A first measurement of the interaction cross section of the tau neutrino
A ?rst measurement of the interaction cross section of the tau neutrino
K.Kodama 1,https://www.sodocs.net/doc/0811925286.html,hida 1,C.Andreopoulos 2,N.Saoulidou 2,a ,G.Tzanakos 2,P.Yager 3,B.Baller 4,D.Boehnlein 4,W.Freeman 4,B.Lundberg 4,J.Mor?n 4,R.Rameika 4,S.H.Chung 5,J.S.Song 5,C.S.
Yoon 5,P.Berghaus 6,M.Kubantsev 6,N.W.Reay 6,R.Sidwell 6,N.Stanton 6,S.Yoshida 6,S.Aoki 7,
T.Hara 7,J.T.Rhee 8,D.Ciampa 9,C.Erickson 9,M.Graham 9,E.Maher 9,b ,K.Heller 9,R.Rusack 9,
R.Schwienhorst 9,J.Siela?9,J.Trammell 9,J.Wilcox 9,T.Furukawa 10,K.Hoshino 10,H.Jiko 10,M.
Komatsu 10,M.Nakamura 10,T.Nakano 10,K.Niwa 10,N.Nonaka 10,K.Okada 10,B.D.Park 10,O.Sato 10,S.Takahashi 10,V.Paolone 11,C.Rosenfeld 12,A.Kulik 11,12,T.Kafka 13,W.Oliver 13,T.Patzak 13,c ,J.Schneps 13
(The DONuT Collaboration)
1
Aichi University of Education,Kariya,Japan
2University of Athens,Athens 15771,Greece
3University of California/Davis,Davis,California 95616,USA
4Fermilab,Batavia IL 60510,USA
5Gyeongsang University,Chiju,South Korea
6Kansas State University,Manhattan,Kansas 66506,USA
7Kobe University,Kobe,Japan
8Kon-kuk University,Seoul,S.Korea
9University of Minnesota,Minneapolis,MN 55455,USA
10Nagoya University,Nagoya 464-8602,Japan
11University of Pittsburgh,Pittsburgh,PA 15260,USA
12University of South Carolina,Columbia,South Carolina 29208,USA
13Tufts University,Medford,MA 02155,USA
a Presently at Fermilab
b Presently at the Massachusetts College of Liberal Arts,North Adams,MA 01247,USA
c Presently at the Universit′e Paris 7,Paris,France The DONuT experiment collecte
d data in 1997and published ?rst results in 2000based on four observed ντcharged-current (CC)interactions.Th
e ?nal analysis o
f the data collected in the experiment is presented in this paper,based on 3.6×1017protons on target usin
g the 800GeV Tevatron beam at Fermilab.The number of observed ντCC interactions is 9,from a total of 578observed neutrino interactions.We calculated the energy-independent part of the tau-neutrino CC cross section (ν+ˉν),relative to the well-known νe and νμcross sections.The ratio σ(ντ)/σ(νe,μ)was found to be 1.37±0.35±0.77.The ντCC cross section was found to be 0.72±0.24±0.36×10?38cm 2GeV ?1.Bot
h results are in agreement with expectations from the Standard Model.PACS numbers:14.60.Lm,13.25.Ft,13.35.Dx,02.50.Sk February 4,2008
I.INTRODUCTION
The tau neutrino,ντ,was assigned its place in the Standard Model after its electrically charged
weak isospin-12partner,the τlepton,was discovered in 1975[1].The observation of identi?able ντ
interactions,in a manner similar to νe [2]and νμ[3]interactions,did not immediately follow.The di?culty of measuring ντinteractions was due to the relative scarcity of the sources of ντand the lack of su?ciently powerful detection methods to unambiguously identify the short-lived τlepton (mean lifetime 2.9×10?13s)produced in ντcharged-current interactions.These challenges were overcome in the observation of four ντinteractions by the DONuT (D irect O bservation of Nu -T au)collaboration,in 2000[4][5],twenty-?ve years after the τwas discovered.Analysis of our full data
a r X i v :0711.0728v 1 [h e p -e x ] 5 N o v 2007
set yielded nearly three times as many neutrino interactions of all?avors as reported in Ref.[4]. This paper reports our?nal results,bringing the DONuT experiment to a completion.
The purpose of the DONuT experiment was to studyντcharged-current(CC)events,
ντ+N→τ?+X,(1a)
ˉντ+N→τ++X.(1b) However,during data taking,DONuT was recording interactions of neutrinos of all?avors:νe CC events
νe+N→e?+X,(2)νμCC events
νμ+N→μ?+X,(3) and neutral-current(NC)events
ν +N→ν +X, =e,μ,τ(4) and analogously for the antineutrinos.
Reaction(1)must be distinguished from charm production in reactions(2)and(3),since the tau-lepton and the charmed particles have comparable lifetimes and decay signatures:
ν +N→ ?+C±+X, =e,μ(5) where C=D,D s,orΛc.Another background considered here were secondary hadron ineractions in NC neutrino events,reaction(4),
ν +N→ν +h±+X, =e,μ,τ,(6)
followed by h±+N→(1or3prongs)+X0
The experimental apparatus and techniques,have been described in detail elsewhere[6][7]and are only summarized here.
The location of vertices in the emulsion data,tagging leptons and the subsequent search for secondary vertices,were accomplished with high e?ciency.This allowed a detailed event-by-event analysis with small and calculable background levels.Further,the large amount of information in the emulsion/spectrometer system permitted the use of powerful multivariate methods yielding probabilities for each candidate event to be signal or background.The measuredντcross section was computed using the?nal sample of allντ,νe,andνμinteractions located in the emulsion.
The organization of this paper is as follows.First we give an overview of the neutrino beam and detector elements.Next,there is a synopsis of triggering and?ltering that produced the interaction sample.We then give important details of the emulsion detector.The analysis is reviewed by outlining the lepton identi?cation procedures,the Monte Carlo,event location in the emulsion and secondary vertex search.After a survey of the entire data set including neutrino interactions of all ?avors,theντcross section analysis is described,systematic error sources are discussed,and the results are presented.
II.NEUTRINO BEAM AND DETECTOR
Primary beam.The number of800-GeV protons that struck the beamdump was measured by devices that integrate charge collected from secondary emission from a foil.These monitors were
calibrated with a beta source before the experiment began.Several times during the course of the run,these devices were calibrated against coil pickups and other monitors installed in the accelerator extraction complex.These checks showed that the primary beam monitors were consistent within5% at intensities of5×1012to1×1013protons per spill.Losses in the beamline were small(≈10?5), and no other corrections were applied.The monitors’output was digitized and recorded at the experiment,and gated by the trigger electronics.A total of3.54×1017protons were recorded during the live-time of the experiment.A systematic uncertainty of5%was assigned to the value of the total number of protons in the beamdump.
