Simulating hadron test beams in liquid argon
SSLAC-PUB-17549
Simulating Hadron Test Beams in Liquid Argon
Alexander Friedland ∗ and Shirley Weishi Li † SLAC National Accelerator Laboratory, 2575 Sand Hill Road, Menlo Park, CA, 94025 (Dated: July 27, 2020)Thorough modeling of the physics involved in liquid argon calorimetry is essential for accuratelypredicting the performance of DUNE and optimizing its design and analysis pipeline. At the fun-damental level, it is essential to quantify the detector response to individual hadrons—protons,charged pions, and neutrons—at different injection energies. We report such a simulation, analyzedunder different assumptions about event reconstruction, such as particle identification and neutrondetection. The role of event containment is also quantified. The results of this simulation can helpinform the ProtoDUNE test-beam data analysis, while also providing a framework for assessing theimpact of various cross section uncertainties.
I. MOTIVATIONS
Energy resolution and the accuracy of energy scale cal-ibration are essential characteristics for a neutrino de-tector operating in a broad-spectrum neutrino beam.Modeling these characteristics for the Deep UndergroundNeutrino Experiment (DUNE) is a nontrivial task. Atthe root of the problem is the nature of the final statesproduced when neutrinos of several-GeV energies inter-act with argon nuclei. These interactions can producemultiple hadrons of different types, which can, in turn,undergo subsequent interactions in the detector medium,distributing energy among even more particles. At firstsight, by collecting all ionization charges, one should beable to measure all this energy calorimetrically. In real-ity, however, different particles create different amountsof detectable charge per unit energy lost, and some en-ergy goes into invisible channels, such as nuclear breakup.As an extreme case, some or all neutrons may be alto-gether missed. Thus, having an accurate model for thedetector response to each particle type is essential foroptimal detector performance.Given the complexity of the problem, a consistent wayto study it is to simulate a large number of fully devel-oped neutrino events [1, 2]. The simulation pipeline inthis approach combines a code modeling the primary neu-trino interaction with another one propagating all result-ing particles through the liquid argon medium. For thefirst code, one can use
GENIE , GiBUU , or another eventgenerator. For the second, the choices are
GEANT4 or FLUKA , both of which model not only ionization losses,but also any subsequent hadronic and electromagneticinteractions of all particles in the detector. The processneeds to be repeated for different flavors of the incomingneutrino and a range of energy of interest. The result isa set of migration matrices describing probabilities con-necting true and reconstructed energies. These matricesare an essential input for any analysis of oscillation sen-sitivity. ∗ [email protected] † [email protected] All this computer-intensive process is necessary just tocharacterize energy resolution in the case of baseline as-sumptions about the detector performance. If one wishesto investigate the impact of various changes to the recon-struction procedure, one needs to rerun the entire sim-ulation pipeline. For example, one may wish to varydetection thresholds, exclude certain particle types, orinvestigate the impact of various particle identification(PID) assumptions. In each case, one obtains a new setof migration matrices, which then can be used for oscilla-tion studies. An example study following this approach ispresented in Ref. [2], where we considered several modelassumptions about the detector performance, specifically,on the values of particle detection thresholds and theavailability of accurate PID information.To gain more insight into the physics dictating neu-trino detection in liquid argon, in this paper, we injectin our simulation volume individual hadron particles—protons, charged pions, neutrons—and investigate thedetector response in each case. This should allow one tounderstand the role of each particle type in neutrino en-ergy reconstruction. Of particular interest is to quantifythe importance of reconstructing secondary neutrons.There are several additional reasons to consider thisstudy. First, our simulations yield “virtual test-beamdata”, which can be used to compare with the actualProtoDUNE [3] test-beam data, an essential step to vali-dating the entire simulation framework for the full events.Second, it may also be used to devise sanity-checks forthe full event simulation results. Such checks are alwaysnecessary when one deals with large simulation frame-works with complex codes.Third, one can use the results on individual particlesto create simplified, flexible codes, in which prescriptionsdescribing the detection process are applied to the out-puts of the neutrino event generator. This is the generalphilosophy of the
