Momentum Analysis of Cosmogenic Muons in theMINOS DetectorsA thesis submitted in partial fulfillment of the requirementfor the degree of Bachelor of Science with Honors inPhysics from the College of William and Mary in Virginia,byDaniel DamianiAccepted for(Honors)Advisor: Prof. Jeffery NelsonProf. John DelosProf. Jan ChaloupkaProf. Nahum ZobinWilliamsburg, VirginiaMay 2006AbstractProper reconstruction of muon tracks requires that the magnetic fields in the two MINOSdetectors be well understood. Previous work revealed problems with the measured ratio ofreconstructed cosmic ray µ+ to µ− in certain regions of the detector indicating that the currentmodel of the field for those sections was unsatisfactory. Modeling of the effects of the ends ofboth detectors and the supermodule gap of the far detector had been left out of the model of themagnetic field because the old finite analysis based method was too memory intensive and slowto use in track reconstruction. A new implementation of the end and supermodule gap effectswas created using a piecewise linear fit to the old end effect model to better model the fieldin the problem regions. The magnetic properties of the detector steel were also characterizedto correct additional problems with the detector magnetic fiel d. Cosmic ray muon data for thenear detector was also analy zed. The charge sign ratio of the muons analyzed was 1.27 ± 0.074which was in line with previous results.iAcknowledgmentsI would first like to thank my advisor Professor Jeff Nelson for making this research possible throughhis guidance, support and always helpful feedback. I would also like to thank Dr. Francisco Yumicevafor his invaluable assistance with my code development and ever present willingness to help. LastlyI wish to thank the Honors Committee for the time they have spent evaluating my research.iiContentsAbstract iv1 Introduction 12 Cosmic Ray Muons 32.1 Basic Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32.2 Energy Loss in Matter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32.3 Charge Sign Ratio . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43 Properties of Ferromagnets 54 Minos Detectors 64.1 Specifications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64.2 Magnetic Field Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95 BH Curve Characterization 115.1 Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115.2 Bdot Calibration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 156 End Effect Impl ementation 186.1 Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 186.2 Results from Fitting Implementation . . . . . . . . . . . . . . . . . . . . . . . . . . . 197 Cosmic Ray Analysis 237.1 Method of Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 237.2 Muon Analysis Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 248 Conclusions 32iiiReferences 34Appendices 36A Fitting Data 36List of Figures1 L3 summary plot of world charge sign ratio data as a function muon momentum(GeV/c) [2]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 Energy spectrum of primary cosmic rays. The region of “steepening” refers to thearea of maximum slope of the data[5]. . . . . . . . . . . . . . . . . . . . . . . . . . . 23 The expected charge sign ratio as a function of muon momentum from Monte Carlo [4]. 44 Example of a major hysteresis loop (dotted line is the ramp up) [11]. . . . . . . . . . 55 Example of a degaussing[12]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66 Field map of the single-plane model of the magnetic field for the far detector. . . . . 87 Field map of the single-plane model of the magnetic field for the near detector. . . . 98 Plot of the charge sign ratio as a function of vertex z-position and dz/ds (indicatesthe direction of entry into the detector)[4]. . . . . . . . . . . . . . . . . . . . . . . . . 109 Diagram of the W&M Bdot system [14]. . . . . . . . . . . . . . . . . . . . . . . . . . 1210 Calibrated 360 torus data (blue) compared with 360 vendor data (red). . . . . . . . 1411 Ramp-up data of 362 (red) and 61680 (blue) toruses. . . . . . . . . . . . . . . . . . . 1512 Overlay plot of all 26 tested MINOS steel sample toruses. . . . . . . . . . . . . . . . 1613 Plot of the averaged MINOS toruses (blue) versus the 360 vendor data (red). . . . . 1614 Plot of the ramp up of the MINOS torus average (blue) vs. …