DONuT beamline.The800-GeV protons from the Tevatron were stopped in a beamdump in the form of a solid block of tungsten alloy.The typical intensity was8×1012protons for20seconds each minute,or about20kW of beam power.Immediately following the beamdump were two dipole magnets with solid steel poles,providing both absorption of interaction products and de?ection of high-energy muons away from the beam center.Following the magnets was an additional18m of passive steel shielding limited to within2m of the beamline.Emerging at the end of this shield,36 m from the beamdump,were neutrinos and muons.The muons were mostly contained in horizontal fan-like distributions on each side of the centerline.The neutrino beam design is shown in Fig.1. Neutrino beam.Neutrinos in the DONuT beam originated from decays of particles within the hadron shower created by a primary proton interaction.Neutrinos from decays of charmed particles are called prompt neutrinos,and neutrinos from decays ofπ±and K±are called non-prompt neutrinos. About97%of the neutrino?ux from the beamdump was composed ofνe andνμ,the rest beingντ. 93%of theνe’s were prompt,whileνμ’s had substantial components of both prompt and non-prompt neutrinos.Allντ’s were prompt.Most of them originated in leptonic decays of D s mesons.The decay mode D s→νττyielded two tau neutrinos within a distance of a few millimeters.This decay length is much less than the interaction length of six centimeters.The calculated neutrino energy spectra of all the neutrinos that interacted in the DONuT target are shown in Fig.2.
Emulsion target.The target-schematically depicted in Fig.3-was the core of DONuT.Its capabilities and performance were matched to the task of recognizing neutrino interactions containing tau leptons.The main component of the target assembly was250kg of nuclear emulsion stacked in modular fashion along the beamline.A total of seven emulsion modules in the target station were exposed,with a maximum of four modules in place at any time during the experiment.
Each module was exposed for a limited time to avoid track density higher than105tracks per cm2that would make the emulsion data analysis ine?cient.To further assist the analysis,single Changeable Sheets were mounted1cm downstream of each emulsion target module and replaced ten times more often.
Scintillating?ber tracker(SFT).Integrated into the emulsion target station were44planes of the SFT built using0.5-mm-diameter scintillating?bers to provide medium-resolution tracking and a time-stamp for each event.
Spectrometer.The emulsion target station was followed by a spectrometer consisting of a large-aperture dipole magnet and up to six drift chambers.A lead-and scintillating-glass electromagnetic calorimeter aided in identifying electrons and measuring their energy.Behind the calorimeter,muons were tagged with a Muon-ID system consisting of three steel walls each followed by two crossed proportional-tube planes.The plan of the spectrometer is shown in Fig.5.
III.SPECTROMETER DATA COLLECTION AND REDUCTION
A.Triggering and data acquisition
Trigger.A trigger for recording neutrino interactions required that no charged particles entered
the emulsion from upstream and at least one charged particle emerged from an emulsion target. The scintillation-counter triggering system included a veto wall upstream of the emulsion target and three hodoscope planes distributed between and downstream of the emulsion modules,shown in Fig.
3.The average trigger rate was5.0Hz,with a livetime of0.89.The trigger e?ciency was calculated using simulated neutrino interactions and measured e?ciencies for all counters.The e?ciency for triggering onνe CC,νμCC,ντCC,and NC interactions was0.98,0.96,0.96,and0.86,respectively. Detailed description of the triggering system can be found in Ref.[7].
Data acquisition.The architecture of the data aquisition was based on the Fermilab DART product [8],using VME-based microprocessors to control the transport of data from the VME bu?ers to a host computer.The host computer served as both the data monitor and as the data logger to tape (Exabyte3500).The average event size was100kB,with a throughput of10MB per beam cycle of one minute.
B.Filtering and scanning
A total of6.6×106triggers from3.54×1017protons on target were recorded.In this data set,only about103neutrino interactions were expected.This implied that the great majority of the triggers were background processes satisfying the simple trigger requirements of Section III A.Data from the electronic detectors were used to extract the neutrino interaction candidates in a two-step process. Software?lter.The time di?erence between any two trigger counter signals was required to be within2.5ns.Data from the SFT and from the drift chambers were then used to reconstruct tracks and to search for a vertex near one of the emulsion targets.Triggers that did not yield a candidate vertex were eliminated.This software?lter reduced the number of recorded triggers by a factor of 300.E?ciencies for keeping neutrino interactions were determined by Monte Carlo studies to be 0.98(for CC events)and0.96(for NC events).
Physicist scan.In the second step,the remaining triggers were scanned individually by a physicist using a graphical display.This step rejected events originating from particle showers produced by high-energy muons and checked for errors in reconstruction and other pathologies.Most of the events were rejected quickly and with high con?dence.This visual scanning reduced the data by another factor of20,yielding866neutrino interaction candidates within one of the emulsion modules which had a visible energy over2GeV.The e?ciency of the physicist scan was found to be(0.86±0.07). The estimated total e?ciency for retaining aντCC interaction with the electronic detectors was 0.72after triggering,?ltering and scanning.Forνe(νμ)CC interactions these e?ciencies were0.73
(0.71),and for NC interactions it was0.64.
C.Neutrino event sample
The resulting sample included866events that were likely neutrino interactions of all?avors with the vertex located within the?ducial volume in the emulsion target.
We report here on the analysis of all the events for which the neutrino interaction vertex was found in the emulsion,referred to thoughout as located events.Although locating the vertex in the emulsion was attempted for each of the866events,only578events were located,as described in Section VII.
Events in the initial sample that were not located in the emulsion were not used in the analysis described below.
IV.THE EMULSION
The DONuT emulsion modules were the?rst modern implementation of a design that interleaves metallic sheets(stainless steel)with emulsion sheets to achieve high mass to increase the number interactions and high precision for tau recognition.As illustrated in Fig.4,two designs of these ‘Emulsion Cloud Chambers’were used in DONuT:both used1-mm thick steel sheets interleaved with emulsion sheets having100μm thick emulsion layers on both sides of a plastic base.The designs di?ered in thickness of the base,one was200μm and the other800μm thick.The third design had 350μm thick emulsion layers on90μm thick base.More details about the emulsion target design can be found in Ref.[6].
After exposure,the emulsion target modules were transported to Nagoya University in Japan, where they were disassembled and individual emulsion sheets developed.The Changeable Sheets were developed at Fermilab.
The information from a small emulsion volume surrounding the interaction point predicted by the spectrometer data was fully digitized and used in a manner similar to the information from an electronic detector.The size of the volume needed to be large enough to contain the vertex but small enough to be compatible with the capabilities of the emulsion scanning machines.