FastMC code employed in the DUNECDR documents [4, 5]. We regard this approach veryuseful for certain problem types, and far from being com-pletely superseded by the full simulations. In connectionwith this point, it is extremely important to establish un-der which conditions the reconstructed energy for a givenhadron type may be described by a Gaussian. a r X i v : . [ h e p - ph ] J u l In our study here, we do not discuss detector signa-tures of electrons, muons, or gamma rays. The reasonis that these particles have already been discussed byus in Ref. [2]: muons leave long tracks, while electronsand gamma rays create electromagnetic showers. In allcases, the total ionization charge is found to be in closecorrespondence with the true particle energy. Thus, theresolution will likely be controlled by the reconstructionalgorithm performance and not by physical processes inparticle propagation, which are the focus of the presentstudy.The presentation is organized as follows. Section IIpresents an overview of our simulation framework anda list of specific reconstruction assumptions consideredin the paper. Section III presents the simulation resultsfor each hadron type. Section III A treats protons andalso explains the reconstruction procedure. Section III Btreats charged pions while Sec. III C is devoted to thestudy of neutrons. Section IV explores the impact oflimited detector volume. Section V discusses some conse-quences of the results of our study, including the physicsdictating the energy resolution and possible applicationsto the development of simplified codes. Finally, Sec. VIsummarizes our main findings.
II. SIMULATION OVERVIEW
Following Ref. [2], our simulations here also employ
FLUKA [6, 7] to model event development in liquid ar-gon.
FLUKA —here we use version 2011.2x.6—is a publiclyavailable, well-tested package that incorporates all rele-vant physics processes, such as ionization and radiativeenergy losses, hadronic inelastic interaction, and particledecays. Among its many strengths is a good descriptionof MeV hadronic physics, as recently demonstrated bythe ArgoNeuT experiment [8].As in Ref. [2], we fully propagate all particles, includ-ing those produced in secondary interactions, but do notconsider detector-specific effects, such as the finite life-time of drifted charges, space charge distribution, wirespacing, electronic noise, or cosmogenic and radiogenicbackgrounds. Such studies are beyond the scope of thepresent paper and will depend on specific detector config-urations and performance characteristics. We are encour-aged, however, by the extremely low levels of electronicnoise in the ProtoDUNE-SP data and assume that thereported issues with the space charge distribution will beadequately resolved.Our emphasis at present is on assessing the physicalimpact of different reconstruction assumptions . Specifi-cally, we aim to elucidate the impact of good PID andneutron detection. We argued in Ref. [2] that these arecrucial factors determining the accuracy of neutrino en-ergy measurements in liquid argon. Here, we deconstructthe argument by considering the reconstruction processfor each hadron type. Accordingly, we analyze threemodel scenarios: 1.
Best reconstruction . One has PID information onall charged particles in an event and applies it toget the ionization energy loss along each trajectory.The detection thresholds are considered to be verylow, motivated by the ArgoNeuT experiment.2.
Charge-only reconstruction . No PID information isavailable for any secondary particles in an event.One collects the total ionization charge and usesit to infer, statistically, the energy of the injectedparticle.3.
Charge-only, no neutrons . In addition to the as-sumption of no PID, any energy imparted to neu-trons at any stage in the process development isconsidered to be completely lost.The first two scenarios were already considered in Ref. [2].The second method is described in detail in Refs. [9, 10]and is currently accepted within the DUNE collaborationas a way of treating the hadronic system [11]. The thirdone is introduced here. It is motivated by the considera-tion of a surface detector, where a high rate of cosmic-rayactivity may impede neutron detection.The significance of these assumptions becomes obviouswhen one considers the anatomy of a hadronic event inliquid argon. Slower particles create more dense chargetracks, which, in turn, leads to more charge loss torecombination. Thus, a relationship between the de-tected charge, dQ/dx , and the true ionization energy loss, dE/dx , depends on the particle type. To be concrete,protons, being more massive, deposit more dense chargetracks, but yield less charge per unit energy lost thancharged pions of the same energy. Neutrons, being elec-trically neutral, do not leave tracks at all. Their presencecan be detected by the secondary ionizing particles theyproduce in their interactions. Since these interactionsoccur some distance away from their starting points, oneends up with secondary proton and pion tracks separatedfrom the main event, and with a spray of small chargedeposits created by the de-excitation gamma rays under-going repeated Compton scattering. For details on bothphenomena, the reader is referred, once again, to Ref. [2].
