OBSERVATION OF THE DALITZ DECAY OF THE FIRST EXCITED STATE OF THE CHARMED-STRANGE MESON

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1 OBSERVATION OF THE DALITZ DECAY OF THE FIRST EXCITED STATE OF THE CHARMED-STRANGE MESON A Diertation Preented to the Faculty of the Graduate School of Cornell Univerity in Partial Fulfillment of the Requirement for the Degree of Doctor of Philoophy by Souvik Da January

2 c Souvik Da ALL RIGHTS RESERVED

3 OBSERVATION OF THE DALITZ DECAY OF THE FIRST EXCITED STATE OF THE CHARMED-STRANGE MESON Souvik Da, Ph.D. Cornell Univerity The branching fraction for a previouly unoberved decay D + D + e+ e i predicted theoretically in thi diertation to be.65% of the branching fraction for the decay D + D + γ. We conduct a earch for the D + D + e + e in 586 pb of e + e colliion data collected with the CLEO-c detector at the Cornell Electron Storage Ring (CESR) operating at a center of ma energy of 47 MeV and oberve it with a ignificance of 6.4 σ over etimated background. The ratio of branching fraction B(D + D + e + e )/B(D + D + γ) i meaured to be (.7.4(tat).6(yt))%, which i within one tandard deviation of uncertainty from the predicted value.

4 BIOGRAPHICAL SKETCH Souvik Da wa born to Tapan and Tanuri Da on Augut, 98 in Kolkata, India. Bred on an abundance of book, toy and love in a family of humble mean, he wa oon convinced in pite of the tagnant life of Kolkata that the world, in the larger cheme of thing, i a magical place that bear invetigation. He gravitated toward phyic and at 4 declared to hi father that he had to be a phyicit. In, he graduated from Don Boco School Park Circu in Kolkata and enrolled in the undergraduate phyic program at St. Stephen College in Delhi. There hi interet in phyic bloomed and beide curricular tudie he worked with phyicit acro the country on a variety of project ranging from condened matter phyic to complex ytem and biophyic. He joined Cornell Univerity a a graduate tudent in and continued hi tradition of wandering between phyic group till he converged on experimental high energy phyic for hi Ph.D. reearch in 6. He worked on the pixel detector for the Compact Muon Solenoid (CMS) experiment at the Large Hadron Collider (LHC), ometime living for month at Fermilab, Illinoi where a part of it wa being fabricated. In early 7, he along with part of the pixel detector wa hipped out to CERN, Geneva. He worked on variou apect of the CMS experiment till the LHC uffered a breakdown in September 8. Thereafter, he witched to the CLEO-c experiment where he worked on the electromagnetic Dalitz decay of the D + meon, which i the content of thi diertation. Souvik look forward to reuming work at the LHC where he hope to occupy himelf with earching for the mechanim of electroweak ymmetry breaking. iii

5 To my parent, Tapan and Tanuri, and my grandparent, Phalguni and Haripada, who taught me to value knowledge above all ele iv

6 ACKNOWLEDGEMENTS I mut acknowledge that any reult in contemporary high energy phyic, epecially from large collaboration like CLEO, owe a lot to many people. Thi analyi i no different and it at the end of decade of effort, drawing on the labor and expertie of hundred who built, maintained, and operated the CLEOc detector and the CESR collider. I mut alo acknowledge the effort that went into making ene of the data, in particular the effort of thoe who meaured the hadronic branching fraction of the D + meon that thi analyi explicitly depend on. Onto more peronal acknowledgement, I mut firt thank my advior, Ander Ryd, for guiding me through thi and many other project in the coure of my graduate career in high energy phyic with exceptional involvement. Thi document would not exit were it not for hi patient guidance and encouragement. I have learned much from him in the field of particle phenomenology, detector hardware, oftware development, tatitic and collaboration politic, and I hope to learn more in the year ahead. I thank David Cael and Jim Alexander for following the progre of thi analyi with o much interet and offering very helpful advice at variou juncture of the effort. I am grateful to Werner Sun for helping me familiarize myelf with CLEO-c oftware. Werner, Dan Riley, David Kreinick and Brian Heltley mut be thanked for helping me reproce large CLEO-c dataet. I thank Peter Onyii for lending u hi expertie on the hadronic decay of D + meon. Brian, Matthew Shepherd and Richard Ehrlich were taked with reviewing thi analyi internally within the CLEO collaboration and for that I thank them. Brian mut alo be thanked for anwering my quetion regarding CLEO-c calorimetry and offering great uggetion for improving the analyi. I alo thank Para v