Once the desired emulsion volume was determined,the individual emulsion sheets were digitized using automatic scanning and digitizing apparatus at Nagoya University.The Nagoya group devel-oped this technology over the years,starting in1974.The DONuT emulsion data were obtained using Ultra Track Selector(UTS)digitizers[9]with scanning rate of1cm2/hour,a factor of?ve improvement over the technology used to obtain the?rst DONuT results of Ref.[4]allowing for greatly increased location e?ciency.
Emulsion data.The UTS automated scanning stations found and digitized track segments(“mi-crotracks”)in the emulsion layers on both sides of the transparent plastic base.Both the position and angle of each segment were computed and recorded in real time.E?ciency for detecting microtracks was measured to be greater than0.97.
Complete tracks were built layer by layer.Each microtrack was examined to see if it had a connectable microtrack in adjacent emulsion layers.Once reconstructed,the tracks were added to a data set unique to the given scan volume.
An important tool used in the o?ine emulsion data processing were high-energy muons from the beamdump that penetrated the shielding and were recorded in the scanned emulsion volume as through-going tracks with little measurable scattering,called“calibration tracks”below.
Data quality checks.A systematic methodology was developed to quantify the quality of tracks found in digitized emulsion images.Two quantities were used:(a)position accuracyσas measured by rms displacement of microtracks from?tted calibration tracks,and(b)emulsion read-out e?ciencyε, representing the fraction of identi?ed calibration-track microtracks actually seen in any one emulsion plate.Emulsion data passed the data quality check whenσ≤1.0μm,andε≥0.9.Reasons for poor data quality could be a damaged emulsion(lost forever),di?culty in emulsion digitization(to be re-digitized),or a systematic problem such as emulsion-sheet slipping within a stack which can be corrected as detailed below.More than50%of events where the predicted vertex was not initially found in the emulsion fell into the poor-data-quality category.
Emulsion-sheet slipping:Occasionally,emulsion sheets slipped one with respect to another during exposure.An alignment method was therefore devised to correct for it using the calibration tracks. The alignment parameters of interest included the distance between the emulsion layers,the relative shifts in transverse direction and the shrinkage of the emulsion layers.Alignment between adjacent sheets was determined within0.2μm.
V.PARTICLE IDENTIFICATION
A.Muons
A muon tag was assigned to a track if there were at least four hits in the six proportional-tube planes of the muon-ID system.The per-tube e?ciency for muons was measured to be 0.96,and the geometrical acceptance of the muon ID system was estimated by Monte Carlo to be 0.76,yielding an overall e?ciency of 0.73.The muon spectra are shown in Fig.6.Muon track momentum could be measured in one of two very di?erent ways:(i)from the curvature in the spectrometer,and (ii)from multiple coulomb scattering (MCS)in the emulsion.
Spectrometer measurement.In the spectrometer,track momentum was measured using a 4T magnet with Bdl =0.75T m.For muons,?p/p was 11%for momentum p of 20GeV/c ,increasing to 100%at p =250GeV/c .
Emulsion measurement.The high spatial precision of the tracking in emulsion,in conjunction with an adequate sampling rate,allowed the calculation of track momentum from the visible scattering of the track’s segments (microtracks)in individual emulsion plates.
A special emulsion track scan was performed on all tracks found in candidate neutrino events for the dual purpose of the multiple coulomb scattering measurement and electron identi?cation (see Section V
B 1below).Momentum was successfully measured using multiple coulomb scattering for 64%of the tracks in the sample.
The method was validated by test-beam experiments which showed that the beam momentum of 0.8and 1.5GeV/c (4Gev/c )could be measured by the emulsion with a resolution of 23%(30%)
[10]([6]).A comparison of track momenta measured with both the emulsion and spectrometer is shown in Fig.10.
The upper limit of the momentum measured this way was determined by the number of samples,the angle of the track,the quality of the emulsion data and the type of emulsion module.A typical upper limit was 25GeV/c .
B.
Electrons 1.Electron identi?cation
The electron analysis was less straightforward since it involved several systems.Since the emulsion modules were two to three radiation lengths thick,most events containing electrons would exhibit showers in the SFT and in the electromagnetic calorimeter.These two electronic detectors were used to ?nd the most likely initial energy of the electron from an algorithm using both energy (pulse height)and geometrical shower development.
A special electron ID scan was performed on all emulsion tracks.This scan followed each track from the vertex to the most downstream plate.An area of 600μm ×600μm centered on the track was digitized in each emulsion plate.Electrons were identi?ed by electron-positron pairs found within 20μm of the track.The electron-ID scan was most e?ective for vertices located in the upstream part of an emulsion module.
The e?ciency for electron tagging using the spectrometer was estimated to be 0.80±0.04.The electron tagging e?ciency using emulsion data varied with path length,with a maximum of 0.86for tracks passing through at least 2X 0.The integrated e?ciency of identifying an electron in the emulsion was 0.66.
The total electron identi?cation e?ciency as a function of energy is shown in Fig.7.
2.Electron energy measurement
The target/?ber system was also used to estimate the electron(or gamma)energy.Since the scintillating?ber system response was calibrated to minimum ionizing particles,the total pulse height in a shower could be summed for each station providing a direct measure of energy.The energy estimates at each station were input variables for an algorithm to compute electron energy from shower development.The calorimeter information was added for showers that penetrated less than six radiation lengths of emulsion(approximate shower maximum).The estimated energy resolution,?E/E,was30%.
Since the beamline could not be con?gured for transport of electrons,electron identi?cation and energy estimate relied heavily on Monte Carlo simulation.A selection of probable electrons from interactions in the most downstream emulsion-target module,analyzed for momentum in the spec-trometer and energy in the calorimeter,showed that the calorimeter calibration was consistent with a calibration method using muons as minimum ionizing particles.
VI.MONTE CARLO SIMULATION
The production of neutrinos in the beamdump,their transport through the shielding system, and their interactions in the emulsion target were simulated with a GEANT3-based Monte Carlo software.The emulsion target and all electronic detectors in the spectrometer were simulated,taking into account their measured e?ciencies and other response characteristics peculiar to each system. The production of charmed particles by800GeV protons in the beamdump were generated using a phenomenological formula,
d2σ
=A e?bp2T(1?|x F|)n(7)
dx F dp2
T
where x F is Feynman x and p T is transverse momentum.The values of b and n in Eq.(7)depend on the charm species.The details of the simulation of neutrino production in the beamdump via charm particle decays are given in Appendix A.If the path of a neutrino originating from a charm decay intersected the emulsion target,a deep-inelastic neutrino-nucleon interaction was generated using LEPTO v6.3.