III. SIMULATION RESULTSA. Protons
Let us illustrate our resolution modeling procedure onthe example of proton test beams. The situation wewould like to emulate is the following: one injects a pro-ton test beam of a known energy E tr into the Proto-DUNE detector, but uses a reconstruction pipeline thatis unaware of the true energy value to analyze each event.First, we generate our simulation dataset, which is usedto model energy resolution in each of our three scenar-ios. For this, we inject protons of energies from 0.01 to3.0 GeV and model the full event development in each Reconstructed proton energy (GeV) N o r m a li z e d p r o b a b ili t y E p , true = Reconstructed proton energy (GeV) best recchargecharge, no nCDR 0.0 0.5 1.0 1.5 2.0 2.5
Reconstructed proton energy (GeV)
Reconstructed proton energy (GeV)
FIG. 1. Distributions of proton reconstructed energies, for four representative values of the true energy, E p = 0 .
1, 0 .
5, 1 .
0, and2 . blue ), (2) only totalionization charge ( orange ), and (3) total ionization charge with neutrons undetected ( green ). For comparison, the dashed curveshows the resolution assumed in the DUNE CDR document [4, 5]. case. Between 0.1 GeV and 3.0 GeV, we sample protonenergy values in 0.05 GeV intervals. To better charac-terize the resolution at low energies, we also generate asecond dataset with below 0.01 GeV energy spacing. Foreach value of the true energy, E tr , we generate 10 events.Let us describe the procedure on the example of thetotal-charge study. The simulation dataset tells us, for agiven value of the true proton energy, E tr , the probabil-ity P ( Q | E tr ) of measuring charge Q . Discretizing (bin-ning) the Q values, we obtain a matrix of probabilitiesconnecting E tr and Q . Explicitly, the matrix element P ( Q ( j ) | E ( i ) tr ) equals the number of events that landed inbin Q ( j ) divided by the number of simulations with E ( i ) tr .For clarity of the argument, we take the values of Q to be equally spaced. Let us likewise consider equallyspaced values of E tr , for the moment neglecting the extrasampling at low energies.Now, suppose we use this simulation dataset to analyzea new event, created by a proton with an unknown valueof E tr . Given the value of Q measured for this event,we can use our matrix as a lookup table, to obtain theprobability P ( E rec | Q ) that the event was created by aproton with energy E rec . Explicitly, P ( E ( j ) rec | Q ( i ) ) is equalto the number of times charge Q ( i ) was obtained in thesimulation with proton energy E ( j ) rec divided by the totalnumber of times charge Q ( i ) was obtained for all energiesin our simulation set.If the first step could be thought of as reading thematrix “horizontally”, for the second step, we read it“vertically.” The requirement of unbiased reconstructionis assured by construction, since our proton energy valuesare drawn from a flat distribution [12]. With relativeprobabilities of different E rec values thus fixed, one onlyneeds to normalize the distribution.Now, suppose we reconstruct in this manner all eventsobtained with the beam of energy E tr . Then wefind a probability distribution of reconstructed energies, P ( E rec | E tr ). This amounts to integrating over all Q val- ues in the intermediate step: P ( E rec | E tr ) = (cid:90) dQP ( E rec | Q ) P ( Q | E tr ) . (1)It can be straightforwardly shown that, if the chargedistribution is Gaussian, P ( Q | E tr ) = 1 √ πσ exp (cid:20) − ( Q − E tr f ) σ (cid:21) , (2)where f is the fraction of energy that on average goes intocharge, the resulting distribution of E rec is also Gaussian,with the width √ σ/f : P ( E rec | E tr ) = (cid:90) dQP ( E rec | Q ) P ( Q | E tr )= f √ πσ exp (cid:20) − ( E rec − E tr ) f σ (cid:21) . (3)Here the probability distribution P ( E rec | Q ) is given by P ( E rec | Q ) = f √ πσ exp (cid:20) − ( Q − E rec f ) σ (cid:21) , (4)which is normalized to one. In a general case, however,the distributions for E rec and Q do not follow the samefunctional form.The application of this procedure to the other two re-construction methods is now straightforward. For thesimulation with no neutrons, all charges created down-stream of any neutron are discarded, with the rest of theprocedure unaffected. In the best-reconstruction case, toeach track in the event, we apply a charge recombinationcorrection factor that is a function of its PID. The re-sulting distribution of the “modified charged” is used inplace of Q .Figure 1 shows the result of applying this procedure toour simulation