First simulation study of trackless events in the INO-ICAL detector to probe the sensitivity to atmospheric neutrinos oscillation parameters
FFirst simulation study of trackless events in the INO-ICALdetector to probe the sensitivity to atmospheric neutrinososcillation parameters
Aleena Chacko, ∗ D. Indumathi,
2, 3, † James F. Libby, ‡ and P.K. Behera § Indian Institute of Technology Madras, Chennai 600 036, India The Institute of Mathematical Sciences, Chennai 600 113, India Homi Bhabha National Institute, Training School Complex,Anushakti Nagar, Mumbai 400085, India (Dated: December 18, 2019)
Abstract
The proposed India-based Neutrino Observatory will host a 50 kton magnetized iron calorime-ter (ICAL) with resistive plate chambers as its active detector element. Its primary focus is tostudy charged-current interactions of atmospheric muon neutrinos via the reconstruction ofmuons in the detector. We present the first study of the energy and direction reconstructionof the final state lepton and hadrons produced in charged current interactions of atmosphericelectron neutrinos at ICAL and the sensitivity of these events to neutrino oscillation parameters θ and ∆ m . However, the signatures of these events are similar to those from neutral-currentinteractions and charged-current muon neutrino events in which the muon track is not recon-structed. On including the entire set of events that do not produce a muon track, we find thatreasonably good sensitivity to θ is obtained, with a relative 1 σ precision of 15% on the mixingparameter sin θ , which decreases to 21%, when systematic uncertainties are considered. ∗ Electronic address: [email protected] † Electronic address: [email protected] ‡ Electronic address: [email protected] § Electronic address: [email protected] a r X i v : . [ phy s i c s . i n s - d e t ] D ec . INTRODUCTION AND MOTIVATION The phenomenon of neutrino oscillations arises when neutrino-mass eigenstates ( ν , ν and ν ) coherently superpose to form neutrino-flavor states ( ν e , ν µ and ν τ ). The masseigenstates and flavor states are related by a 3 × θ , θ and θ ) and the CP -violating Dirac phase δ CP . Alongwith the dependence on these four parameters, the oscillation probability depends uponthe mass-squared differences ∆ m ij ≡ m i − m j , ( i (cid:54) = j ), with i and j being any of the masseigenstates. As only two of the three values of ∆ m ij are independent, oscillations areusually parametrized by ∆ m and ∆ m . Hence, measurements of neutrino oscillationsare only sensitive to the ∆ m ij and not to the neutrino masses.Recent measurements from solar and reactor data [2] give the best-fit value of the “solarparameters” as, sin θ = 0 . +0 . − . and ∆ m = (7 . ± . × − eV [3]. Further-more, reactor ¯ ν e data precisely determines the mixing angle, θ [4–6]. Measurementsof atmospheric and accelerator neutrinos are sensitive to the “atmospheric parameters”∆ m and θ . While | ∆ m | = 2 . ± . × − eV [7] has been measured, its sign,which determines the neutrino mass ordering, as well as the octant of θ are currentlyunknown. Current and near-future experiments [8–10] can confirm the sign of ∆ m beingpositive (normal ordering or hierarchy, NH) or negative (inverted ordering or hierarchy,IH), as well as resolve the octant problem i.e. , θ = π/ θ < π/ θ > π/ θ , with a best fit value of sin θ = 0 . +0 . − . .The proposed magnetized iron calorimeter (ICAL) detector at the India-based NeutrinoObservatory (INO) is an experiment that can probe the mass hierarchy [12]. The ICALis most sensitive to atmospheric muon neutrinos (and anti-neutrinos), where the longtracks of muons produced in charged-current interactions of muon neutrinos (CC µ ) via ν µ N → µ − X ( ν µ N → µ + X ) can be used to reconstruct both the magnitude and directionof their momenta, as well as the charge of the muon. Here X is any set of final-statehadrons. The advantage of having a magnetised iron calorimeter is its ability to clearlydistinguish µ + from µ − , which allows the differing matter effect for neutrinos and anti-neutrinos to be used to access the mass hierarchy. Hence analyzing muon events willyield the bulk of the sensitivity to oscillation parameters. Several studies of atmosphericneutrino oscillation parameters using muon events at INO have been reported [13–16].Since neutrino experiments are statistically limited, any neutrino interactions that can2e reconstructed in addition to the CC µ events in which there is muon track can poten-tially improve the sensitivity to oscillation parameters. Here we study the contributionfrom the sub-dominant electron-neutrino events, even though the detector configurationpresents challenges in reconstructing the electron events correctly. In addition, CC µ events in which no track is reconstructed are considered, because they have an almostidentical topology to the electron-neutrino interactions.The ICAL will have sensitivity to atmospheric electron neutrinos (and anti-neutrinos)through the charged-current interaction (CC e ), ν e N → eX ( ν e N → e + X ). So only thefinal-state electromagnetic and hadronic showers can be used to reconstruct the event.The passive elements between each sampling layer in the ICAL are iron plates of 5.6 cmthickness, which corresponds to approximately three radiation lengths, so the detectorwill have limited capability to reconstruct the electromagnetic showers produced