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Brick finding efficiency in muonic decay tau neutrino
events
I. Laktineh
To cite this version:
21January, 2002
Brick Finding EÆciency in
Muonic Decay Tau Neutrino Events
I.Laktineh [email protected]
InstitutdePhysiqueNucleairedeLyon UniversiteClaudeBernardLyonI
F-69622Villeurbannecedex
Abstract
An essential issue in OPERA is the nding of the right brick in which the neutrino interaction takesplace. This is acrucial point when lookingfor evidence of tau neutrino appearance through the detection of a tau. The tau decays in many channels but the muonic decay mode isby far the most relevant channel for a detector like OPERAsince the presence of themuoninthe nal state couldbe detected thanksto thespectrometer. Finding the right brick will then allow to search for a tau-muon kink inside the nuclear emulsions.
The neutrino charged current interactions through which the tau is produced, are of two kinds, either quasi-elastic (QE) or deep inelastic scattering (DIS). In the rst case, only a tau is produced while anadditionalhadronic shower is present in the second. An important issue related to the wall nding is the presence in part of the neutrino inter-action events of back-scattered particles. This may fake the information concerning the position of the brick in which the interaction vertex is present. Back-scattering is more present in DISevents (50%) than inQE ones (10%) which explains why the wall nding eÆciency willdepend onthe natureof the neutrino interaction. The back-scattered par-ticlesare usuallylow-energyones anddeviatedfromthe eventaxis. The planecontaining the strips touched by those particlesis easily distinguished. However insome events the back-scattered particlesare eitherenergetic orlocatedonthe event axisoreven both. In this caseit isdiÆculttoseparate theback scattered particlesfromthose producedinthe forward directionof the event determined by the neutrino beam. This last scenariomay happen for events for which the reaction takes placeat the beginingof the brick.
In order to get rid of those touched strips due to back-scattered particles as well as those due to electronic noise, Hough Transform (HT) is used. This helps at least to clean theeventsfromisolatedand disconnected strips. The next step istoselectthe rst scintillator planes of each event in order to determine which of those planes is the one located after the vertex in the downstream directionwith respect to the neutrino beam. The touched strips in the following planes are then used to determine the visibleenergy event axisinboth(z,x) and (z,y) planes. Theintersectionofthose twoaxeswith the rst plane determines the brick inwhich the interaction vertex is located.
In this paper the rst section will be devoted to explain how the Hough Transform is used for cleaning each event. In the second section, the selection of the rst planes and events classi cation will be detailed and the variables used in the di erent neural networks will be explained. The results of wall nding eÆciency are then quoted in the third section. In the lastsectionthe methodused to nd the (x,y) interaction position is shown with the totaleÆciency of the brick nding.
2 Hough Transform for event cleaning
expressed using polarcoordinates (;):
=xcos+ysin
It isclearthateachhitgivesbirthtoasinusoidalcurve. Thehits locatedonthesame straight line will have their curves intersecting in the (;) related to that very line as shown in gure 1. In practice the number of orientations should be limited and chosen according to the experimental angular resolution in order to obtain the di erent curves intersection. This can be achieved by constructing a bi-dimensional histogram of (;) where each hit contributes to ll a number of bins located on its sinusoidal curve. The di erentstraightlines of the eventscan then bedetermined by pickingup the most lled bins of the histogram.
InOPERAthebrickswallsareperpendiculartothebeamaxisandeachwallisfollowed by a scintillators wall made of two planes. The rst one is y-coordinate scintillators plane whereas the second is x-coordinate one. Seen from the scintillators, each event is a sum of strips in (y,z) and (x,z) planes. An important part of the back-scattered particlesarelowenergy onesand deviatedfromthe principalgeometric eventaxis(which often coincides with the outgoing muon). Electronic noises as well as neutral particles interactions are disconnected strips for the former or showers of strips for the latter. In all these con gurations the HT method can be used to eliminate or at least reduce the associated strips making the vertex location much more easier.