set. Four representative values of the trueproton energy are considered: 0.1, 0.5, 1.0, and 2.0 GeV.We see that the character of the distribution changes Reconstructed π − energy (GeV) N o r m a li z e d p r o b a b ili t y E π − , true = Reconstructed π − energy (GeV) best recchargecharge, no nCDR 0.0 0.5 1.0 1.5 2.0 2.5 Reconstructed π − energy (GeV) Reconstructed π − energy (GeV) FIG. 2. Same as Fig. 1, but for the π − reconstructed energies. as one goes from low to high energy values: at 2 GeV,the E rec distributions with neutrons are well-describedby Gaussians, while at 0.1 GeV the distribution is dom-inated by a sharp spike, where essentially all proton en-ergy is recovered. The 0.5 GeV represents a transitionbetween these regimes. This observation will prove cru-cial for our discussion in Sec. V below. But first, we turnto the corresponding results for the other hadrons. B. Charged pions
Understanding the propagation of charged pions is alsoof direct relevance to DUNE calorimetry. As illustratedin Ref. [2], interactions of 4 GeV neutrinos can createhadronic showers with multiple pions, with energies inthe hundreds of MeV range. Even 1–2 GeV pions arenot uncommon in such events. Therefore, it is certainlyworth considering charged pion test beams, and indeedProtoDUNE has collected such data.In Fig. 2, we simulate charged pion beams, with ener-gies 0.2, 0.5, 1 and 2 GeV. The histograms in the figurecorrespond to π − ; for positively charged pions, the resultsare very similar. The reconstruction assumptions and theanalysis are the same as considered earlier for protons.We see that the basic results for pions and protons arequalitatively similar: the distributions of reconstructedenergies are non-Gaussian at the lowest energies and be-come Gaussian at higher energies. One notable quantita-tive difference is that the gaussianity sets in at a smallerenergy for pions than for protons. This has a naturalphysical explanation in terms of the ionization rates inthe two cases. With energy loss having a ∝ v − leadingvelocity dependence, slower particles lose energy fasterper unit distance traveled. Since protons of a few hun-dred MeV are nonrelativistic, their ionization rates arehigher than for pions of the same kinetic energy. Thus,protons are more likely than pions to come to rest be-fore undergoing hadronic interactions, and it is repeatedhadronic interactions that create Gaussian distributionof reconstructed energies. C. Neutrons
We have seen that neutron detection has a dramaticimpact on the accuracy of the calorimetric energy recon-struction by liquid argon detectors. Let us now take adeeper dive into the subject by analyzing neutron prop-agation and interactions.First of all, one should be more precise about whatis meant by neutron detection. As already mentionedin Sec. II, a neutron traveling through the liquid argonmedium does not, by itself, create an ionization track.Its energy is lost via interaction with multiple argon nu-clei, and it is through the secondary particles created inthese interactions that the presence of the neutron canbe revealed. Importantly, the secondary charged parti-cles carry only a fraction of the original neutron energy—some of the energy is lost to nuclear breakup. Hence, adirect calorimetric measurement of the neutron energy isnot possible. One recovers only part of the energy anduses a simulation-based model to infer the likely energyrange of the original neutron.At a more detailed level, one has to consider the dif-ferent signatures that can be created in neutron inter-actions. A neutron can excite an argon nucleus, or itcan knock out one or more nucleons from it, leaving thedaughter nucleus in an excited state. The de-excitationgammas undergo Compton scattering in the medium,and the recoil electrons leave small ionization charge de-posits [13]. Since a given neutron interacts with manyargon nuclei in this way, many recoil electrons are scat-tered over an extended region. The resulting spray ofsuch small charges, from many nuclear interactions, is, inprinciple, observable, as demonstrated by the ArgoNeuTanalysis [8].A more prominent signature comes from energeticknock-out products. In particular, a sufficiently ener-getic proton can create a distinct track that is detachedfrom the main event. Such tracks can be identified asprotons, thus enabling proper charge recombination cor-rection. In Fig. 3, we depict a spectrum of the leading(highest energy) protons created in propagation of neu-trons of two starting kinetic energies: 0.5 and 1 GeV.
