{"title": "Vertex Identification in High Energy Physics Experiments", "book": "Advances in Neural Information Processing Systems", "page_first": 868, "page_last": 874, "abstract": null, "full_text": "Vertex Identification in High Energy \n\nPhysics Experiments \n\nGideon Dror* \n\nDepartment of Computer Science \n\nThe Academic College of Tel-Aviv-Yaffo, Tel Aviv 64044 , Israel \n\nHalina Abramowiczt David Hornt \n\nSchool of Physics and Astronomy \n\nRaymond and Beverly Sackler Faculty of Exact Sciences \n\nTel-Aviv University, Tel Aviv 69978 , Israel \n\nAbstract \n\nIn High Energy Physics experiments one has to sort through a high \nflux of events, at a rate of tens of MHz, and select the few that are \nof interest. One of the key factors in making this decision is the \nlocation of the vertex where the interaction , that led to the event , \ntook place. Here we present a novel solution to the problem of \nfinding the location of the vertex, based on two feedforward neu(cid:173)\nral networks with fixed architectures, whose parameters are chosen \nso as to obtain a high accuracy. The system is tested on simu(cid:173)\nlated data sets , and is shown to perform better than conventional \nalgorithms. \n\n1 \n\nIntroduction \n\nAn event in High Energy Physics (HEP) is the experimental result of an interaction \nduring the collision of particles in an accelerator . The result of this interaction is \nthe production of tens of particles, each of which is ejected in a different direction \nand energy. Due to the quantum mechanical effects involved, the events differ from \none another in the number of particles produced , the types of particles, and their \nenergies. The trajectories of produced particles are detected by a very large and \nsophisticated detector. \n\n\u2022 gideon@server.mta.ac.il \nthalina@Dost.tau.ac.i1 \n*hom@n;uron.tau.ac.il \n\n\fVertex Identification in High Energy Physics Experiments \n\n869 \n\nEvents are typically produced at a rate of 10 MHz, in conjunction with a data \nvolume of up to 500 kBytes per event. The signal is very small, and is selected from \nthe background by multilevel triggers that perform filtering either through hardware \nor software. In the present paper we confront one problem that is of interest in these \nexperiments and is part of the triggering consideration. This is the location of the \nvertex of the interaction. To be specific we will use a simulation of data collected by \nthe central tracking detector [1] of the ZEUS experiment [2] at the HEP laboratory \nDESY in Hamburg, Germany. This detector, placed in a magnetic field , surrounds \nthe interaction point and is sensitive to the path of charged particles. It has a \ncylindrical shape around the axis, z, where the interaction between the incoming \nparticles takes place. The challenge is to find an efficient and fast method to extract \nthe exact location of the vertex along this axis. \n\n2 The Input Data \n\nAn example of an event, projected onto the z = 0 plane, is shown in Figure 1. Only \nthe information relevant to triggering is used and displayed. The relevant points, \nwhich denote hits by the outgoing particles on wires in the detector , form five rings \ndue to the concentric structure of the detector. Several slightly curved particle \ntracks emanating from the origin, which is marked with a + sign, and crossing \nall five rings, can easily be seen. Each track is made of 30-40 data points. All \ntracks appear in this projection as arcs, and indeed, when viewed in 3 dimensions, \nevery particle follows a helical trajectory due to the solenoidal magnetic field in the \ndetector. \n\n. \"1: .. -\n\n60 \n\n40 \n\n20 \nEo \n.\u00a3 \n\n-20 \n\n-40 \n\n-60 \n\n-60 -40 -20 \n\n0 \n\nx[cml \n\n20 \n\n40 \n\n60 \n\nFigure 1: A typical event projected onto the z = 0 plane. The dots, or hits , have \na two-fold ambiguity in the determination of the xy coordinates through which the \nparticle has moved. The correct solutions lie on curved tracks that emanate from \nthe origin. \n\nEach physical hit is represented twice in Fig. 1 due to an inherent two-fold ambiguity \nin the determination of its xy coordinates. The correct solutions form curved tracks \nemanating from the origin. Some of those can be readily seen in the data. Due to \nthe limited time available for decision making at the trigger level, the z coordinate \nis obtained from the difference in arrival times of a pulse at both ends of the CTD \nand is available for only a fraction of these points. The hit resolution in xy is \n'\" 230 J.lm , while that of z-by-timing is ::: 4 cm. The quality of the z coordinate \n\n\f870 \n\nG. Dror. H. Abramowicz and D. Hom \n\ninformation is exemplified in figure 2. Figure 2(a) shows points forming a track of \na single particle on the z = 0 projection. Since the corresponding track forms a \nhelix with small curvature, one expects a linear dependence of the z coordinate of \nthe hits on their radial position, r = J x 2 + y2. Figure 2(b) compares the values of \nr with the measured z values for these points. The scatter of the data around the \nlinear regression fit is considerable. \n\n35,--,--,-,1---,1-...,--,..