The simulated particles from the interaction were recorded in each detector and“digitized”as appropriate for electronics used in the experiment.This Monte Carlo data was stored in the format used by the data acquisition system and was analyzed in the same manner as experimental data. In addition,a separate?le was generated with data from the charged particles within the emulsion sheets.The data contains microtracks in each emulsion layer,but it does not directly simulate the algorithms used in the UTS emulsion digitizers.
The Monte Carlo was the primary tool for computing acceptance of the neutrino?ux in the emul-sion target needed for the cross section analysis.It was also used to establish selection cuts,develop electron identi?cation algorithms,and probe systematic e?ects from charm particle production un-certainties.
VII.EVENT LOCATION IN THE EMULSION
Two methods were used by DONuT to locate neutrino inetraction vertices in the emulsion target, both starting with extrapolation of spectrometer tracks back to the emulsion target.The SFT was the principal device for making the initial vertex prediction.
A.Event location by Netscan
Netscan event location was a multi-step process.Initially,information from the electronic detec-tors was used to?t charged-particle tracks,and reconstruct a neutrino-interaction vertex whenever possible.The resolution of these detectors enabled vertex predictions with a precision of about1 mm transverse and5mm along the neutrino beam direction.Next,both the position and size of the scanning volume were determined using the spectrometer prediction,and all microtracks within the scanning volume were digitized.
After the necessary alignment of the emulsion data,track pairs were examined to see if they formed a vertex.The following selection criteria were applied:
?Tracks must start within the volume and cannot be connected to any aligned microtracks in two adjacent upstream emulsion layers to reject penetrating muon tracks.
?Tracks must be constructed from at least three microtracks and have a goodχ2?t.These requirements reduce the number of low momentum tracks.
?The remaining tracks were tested for vertex topology.Tracks were associated when the impact parameter at the best vertex position was less than5μm.
Out of the total of～104?105microtracks per5×5×15mm3emulsion volume,only a few vertex candidates remained after the three requirements were imposed.To con?rm a vertex candidate,(i) the emulsion plates near the vertex point were examined by a physicist using a manually controlled microscope to check for consistency of the neutrino interaction hypothesis(i.e.neutral particle interaction),and(ii)the emulsion track information was compared with the hits in the SFT to verify that all tracks were associated with the same event.For interaction vertices that passed all the checks,all tracks in the event were re?t using the emulsion information.
B.Event location by Backscan using Changeable Sheets
The Changeable Sheets were used when the vertex prediction was problematic:the event was either too complex to have an accurate vertex prediction made,or,on the other hand,only one charged track was reconstructed in the SFT,so that the interaction point was constrained only in the two transverse dimensions.In this case,the SFT track was extrapolated to the CS position and the emulsion data in this sheet was searched for a track matching both position and angle.If found,the track could be followed into the emulsion target module with much greater accuracy to greatly reduce ambiguity in high track-density regions.The SFT-CS matched tracks were followed upstream,through the sheets of the target module,using emulsion scanning within a cylindrical volume(used in Ref.[4])or within a conical volume with transverse dimensions increasing along the track,used in this analysis.The latter scan resulted in much larger emulsion volume being scanned to increase event location e?ciency,but also greatly increased the digitizer work load.This was only possible when UTS digitizers became available.
If a track penetrated all the way to the most upstream sheet,the track was rejected.If the track was found to be missing in upstream sheets,it was assumed to originate in the space between emulsion layers.All tracks followed in this way were checked to ensure that they did not originate as an e+e?pair,a secondary interaction or as an emulsion ine?ciency causing a gap in a throughgoing track.If these background hypotheses were rejected,the track was assumed to originate from a primary vertex of a neutrino interaction.All other emulsion tracks that passed within5μm of this track’s endpoint were checked to see if they were likely to originate in the same interaction.
C.Special cases
Special methods were developed for events with large number of hits in SFT,for which the total pulse height exceeded the equivalent of650minium ionizing tracks and no3-D tracks could be reconstructed.These large-pulse height events are called LP events below.
In the modi?ed CS scan,a large area(>1cm2)was scanned in the CS nearest to the upstream end of a large SFT shower,and electron signature was searched for in the form of clustered parallel microtracks.If found,the electron was followed by backscan to the vertex.Alternatively,a line was drawn through the shower core in the SFT to better pinpoint the CS area to be scanned,with a typical size of5×5mm2.In this case,no electron signature was required,and all tracks matching the line in position and angle were followed back.
In the modi?ed Netscan,a number of lines were drawn in u-and v-projection and extrapolated into the emulsion module.If a candidate vertex region was found,Netscan was applied over an oversized volume,typically13×13×20mm3.
The two methods yielded similar numbers of events,with a total of58LP events located in the emulsion,of which31wereνe events,9νμevents,2ντevents and16NC events.
D.Location e?ciency
The overall e?ciency for locating the primary vertex in the emulsion was given directly as the ratio of the number events found and the number of events tried.This ratio is578/866or0.667±0.036. We note that each module corresponded to2.5to3radiation lengths and0.2interaction lengths,so secondary interactions were a common occurrence.Resulting large hadron/electromagnetic showers hampered track reconstruction and vertex location.There were188events classi?ed as LP events, or22%of the total of866.A total of58LP events were located in the emulsion,representing a location e?ciency of0.31±0.05,to be compared to0.77±0.04location e?ciency for the regular events(520located out of a total of678).
We investigated the located-event sample for possible biases.Fig.8displays the distance along the beam direction between the vertex and the downstream edge of an emulsion module,for all7 modules.The distribution is consistent with being independent of z,withχ2/ndf to a straight line of1.7.The vertex distribution in the transverse plane(not shown)is uniform,as expected.The located-event charged multiplicity distribution is compared with expectation in Fig.9.We conclude that the bene?t of using a combination of di?erent location methods was to have uniform location e?ciency.
VIII.SECONDARY VERTEX ANALYSIS
A.Decay search criteria
For the located events,the emulsion was digitized again in a smaller volume containing the vertex and optimized for the decay search,typically2.5mm×2.5mm×12mm.The track reconstruction algorithm was the same as that used for vertex location.The decay search was divided into two categories distinguished by topology:
1.Long-decay search:Decays in which the candidate parent track passed through at least one
emulsion layer.
2.Short-decay search:Decays in which only the daughter track was recorded in emulsion.
The strategy was common for both decay topologies under consideration.Once a secondary vertex was found,the event was classi?ed as a one-prong decay,unless additional tracks were found to be associated with the same secondary vertex constituting a three-prong decay.
Tau and charm decays were obtained from the data in a two-step process:(i)?nding secondary vertices in emulsion data using geometrical cuts,described in this Section,and(ii)subsequently imposing topological and kinematical cuts to isolate the signal from the background,described in Section VIII B.