Leading proton kinetic energy (GeV) N o r m a li z e d p r o b a b ili t y FIG. 3. Kinetic energy distributions of the most energeticprotons produced by 0.5 GeV and 1.0 GeV neutrons.
Estimating the threshold for proton identification to be30 MeV, we see that a large fraction of the knock-outprotons could be identified.This remains true even at lower neutron energy. Forexample, for a 300 MeV neutron, on average, 34% of theenergy goes into knock-out protons above the 30 MeVthreshold, according to our simulations. Additional 4%of the energy goes into protons below that threshold, 40%is lost to nuclear breakup, 14% goes into gammas, 4% isimparted to heavy ions knocked out of the nuclei, 2% goesto nuclear recoil, and, finally, 2% to pions produced inhadronic collisions. Thus, the full energy budget is quitecomplicated, and the accuracy of energy reconstructiondepends on how much of that energy can be recovered.Three comments about these numbers are in order.First, the process is highly stochastic, and event-to-eventvariations are found to be large. For example, the energyfraction in the leading proton has a range of 38 ± FLUKA , and direct test-beammeasurements are highly desirable to validate the simu-lations.The sub-threshold protons and the heavy ions appearas part of the spray. Unlike Compton-recoil electrons,these low-energy hadrons are subject to large chargerecombination. Thus, if one wished to use the mea-sured charge in the spray to improve the neutron energyreconstruction—compared to what is possible from the leading proton alone—the composition of the spray mustbe reliably understood. This provides another motiva-tion for neutron test-beam studies.It is essential that experiments carry out quantitativemeasurements of the leading proton energy distributionand other physics described above. We are greatly en-couraged by the plans of ProtoDUNE to conduct a cal-ibration study with a pulsed neutron source. Anothersetup with the capabilities to study neutron interactionsin liquid argon is the mini-CAPTAIN detector. This ex-periment already ran and collected data at LANL [14],in a neutron beam with energies between 100 and 800MeV, but so far has only presented total cross sectionresults. We encourage the collaboration to analyze thedistribution of the resulting proton energies.To this end, we simulate energy reconstruction ex-pected from a neutron test beam. In Fig. 4, we presentresults for neutrons of initial energies of 0.1, 0.5, 1.0, and2.0 GeV.