by theelectrons. Previous simulation studies have characterized the sensitivity of ICAL to thehadron energy [17, 18] and preliminary results are available [19] on its sensitivity to thehadron direction. Both the energy and direction are reconstructed through the patternof hits that will be left by the hadronic shower in the detector. In this paper, for thefirst time, a detailed simulation study is made of the ability of the ICAL to reconstructelectrons and determine the ν e momentum, and to examine the sensitivity of these eventsto neutrino-oscillation parameters. Such CC e events appear as “trackless” events in thedetector, in contrast to most CC µ events, where a final-state muon often produces a longtrack.Note that there are other sources of trackless events, namely, neutral current (NC)events, where the final state lepton is not observed in the detector, as well as those CC µ events where the reconstruction algorithm for the muon track fails. In all these tracklessevents, only a shower is obtained; note, however, that for CC e /CC µ events, the showerincludes hits from both electron/muon and the associated hadrons in the interaction whilefor NC events the shower is due to the hadrons alone. We analyze these trackless eventsand show that they have good sensitivity to the oscillation parameter θ .The rest of the paper is arranged in the following manner. We begin with the analysisof the pure CC e sample in a hypothetical ICAL-like detector that is fully efficient and hasperfect reconstruction of CC e events. In Sec. 2 we identify the regions in electron-neutrinoenergy and direction space, where there is sensitivity to the oscillation parameters. InSec. 3 we briefly describe the salient parts of the GEANT4 [20, 21] ICAL detector codethat are used in the analysis, and also briefly discuss the generation of events in the3etector using the NUANCE neutrino generator [22]. In Sec. 4, we perform a χ analysisto determine the sensitivity of CC e events to the neutrino-oscillation parameters, assuminga hypothetical ICAL-like detector. In Sec. 5, we consider the realistic case of sensitivity tooscillation parameters of the combined trackless sample of CC e , NC, and trackless CC µ events in the proposed ICAL detector at INO, including systematic uncertainties as well.We conclude with a discussion in Sec. 6. II. THE OSCILLATION PROBABILITIES
Detailed simulations studies indicating the potential of the ICAL to measure ∆ m and θ have been performed using the dominant CC µ channel; these studies use reconstructedinformation about the muon momentum (magnitude and direction), the muon charge, andhadronic shower. Therefore, the contribution of CC µ events in determining the oscillationparameters is well-understood. Here we study the complementary set of events where notrack could be reconstructed in the event sample. These events include CC e events, whichhave hitherto not been studied with the ICAL.Figure 1 shows the relevant oscillation probabilities for CC e events, P ee and P µe , as afunction of the zenith angle θ ν (direction of the neutrino with respect to the verticallyupward direction) for a single value of neutrino energy ( E ν = 5 GeV). Here P ee is thesurvival probability of ν e and P µe is the probability of conversion of ν µ to ν e [23]. Inthe top panel of Fig. 1, P ee and P µe , are shown for three different values of ∆ m whilethe bottom panel shows their behaviour for three different values of θ . As can be seenfrom Fig. 1, the oscillation probability P µe is sensitive to both ∆ m as well as θ whilethe survival probability P ee is sensitive to ∆ m alone. In addition, the effect of the∆ m variation is opposite for both probabilities i.e. , P ee increases with increasing ∆ m , P µe decreases with increasing ∆ m and vice versa. The true values of the oscillationparameters used in this analysis is given in Table I, along with the 3 σ confidence level(C.L.) for the parameters. We assume the normal ordering throughout this paper, unlessotherwise stated, because trackless events have no sensitivity to mass-ordering as ν and¯ ν are indistinguishable.To see a significant oscillation signature in the distributions of electron events, eitherthe survival probability P ee should be significantly less than 1 or the appearance prob-ability P µe should be significantly greater than 0. Therefore, we explore the parametersensitivity in the regions where P ee < . P µe > . θ ν and E ν (deg) n q ee P eV -3 · = 2.35 m D eV -3 · = 2.45 m D eV -3 · = 2.55 m D E = 5 GeV (deg) n q e m P eV -3 · = 2.35 m D eV -3 · = 2.45 m D eV -3 · = 2.55 m D E = 5 GeV (deg) n q ee P (cid:176) = 53 q (cid:176) = 45 q (cid:176) = 37 q E = 5 GeV (deg) n q e m P (cid:176) = 53 q (cid:176) = 45 q (cid:176) = 37 q E = 5 GeV
FIG. 1: P ee (top left) and P µe (top right) as a function of zenith angle, shown for three valuesof ∆ m (2 . × − eV [dotted blue line], 2 . × − eV [solid black line], 2 . × − eV [dashed red line]). P ee (bottom left) and P µe (bottom right) as a function of zenith angle, shownfor three values of θ [left] (53 ◦ [dotted blue line], 45 ◦ [solid black line], 37 ◦ [dashed red line]).TABLE I: Oscillation parameter values assumed for the analysis [24]. The values of sin θ ,sin θ and ∆ m have been fixed at their central value, because marginalizing them over theirpresent 3 σ range causes very little change in the results.Parameter Value 3 σ rangesin θ .