7 Naik for fielding random quetion about the detector and oftware at equally random time of the day or night. I am grateful to Pattie Place, the Thei Advior of the Graduate School at Cornell Univerity, for weeding out typeetting error from thi document. Finally, I thank Cornell Univerity, the Department of Phyic and the Laboratory for Elementary Particle Phyic for accepting my candidacy and giving me uch an extraordinary opportunity to work at the very frontier of phyic. vi

8 TABLE OF CONTENTS Biographical Sketch iii Dedication iv Acknowledgement v Table of Content vii Lit of Table x Lit of Figure xvii Introduction A Theoretical Prediction for the Ratio of Branching Fraction B(D + D + e+ e )/B(D + D + γ) 6. Rate for D + D + γ Rate for D + D + e+ e The CLEO-c Detector 6. The Tracking Sytem The Calorimeter Analyi Method to Search for the D + D + e + e and Meaure the Ratio of Branching Fraction B(D + D + e+ e )/B(D + D + γ) 6 4. Background for D + D + e + e Selection Criteria for Recontructing D + D + e+ e Track Quality Requirement for the Soft e + e Pair Ma of the D + Meon, m D Beam Contrained Ma of the D + Meon, Ma Difference between the D + and the D + Meon, δm d between the e + and e Track φ between the e + and e Track Selection Criteria for Recontructing D + D + γ Shower Criteria for the Photon Dataet Ued Generic Monte Carlo Continuum Monte Carlo Reproceing Data to Fit Track with the Electron Ma Hypothei Monte Carlo Generation and Validation Optimization of Selection Criteria for the D + D + e+ e D + K + K π D + K S K D + ηπ+ ; η γγ D + η π + ; η π + π η; η γγ D + K+ K π + π D + π + π π vii

9 4.7.7 D + K + K ; K + K S π+, K K π D + ηρ+ ; η γγ; ρ + π + π D + η π + ; η ρ γ Efficiency of Selection Criteria for the Recontruction of D + D + e+ e Etimation of Background in the Signal Region of D + D + e + e Determining the Shape of the Ditribution Determining the Shape of the δm Ditribution Etimating the Background in the D + K + K π + Mode Etimating the Background in the D + K S K + Mode Etimating the Background in the D + ηπ+ ; η γγ Mode Etimating the Background in the D + η π + ; η π + π η; η γγ Mode Etimating the Background in the D + K + K π + π Mode Etimating the Background in the D + π+ π π + Mode Etimating the Background in the D + K + K ; K + KS π+ ; K K π + Mode Etimating the Background in the D + ηρ+ ; η γγ; ρ + π + π Mode Etimating the Background in the D + η π + ; η ρ γ Mode 4.9. Summary of Etimated Background in the Variou Mode 4.9. Predicted Signal Significance Signal Yield and Selection Efficiencie for D + D + γ D + K+ K π D + K S K D + ηπ+ ; η γγ D + η π + ; η π + π η; η γγ D + K+ K π + π D + π+ π π D + K + K ; K + KS π+ ; K K π D + ηρ+ ; η γγ; ρ + π + π D + η π + ; η ρ γ Un-blinding Data and Reult D + K+ K π D + K S K D + ηπ+ ; η γγ D + η π + ; η π + π η; η γγ D + K + K π + π D + π+ π π D + K + K ; K + K S π+ ; K K π D + ηρ + ; η γγ; ρ + π + π D + η π + ; η ρ γ Comparion of m e + e between Data and Monte Carlo Simulation viii

10 4.. A Re-evaluation of All D + Branching Fraction Sytematic Uncertaintie from the Tracking of Soft Electron and Photon Method Method Reult and Concluion A Plot Ued to Optimize Selection Criteria for D + D + e+ e 5 A. D + K S K A. D + ηπ+ ; η γγ A. D + η π + ; η π + π η; η γγ A.4 D + K + K π + π A.5 D + π+ π π A.6 D + K + K ; K + K S π+, K K π A.7 D + ηρ + ; η γγ; ρ + π + π A.8 D + η π + ; η ρ γ Bibliography 64 ix