IV. EFFECTS OF LIMITED VOLUME
As the next step, we will consider what happens if thedetection volume is limited. This study has two moti-vations. From the practical side, such a situation couldbe realized in ProtoDUNE [3], if one analyzes ionizationcharges collected in a single anode plane assembly, orlight detected by a single light collection bar [15]. It mayalso have implications for the design of near detectors, aswe noted in Ref. [2]. From the conceptual point of view,we would like to understand how the spatial developmentof the events impacts the accuracy of calorimetric mea-surements.We consider proton beams with two initial energy val-ues, 2 GeV and 7 GeV. The first case is motivated by therelevance to the DUNE experiment, where the neutrinoenergy varies in the ∼ × × × × × × × × ∼
80 cm, the fraction of unscat-tered protons exiting the 2 m × × Reconstructed neutron energy (GeV) N o r m a li z e d p r o b a b ili t y E n , true = Reconstructed neutron energy (GeV) best recchargeCDR 0.0 0.5 1.0 1.5 2.0 2.5
Reconstructed neutron energy (GeV)
Reconstructed neutron energy (GeV)
FIG. 4. Distributions of the neutron reconstructed energies, for four representative values of the true energy, E n = 0 .
1, 0 . .
0, and 2 . blue ), and (2)only total ionization charge ( orange ). For comparison, the dashed curve shows the resolution assumed in the DUNE CDRdocument. Energy-equivalent charge (GeV) N o r m a li z e dd i s t r i b u t i o n Energy-equivalent charge (GeV) N o r m a li z e dd i s t r i b u t i o n Energy-equivalent charge (GeV) N o r m a li z e dd i s t r i b u t i o n Energy-equivalent charge (GeV) N o r m a li z e dd i s t r i b u t i o n Energy-equivalent charge (GeV) N o r m a li z e dd i s t r i b u t i o n Energy-equivalent charge (GeV) N o r m a li z e dd i s t r i b u t i o n FIG. 5. Distribution of ionization charges created by an injected proton in cubic volumes of length 2 m, 3 m, and 5 m. Thetop row corresponds to injected proton energy of 2 GeV, the bottom row to proton energy of 7 GeV. The dashed curves in thetop row show the corresponding Gaussian fits. ∼ exp( − / . ∼ × × × × − − z (m) − − − x ( m ) − − − − C h a r g e d e p o s i t i o n i n t e n s i t y ( a r b . u n i t s ) FIG. 6. Distribution of ionization charges created by injecting4 × protons of 2 GeV kinetic energy at position (0 , , z direction.All charges have been projected along the y direction. Thesolid contours show the regions enclosing 95% and 99% of thetotal charge. The dashed lines show the 2 m × × × × × × tribution of the ionization charge in our simulation. Fig-ure 6 shows the distribution of charges found after inject-ing 4 × protons at position (0 , , z direction. The y coordinate has been suppressed,so that the graphics shows the charge projection ontothe ( x, z ) plane. The contours show the regions enclos-ing 95% and 99% of the total charge. The cubic volumesconsidered above are shown with dashed lines.We clearly see that the smaller volumes fail to enclosethe full charge distribution. Even the 5-m box misses afew percent of the ionization charge. These charges forman extended “halo” and are induced mostly by diffusingneutrons. Interestingly, some of the charge lies in thebackward direction (at negative z ). This charge cannotbe captured at ProtoDUNE, but may be detected in theDUNE far detector.For 7 GeV injected protons, the effects of the limitedvolume are even more pronounced, as indicated by anextended shoulder between the unscattered spike and thepeak of the scattered distribution.This shows that behind seemingly simple Gaussian res-olution curves seen in Sec. III lies a complicated dynam-ical picture of shower development. The resolution of adetector may thus be affected by its geometry and otherrelevant considerations, such as requirements to fiducial-ize the detection volume to eliminate cosmic-ray-inducedand other contamination. V. DISCUSSION
The results of our large-volume simulations can besummarized by plotting the energy resolution for eachparticle type, as a function of energy. This is shown inFig. 