307 0.268 - 0.346sin θ .
51 0.39 - 0.63sin θ . m [10 − eV ] 7 .
53 6.99 - 8.07∆ m [10 − eV ] 2 .
45 2.3 - 2.6 δ CP [deg] 0 0 - 360 to establish whether there is enough sensitivity to proceed with further studies. Fig. 2shows P ee and P µe as a function of E ν and cos θ ν . As expected both P µe and P ee show5otential sensitivity in the region where E ν > θ ν >
0, which correspondsto upward-going neutrinos, with the highest sensitivity in the region around E ν ∼ θ ν ∼ . (GeV) n E nq c o s <0.8 ee P <0.8 ee P (GeV) n E nq c o s >0.1 e m P >0.1 e m P FIG. 2: P ee < . P µe > . E ν and cos θ ν . III. EVENTS GENERATION AND ANALYSIS
Atmospheric neutrinos originate from the decay of particles in hadronic showers gener-ated by cosmic rays, which are primarily composed of protons, interacting with the upperatmosphere. The hadronic showers contain many charged pions that subsequently decayalmost exclusively via the following chain: π ± → µ ± + ν µ ( ν µ ); µ ± → e ± + ν e ( ν e ) + ν µ ( ν µ ) . It can be seen that the flux of muon neutrinos (Φ µ ) is approximately twice the electron-neutrino flux (Φ e ), especially at low energies where the muon subsequently decays beforereaching the surface of the earth. These neutrinos interact with matter through CC andNC interactions. A. Event generation with the NUANCE neutrino generator
Atmospheric neutrino interactions in the 50 kton ICAL detector for an exposure time of100 years are simulated using the NUANCE neutrino generator, incorporating the Honda-3D atmospheric neutrino flux [25]. NUANCE generates these events for different crosssections, including quasi-elastic, resonance and deep-inelastic scattering. Since generatingNUANCE events for various oscillation parameters is quite time consuming, it is generated6nce for a specified detector exposure time and the oscillation effects are later includedevent-by-event using the accept-or-reject method.The number of events N Pα ( α = e, µ, τ ) that occur via the processes P , P = CC orNC, in a detector with N D targets during an exposure time T , is related to the productof the flux times the cross section. Therefore, N Pα = N D × T (cid:90) dE ν d cos θ ν (cid:20) P eα d Φ e dE ν d cos θ ν + P µα d Φ µ dE ν d cos θ ν (cid:21) σ Pα ( E ν ) , (1)where σ Pα is the cross section for the interaction of neutrino flavour ν α via process P inthe detector. Here Φ e and Φ µ are the electron and muon atmospheric neutrino fluxesrespectively. A similar expression holds for anti-neutrinos as well.In particular, N CC e and N CC µ correspond to CC e and CC µ interactions in ICAL. Notethat (cid:88) α P βα = 1 , for β = e, µ , the sum of all NC interactions N NC ≡ N NC e + N NC µ + N NC τ , is independent of oscillation probabilities, thus the oscillation parameters. Therefore, only N CC e and N CC µ are sensitive to the neutrino-oscillation parameters. B. Analysis of pure CC e events To understand the potential sensitivity to θ we start by performing a study assuminga hypothetical ICAL-like detector with 100% reconstruction efficiency and perfect reso-lution. This provides a benchmark for the maximum amount of information regardingneutrino oscillations that can be extracted from the ICAL data.First a sample corresponding to five years of exposure that contains unoscillated ν e and ν µ fluxes is considered. Then the following simulation algorithm is used to incorporateoscillations for CC e events. The CC e events have contributions from the ν e fluxes via thefirst term in Eq. 1, viz. , Φ e σ CCe , weighted by P ee , and similarly from the ν µ flux via thesecond term. The weight is implemented as follows. A uniform random number r between0 and 1 is generated. Those events for which P ee > r are taken to be survived electronevents. Similarly, NUANCE events are generated in which the electron and muon fluxesare swapped. This corresponds to events from the second term, viz. , Φ µ σ CCe , weightedby P µe . Then the oscillation probability P µe is calculated for every swapped ν e event; see7q. 1. Those events for which P µe > r (cid:48) , where r (cid:48) is a uniform random number between 0and 1, are taken to be oscillated electron events. Fig. 3 shows the fraction of CC e eventsarising from survived and oscillated fluxes. Approximately 94% of ν e events survive, whileonly ∼
3% of ν µ events oscillate into ν e due to the smallness of θ . However, note thatthese events are direction dependent; in addition, they arise from a term containing theatmospheric muon neutrino fluxes, as can be seen from Eq. 1, which are roughly twice theelectron neutrino fluxes; hence the contribution of these events, roughly 6% of the totalelectron neutrino events, will turn out to be significant. ) e F Without Oscillation (Entries 9949 n q cos - - e v e n t s / b i n e n ) e F Without Oscillation (Entries 9949 ) e s e F ee survived events (P e n ) e F ee With Oscil (PEntries 9342) e F ee With Oscil (PEntries 9342 ) m F Without Oscillation (Entries 22604 n q cos - - e v e n t s / b i n mn ) m F Without Oscillation (Entries 22604 ) e s m F e m oscillated events (P m n ) m F e m With Oscillation (PEntries 567) m F e m With Oscillation (PEntries 567 ) m F e m With Oscill (P
Entries 567
FIG. 3: Simulated cos θ distributions for CC e events arising from survived ν e (left) and oscillated ν µ events (right), with (solid blue line) and without (dashed red line) including oscillationprobabilities P αe . Figure 4 shows the ratio of oscillated to unoscillated events of the total (survivedand oscillated) electron events. The oscillation signature is most prominent for up-goingneutrinos (cos θ > .