11 LIST OF TABLES. Branching fraction of the known decay of the D Integrated luminoity correponding to the CLEO-c dataet ued in thi analyi. The tatitical uncertaintie are added in quadrature, while the ytematic uncertaintie are added linearly. Thereafter, thee two form of uncertaintie are added in quadrature to give u the total uncertainty we ue for the analyi and the remainder of thi document Number of ignal and background event retained by optimized election criteria in ignal and background Monte Carlo imulation where electron track have been fitted to the pion ma hypothei. The number are normalized to 586 pb of integrated luminoity Number of ignal and background event retained by optimized election criteria in ignal and background Monte Carlo imulation where electron track have been fitted to the electron ma hypothei. The number are normalized to 586 pb of integrated luminoity Selection criteria for data with electron track fitted to the pion and electron ma hypothee in the D + K + K π + decay mode Number of ignal and background event left in 586 pb of pion and electron-fitted imulation ample in the D + K + K π + decay mode Selection criteria for data with electron track fitted to the pion and electron ma hypothee in the D + K S K + decay mode Number of ignal and background event expected in pion and electron-fitted data in the D + K S K + decay mode Selection criteria for data with electron track fitted to the pion and electron ma hypothee in the D + ηπ + ; η γγ decay mode Number of ignal and background event expected in pion and electron-fitted data in the D + ηπ+ ; η γγ decay mode Selection criteria for data with electron track fitted to the pion and electron ma hypothee in the D + η π + ; η π + π η; η γγ decay mode Number of ignal and background event expected in pion and electron-fitted data in the D + η π + ; η π + π η; η γγ decay mode Selection criteria for data with electron track fitted to the pion and electron ma hypothee in the D + K+ K π + π decay mode Number of ignal and background event expected in pion and electron-fitted data in the D + K+ K π + π decay mode x

12 4.4 Selection criteria for data with electron track fitted to the pion and electron ma hypothee in the D + π+ π π + decay mode Number of ignal and background event expected in pion and electron-fitted data in the D + π + π π + decay mode Selection criteria for data with electron track fitted to the pion and electron ma hypothee in the D + K + K decay mode Number of ignal and background event expected in pion and electron-fitted data in the D + K + K decay mode Selection criteria for data with electron track fitted to the pion and electron ma hypothee in the D + ηρ + ; η γγ; ρ + π + π decay mode Number of ignal and background event expected in pion and electron-fitted data in the D + ηρ + ; η γγ; ρ + π + π decay mode Selection criteria for data with electron track fitted to the pion and electron ma hypothee in the D + η π + ; η ρ γ decay mode Number of ignal and background event expected in pion and electron-fitted data in the D + η π + ; η ρ γ decay mode Selection efficiencie for recontructing the D + D + e + e ignal in each of the hadronic decay mode of the D + that thi analyi deal with Maximum likelihood fit parameter for the MC hape in ditribution Maximum likelihood fit parameter for the data hape in ditribution Maximum likelihood fit parameter for the MC hape in δm ditribution Maximum likelihood fit parameter for the Data hape in δm ditribution Maximum likelihood fit parameter to etimate background in the D + K+ K π + mode Etimate of the background in the ignal region of the D + K + K π + mode uing four fit outlined above Maximum likelihood fit parameter to etimate background in the D + K S K + mode Etimate of the background in the ignal region of the D + K S K + mode uing four fit outlined above Maximum likelihood fit parameter to etimate background in the D + ηπ + ; η γγ mode Etimate of the background in the ignal region of the D + ηπ + ; η γγ mode uing four fit outlined above Etimate of the background in the ignal region of the D + η π + ; η π + π η; η γγ mode uing four fit outlined above xi