7, where injection energies up to 3 GeV are consid-ered. The colored curves correspond to the three recon-struction scenarios we consider, as labeled. The dashedcurves indicate the resolution assumed in the CDR doc-ument [4, 5].We immediately see that the role of neutrons is abso-lutely crucial for the accuracy of charge hadron energyreconstruction: the green curves, which correspond todiscarding all neutrons, show the resolution that is sig-nificantly worse than the other two cases. This is in linewith what we already discussed in Sec. III for specific en-ergy values. Even though the average fraction of energythat goes into secondary neutrons is quite stable, about20%, the event-by-event variation of this fraction is verylarge [2].Let us now turn to the other two reconstruction sce-narios. Notably, at sufficiently high energies, the frac-tional energy resolution is well fit by a E − / scal-ing law. Specifically, for protons we obtain 42% / √ E for the charge-only method and 25% / √ E for the best-reconstruction method. For charged pions, we find42% / √ E for the charge-only method and 21% / √ E forthe best-reconstruction method. For neutrons, the cor-responding relationships are 40% / √ E for the charge-only method and 23% / √ E for the best-reconstructionmethod. The first observation, therefore, is that at highenergies, the energy resolution performance is remarkablysimilar for each particle type.The second observation is that the E − / law breaksdown at lower energies, and the fractional resolution ac-tually improves as the energy is decreased to 0.1 GeV.Let us discuss the underlying reasons for this behavior.At the most basic level, liquid argon detectors operateas calorimeters, in which ionization charge deposited byparticles created as a result of neutrino interactions isused to infer the total energy. Conversion from chargeto energy involves, however, a number of steps that eachintroduce uncertainty. The size of this uncertainty de-pends on the amount of additional information gained inthe reconstruction process. Let us summarize the rele-vant factors:a. For a given final state track, the first consideration isits PID. Conversion from charge deposited along a trackto energy needs to correct for charges lost to recombina-tion. This correction is higher for slow-moving protonsthan for minimally ionizing fast pions and muons.b. The next fundamental ingredient in the energy re-construction of charged hadrons is their interactions inthe medium. Indeed, once the particle type is identi-fied, dQ/dx along its trajectory can be reasonably wellrelated to dE/dx , until the particle undergoes a hadronicinteraction with a background argon nucleus.In hadronic collisions, the energy flow is affected by Proton kinetic energy (GeV) F r a c t i o n a l r e s o l u t i o n ( % ) best recchargecharge, no nCDR 0.0 0.5 1.0 1.5 2.0 2.5 3.0 π − total energy (GeV) F r a c t i o n a l r e s o l u t i o n ( % ) best recchargecharge, no nCDR 0.0 0.5 1.0 1.5 2.0 2.5 3.0 Neutron kinetic energy (GeV) F r a c t i o n a l r e s o l u t i o n ( % ) best recchargeCDR FIG. 7. Simulated hadron energy resolution as a function of its true energy. Left to right: protons, negative pions, and neutrons. several processes:i. Some energy is lost to the breakup of the targetnucleus. Some can be emitted by de-excitation gammarays, which create small charge deposits that may be de-tected with a varying degree of efficiency, depending onthe detection thresholds.ii. Energy can be imparted to one or more hadrons,such as secondary pions created in the collision, nucleonsknocked out of the nucleus, or a combination of pionsand nucleons. For each secondary track, the accuracy ofconversion from charge to energy loss again depends onwhether PID information is available.iii. Some of the knocked-out nucleons in the last stepcould be neutrons, and these present a special challenge,as discussed in Sec. III C. They do not leave tracks andcan dissipate energy by exciting and breaking up numer-ous argon nuclei, resulting in a spray of small charge de-posits. They may also produce tertiary charged hadrons,which are likewise detached from the main event. Energyreconstruction depends on whether and how often suchdetached charge deposits can be identified with the mainevent.Above all, the main conclusion here is this: the na-ture of the energy resolution is dictated by the frequencyof hadronic collisions. Hadrons above 1 GeV (and theirproducts) are expected to undergo multiple collisions. Inthis regime, the distribution of energy among the sev-eral channels becomes stochastic, and the reconstructedenergy distribution approaches a Gaussian form. No-tice that the widths of the Gaussians, which have beenderived earlier, are found to be very similar for thethree hadron types. They are controlled by the similarhadronic interaction rates.On the other hand, at lower energies, the interac-tions are only sporadic, and the distributions of recon-structed energies become more and more asymmetric.The Gaussian width prescriptions obtained at higher en-ergies break down at these energies. For protons of ∼