5) with E ν ∼ µ events are generated using the same algorithm.The sensitivity of CC µ events to the oscillation parameters ∆ m and θ , via the dom-inant term proportional to P µµ , is well-understood and is not repeated here. Again, the“swapped events” in this case are also small due to the smallness of P eµ . Finally, five-yearsamples of NC events are generated in the same way and are independent of P βα .The sensitivity and oscillation studies presented so far are for generator level events.For the studies that simulate the ICAL we need to reconstruct the events by a GEANT4-based detector simulation of the ICAL detector, and furthermore, select the tracklessevents in this sample. 8 n q cos - - un o s c / N o s c N h5Entries 10Mean 0.008202RMS 0.5763 e F )/ m F e m +P e F ee total events (P e n h5Entries 7Mean 4.193RMS 2.824 (GeV) n E un o s c / N o s c N h5Entries 7Mean 4.193RMS 2.824 e F )/ m F e m +P e F ee total events (P e n FIG. 4: Ratio of oscillated to unoscillated CC e events as a function of cos θ ν (left) and E ν (right), corresponding to five years of data. C. Event generation with GEANT
A part of the INO proposal is the construction of a 50 kton magnetised ICAL [26].The ICAL will be built in three modules each with a size of 16 m ×
16 m × . × width × height). Each module will comprise of 151 layers of 5.6 cm thick iron plates,which will be magnetised to a strength of about 1.5 T using copper coils. The activedetector elements of the ICAL will be the resistive plate chambers (RPCs) [26]. TheRPCs are gaseous detectors constructed by placing 2 mm spacers between two 3mm thickglass plates of area 2 m × µ events. The CC e events form the sub-dominant signal, both due to smaller fluxes andalso because ICAL is optimised for detecting CC µ events. We also have NC interactions,but the cross section for these interactions are small compared to CC µ interactions [27].The NUANCE-generated events are passed through the GEANT4-based simulation ofthe ICAL detector. Each event leaves a pattern of hits in the sensitive RPC detector.Long track-like events are typically associated with the minimum-ionising muons. Usinginformation about the local magnetic field that is incorporated into the GEANT code, a9alman-filter algorithm [28] is used to identify and reconstruct possible “tracks” whichcan be fitted to yield the particle momentum and sign of charge. Events where no trackcould be reconstructed are identified as trackless events . Notice that events which passthrough less than four layers of the detector are not sent to the Kalman filter for trackreconstruction and hence are included in the trackless events sample. The compositionof this sample is shown in Fig. 5. While roughly half the events in the vertical bins arefrom CC e events, the bins in the horizontal direction are dominated by trackless CC µ events. (About 1% of the time, an energetic pion from a hadron shower may give a trackand the event may be misidentified as a CC µ event.) In order to analyze these events weneed to calibrate the hits to the energy and direction associated with each event. We firstconsider the CC e events alone. e CCEntries 82434 reco q cos - - N u m b er o f e v e n t s e CCEntries 82434 m trackless CCEntries 93744 m trackless CCEntries 93744NCEntries 59871NCEntries 59871 FIG. 5: cos θ reco distribution for five-year samples of CC e (blue solid line), trackless CC µ (reddotted line) and NC (green dashed line) events. D. Direction reconstruction of trackless events
To reconstruct the direction of the shower, we use a method referred to as the raw-hit method [19]. A charged particle, produced by the interaction of neutrinos with thedetector, while passing through an RPC, produces induced electrical signals. These signalsare collected by copper pick-up strips of width 2 cm, which are placed orthogonal to eachother on either side of the RPC. The center of the pick-up strips defines x or y coordinateof the hits and the center of the RPC air-gap defines the z coordinate. The signals in thecopper strips thus provide either ( x, z ) or ( y, z ) information and are considered as “hits”,which are used to reconstruct the average energy and direction of the shower. Due to10he coarse position resolution of the ICAL detector, it is difficult to distinguish betweenelectron and hadron showers. Since in CC e and CC µ trackless events the shower actuallyarises from both the electron/muon and hadrons in the final state, the net reconstructeddirection will point back to that of the original neutrino, especially at higher energies sincethe final state particles from such events are forward-peaked. This is in contrast to thedirection reconstruction of showers in CC µ events where the muon track is reconstructed;here, the direction of the shower determines the net direction of the hadrons alone, sincethe direction of the muons can be independently determined. Finally, since the final statelepton is not detected in NC events, the shower direction is that of the hadrons in theevent, just as in the case of CC µ events with track reconstruction.If two or more x and y strips have signals within a single RPC in an event, there isan ambiguity in the definition of the ( x, y ) hit position. One or more of the positions arefake and are referred to as a ghost hit . Therefore, the reconstruction is done separately inthe x - z and y - z planes to avoid these ghost hits. Since the electron or hadron showers areinsensitive to the magnetic field, the average direction of the shower is reconstructed as, θ reco = tan − (cid:113) m x + m y ; φ = tan − (cid:18) m y m x (cid:19) , (2)where m x [ y ] are the slopes of straight line fits to the ( x, z ) [( y, z )] hit positions. Thesimulation requires that the hits are within a timing window of 50 ns to ensure theyare only from the event under consideration. Requirements on the minimum number oflayers with hits ( ≥