1.Long-decay search
The Long-decay search for one-prong decays imposed the following criteria:
?The parent track had one or more microtracks,and a daughter track had three or more micro-tracks.
?The parent track length:L dec<10mm.
?The impact parameter b p of the parent track with respect to the primary vertex:(i)b p<5μm if there were at least two microtracks,or(ii)b p<(5+0.01×δz)μm if there was one microtrack, whereδz is the distance from the parent microtrack to the vertex.
?The minimum distance,d min,between extrapolated parent and daughter tracks:(i)d min<5μm if there were at least two parent microtracks,or(ii)d min<(5+0.01×δz)μm if there was only one parent microtrack.
?(i)The angle between the daughter and parent tracks:α>4times the angular measurement error,or(ii)The impact parameter b d of the daughter with respect to the primary vertex:b d> 4times the error in the position.
Candidate tracks passing the above criteria were checked in the emulsion by a physicist using a microscope to ensure that(i)the daughter track could not be associated with emulsion tracks upstream of the vertex,(ii)that it was not a part of a e+e?pair,and(iii)that there were no alignment problems.
2.Short-decay search
The Short-decay search for one-prong decays required the following criteria:
?The daughter track had at least three microtracks.
?The daughter-track impact parameter(IP)with respect to the primary vertex:b d<200μm.
?The daughter-track IP w.r.t.the primary vertex:b d>4×σIP,whereσIP is the error on the impact parameter.
Each candidate daughter track was checked visually to insure that it could not be connected to microtracks upstream of the vertex.
B.Tau and charm recognition
To extract theντsignal from events passing the secondary-vertex selection,a set of topological and kinematical criteria was?rst applied as described in Section VIII B1below.In the second step, the amount of signal and background was determined using a multivariate technique featured in Section VIII B2.
1.Topology and kinematical cuts
ντevent topology.TheντCC interactions,reaction(1),produce aτlepton that typically decays within2mm of its origin.Thus,the topological signature forντevents is a track from the primary vertex that gives a secondary vertex at a short distance consistent with the kinematics of the de-cay.There must be no other lepton from the primary vertex.The topological signature of charm production in reaction(5)is very similar toντevents.Tau and charm events were distinguished primarily by presence of an electron or muon at the interaction vertex.Thus,aνe or aνμCC interaction together with a failure in lepton identi?cation constitutes the primary background to the tau sample.The second background considered here were interactions of hadrons produced in neutrino NC interactions,reaction(6),that appeared in the emulsion with a topology of a one-prong or three-prong interaction(or decay).
Kinematical cuts.The following set of criteria were derived from Monte Carlo studies to e?ciently extract theντsignal with minimal background.It is a modi?ed version of the selection criteria of Ref.[4].Long one-prong and trident decays were accepted when the following conditions were satis?ed:
?Parent-track angle w.r.t.neutrino direction:θp<0.2rad.
?Daughter-track angle w.r.t.parent direction:θd<0.3rad.
?Kink angle:α<0.25rad.
?Daughter-track IP:b d<500μm.
?Transverse momentum of the daughter w.r.t.parent track:p T>250MeV/c for hadrons,and p T>100MeV/c for electrons and muons.
?Daughter momentum:p d>1GeV/c.
Events passing these criteria that did not have an identi?ed electron or muon track from the primary interaction vertex were selected asντcandidate events.In the case of trident secondary vertices,at least one of the secondary tracks must pass all of the above requirements.Fig.11shows the distribution of number of kinks versus transverse momentum,p T,of the daughter w.r.t the parent track,for all tracks satisfying the above criteria except the transverse momentum cut.One can see that p T is an impressive discriminant.There are198tracks,but almost all are within the steeply falling peak at low p T due to hadronic background,reaction(6).All but one of the other tracks are classi?ed as either tau or charm decays following the multivariate analysis outlined in the next section.
For Short decays,all the cuts were the same but one:the kink angleαcannot be de?ned since the parent direction is unknown.Here the kink angle was replaced by the“minimum kink angle”, obtained by extrapolating the daughter track back to the steel plate and placing the“decay vertex”at the point where this extrapolation intersects the downstream face of the plate.This was the most conservative assumption,since it also minimized the transverse momentum assigned to the decay.
2.Mutivariate analysis
Only events selected by secondary vertex analysis detailed above were submitted to the multivariate analysis employed to determine the probability that individual events represented one of the following interaction types,each with a one-prong or a three-prong secondary vertex:
1.ντCC events,reaction (1).
2.Charm production,reaction (5).
3.Neutrino NC events with a secondary hadron interaction,reaction (6).
No other physical process,subject to the topological and kinematical cuts above,was deemed to be a signi?cant part of the background.
A set of quantities was chosen that could be easily and unambiguously measured in the emulsion data (supplemented by spectrometer information)and that could discriminate between the three hypotheses.Note that all these quantities are independent of the neutrino production and interaction processes.For n parameters,an n -dimensional probability density distribution for each hypothesis was computed using Monte Carlo generated events.Then the relative probability of event k sampled from the distribution of hypothesis i can be written as
P ({x k }|i )=W i P ({x k }|i ) j W j P ({x k }|j )
(8)
where {x k }is a set of parameters describing event k ,P ({x k }|i )is the probability density function for hypothesis i evaluated for x k determined from the data,and W i is the prior probability of the event being an i -type event.Note that the W i are independent of {x k },and give the probability of a neutrino interaction of type i occurring within the emulsion ?ducial volume using full MC simulation starting with neutrino production in the beamdump through its interaction in the emulsion target.The parameter set {x k }for events selected as tau candidates included L dec ,α,p d ,θp ,and b d ,introduced above.In addition,?φwas added,which represents the angle in the plane transverse to the neutrino beam between the parent direction and the vector sum of unit vectors of the remaining tracks at the primary vertex,expected to peak at 180?for ντCC events,and to distribute uniformly for the other two hypotheses.
Hence,for one-prong decay candidates resulting from the Long-decay search,the set {x }={L dec ,α,p d ,θp ,?φ}was used,and {x }={L dec ,θp ,?φ, b d }was used for three-prong de-cays.
Simulated distributions used as input to the multivariate method are illustrated in Figures 12-14for all three hypotheses.Fig.12shows the ?φangle in the transverse plane,used for both one-and three-prong topologies,which discriminates very strongly against both charm and hadronic-interaction background.Fig.13shows the αdecay angle used for the one-prong topology,which discriminates strongly against the hadronic-interaction background,and provides modest discrimi-nation against charm.Fig.14shows b d ,sum of the daughter-track impact parameters,used for the three-prong topology.This quantity is related to ct for this event,where t is this parent’s lifetime in its rest frame.Since τ-lepton has shorter lifetime than charmed mesons, b d discriminates very strongly against the hadronic-interaction background,and provides strong discrimination against charm.Note that these one-dimensional distributions do not provide information about correlations among the multivariate parameters which are taken into account in the calculation.