-----.1--1.----, 10~~-~-,..--~-~-~~-, \n\n301-\n\na) \n\n25f(cid:173)\n~20f-\n>-\n\n101-\n\n51-\n\n... ; \n\n90 \n\n80 \n\nb) \n\n:-r. \n\n-\n-\n\n70 \n\nE \n\n- ~60 \n\nN \n\n_ \n\n-\n\n-\n\n50 \n\n40 \n\n30 \n\n20 \n\nI I I ' I \n10 \n\n50 \n\n70 \n\n20 \n\n30 \n\n60 \n\n40 \nx [cm) \n\n80 \n\n1~5 20 \n\n25 \n\n30 \n\n35 \nr[cm) \n\n40 \n\n45 \n\n50 \n\n55 \n\nFigure 2: A typical example of uncertainties in the measured z values: (a) a single \ntrack taken from the event shown in figure 1, (b) the z coordinate vs r = Jx 2 + y2 \nthe distance from the z axis for the data points shown in (a). The full line is a \nlinear regression fit. \n\n3 The Network \n\nOur network is based on step-wise changes in the representation of the data, moving \nfrom the input points, to local line segments and to global arcs. The nature of \nthe data and the problem suggest it is best to separate the treatment of the xy \ncoordinates from that of the z coordinate. Two parallel networks which perform \nentirely different computations, form our final system. The first network, which \nhandles the xy information is responsible for constructing arcs that correctly identify \nsome of the particle tracks in the event. The second network uses this information \nto evaluate the z location of the point where all tracks meet. \n\n3.1 Arc Identification Network \n\nThe arc identification network processes information in a fashion akin to the method \nvisual information is processed by the primary visual system [3]. \n\nThe input layer for this network is made of a large number of neurons (several tens \nof thousands) and corresponds to the function of the retina. Each input neuron \nhas its distinct receptive field. The sum of all fields covers completely the relevant \ndomain in the xy plane. This domain has 5 concentric rings, which show up in \nfigure 1. The total area of the rings is about 5000 cm2 , and covering it with 100000 \ninput neurons leads to satisfactory resolution. A neuron in the input level fires \nwhen a hit is present in its receptive field. We shall label each input neuron by the \n(xy) coordinates of the center of its receptive field. \n\nNeurons of the second layer are line segment detectors. Each second layer neuron \nis labeled by (XY a), where (X, Y) are the coordinates of the center of the segment \n\n\fVertex Identification in High Energy Physics Experiments \n\n871 \n\nand 0' denotes its orientation. The activation of second layer neurons is given by \n\nVXYa = g(2:: J XY a ,xy V xy -\n\n( 2 ) , \n\nxy \n\nwhere \n\nlxY a ,ry = { ~1 ifr.L < O.5cmArll < 2cm \n\nifO.5cm< r.L < 1cmArii < 2cm \notherwise \n\n(1) \n\n(2) \n\nand g( x) is the standard Heaviside step function . rll and r.L are the parallel and \nperpendicular distances between (X , Y) and (x, y) with respect to the axis of the \nline segment, defined by 0' . It is important to note that at this level , values of the \nthreshold 82 which are slightly lower than optimum are preferable, taking the risk \nof obtaining superfluous line segments in order to reduce the probability of missing \none. Superfluous line segments are filtered out very efficiently in higher layers. \n\nFigure 3 represents the output of the second layer neurons for the input illustrated \nby the event of figure 1. An active second layer neuron (XY 0') is represented in \nthis figure by a line segment centered at the point (X , Y) making an angle 0' with \nthe x axis. The length of the line segments is immaterial and was chosen only for \nthe purpose of visual clarity. \n\n60 \n\n40 \n\n20 \nE 0 ~ \n>-\n-20 \n\n-40 \n\n-60 \n\n\"Z \n\n.... \n~ .~ \n1'1( #- .>~~ . \ns \n\n~.::.. ~ \n\n~ , \n~ ~. ' \n~ . \n\n\"\\0 \n\n-t!