2) and minimum number of hits per event n hits ( ≥
3) are applied atthe reconstruction level to ensure that there are sufficient hits passing through enoughlayers to fit a straight line. Around 46% of the events satisfy these criteria. The timeinformation from each of these hit distributions i.e. , the slopes of the t x vs. z and t y vs. z distributions, allows us to reconstruct whether the event is an up-going or down-goingone. Approximately 10% of events have time slopes from the t x - z and t y - z distributionsof opposite signs; these events are discarded. Figure 6 shows an example of an up-goingevent and the corresponding position of hits in that event in the x - z and y - z planes.The reconstruction efficiency (cid:15) reco and relative directional efficiency (cid:15) dir are given by, (cid:15) reco = N reco N , (cid:15) dir = N (cid:48) reco N reco , (3)where N reco is the number of events reconstructed from the total number of events ( N ) and N (cid:48) reco is number of the events correctly reconstructed as up-going or down-going. Figure 7shows (cid:15) reco and (cid:15) dir as functions of cos θ ν . The E ν and cos θ ν averaged values of (cid:15) reco and11 (m) - - - - - - ( n s ) x t / ndf c – – c – – z (m) - - - - - - ( n s ) y t - / ndf c – – c – – z (m) - - - - - - x ( m ) / ndf c – – - / ndf c – – - z (m) - - - - - - y ( m ) - - - - - / ndf c – - p1 0.07751 – - / ndf c – - p1 0.07751 – - FIG. 6: Example fits (top panel) to z vs. t x (left) and z vs. t y (right) distributions for one eventwhich was produced by an electron neutrino with E ν = 1.59 GeV and cos θ ν = 0.48. Fits to thedistribution (bottom panel) of z - x (left) and z - y (right) hits for the same example event. Here p p (cid:15) dir are (41 . ± . . ± . θ ν distribution before and after reconstruction. Notice thatangular smearing leads to an excess of events in the vertical directions compared to theNUANCE level events while leaving very few events in the horizontal bins.12 q cos - - ( % ) rec o ˛ n q cos - - ( % ) d i r ˛ up going eventsdown going events FIG. 7: Reconstruction efficiency, (cid:15) reco (left) and the relative directional efficiency (cid:15) dir (right) asa function of cos θ ν . Note that the y -axis scales on the two graphs are different. e n q cosEntries 198945 q cos - - e v e n t s / b i n e n e n q cosEntries 198945 reco q cosEntries 82433 reco q cosEntries 82433 FIG. 8: The distribution of the cos θ ν (dashed red line) and reconstructed cos θ reco (solid blueline). E. Energy reconstruction of trackless events
The total energy reconstructed from the hit information is labelled as E reco . As dis-cussed above, for the CC e and CC µ events sample, this should give the incident neutrinoenergy while for NC events, this is the hadron energy in the final state. It is not possibleto obtain the reconstructed energy directly from the hit information; rather it is inferredvia a calibration of the number of hits as a function of the true energy. Taking intoconsideration the same selection criteria applied for direction reconstruction, we removethree hits from each event so that we calibrate true energy vs. ( n hits − e events). For each of these hitdistributions, the mean of number hits n ( E ) is plotted against the mean energy E of13vents within a specific energy range. This data is then fit to,¯ n ( E ) = n − n exp( − ¯ E/E ) , (4)where n , n and E are constants, as shown in the right side of Fig. 9. h6Entries 1359Mean 0.1285 – – nhits F re qu e n c y h6Entries 1359Mean 0.1285 – – : (5.9 - 6.4) GeV n E (GeV) n E M e a n nh i t s / ndf c – – – c – – – hits (n FIG. 9: Left: example of hits distribution in the E ν range (5.9 to 6.4) GeV. Right: n ( E ) vs. E with the fit superimposed. After obtaining the values of constants n , n and E , we invert Eq. 4 to estimate thereconstructed energy, E reco . In Fig. 10, which shows the E ν distribution before and afterreconstruction, we see that the reconstructed events have shifted towards high energy.Most of the low energy events are reconstructed as high energy events because of theupper tail in n hits distribution (see Fig. 9), because of which we have more reconstructedevents with higher energy. n EEntries 82433
E (GeV) e v e n t s / b i n e n n EEntries 82433 reco
EEntries 80655 reco
EEntries 80655
FIG. 10: Distribution of true E ν (dashed red lines) and reconstructed E reco (solid blue lines)energy for CC e events. . Sensitivity after reconstruction Using the simulation algorithm the oscillations were again incorporated in the unoscil-lated flux of reconstructed θ reco and E reco . Figure 11 shows the ratio of oscillated tounoscillated cos θ reco and E reco distributions for selected events. As seen in Fig. 4, wherewe had taken a sample corresponding to five-year data assuming 100% efficiency andperfect resolution, even after reconstruction the oscillation signature is still prominent inregions where E ν > θ ν > . h5Entries 10Mean 0.003878RMS 0.5769 reco q cos - - - - - un o s c i / N o s c i N h5Entries 10Mean 0.003878RMS 0.5769 e F )/ m F e m +P e F ee reconstructed events (P e n h5Entries 7Mean 4.191RMS 2.835 (GeV) reco E un o s c / N o s c N h5Entries 7Mean 4.191RMS 2.835 e F )/ m F e m +P e F ee reconstructed events (P e n FIG. 11: Ratio of oscillated to un-oscillated CC e events as a function of cos θ reco (left) and E reco (right), for 50 ×
100 kton-years of exposure time.