In our case, two histograms, one for x and the other for y-oriented strips, of 50bins, covering a 2 range for the ()axis, and 50 bins, covering up to itsmaximum possible value, are lled by all the touched strips in each event. In each histogram the most populated bin was singled out and its value used as a reference. Bins with values more than 95% of the reference are kept. Hits belonging to straight lines associated with the previous bins are taggedas HT-strips. In gure 2 the selected HTstrips are shown with respecttoalltouchedstrips forone ofthemuonicdecaytau eventsinboth(y,z) and(x,z) orientations.
Foreventsinwhichallthe hitstripsare locatedinone scintillatorswall, allthe strips are considered as HT-strips since the Hough transformis useless in this case.
3 Scintillators walls selection
Animportantstepin ndingtherightwallinthe newalgorithmisapreliminaryselection ofsome scintillatorswalls(uptofour)whichare likelytobecandidatesforbeing the rst downstream wall after the vertex. The choice of the rst of these walls is of the utmost importancesince inthe absence of back-scattered particles the rst touched scintillators wallistheoneofinterestwhileinthepresenceofback-scatteredparticlesthe rsttouched wall and even one ortwo successive wallsare tobe eliminated.
reinteracting far behind the vertex.
Starting from the rst wall ful lling the previous condition, only scintillators walls containingat least one HT strip for eachorientation(x and y) are kept.
For events with lownumber of strips(less than 2.5strips/plane) the rst scintillators wallisselectedevenif itdoesnot ful llthe previousconditionandwallswithatleasttwo strips areselected even ifthey are not HTselected ones. This isintented tolimitthe loss of eÆciency forQE for which back scattering is low.
For eachselected scintillatorswall the followingvariables are then estimated:
Number of photo-electrons detected ineach selected scintillators wall
Number of hitstrips in each selected scintillators wall
The geometric dispersion of the strips ineach selected wall calculated as:
= q 2 x + 2 y where x ( y
) is the dispersion in the x(y) oriented plane de ned as the maximum distance of any two strips inthis plane
The mean distance of the strips of each plane with respect to the event principal axis de ned by the HT strips of the rst scintillators planes of each event (except the very rst one). The determination of the event principal axiswill be presented inth x-y vertex positiondeterminationsection.
4 Wall nding eÆciency
The muonic decay tau events are separated inthree categories depending onthe number of the selected walls and on the mean number of strips per wall of scintillators. This separationismotivatedbythefactthattheneuralnetworkperformanceusedtolocatethe rightwallisimprovedbyseparataingQE-likefromDIS-likeeventsandalsobyseparating events with smallshower developmentfromthose ofimportantone. The threecategories of events are de ned as follows:
Events with less than two touched wallsof planes of scintillators
Eventswithmorethantwotoucheswallsofplanesandameannumberofstrips/wall less than 2.5
Eventswithmorethantwotouchedwallsofplanesandameannumberofstrips/wall more than 2.5
feed forward, standard back propagation option. The number of hidden layers used in this NN is one with as many nodes as the number of used variables.
The number of the outputs is one for the rst category and 3 for the others. The outputsgivethe probability ofeach ofthe considered wallsto bethe rst plane afterthe vertex. In gure3theweightof each variableusedintheneuralnetworkisshown forone of the threeneuralnetworks. Figure3shows that the collected energyof the scintillators walls is by far the most important one. The training and the validationof these NN use asmany as24000events. 6000 eventsare then used todeterminethe eÆciency of nding the right wallof brick. 30% of these events are QEevents.
The events used inthis study are tau neutrino eventswith the same energy spectrum as the LNGS muon neutrino beam one [4]. Taking into account the oscillation e ect on the energy spectrum will not a ect the result of the present analysis. This can be seen in gure 4 which shows that the wall nding eÆciency does not depend onthe neutrino energy.
Intable1theeÆciencyandtheproportionforeachofthethreecategoriesoftau-muon events are shown.