100 MeV energy, the high-energy Gaussian width failsdramatically. Instead, the energy can be reconstructed with very good accuracy, assuming good PID.As a corollary, for protons and charged pions, the worstrelative resolution occurs at energies of several hundredMeV, as seen in the graphs. We see that this behavioris not captured by the assumptions of the CDR (shownwith dashed curves).Given the crucial role of the hadronic interactions, it isessential that our predictions for them (made with
FLUKA )be directed tested with ProtoDUNE. This applies notonly to the frequency of collisions, but to the statisticsof the final states produced.Let us now consider some important applications forour results. Consider two types of problems: • estimating the impact of various detectorchanges—such as gradually improving neutrondetection efficiency, or improving PID; and, • understanding the impact of various cross sectionuncertainties, especially the impact of several con-tinuously varied parameters in the model.For example, suppose one considers changes to the pionproduction model for neutrino-nucleon interactions, toreduce the tensions with the electron scattering data [16].This adjustment may result in the modification of theproperties of the hadronic final states [17]. One wouldlike to be able to gauge the impact of these changes onneutrino energy reconstruction, without having to regen-erate the full event simulation set after each incrementaladjustment, which carries prohibitive computing costs.This calls for the need to build simplified codes, aswe mentioned in the Introduction. Such codes would,instead of simulating full events in the detector, applycertain “smearing” prescriptions to the final-state parti-cles outputted by the neutrino-nucleus event generator,in the spirit of FastMC [4, 5]. Such a framework wouldgive approximate answers to the questions of energy reso-lution and energy scale calibration, in response to variousassumptions about cross section physics or detector per-formance. It can also be used to explore sensitivity tovarious new physics scenarios.Our virtual test-beam simulations provide crucial in-put into such a framework. As we saw, it gives not onlythe width of the distribution of reconstructed energy,but also when the energy of a particle can be Gaussian-smeared and when a different functional form must beused.
VI. CONCLUSIONS
In summary, the two main lessons of our investigationsin this paper are as follows. First, the energy resolution ofliquid argon time-projection chamber detectors stronglydepends on the detector parameters and performance.Among the relevant factors are the detector geometry,which may impact event containment, and the quality ofevent reconstruction. In particular, inability to recon-struct detached charge deposits due to neutrons leads toa large resolution penalty.Second, for hadrons with energies in the GeV range,the resulting distributions of reconstructed energies areoften non-Gaussian. Namely: • With neutrons dropped, we consistently find a verynon-Gaussian charge distribution, even when thedetection volume is large. • Conversely, in a limited volume (2 m × × • We have considered a total charge measurementwith no PID corrections. In a large volume, withdetached charges created by neutrons, the distribu-tion starts approaching Gaussian at 2 GeV. • The best-case scenario is when the charges are col-lected over a large volume, neutron-induced chargesare included and full PID corrections are imple-mented. In this case, the distribution is Gaussianeven at 1 GeV. • Even in the best-case scenario, however, at lowhadron energies the distribution is always non-Gaussian; this happens for proton energies (cid:46) . (cid:46) . O (1 GeV), the shower maynot be developed, as we have seen here.Our findings have two major applications. First, theycan be directly applied to the analysis of the test beamProtoDUNE data. The comparison should make it pos-sible to validate the parameters of the simulation frame-work, as well as help guide the analysis of the experimen-tal data.Second, they have implications for how the physicsreach of liquid argon experiments is assessed. In situa-tions where one is interested in general estimates of sen-sitivity to Beyond-the-Standard-Model scenarios, it maybe acceptable to approximate the detector response withsimple Gaussian errors. However, when accurate mod-eling is required—for example, in studying sensitivity tospecific oscillation parameters—detailed, realistic modelsof the near and far detector are required for the resultsto be credible.We hope that the present study will help with con-structing such detailed models. ACKNOWLEDGMENTS
We are grateful to Flavio Cavanna and Yun-Tse Tsaifor useful discussions. We owe special thanks to the
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