- ~ \n~ \n\n... \n\n~ \n\n~1t ~ \n..,. ~ , . \nl-\n-J.. \n\ni-!. \n\nI' \n\n;J \n\n\"'\" \" \n\n'\" \n\n-60 -40 -20 \n\n0 \n\nxfcml \n\n20 \n\n40 \n\n60 \n\nFigure 3: Representation of the activity of second layer neurons XY 0' for the input \nof figure 1 taken by plotting the appropriate line segments in the xy plane . At some \nXY locations several line segments with different directions occur due to the rather \nlow threshold parameter used , 82 = 4. \n\nNeurons of the third layer transform the representation of local line segments into \nlocal arc segments. An arc which passes through the origin is uniquely defined by \nits radius of curvature R and its slope at the origin. Thus , each third layer neuron \nis labeled by '\" 8 i , where 1\"'1 = 1/ R is the curvature and the sign of '\" determines \nthe orient ation of the arc. 1 < i < 5 is an index which relates each arc segment to \nthe ring it belongs to. \n\n- -\n\nThe mapping between second and third layers is based on a winner-take-all mech(cid:173)\nanism. Namely, for a given local arc segment, we take the arc segment which is \nclosest to being tangent to the local arc segment. \nDenoting the average radius of the ring i ( i=1 ,2, ... 5) by rj and using f3i = sin -1 (y) \n\n\f872 \n\nG. Dror. H. Abramowicz and D. Horn \n\nthe final expression for the activation of the third layer neurons is \n\nV\",lIi = maxe \n\n_0 2 \n\n0<3 \n\n2 \n\ncos (() - 2f3i - 0:), \n\n(3) \n\nwhere 6 = 6(X , Y, \"', (), i) = J(X - ri cos((} - f3d)2 + (Y - ri sin(() - f3d)2 is simply \nthe distance of the center of the receptive field of the (XY 0:) neuron to the (\"'(}) \narc. \n\nThe fourth layer is the last one in the arc identification network. Neurons belonging \nto this layer are global arc detectors. In other words, they detect projected tracks \non the z = 0 plane. A fourth level neuron is denoted by \"'(} , where\", and () have the \nprevious meaning, now describing global arcs. Fourth layer neurons are connected \nto third layer neurons in a simple fashion , \n\nVd = g( L 6\"\"\",,611 ,11' V\"\"II'i - (}4) . \n\n\",'II' i \n\n(4) \n\nFigure 4 represents the activity of fourth layer neurons. Each active neuron \"'(} is \nequivalent in the xy plane to one arc appearing in the figure . \n\n. ~-\n\n~ \n\n60 \n\n40 \n\n20 \n\nE \n~o \n>-\n-20 \n\n-40 \n\n-60 \n\n-60 -40 -20 \n\nf< \n\nx em] \n\n20 \n\n40 \n\n60 \n\nFigure 4: Representation of the activity of fourth layer neurons \"'(} for the input of \nfigure 1 taken by plotting the appropriate arcs in t he xy plane. The arcs are not \nprecisely congruent to the activity of the input layer which is also shown , due to \nthe finite widths which were used, il\", = 0.004 and il(} = 7r/20. This figure was \nproduced with (}4 = 3. \n\n3.2 z Location Network \n\nThe architecture of the second network has a structure which is identical to the first \none, although its computational task is different. We will use an identical labeling \nsystem for its neurons , but denote their activities by v xy . The latter will assume \ncontinuous values in this network. \n\nA first layer neuron of the z-location network receives its input from the same \nreceptive field as its corresponding neuron in the first network. Its value, vxy , is the \nmean value of the z values of the points within its receptive field . If no z values are \navailable for these points , a null value is assigned to it. \nThe second layer neurons compute the mean value v XY a = (v xy ) of the z coordinate \nof the first layer neurons in their receptive field , averaging over all neurons within \n\n\fVertex Identification in High Energy Physics Experiments \n\n873 \n\nthe section \n\n{xy II(x - X) sina - (y - Y) cosal < 0.5cm/\\ (x - X)2 + (y - y)2 < 4cm2} , \n\nwhich corresponds to the excitatory part of the synaptic connections of equation \n(2). If null values appear within that section they are disregarded by the averaging \nprocedure. If all values are null , VXYa is assigned a null value too. This Z averaging \nprocedure is similarly propagated to the third layer neurons. \n\nThe fourth layer neurons evaluate the Z value of the origin of each arc identified \nby the first network. This is performed by a simple linear extrapolation. The final \nz estimate of the vertex, Znet , which should be the common origin of all arcs, IS \ncalculated by averaging the outputs of all active fourth layer neurons. \n\n4 Results \n\nIn order to test the network, we ran it over a set of 1000 events generated by a \nMonte-Carlo simulator as well as over a sample of physical events taken from the \nZEUS experiment at the HEP laboratory DESY in Hamburg. For the former set \nwe compared the estimate of the net Znet with the nominal location of the vertex z, \nwhereas for the real events in the latter set , we compared it with an estimate Zrec \nobtained by full reconstruction algorithm , which runs off-line and uses all available \ndata. Results of the two tests can be compared since it is well established that the \nresult of the full reconstruction algorithm is within 1 mm from the exact location \nof the vertex. \n\nNetwork \n\n=-2.7\u00b1O.2 \n(1 = 6.1 \u00b1O.2 \n\nz \n\n140 \n\n120 \n\n100 \n\n80 \n\n60 \n\n40 \n\nHistogrom \n\n= 1.9\u00b1O.3 \n(1 = 8.4\u00b1O.3 \n\nz \n\n140 \n\n120 \n\n100 \n\n80 \n\n60 \n\n40 \n\n20 J ~~ 20 \n\n0 \n\n0 \n\n-40 \n\n-20 \n\n0 \n\n20 \n\n40 \n\nAz [em] \n\nFigure 5: Distribution of ~ z = Ze8timate - Zexact values for two types of estimates, \n(a) the one proposed in this paper and (b) the one based on a commonly used \nhistogram method. \n\nWe also compared our results with those of an algorithmic method used for trig(cid:173)\ngering at ZEUS [4]. We shall refer to this method as the 'histogram method '. The \nperformance of the two methods was compared on a sample of 1000 Monte-Carlo \nevents. The network was unable to get an estimate for 16 events from the set , \nas compared with 15 for the histogram method (15 of those events were common \n\n\f874 \n\nG. Dror, H. Abramowicz and D. Horn \n\nIn Figure 5 we compare the distributions of ~z = Znet - Zexact and \nfailures). \n~Z = Zhist - Zexact for the sample of Monte-Carlo events, where Zexact is the gen(cid:173)\nerated location of the vertex. Both methods lead to small biases, -2.7 cm for Znet \nand 1.9 cm for Zhist . The resolution, as obtained from a Gaussian fit , was found \nto be better for the network approach (0- = 6.1 cm) as compared to the histogram \nmethod (0- = 8.4cm). In addition, it should be noted that the histogram method \nyields discrete results, with a step of 10 cm, whereas the current method gives con(cid:173)\ntinuous values. This can be of great advantage for further processing. Note that \noff-line, after using the whole CTD information, the resolution is better than 1 mm. \n\n5 Discussion \n\nWe have described a feed forward double neural network that performs a task of \npattern identification by thresholding and selecting subsets of data on which a simple \ncomputation can lead to the final answer. The network uses a fixed architecture, \nwhich allows for its implementation in hardware, crucial for fast triggering purposes. \n\nThe basic idea of using a fixed architecture that is inspired by the way our brain \nprocesses visual information, is similar to the the raison d 'etre of the orientation \nselective neural network employed by [5]. The latter was based on orientation se(cid:173)\nlective cells only, which were sufficient to select linear tracks that are of interest in \nHEP experiments. Here we develop an arc identification method, following similar \nsteps. Both methods can also be viewed as generalizations of the Hough trans(cid:173)\nform [6] that was originally proposed for straight line identification and may be \nregarded as a basic element of pattern recognition problems [7]. Neither [5] nor \nour present proposal were considered by previous neural network analyses of HEP \ndata [8] . The results that we have obtained are very promising. We hope that they \nopen the possibility for a new type of neural network implementation in triggering \ndevices of HEP experiments. \n\nAcknowledgments \n\nWe are indebted to the ZEUS Collaboration whose data were used for this study. \nThis research was partially supported by the Israel National Science Foundation . \n\nReferences \n\n[1] B. Foster et al. , Nuclear Instrum. and Methods in Phys. Res. A338 (1994) 254. \n[2] ZEUS Collab., The ZEUS Detector, Status Report 1993, DESY 1993; M. \n\nDerrick et al. , Phys. Lett. B 293 (1992) 465 . \n\n[3] D. H. Hubel and T . N. Wiesel, J. Physiol. 195 (1968) 215. \n[4] A. Quadt , MSc thesis, University of Oxford (1997) . \n[5] H. Abramowicz , D. Horn , U. Naftaly and C . Sahar-Pikielny, Nuclear Instrum. \nand Methods in Phys. Res. A378 (1996) 305; Advances in Neural Information \nProcessing Systems 9, eds. M. C . Mozer , M. J. Jordan and T. Petsche, MIT \nPress 1997, pp. 925- 931. \n\n[6] P. V. Hough , \"Methods and means to recognize complex patterns\", U.S. patent \n\n3.069.654. \n\n[7] R. O. Duda and P. E. Hart, \"Pattern classification and scene analysis\" , Wiley, \n\nNew York, 1973. \n\n[8] B. Denby, Neural Computation, 5 (1993) 505. \n\n\f", "award": [], "sourceid": 1546, "authors": [{"given_name": "Gideon", "family_name": "Dror", "institution": null}, {"given_name": "Halina", "family_name": "Abramowicz", "institution": null}, {"given_name": "David", "family_name": "Horn", "institution": null}]}