, equivalently, drift time), because of the finite electron lifetime.
If this exponential decay of the collected charge can be measured, the electron lifetime can be deduced.
The plot compares the performance of three different lifetime estimators for simulated data. Method 1 uses slices from an individual track which crosses both the cathode and the anode planes, and therefore provides data for a range of drift distances; method 2 uses the same type of muon tracks, but instead of taking them track by track it takes them time slice by time slice, and for each time slice fits a Landau-Gaussian convolution to the whole data sample.
Method 3 uses a sample of tracks that are directed approximately parallel to the wire planes, so that the whole of each track falls in a single time slice.
It can be seen that all three methods would be equally effective if the electron lifetime in SBND were rather short (< 4 ms or so), but method 1, and to a lesser extent method 3, tends to underestimate longer lifetimes.
Method 3 has the advantage that the muons are selected by using the segmentation of SBND's cosmic ray tagger, a system of strips of plastic scintillator surrounding the TPC, and so minimal reconstruction is required—this technique could be implemented as a real-time (or nearly real-time) argon purity monitor.