13 4.4 Maximum likelihood fit parameter to etimate background in the D + K+ K π + π mode Etimate of the background in the ignal region of the D + K + K π + π mode uing four fit outlined above Maximum likelihood fit parameter to etimate background in the D + π + π π + mode Etimate of the background in the ignal region of the D + π + π π + mode uing four fit outlined above Maximum likelihood fit parameter to etimate background in the D + K + K mode Etimate of the background in the ignal region of the D + K + K mode uing four fit outlined above Maximum likelihood fit parameter to etimate background in the D + ηρ + ; η γγ; ρ + π + π mode Etimate of the background in the ignal region of the D + ηρ + ; η γγ; ρ + π + π mode uing four fit outlined above Maximum likelihood fit parameter to etimate background in the D + η π + ; η ρ γ mode Etimate of the background in the ignal region of the D + η π + ; η ρ γ mode uing four fit outlined above Summary of the etimate for the background in the ignal region for all the mode we have tudied The projected ignal ignificance expected for each individual 4.46 hadronic decay mode of the D +, a well a mode combined Signal yield and efficiencie for D + D + γ from all the mode of decay of the D + relevant for our meaurement of the ratio B(D + D + e + e )/B(D + D + γ). B(D + i) i the known branching fraction for D + to decay via the i th hadronic mode we are tudying. ɛd i γ i the efficiency of our election criteria for the 4.47 mode. ND i γ i the ignal yield oberved for thi mode Signal yield and efficiencie for D + D + γ from all the mode of decay of the D + relevant for our meaurement of the ratio B(D + D + e+ e )/B(D + D + γ) in Generic Monte Carlo. B(D + i) i the known branching fraction for D + to decay via the i th hadronic mode we are tudying. ɛd i γ i the efficiency of our election criteria for the mode. ND i γ i the ignal yield oberved for thi mode. B(D + D + γ) i the branching fraction for D + D + e+ e inferred from thi mode. Error [] on the inferred branching fraction i the tatitical error from the final fit. Error [] encapulate the ytematic uncertaintie from the ignal efficiency and the uncertainty in the number of produced generic MC event a decribed in Section xii

14 4.48 Selection criteria for D + D + γ event where D + K + K π +. The δm cut ha been widened to accommodate the wider peak for the ignal in thi ditribution ɛd i γ i the efficiency of our election criteria for the mode. Ni D γ i the ignal yield oberved in generic Monte Carlo for thi mode. B(D + D + γ) i the branching fraction for D + D + e + e inferred from thi mode. Error [] on the inferred branching fraction i the tatitical error from the final fit. Error [] encapulate the ytematic uncertaintie from the ignal efficiency and the uncertainty in the number of produced generic MC event ɛd i γ i the efficiency of our election criteria for the mode. Ni D γ i the ignal yield in data oberved for thi mode Selection criteria for D + D + γ event where D+ K S K +. The δm cut ha been widened to accomodate the wider peak for the ignal in thi ditribution ɛd i γ i the efficiency of our election criteria for the mode. Ni D γ i the ignal yield in generic Monte Carlo oberved for thi mode. B(D + D + γ) i the branching fraction for D + D + e+ e inferred from thi mode. Error [] on the inferred branching fraction i the tatitical error from the final fit. Error [] encapulate the ytematic uncertaintie from the ignal efficiency and the uncertainty in the number of produced generic MC event ɛd i γ i the efficiency of our election criteria for the mode. Ni D γ i the ignal yield in data oberved for thi mode Selection criteria for D + D + γ event where D + ηπ + ; η γγ. The δm cut ha been widened to accomodate the wider peak for the ignal in thi ditribution ɛd i γ i the efficiency of our election criteria for the mode. Ni D γ i the ignal yield in generic Monte Carlo oberved for thi mode. B(D + D + γ) i the branching fraction for D + D + e + e inferred from thi mode. Error [] on the inferred branching fraction i the tatitical error from the final fit. Error [] encapulate the ytematic uncertaintie from the ignal efficiency, the integrated luminoity and the production cro ection for D D ɛ i D γ i the efficiency of our election criteria for the mode. Ni D γ i the ignal yield oberved in data for thi mode. B(D + D + γ) i the branching fraction for D + D + e+ e inferred from thi mode. Error [] on the inferred branching fraction i the tatitical error from the final fit. Error [] arie from the uncertainty in the branching fraction for D + i. Error [] encapulate the ytematic uncertaintie from the ignal efficiency, the integrated luminoity and the production cro ection for D D. Error [4] encapulate the ytematic error ariing from the fit xiii