The multivariate analysis was also used for events from the Short-decay search.Here,the parent direction is unknown,and hence θp ,αand ?φare unkown.The true decay point must have been
in the same steel plate that contained the interaction vertex,lying on a line made by projecting the candidate daughter track upstream.Along this line within the steel,the parameters L dec,α,θp,and ?φvary continuously,so that probabilities for the three hypotheses also vary.To make a de?nite and conservative estimate,the values of all three probabilities were measured at the point along the line where the tau-hypothesis probability was minimum.
Table I summarizes the prior probabilities for both kink and trident topologies and di?erent ma-terials of the emulsion target.Resulting hypothesis probabilities for theντevent candidates are presented in Section IX D below.
C.Decay search e?ciencies
The e?ect of cuts applied during the secondary vertex search was determined by Monte Carlo calculation for all three hypotheses,tau,charm,and hadronic interaction.The secondary-vertex search e?ciency was checked by using secondary hadronic interactions found as a byproduct of the track-by-track electron ID scans.The number of interactions expected has a well-understood value depending on path length in a given material(emulsion,steel or plastic).The number of interaction vertices of all multiplicities was estimated to be31.The total number of found interactions was27, yielding an e?ciency of0.87,consistent with a Monte Carlo derived e?ciency of0.86.
The fractions of events remaining after selections described in Secions VIII A and VIII B1are listed in Table II.The estimate for the overall systematic uncertainties in these e?ciencies is5%of the value.
IX.SUR VEY OF DATA
A.Expected composition
The expected number of interactions for reactions(2)-(4)was predicted using the DONuT Monte Carlo simulating the same event-selection procedure that was applied to the data.Charged-current ineractions of all?avors were selected by identifying a lepton at the primary vertex.All neutrino interactions without an identi?ed lepton were considered to be“e?ective neutral-current”events, NC e?.These NC e?events therefore included CC events with a lepton that escaped detection. Table III shows the expected number of events of all four interaction types.Note that although the prompt and non-prompt components(see Section II)are separated in the simulation,they are not distinguishable in the data.
B.νμCC events
The identi?cation of muons using the spectrometer was straightforward and e?cient,so this cat-egory of interactions was considered the most reliable.The number ofνμCC events found was225 events,which gives the fraction ofνμCC to the total(578)as0.39±0.03.
The fraction of promptνμCC events was estimated both by Monte Carlo and from the data. Averaging over several algorithms,the MC estimate is0.61±0.03.An estimate from combining results from analyses based on data(number ofνe CC interactions,?tting to the muon spectrum and data taken with a half-density beamdump)gives0.59±0.06.The estimated number of prompt νμCC interactions is thus133±16.
The ratio of the number ofνμinteractions with outgoingμ+to the number ofνμinteractions withμ?was computed fromνμandνμcross sections taking into account detector e?ciency and
acceptance.The resulting expected ratio was0.63.The same fraction determined in the578-event data sample was0.67±https://www.sodocs.net/doc/0811925286.html,ing this measured ratio,the ratio of integratedνμandνμ?uxes was found to be1.05±0.13.
There are three events in the located sample that have two identi?ed muons.One event has muons of opposite sign with one from the primary interaction vertex and the other from a secondary decay vertex.This event is identi?ed as aνμCC interaction producing a charmed meson.The other two dimuon events have same-sign tracks,where one of the tracks is likely a chargedπdecaying in-?ight.
C.νe CC events
The expected mean energy of outgoing electrons inνe CC interactions was52GeV,with22%of events having electron energies below20GeV.Approximately15%of NC events have at least one electron with energy less than20GeV.Therefore,a low-energy cut is applied to the electron sample to reduce background from events that are notνe CC events.Table IV summarizes the result of a Monte-Carlo-based study to optimize this cut and to estimate the NC background as a function of energy.For cuts of18GeV and higher,there is little change in signal-to-background ratio and a cut of20GeV was chosen.A total of120νe CC and NC e?events passed the cut.The NC e?background fraction is estimated in Table IV to be0.174,so the best estimate for the number ofνe CC events (with a20-GeV electron cut)is given as120×(1?0.174)=99±9,as determined by the electronic detector data.To compare this number to the second identi?cation method which follows,it must be divided by the electronic identi?cation e?ciency(0.80),yielding124±11.
The set of events with electrons identi?ed in the emulsion was analyzed independently.There were 82events with primary electrons found in the emulsion data alone.Of these,62electrons passed the 20GeV minimum energy cut.The electron-identi?cation e?ciency of this procedure was found to be independent of energy.The number ofνe CC,corrected by the e?ciency,was62/0.66=94±12.
D.ντCC events
The methods of selecting theντevents described in Section VIII were applied to the578located events.The multivariate analysis(Section VIII B2)was performed for each selected event.Events with P(τ)>0.5are listed in Table V.We estimate the number ofντ,charm,and hadronic interaction events in our?nal sample by summing up the hypothesis probabilities in Table V,yielding7.5ντevents,1.26charm events,and0.22hadronic interactions.
The charm and hadronic-interaction backgrounds can also be estimated in the tau sample using one-dimensional cuts on Monte Carlo events without any reference to the correlations between vari-ables.This simpler analysis gives an estimate of the background from charm decays and hadronic interactions in the nine selected events as1.1and0.9events,respectively.In comparing the results between the two analyses,it is important to note that the multivariate method accounts for cor-relations between parameters and results depend on the particular set of candidate events.This last point is signi?cant due to the small number of tau events.The similarity of the charm back-ground from the two analyses demonstrates the similarity in the topological signature of tau and charm decays.The hadronic interaction background,however,shows little correlation between par-ent track length and‘decay’(interaction)topology,and simple one-dimensional cuts overestimate this background.
E.Charm production in neutrino interactions
Integrating over the expected neutrino energy spectrum,the average charm production fraction, normalized to the number ofνμandνe CC interactions,is0.066±0.008[11].This fraction includes production of D0,D±,D s,andΛc.Including only charged charmed hadrons reduces the fraction to 0.028±0.006.The expected number of charged charm events is the product of the total number of located events(578),the fraction of CC events(0.62),the e?ciency for observing the secondary decay(0.45±0.05)and the charged charm fraction(0.028).The result is4.5±1.0events,where the error represents the uncertainties in cross sections and branching ratios.The observed number of charged charm events in our sample is7events,with an estimated background level of2.2events, which is consistent with our prediction.