IV. SENSITIVITY OF ELECTRON EVENTS TO OSCILLATION PARAME-TERS
To assess the sensitivity of pure CC e events in ICAL to oscillation parameters, a χ analysis is performed assuming an ICAL-like detector that can also perfectly reconstructand discriminate such pure CC e events; the analysis including all trackless events ispresented in the next section. First, a set of 100 years of data is simulated with the truevalues of the oscillation parameters as given in Table I, which is later scaled down to10 years for the statistical analysis. The simulated data are then fit to the theoreticalexpectation for a set of oscillation parameters varied in their 3 σ ranges, by binning it inten cos θ reco bins of equal width and seven E reco bins of unequal width in the range 0 to10 GeV (see Fig. 11). The fit is the minimization of a Poissonian χ χ = 2 (cid:88) i (cid:88) j (cid:34) ( T ij − D ij ) − D ij ln (cid:18) T ij D ij (cid:19)(cid:35) , (5)15here T ij and D ij are the “theoretically expected” and “observed number” of eventsrespectively, in the i th cos θ reco bin and j th E reco bin. We find that this hypotheticalcase with a sample of just CC ν e events, without including other trackless events andsystematic uncertainties, does show sensitivity to neutrino oscillation parameters.Figure 12 shows the effect of binning in cos θ reco and E reco separately, as well as binningin both observables. With binning in cos θ reco alone, we find that it is possible to obtaina relative 1 σ precision on sin θ of 20%. There is no significant change when the eventsare binned in both observables. Therefore, for the rest of the analysis we present resultsfrom fits to cos θ reco bins alone, with events summed over all E ν . Since the effect ofincreasing (decreasing) ∆ m leads to an increase (decrease) and decrease (increase) in P ee and P µe , respectively (Fig. 1 top panel), sensitivity to ∆ m from CC e events in ICALis inconsequential. Hence in the rest of the paper we consider the sensitivity to θ alone.We now consider a realistic analysis of all trackless events. q sin cD reco q cos reco E reco ,E reco q cos s s s FIG. 12: ∆ χ as a function of sin θ with bins in cos θ reco (solid blue lines) alone, E reco (dottedred lines) alone and in both (dashed green lines) cos θ reco and E reco . “Data” were generated withtrue sin θ = 0 . Relative 1 σ precision is defined as 1 / th of the ± σ variation around the true value of the parameter[12]. . REALISTIC ANALYSIS OF TRACKLESS EVENTS IN ICALA. Selection criteria Since the CC e events have been reconstructed through their showers (both electro-magnetic and hadronic), the NC events that produce showers (only hadronic) may bemisidentified as CC e events, even though we expect the shower pattern to be differentin these two cases. A useful set of parameters to separate these events is the number oflayers ( l ) that the shower has traversed and the average hits per layer ( s/l ) in an event, s being the number of hits in that layer [29]. While both CC e and NC events are ex-pected to traverse fewer layers than CC µ events (since the muon is a minimum-ionisingparticle that leaves long “tracks” in the detector), it is expected that CC e events willhave larger s/l because of the nature of the events. In addition, sometimes, due to largescattering or low energies giving a small number of hits, the Kalman-filter algorithm failsto reconstruct even a single track for CC µ events. Hence such “trackless” events alsohave showers as their signatures in the detector and can also be misidentified as CC e orNC events. In a realistic analysis with a detector such as ICAL, all these events need tobe considered together. It turns out that this fraction is substantial; about 53% of thetotal CC µ events, which occurs because of the large fluxes at low energies. Such eventshave very small s/l ∼ . s/l > e events,but it decreases the number of events in the sample, especially since a large fraction ofCC e events correspond to low energies and hence traverse fewer layers. Here, efficiency isdefined as the percentage of CC e events passing the s/l selection in total CC e events andpurity is the percentage of CC e events in all type of events passing s/l selection.Different selection criteria on s/l , s/l > s/l > . s/l > .
