A Search for Rare Decay D0 --> mu+mu - High Energy Physics UPRM

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”4.6 Analysis Methodology 68signals that are small when background noise is present. This technique is based on acombination of a two dimensional confidence region and a large sample approximation tothe likelihood-ratio test statistic. Automatically it quotes upper limits for small signals andalso two-sided confidence intervals for large samples.The technique of Feldman and Cousins [25] does not consider the amount ofuncertainty in the background.The new Rolke and López technique deals with thebackground uncertainty as a statistical error. The technique performs very well. It hasgood power and has correct coverage. This method can be used for two situations: whensidebands data give an estimated background rate and when it comes from Monte Carlo. Itcan also be used if there is a second background source in the signal region.To understand the results of this technique we will need the following notation: x willrepresent the observed events in our signal region, y will be the events in the backgroundregion • and will be the ratio of the sidebands background to the signal background. Theexpected background rate is –˜—Q›š¦• and the Sensitivity Number, œN … D† ƒo‡‰ˆ_‡Šn‹, isdefined as the average 90% upper limit for an ensemble of experiments having an averageof y events in the sidebands and no true signal. Table 4.3 gives the sensitivity numbers fordifferent values of the confidence • level, and y. During the various stages of this analysiscomputer routines provided by Rolke and López were used to calculate sensitivity numbersand confidence limits. The value • of for each set of cuts was determined as explained inSection 4.7. The sensitivity numbers were used to select the optimum set of cuts. Then theconfidence limits were computed from the values of x, y • and for that set of cuts. Examplesof confidence limits are given in Table 4.4
4.6 Analysis Methodology 69”Table 4.3: Sensitivity number as per Rolke and López. The number ofbackground events in the sidebands is y. The estimated background rate isC.L.C.L.–—ž›š¦• . Ÿ ¡ŸŸ¡•¢—¤£ •¢—¦¥ •¢—§£ •¢—¦¥0 2.21 2.21 4.52 4.521 3.31 2.82 6.22 5.35y2 3.97 3.17 7.12 6.143 4.62 3.49 8.17 6.454 5.29 4.03 8.99 7.125 5.90 4.23 9.77 7.436 6.37 4.60 10.52 8.007 6.86 4.79 11.21 8.308 7.23 5.14 11.85 8.869 7.64 5.32 12.51 9.0210 8.01 5.62 13.04 9.5211 8.40 5.78 13.55 9.7612 8.71 6.08 14.15 10.1413 9.09 6.19 14.63 10.3714 9.39 6.45 15.14 10.7615 9.71 6.59 15.64 10.964.6.3 Determination of Sensitivity and Confidence LimitsWe define the experimental sensitivity as the average upper limit for the branchingratio that would be obtained by an ensemble of experiments with the expected backgroundand no true signal. Therefore, the experimental sensitivity is calculated in the same way asthe branching ratio except that the sensitivity number is used for the number of observedsignal events. For each particular set of • cuts, is determined as explained in Section 4.7.3.is the predicted level of background, b. Having this in mind, we can determine the›š¦•
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A Search for the Rare Decay D£¥¤
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ResumenEste trabajo de tesis presen
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AcknowledgmentsThere are so many pe
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to work on their experiment. To all
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extremos que ésta nos presenta. Y
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amigos de universidad, Arnulfo Barr
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1.2.1 Conservation of Angular Momen
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4. Vertex z Positions . . . . . . .
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List of Tables2.1 Chronological bra
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2.4 The FOCUS Spectrometer . . . .
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M2: Magnet Number 2.: Lorentz Dimuo
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1.1 The Standard Model 2`the branch
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families of matter. These are divid
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The Standard Model 6Each of the thr
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ŽuŽd’ ‘ “”“ “-• —
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%1.2 Conservation Laws 10current be
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Conservation Laws 12`1.2handed lept
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Conservation Laws 14`1.2A §Aº‰
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However, these states are +63-1.3 C
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Page 42 and 43: W¦¨ , , and © o ¨ cÏ Î7Ô¦Ca
Page 44 and 45: 1.4 GIM Mechanism 22`1.4 GIM Mechan
Page 46 and 47: 1.5 Rare and Forbidden Decays 24whe
Page 48 and 49: 55 q z4so ¤ pj¥4osoÛ { J zF45 (1
Page 50 and 51: Notice that AA5 q z ¤ q z oiÛ z?
Page 52 and 53: Chapter 2Previous Works2.1 FCNC Dec
Page 54 and 55: ŠŠz‘i2.2 Previous Searches for
Page 56 and 57: ˜¥˜‘2.2 Previous Searches for
Page 58 and 59: ··i2.2 Previous Searches for Rare
Page 60 and 61: i2.3 FOCUS 382.3 FOCUS2.3.1 Introdu
Page 62 and 63: ¥i2.3 FOCUS 40were transmited with
Page 64 and 65: i2.3 FOCUS 42the experimental targe
Page 66 and 67: Chapter 3ObjectivesAs a departure p
Page 68 and 69: Chapter 4ProcedureThis chapter will
Page 70 and 71: 4.2 Reconstruction Process 48Recons
Page 72 and 73: 4.3 Data Selection 50Figure 4.1 sho
Page 74 and 75: °4.3 Data Selection 52Using inform
Page 76 and 77: i4.3 Data Selection 54to detect muo
Page 78 and 79: ›4.3 Data Selection 56Information
Page 80 and 81: kŸnJÑ,ššJBn©kŸnJšz¥{{[“
Page 82 and 83: 4.3 Data Selection 60iReconstructio
Page 84 and 85: ‘°4.3 Data Selection 62iTable 4.
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Page 88 and 89: 4.5 Monte Carlo Simulation 66ia spe
Page 92 and 93: signal region and determined the co
Page 94 and 95: sideband was defined as £Í£¥Í
Page 96 and 97: ƒ”4.7 Background Study 74K†«
Page 98 and 99: 4.7 Background Study 76”Figure 4.
Page 100 and 101: 4.8 Optimization of the Selection C
Page 102 and 103: ISOS ïþëÿ÷ ¡ ü&ë&÷¢üÕë
Page 104 and 105: 5.2 Background Ratio 82”Figure 5.
Page 106 and 107: 5.3 Skimming Results 84”Figure 5.
Page 108 and 109: ”5.4 Cut Optimization Results 86b
Page 110 and 111: ¥£¨ … D† ƒ ‡ ˆ ‡ Š
Page 112 and 113: … D† ƒo‡ ˆ ‡ Š ‹ —£
Page 114 and 115: List of References[1] M. Herrero, T
Page 116 and 117: æææ”Bibliography 94[19] T. Sj
Page 118 and 119: æˆææBibliography 96”[37] Ferm
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