15 4.57 Selection criteria for D + D + γ event where D + η π + ; η π + π η; η γγ. The δm cut ha been widened to accomodate the wider peak for the ignal in thi ditribution ɛd i γ i the efficiency of our election criteria for the mode. Ni D γ i the ignal yield oberved in generic Monte Carlo for thi mode. B(D + D + γ) i the branching fraction for D + D + e + e inferred from thi mode. Error [] on the inferred branching fraction i the tatitical error from the final fit. Error [] encapulate the ytematic uncertaintie from the ignal efficiency, the integrated luminoity and the production cro ection for D D ɛd i γ i the efficiency of our election criteria for the mode. Ni D γ i the ignal yield in data oberved for thi mode. B(D + D + γ) i the branching fraction for D + D + e+ e inferred from thi mode. Error [] on the inferred branching fraction i the tatitical error from the final fit. Error [] arie from the uncertainty in the branching fraction for D + i. Error [] encapulate the ytematic uncertaintie from the ignal efficiency, the integrated luminoity and the production cro ection for D D. Error [4] encapulate the ytematic error ariing from the fit Selection criteria for D + D + γ event where D + K + K π + π. The δm cut ha been widened to accomodate the wider peak for the ignal in thi ditribution ɛd i γ i the efficiency of our election criteria for the mode. Ni D γ i the ignal yield oberved in generic Monte Carlo for thi mode. B(D + D + γ) i the branching fraction for D + D + e + e inferred from thi mode. Error [] on the inferred branching fraction i the tatitical error from the final fit. Error [] encapulate the ytematic uncertaintie from the ignal efficiency, the integrated luminoity and the production cro ection for D D ɛd i γ i the efficiency of our election criteria for the mode. Ni D γ i the ignal yield oberved in data for thi mode. B(D + D + γ) i the branching fraction for D + D + e+ e inferred from thi mode. Error [] on the inferred branching fraction i the tatitical error from the final fit. Error [] arie from the uncertainty in the branching fraction for D + i. Error [] encapulate the ytematic uncertaintie from the ignal efficiency, the integrated luminoity and the production cro ection for D D. Error [4] encapulate the ytematic error ariing from the fit Selection criteria for D + D + γ event where D+ π+ π π +. The δm cut ha been widened to accomodate the wider peak for the ignal in thi ditribution xiv

16 4.64 ɛ i D γ i the efficiency of our election criteria for the mode. Ni D γ i the ignal yield oberved in generic Monte Carlo for thi mode. B(D + D + γ) i the branching fraction for D + D + e+ e inferred from thi mode. Error [] on the inferred branching fraction i the tatitical error from the final fit. Error [] encapulate the ytematic uncertaintie from the ignal efficiency, the integrated luminoity and the production cro ection for D D ɛd i γ i the efficiency of our election criteria for the mode. Ni D γ i the ignal yield oberved in data for thi mode. B(D + D + γ) i the branching fraction for D + D + e+ e inferred from thi mode. Error [] on the inferred branching fraction i the tatitical error from the final fit. Error [] arie from the uncertainty in the branching fraction for D + i. Error [] encapulate the ytematic uncertaintie from the ignal efficiency, the integrated luminoity and the production cro ection for D D. Error [4] encapulate the ytematic error ariing from the fit Selection criteria for D + D + γ event where D + K + K. The δm cut ha been widened to accomodate the wider peak for the ignal in thi ditribution ɛd i γ i the efficiency of our election criteria for the mode. Ni D γ i the ignal yield oberved in generic Monte Carlo for thi mode. B(D + D + γ) i the branching fraction for D + D + e + e inferred from thi mode. Error [] on the inferred branching fraction i the tatitical error from the final fit. Error [] encapulate the ytematic uncertaintie from the ignal efficiency, the integrated luminoity and the production cro ection for D D ɛ i D γ i the efficiency of our election criteria for the mode. Ni D γ i the ignal yield oberved in data for thi mode. B(D + D + γ) i the branching fraction for D + D + e+ e inferred from thi mode. Error [] on the inferred branching fraction i the tatitical error from the final fit. Error [] arie from the uncertainty in the branching fraction for D + i. Error [] encapulate the ytematic uncertaintie from the ignal efficiency, the integrated luminoity and the production cro ection for D D. Error [4] encapulate the ytematic error ariing from the fit Selection criteria for D + D + γ event where D+ ηρ +. The δm cut ha been widened to accomodate the wider peak for the ignal in thi ditribution xv