8, and s/l >
2, were usedand the sensitivity to sin θ determined. It was found that the sensitivity is dominatedby the statistics, since the harder cuts decrease the total number of events available in theanalysis. While efforts are on going to improve the Kalman-filter algorithm, as well as toimprove the efficiency of separating the CC e from the NC and trackless CC µ events, inwhat follows, we include all events (CC e , NC and trackless CC µ ) in the analysis and donot apply any further selection criteria on s/l .In the next section of this paper, we examine the effect of the inclusion of all thesetrackless events on the sensitivities to the neutrino-oscillation parameters.17 umber of layers (l) M e a n s /l e CC m CC e NC m NC FIG. 13: Mean of average hits per layer( s/l ) as a function of number of layers( l ) for CC e (bluetriangle), trackless CC µ (red star) and NC (pink circle for NC e and green square for NC µ )events. B. χ analysis of the entire sample of trackless events We now repeat the χ analysis, including all trackless events. As before, the parametersnot being studied are fixed at their true values as given in Table I. Since θ is so preciselyknown, it is also kept fixed in the analysis. We consider the inclusion of systematic errorsin the next section.With the inclusion of all trackless events, the Poissonian χ without systematics is: χ = 2 (cid:88) i (cid:20) T i − D i − D i ln (cid:18) T i D i (cid:19)(cid:21) , (6)where T i now include the original CC e events, and both the NC and trackless CC µ eventsas well, in the i th cos θ reco bin. The result of the analysis for the sensitivity to sin θ is shown in Fig. 14. It can be seen that inclusion of all trackless events increases therelative 1 σ precision on sin θ to 15%. The improvement in sensitivity to sin θ can beunderstood as the effect of inclusion of the low energy trackless CC µ events ( ∼
42% oftotal CC µ events), since NC events do not have sensitivity to oscillation parameters andsimply improve the overall normalization uncertainties. C. Including systematic uncertainties
So far, we have not considered the effect of systematic uncertainties on the sensitiv-ities. We incorporate them through the pull method [30, 31], where each independent18 q sin cD CCeCCe+bkg s s s CCeAll trackless
FIG. 14: ∆ χ as a function of sin θ with only CC e events (solid blue lines) compared withthe sensitivity when all trackless events (dotted red lines) are included. source of systematic uncertainty is added to the difference of the theoretically expectedand observed events through an univariate gaussian random variable ( ξ ) referred to as the pull . To avoid overestimation of the systematic uncertainties, penalties are implementedby adding ξ terms. We consider two sources of systematic uncertainties: ( i ) a 5% un-certainty on the flux dependency on θ ν [30] and ( ii ) a 2% uncertainty on the efficiency ofreconstruction. In principle, it is possible to include an additional systematic uncertaintydue to the overall flux normalisation; however, a detailed analysis of the higher energy( E ν > µ events [32] has shown that such a detector can determine the overallnormalisation to about 1.5% and hence we ignore this source of uncertainty.
1. Uncertainties due to reconstruction
The uncertainty on the efficiency of reconstruction of the evernt is uncorrelated betweenCC e , CC µ and N C events. This is because the contribution from CC µ events includesmainly the low energy events (which do not have sufficient hits to be reconstructed inthe Kalman filter) while the entire CC e sample corresponds to low energies since theelectron-neutrino fluxes are much softer than the muon-neutrino fluxes (the latter arisesonly in the secondary three-body decay of the cosmic muons). On the other hand, thereconstruction efficiency for NC events is small because they do not survive the minimumnumber of hits ( ≥
3) criterion required to reconstruct their direction, which is the resultof the final-state neutrino taking away a substantial part of the available energy. WhileCC e events also arise from a softer flux spectrum, the presence of electrons in the final19tate adds to the total number of hits and hence more CC e events pass these selectioncriterion. In any case, it can be seen that the reconstruction efficiencies of the differentevents contributing to the analysis have different origins and are hence uncorrelated. Wetherefore apply a 2% systematic uncertainty on the reconstruction efficiencies, but includethem in the analysis as three different uncorrelated pulls, one for each channel.With the addition of these systematics, the χ now becomes, χ = min { ξ } (cid:88) i (cid:26) N i ( ξ ) − D i − D i ln (cid:20) N i ( ξ ) D i (cid:21)(cid:27) + ξ Z + ξ e + ξ CC µ + ξ NC , (7)where the total events are given in terms of the CC e ( T CC ei ), CC µ ( T CC µi ) and NC ( T NC i )events as, N i ( ξ ) ≡ (cid:110)(cid:16) T CC ei + T CC µi + T NC i (cid:17) (1 + π i ξ Z ) + π reco i (cid:16) T CC ei ξ CC e + T CC µi ξ CC µ + T NC i ξ NC (cid:17)(cid:111) , (8)where π i is the correlated systematic uncertainty in the zenith-angle dependence for thedifferent sets of events, and ξ Z is the corresponding pull. Although the same uncorrelatederror π reco i is applied across all sets of events, three different pulls are applied to the CC e ( ξ T ), trackless CC µ component ( ξ CCµ ) and NC component ( ξ NC ) respectively, to accountfor the varying signatures of these events.The analysis is repeated with the inclusion of uncertainties on all three types of tracklessevents. As expected, the sensitivity decreases, as can be seen in Fig. 15, which shows ∆ χ as a function of sin θ with and without pulls. The results are also then marginalizedover the 3 σ range of the remaining neutrino oscillation parameters (excluding the solarparameters), as given in Table I and the result plotted in Fig. 15. The inclusion ofsystematic uncertainties as well as marginalisation, reduces the relative 1 σ precision onsin θ from 15% to 21%. VI. DISCUSSIONS AND CONCLUSIONS