Category Composition(%) EÆciency(%)
rst 5.6 93.41:4
second 41.5 91.70:6
third 52.9 85.6 0:6
Table 1
Taking into account the proportion of each category the total wall brick nding eÆ-ciency is found to be:
WallBrick FindingEÆciency =88.60:4%
5 X-Y vertex position determination
Once the right wall is found, the event principal axis is used to determine the x-y position of the vertex. The determination of this axis is identical to the one used to estimate the strips distance variable mentioned before, except that here we include the rst touched plane when it is the rst plane after the vertex. In the following we give a short description of this determination.
The event direction in both (x,z) and (y,z) planes, is determined using selected hit strips. These strips are chosen according to the event topology:
Only HT-selected strips are used when they satisfythe followoing requirements:
Thedistance ofthestriptothe geometriccentre ofthe hitstripsisless thanD.The initialvalue of D is 30cm. It isthen decreased step by step ( 3 cmeach)until the t of the straight linepassing by all the chosen strips is goodenough (
2
5). In any case the value of Dcould not go under5 cm.
N=7for events with numberof strips perwall of scintillators planes more than 2.5
N=2when only two wallsare selected
These numbers take account of the di erent topologies encountered inthe muonic tau's decay events.
The selected stripsare then usedto ttwo lines,one inthe (x,z)plane andone inthe (y,z)plane. Theintersectionsof thetwo ttedstraightlineswiththe rstscintillatorwall afterthe right brick wall,are considered asthe predicted (x,y) coordinates of the vertex. The brick locatedinthe rightwalland containingthe predicted(x,y) coordinates isthen considered as the rightbrick.
Comparison between the predictedbrickand the one withinwhich theneutrino inter-action takes place shows that in events where the right wall was correctly predicted, the brick prediction is correctfor 81.7% of the events.
Vertex Brick FindingEÆciency = 81.7 0:5%
6 Conclusion
The total eÆciency of nding the brick in which the neutrino interaction takes place in the muonictau decay events isimproved usinga newalgorithm. The newalgorithmuses the Hough Transform technique as a preselection of the signi cant strips. The neural network technique is then used after separating the events in three categories according to their topolgy. Once the wallis found, a t of the event thrust in both (x,z) and (y,z) is done todetermine the right brick. The total eÆciency of nding the right brick in the muonic decay of tau neutrino events is then estimated to be 72.3%.
Brick FindingEÆciency = 72.30:6%
Optimisation of the previous algorithm willcertainly allow to improve this eÆciency especiallyin the vertex coordinates determinationwhere more sophisticated tracking al-gorithmusingtopoplogiesofone, twoand many branches canbeused. The improvement onthe wall ndingeÆciencycan alsobepossiblebystudyingthoroughlytheHTcriterion selectionand by improving the separation between QE-likeand DIS-likeevents.
[1] M. G. Moret et al. OPERA internal note 23 May 2001, 'Brick nding eÆciency: comparisons between several scintillator tracker options'.
[2] HOUGHP.V.CMethodsandmeansforrecognizing complexpatterns.UnitedStates Patents, n.3, 069, 654, 18December1962.
[3] A.Zell et al. SNNS User manual, Version 4.1, Report N 6/95. SNNS is(c) (Copy-right) 1990-95 SNNS Group, Institue of Parellel and Distributed High-Performance Systems(IPVR),University of Stuttgart, Breitwiesentrasse 20-22, 70565 Stuttgart, Germany.
var1: numberof photo-electrons in the rst plane var2: dispersion in the rst plane
var3: nbof strips in the rst plane
var4: distance with respect tothe event axis inthe rst plane
var5: ratio of the numberof photo-electrons in the rst plane with respect tothe second one
var6: numberof photo-electrons in the second plane var7: dispersion in the secondplane
var8: nbof strips in the second plane
var9: distance with respect tothe event axis inthe second plane var10: numberof photo-electrons in the third plane
var11: dispersion inthe thirdplane var12: nb of strips in the third plane
var13: distance with respect tothe event axisin the third plane var14: total numberof photo-electrons in the event
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