X.NU-TAU CROSS SECTION
A.Analyses
Two methods were used to measure the cross section forντ-nucleon CC interactions.The primary analysis determined the ratio of theντ-nucleon cross section and theνe-nucleon orνμ-nucleon cross section.Systematic uncertainties in neutrino production that a?ected all?avors equally canceled in the relative measurement.Electronic triggering e?ciencies and neutrino interaction selection e?ciencies were high and for CC events showed no dependence on?avor.However,some corrections applied to the data did not cancel,and their uncertainties contribute to the systematic error.Since only the promptνμare relevant in the relative cross section calculation,the uncertainty in the prompt fraction was included in the systematic error of theσ(ντN)toσ(νμN)ratio.Similarly, the systematic uncertainty related to the energy cut and the NC background subtraction in theνe sample was included in theσ(ντN)toσ(νe N)ratio.Theντanalysis required the secondary vertex search,and this e?ciency(0.46)is applied to theντevents.
The second technique measured the absolute cross section forντN CC interactions.All electronic, event selection and analysis e?ciencies appear explicitly in the calculation.
The cross section calculations required an estimate for the number of neutrino interactions in the emulsion target,corrected for e?ciency and acceptance.It was important to account for correlations between acceptance and energy.The number of interactions of each?avor in the experiment can be written as
N int=N tgt
ν
N pot
·N pot·ε·
σconst
Area
·
M tgt
m nucleon
·
f
N MC
ν
EKT t=σconstεCf
EKT t
(9)
where the sum is over neutrinos generated by Monte Carlo in the beamdump with energy E,and with kinematic suppression factor K(E).The binary T was equal to one if the neutrino passed within the target?ducial volume and the binary t was equal to one if the interaction generated a
trigger.The number of neutrinos generated in the Monte Carlo is denoted by N MC
νand the number
passing through the emulsion is N tgt
ν.The area is taken to be the size of the emulsion,50cm×50
cm.For the Monte Carlo events,the simulated trigger also incorporated the muon identi?cation for νμinteractions.The electron identi?cation,with its e?ciencies,was not incorporated directly into t but it,as well as other electronic and analysis e?ciencies,were incorporated intoε.The number of protons accumulated in the beamdump(N pot)and the fraction of the neutrino?ux(f)intercepting the emulsion are explicitly shown.The quantity C incorporates the energy-independent factors and it depends on neutrino?avor.The angle brackets indicate that the mean value of the sum of the
products is used.The Monte Carlo gives f and the mean value of the sum directly and the constants of Eq.(9)are incorporated into C.The values of C and the sum that were used in this analysis are listed in Table VII.
The total CC cross sections per nucleon can be written
σν
=σconst
ν
E K(E), =e,μ,τ(10)
whereσconst
ν is the energy-independent factor of the cross section of?avor ,and K gives the part of
the tau-neutrino cross section that depends on kinematic e?ects due to theτ-lepton mass(see Fig.
15).In the DONuT energy range(Fig.2),the factor K can be safely taken to be unity forνe and νμCC interactions.With this notation,the relative cross sections can be written,
σconst τ
σconst =
N exp
τ
N exp
i
·
C
Cτ
·
f
ET t
fτ
EKT t
τ
·
ε
ετ
, =e,μ(11)
Theεi denote e?ciencies for lepton identi?cation only.The e?ciency of the secondary vertex search is included inετ.
The absoluteντcross section is computed from the following expression,
σconst τ=
N exp
τ
εTOT·Cτ·(f
EKT t )
τ
(12)
whereεTOT is the product of all experimental e?ciencies
εTOT=εFS·εtrig·εloc·ετ.(13) The e?ciencies in Eq.(13)are as follows:?ltering and scanning(0.85±0.06),trigger with live-time (0.79±0.02),location in emulsion(0.64±0.04),and secondary vertex?nding(0.46±0.02),yielding εTOT=0.20±0.02.
B.Systematic uncertainties
The cross section results from this experiment depend on predicting the neutrino?uxes of each ?avor.The value of C in Eq.(11)and Eq.(12)depends linearly on the total charm production cross section in pN interactions in the beamdump.And the value of f times the term in the brackets depends on the angular distribution of charm in the pN center-of-momentum frame.Most of the systematic uncertainty in the cross section results was due to these two terms.We examine each in more detail.
The factor C contains the number of neutrinos produced in the beamdump,so it is sensitive to variations in total cross section,branching ratios and target atomic number e?ects,which we parameterize by Aα.The relative errors for charm production ofνe andνμis taken to be the same for both:0.10from charm total cross section,0.16from branching ratios and0.14from the A dependence.We adopt the convention to add the errors in quadrature where values are derived from several sources and not likely to be correlated.This gives a total relative error of0.23for C e and Cμ.The estimated uncertainty in Cτdepends almost entirely on D s production and decay.The relative uncertainties are computed to be0.15,0.23and0.14for cross section,branching ratio and A dependence,respectively.Added in quadrature,this gives0.31for the relative uncertainty in Cτ.In the results for the relative cross section measurement,below,the uncertainty in the A dependence is not included in the second,systematic error.
The factor fΣEKT t is sensitive to kinematic uncertainties in charm production,with the e?ects manifested in the variation of the parameter n of Eq.(7).Both the neutrino energy(and hence
number of interactions)and the fraction of the neutrino?ux within the emulsion are a?ected.We compute the amount of variation in the number of accepted Monte Carlo events and assign it to the
systematic error in fΣEKT t.We assume n=8.0±0.8for both D+
s and D?
s
production,but in
computing the relative error,allow n to be di?erent by±2.0for D?
s .This gives a relative uncertainty
of+0.31and-0.23inντproduction.The uncertainties in fΣEKT t forνe andνμwere computed analogously,yielding+0.30and-0.20.The positive uncertainty corresponds to a decrease in n by two units.
Forνe andνμCC interactions we can estimate C e,μfrom the number of interactions in the data, given the values of fΣEKT t and the e?ciencies computed from the Monte Carlo.This provides a systematic check on C.The values are C e=1.47×1040cm?2and Cμ=1.79×1040cm?2(prompt muons only).These are compared with1.64×1040and1.55×1040,respectively from Table VII,which were extracted from Monte Carlo simulations with values of the parameter n discussed above.This indicates that the systematic uncertainty in the charm cross sections is within the values(+0.30, -0.20)estimated above.