Simulation studies of charged-current atmospheric muon neutrino events, CC µ , in theICAL detector have established its capability to precisely determine the so-called atmo-spheric parameters θ and ∆ m , including its sign (the neutrino mass ordering issue)through the observation of earth matter effects in neutrino (and anti-neutrino) oscillations.In this paper, for the first time, we consider the contribution to the sensitivity to atmo-spheric neutrino oscillation parameters from trackless events in the ICAL detector whereno track (typically assumed to be a muon) could be reconstructed. Such events arise from20 q sin cD All tracklessAll trackless : with pullsAll trackless : with pulls & marginilasation s s s All tracklessAll trackless : with pullsAll trackless : with pulls& marginalisation
FIG. 15: ∆ χ as a function of sin θ for all trackless events without pulls (blue solid lines),with pulls (red dashed lines) and with pulls after marginalisation (green dotted lines). charged current electron and muon events as well as from neutral current interactions inthe detector.We used a simulated sample generated by the NUANCE neutrino generator, whichcorresponds to 100 years (or equivalently to 5000 kton-years) of data, in which the responseof ICAL is modelled by GEANT4. Using pure CC e events, we first studied the simulationresponse of an ICAL-like detector with electron separation capability to CC e events andshowed that the detector is capable of reconstructing the energy and direction of the finalstate shower (of the combined electron and hadrons in the final state) with reasonableaccuracy and efficiency. These reconstructed observables are then used in a χ analysis.It is shown that there was sufficient sensitivity to θ .However, it turns out that the ICAL will not be able to cleanly separate CC e events(containing both electron and hadrons in the final state) from NC events (with onlyhadrons in the final state) or CC µ events (where the muon track failed to be recon-structed). While various selection criteria are applied, in particular, the number of hitsper layer, to try and improve the discrimination to electron events, these requirementsled to worse sensitivities to the oscillation parameters, since the analysis is statistics dom-inated. We therefore analyze the total collection of so-called “trackless events” arisingfrom CC e , CC µ and NC events. The increased statistics as well as the known sensitivityof CC µ events to oscillation parameters changed the sensitivity to sin θ significantly.We summarize our results in Table II where we show the results when the events arebinned in the polar angle cos θ alone; we also show that there is hardly any change insensitivity when we include energy binning as well.21n summary, neutrino experiments are low counting experiments and hence it is impor-tant to reconstruct and analyse all possible events in neutrino detectors. A first study ofthe sub-dominant trackless events at the proposed ICAL detector at INO indicates thatthese will be sensitive to θ and hence need to be considered as well. Binning in cos θ reco Relative 1 σ precisionon sin θ CC e θ for pure CC e events, all trackless events and all trackless eventswith systematic uncertainties. Acknowledgements : We thank Gobinda Majumder and Asmita Redij for developingthe ICAL detector simulation packages. [1] B. Pontecorvo, J. Exp. Theor. Phys. , 247 (1958); Z. Maki, M. Nakagawa, and S. Sakata,Prog. Theor. Phys. , 870 (1962).[2] A. Gando et al . (KamLAND Collaboration), Phys. Rev. D , 033001 (2013).[3] K. Abe et al . (Super-Kamiokande Collaboration), Phys. Rev. D , 052001 (2016).[4] F. An et al . (Daya Bay Collaboration),Phys. Rev. D , 072006 (2017).[5] Y. Abe et al . (Double Chooz Collaboration), JHEP (2016) 163.[6] J. H. Choi et al ., (RENO Collaboration) , Phys. Rev. Lett. , 211801 (2016).[7] M. Tanabashi et al . (Particle Data Group), Phys. Rev. D , 030001 (2018) and 2019update.[8] S. Adri´an-Mart´ınez, et al . (KM3NeT collaboration), JHEP (2017) 008.[9] M. G. Aartsen et al ., (IceCube Collaboration) Phys. Rev. Lett. , 071801 (2018).[10] B. Abi et al . (DUNE Collaboration), arXiv:1807.10334.[11] I. Esteban et al. , JHEP (2019) 180.[12] S. Ahmed et al . (ICAL Collaboration), Pramana , 79 (2017).[13] T. Thakore, A. Ghosh, S. Choubey and A. Dighe, JHEP (2013) 058.[14] A. Ghosh, T. Thakore and S. Choubey, JHEP (2013) 009.[15] M.-M. Devi, T. Thakore, S. K. Agarwalla and A. Dighe, JHEP (2014) 189.
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