10 - H1 - Desy

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82 Photon signal extraction n∏ var p MV S(B) A (i) = k=1 p S(B),k (x k (i)). (6.12) This approach assumes statistical independence of all the input variables, which is usually not fully true. The output of the MVA is a likelihood ratio, denoted further as a discriminator D. For an event i it is calculated as D(i) = p MV A S p MV S A (i) (i) + p MV B A (i) . (6.13) It can be shown that in absence of model inaccuracies (such as correlations between input variables, or an inaccurate probability density model), the ratio given by equation 6.13 provides optimal signal from background separation for the given set of input variables []. Some other, alternative, mostly more advanced classifier definitions have been also studied for their possible application in this analysis. The result of this study is presented in appendix B together with a short discussion of their advantages and disadvantages. The classifier has been trained independently in double differential bins of transverse energy and pseudorapidity summarised in appendix in table A-1. The choice of both dimensions has been motivated by a brief discussion in section 6.1. The discriminator distribution for both signal and background is presented in figure 6.7 as studied with the evaluating sample. The discriminator, by definition restricted to the range 0 < D < 1, tends to peak near one for the signal events and near zero for the background events. In addition to the separation, defined in 6.1.2, for the peaked distributions as in the case od D, one can study the significance 〈G〉 of the classifier being equal to the difference between the classifier means for signal and background divided by the quadratic sum of their root-meansquares. ∫ pS (x) − p B (x) 〈G〉 = p 2 S (x) + (6.14) p2 B (x)dx, The transverse energy dependence of both benchmark quantities are shown in the fig 6.8 for each LAr wheel separately. As a reference, in the same plot, the separation of the best discriminating input variable - R T is shown. One can see the advantage of combining more than one input variable, as the discriminator separation is higher than the separation of the single input variable. There is no advantage though in the cases where the best input variable is highly dominant, as for CB3, FB1 and FB2 LAr wheels, where separation power of R T is much higher than of all other input variables. Again, one can see the consistent drop of both, the separation and significance with the transverse energy following the dependence of the input variables. The maximum likelihood method chosen in this analysis, is valued for its transparency, simplicity and speed. At the same time, the method’s limitations are numerous. Particularly, the incorrect treatment of correlations between input variables is believed to lead to dimunision of the discrimination performance [116]. In the statistical theory there are other, more advanced classifier definitions, developed for improvement of the performance.
6.3 Classifier 83 E1 CB1 CB2 CB3 FB1 FB2 FB3 E 2 E 3 E 4 E 5 E 6 Signal Background E 7 E 8 Figure 6.7: Discriminator signal and background distribution binned in a transverse energy and a pseudorapidity of the incoming particle. The discriminator introduced in this chapter is used during the final cross section determination as an input variable for the unfolding presented in chapter 8.
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PROMPT PHOTON PRODUCTION IN PHOTOPR
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Abstract This thesis presents measu
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x Contents 4 Event reconstruction a
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xii Contents
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xiv Contents the two photon decay c
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xvi Contents
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2 Theoretical framework Gene- Quark
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4 Theoretical framework charged W
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6 Theoretical framework Neutral and
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8 Theoretical framework α s 0.20 H
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10 Theoretical framework 1.2.4.1 DG
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12 Theoretical framework for the em
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14 Theoretical framework F 2 ⋅ 2
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- - 2) 9O9O9 4 - 70 6- - 7 - Q-
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18 Theoretical framework e e e a) b
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20 Theoretical framework than in th
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22 Theoretical framework ZEUS dσ/E
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24 Theoretical framework claim thou
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26 Theoretical framework Figure 1.2
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28 Theoretical framework Inclusive
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30 Theoretical predictions partons
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Page 54 and 55: 38 Theoretical predictions contribu
Page 56 and 57: 40 The H1 experiment at HERA Hall N
Page 58 and 59: 42 The H1 experiment at HERA y θ z
Page 60 and 61: 44 The H1 experiment at HERA resolu
Page 62 and 63: 46 The H1 experiment at HERA the el
Page 64 and 65: 48 The H1 experiment at HERA under
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Page 68 and 69: 52 Event reconstruction and presele
Page 80 and 81: 64 Prompt photon selection the rema
Page 82 and 83: 66 Prompt photon selection ∆η <
Page 84 and 85: 68 Prompt photon selection reconstr
Page 86 and 87: 70 Prompt photon selection Events 5
Page 88 and 89: 72 Prompt photon selection Selectio
Page 90 and 91: 74 Photon signal extraction γ π0
Page 92 and 93: 76 Photon signal extraction Events
Page 94 and 95: 78 Photon signal extraction CB1 CB2
Page 96 and 97: 80 Photon signal extraction Figure
Page 100 and 101: 84 Photon signal extraction 〈S〉
Page 102 and 103: 86 Calibration and tuning • Backg
Page 104 and 105: 88 Calibration and tuning χ 2 /NDF
Page 106 and 107: 90 Calibration and tuning energy on
Page 108 and 109: 92 Calibration and tuning D Ej 1.1
Page 110 and 111: 94 Calibration and tuning
Page 112 and 113: 96 Cross section building The corre
Page 114 and 115: 98 Cross section building • L-cur
Page 116 and 117: 100 Cross section building (Reconst
Page 118 and 119: 102 Cross section building 8.2.1.1
Page 120 and 121: 104 Cross section building Figure 8
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Page 142 and 143: f f f f f f f f f f f f 126 Cross s
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Page 146 and 147: 130 Results description of the shap
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132 Results 9.2 Prompt photon + jet
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134 Results [pb] LO dσ / dx γ 100
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136 Results 9.3 NLO corrections The
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138 Results [pb/GeV] dσ / dp 15 10
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140 Results transverse momentum imb
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142 Results [pb/GeV] γ dσ / E T 2
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144 Conclusions and outlook is cons
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A Analysis Binning 147 A Analysis B
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A Analysis Binning 149 Bin E γ T,O
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B Alternative classifier definition
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C Cross Section Tables 153 C Cross
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C Cross Section Tables 155 η γ E
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C Cross Section Tables 157 η γ d
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C Cross Section Tables 159 η jet d
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C Cross Section Tables 161 x LO γ
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C Cross Section Tables 163 x LO γ
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List of Figures 1.1 Lowest order Fe
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List of Figures 167 6.2 Shower shap
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List of Tables 169 List of Tables 1
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List of Tables 171 C-8b Corrections
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References [1] C. Amsler et al.,
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References 175 [32] R. Nisius, “T
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References 177 [63] P. A. Aarnio et
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References 179 [97] W. Braunschweig
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References 181 [129] J. M. Butterwo
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