C.Results
The relative cross sections were obtained from Eq.(11)using the observed number of interactions, corrected by e?ciency and kinematic factors.Inserting the values from Table VIII yields
σconst ντσconst νe =1.58±0.58±0.91and
σconst
ντ
σconst
νμ
=1.16±0.42±0.65(14)
The?rst error in the results is the statistical error,the second is the estimated sytematic uncer-tainty.The systematics of these two results are correlated,since the same assumptions regarding charm production were made for bothνe andνμproduction.Therefore,the two cross section may be averaged without introducing other uncertainties.The result is
σconst
ντ
σconst
νe,μ
=1.37±0.35±0.77(15)
The absoluteντ-nucleon cross section was computed using the factors of Table VII inserted into Eq.(12):
σconst
ντ
=0.72±0.24±0.36×10?38cm2GeV?1(16)
The?rst error is statistical,the second one systematic.
Lack of knowledge of the charge of theτlepton implies that the result,Eq.(16),represents an
average ofντandˉντcross sections.The measured value ofσconst
ντis to be compared with the average
ofνμandˉνμcross section factors,0.51×10?38cm2[12],assuming equal?uxes of neutrinos and antineutrinos in the DONuT beam.Hence,theντresult,Eq.(16),is consistent with Standard Model assuming lepton universality.As discussed in Section IX B,the?ux of neutrinos in the DONuT beam is approximately equal to the?ux of antineutrinos,which has been assumed for the results given above.The actual value of the ratio ofˉνμandνμ?uxes in the DONuT beam was measured to be1.05±0.13.Thisν-ˉνimbalance taken at face value would result in a negligible correction to the relative cross section if one assumes that it applies to all?avors equally.The absolute cross section would be reduced by about2.5%.
XI.CONCLUSIONS
The identi?cation of a set of likelyντinteractions with small background has enabled a?rst direct measurement of theντcharged-current cross section.The values obtained are consistent with the Standard Model expectation of unity for the relative cross sections.Since the uncertainty from hadronic charm production and decay is larger than the statistical error,these results can be improved with better data from charm production experiments.
XII.ACKNOWLEDGMENTS
We would like to thank the support sta?s at Fermilab and the collaborating institutions.We acknowldge the support of the U.S.Department of Energy,the Japan Society for the Promotion of Science,the Japan-US Cooperative Research Program for High Energy Physics,the Ministry of Education,Science and Culture of Japan,the General Secretariat of Research and Technology of Greece,the Korean Research Foundation,and the DOE/OJI Program.
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TABLE I:Summary of the prior probabilities for the multivariate analysis.
Material Number of Prior probabilities W
decay prongs Tau decay Charm decay Hadron int.
?3?3?5
Emulsion32.7×10?31.9×10?32.0×10?4
Plastic11.6×10?21.2×10?37.5×10?6
Plastic32.7×10?31.9×10?36.7×10?5
Steel11.6×10?21.2×10?35.1×10?4
Steel31.6×10?21.2×10?35.6×10?3
TABLE II:E?ciencies for identifying the secondary vertex inντinteractions,in charm-producingνe andνμinteractions,and inνNC events with secondary hadronic interactions.(Kink-daughter type is given in parentheses.)
Decay Topologyντ→τ?ˉντ→τ+ν→charmˉν→charm Hadron interactions
1-prong(Hadron)0.390.390.260.320.72
1-prong(Electron)0.490.510.350.36
1-prong(Muon)0.500.540.340.33
3-prong decay0.580.620.450.560.84
All0.460.470.340.400.76
TABLE III:Expected composition of the beamdump neutrino beam.The distinction ofνμfrom prompt(charm decay)and non-prompt(πand K decay)sources can be made only for Monte Carlo.The NC e?category includes all events not classi?ed as charged-current.
νe CCνμCCνμCCντCC NC e?
prompt non-prompt
MC fraction0.1810.1990.1590.0180.442
MC fraction×5781051159210256
Data1202259224
Di?erence15±1518±21?1±4?32±22
TABLE IV:Results of a systematic study of classifyingνe CC events as a function of electron energy.N data
e
includes bothνe CC events and a background of NC e?events misidenti?ed asνe CC events.The last column gives the estimated true number of CCνe events after subtracting background and correcting for e?ciency,and should be constant in energy if systematics are small.Events with energy less than20GeV were rejected from the CCνe set and therefore assigned to the NC e?set.
Energy cut N data
e N data(NC e?)ε(νe CC)NC e?bkg N corr
e
(GeV)
151442070.7470.239154 181342170.6930.194161 201202310.6350.174166 251042470.5730.160163 30912600.5140.153165
TABLE V:List of ντevents with parameters used in the analyses and the result of the multivariate analysis.(?)Event 3139/22722was a Short decay so the probability values listed are at the tau probability minimum.
Event Daughter L dec αb d ?φθp p d P (τ)P (c )P (int )
(mm)(rad)(μm)(rad)(rad)(GeV/c )
3024/30175e 4.470.093416 1.090.030 5.20.530.470.00
3039/019100.280.08924 2.710.065 4.60.960.040.00
3140/22143μ 4.830.01260 1.670.04022.20.970.030.00
3333/17665e 0.660.0118 2.840.016590.980.020.00
3024/18706e 1.710.01423 2.960.04350 1.000.000.00
3139/22722?0.440.02712 1.710.15515.80.500.290.21
3296/188160.800.05438 1.740.140 5.00.710.290.00
0.190148 1.3
0.130112 1.9
3334/199208.880.017147 3.110.04111.6 1.000.000.00
0.0119815.7
0.01194 3.2
3250/017130.830.133110 2.830.028 1.30.870.120.01
0.192161 2.4
0.4423550.5
Total 7.5 1.260.22
TABLE VI:Quantities used in the analysis to compute neutrino cross sections.The charm production cross section in a material of atomic number A is assumed to be proportional to A α.The di?erential cross section is assumed to be given by Eq.(7).
Quantity Value
σ(pN →D ±X)21±2μb
σ(pN →D 0X)39±3μb
σ(pN →D s X)7.9±1.2μb
σ(pN →Λc X)8±5μb
σtot (pW)1650mb
α0.99±0.03
n 8.0±0.8
b 0.83±0.22(GeV/
c )?2
TABLE VII:Monte Carlo derived factors in the cross section analysis.Type C f P EKT t ×1040cm ?2GeV
νe 1.64±0.384.62+1.41?0.94νμ1.55±0.364.33+1.32?0.88ντ0.222±0.0852.23+0.69?0.52
TABLE VIII:The values for the factors of Eq.(11)giving the relative cross sections.The number of observed ντinteractions is the sum of the probabilities listed in Table V,column 7.The values of C and f P EKT t ,columns four and ?ve,are listed in Table VII.x N exp νx ε(νx )/ε(ντ)C x /C τf P x /f P ττ7.5
e 991.36±0.087.40±3.252.07±0.78
μ1381.57±0.107.01±2.981.94±0.71