17 4.7 ɛ i D γ i the efficiency of our election criteria for the mode. Ni D γ i the ignal yield oberved in generic Monte Carlo for thi mode. B(D + D + γ) i the branching fraction for D + D + e+ e inferred from thi mode. Error [] on the inferred branching fraction i the tatitical error from the final fit. Error [] encapulate the ytematic uncertaintie from the ignal efficiency, the integrated luminoity and the production cro ection for D D ɛd i γ i the efficiency of our election criteria for the mode. Ni D γ i the ignal yield oberved in data for thi mode. B(D + D + γ) i the branching fraction for D + D + e+ e inferred from thi mode. Error [] on the inferred branching fraction i the tatitical error from the final fit. Error [] arie from the uncertainty in the branching fraction for D + i. Error [] encapulate the ytematic uncertaintie from the ignal efficiency, the integrated luminoity and the production cro ection for D D. Error [4] encapulate the ytematic error ariing from the fit Selection criteria for D + D + γ event where D + η π + ; η ρ γ. The δm cut ha been widened to accomodate the wider peak for the ignal in thi ditribution ɛd i γ i the efficiency of our election criteria for the mode. Ni D γ i the ignal yield oberved in generic Monte Carlo for thi mode. B(D + D + γ) i the branching fraction for D + D + e + e inferred from thi mode. Error [] on the inferred branching fraction i the tatitical error from the final fit. Error [] encapulate the ytematic uncertaintie from the ignal efficiency, the integrated luminoity and the production cro ection for D D ɛ i D γ i the efficiency of our election criteria for the mode. Ni D γ i the ignal yield oberved in data for thi mode. B(D + D + γ) i the branching fraction for D + D + e+ e inferred from thi mode. Error [] on the inferred branching fraction i the tatitical error from the final fit. Error [] arie from the uncertainty in the branching fraction for D + i. Error [] encapulate the ytematic uncertaintie from the ignal efficiency, the integrated luminoity and the production cro ection for D D. Error [4] encapulate the ytematic error ariing from the fit Data and etimated background in the ignal region ued to etimate the number of ignal event found in each mode and the correponding ignificance of the ignal. Expected number of ignal event from Monte Carlo imulation alo lited The ratio of branching fraction B(D + D + e + e )/B(D + D + γ) inferred from the ignal yield and efficiencie of each and all mode xvi

18 LIST OF FIGURES. A Feynman diagram for the D + D + γ proce A Feynman diagram for the D + D + e+ e proce Cutaway chematic of the CLEO-c detector Quarter-view chematic of the CLEO-c detector The inner drift chamber Stereo angle in the outer drift chamber A chematic howing a e + e colliion producing a D + D pair where the D + decay to a D + and a e + e via the decay we are earching for in thi diertation An illutration of d between the oft e + e track of the ignal and converion event An illutration of φ between the oft e + e track of the ignal and converion event (Left) The difference between the recontructed and Monte Carlo generated electron energy plotted againt the generated electron energy when the electron have been fitted to track uing the pion ma hypothei. (Right) The difference when the electron are fitted to track uing the electron ma hypothei (a) The analytical expreion for the ditribution of k overlaid with the ditribution of the corrected m ee from the Monte Carlo. (b) A zoom into the region betweeen GeV and m e to illutrate the cloe match near the peak Optimization plot for the m D + election criterion in the D + K + K π + mode uing pion-fitted track in the imulated ample. The top left plot i the ditribution of m D + in the ignal Monte Carlo ample. The top right plot graph the number of ignal MC ample event accepted by the criterion a we increae the cut width plotted on the x-axi. The plot in the econd and third row correpond to the generic and continuum MC ample. The bottom left how the ignificance of the ignal over background. The bottom right plot how the preciion of the ignal Optimization plot for the election criterion in the D + K + K π + mode uing pion-fitted track in the imulated ample. The top left plot i the ditribution of in the ignal Monte Carlo ample. The top right plot graph the number of ignal MC ample event accepted by the criterion a we increae the cut width plotted on the x-axi. The plot in the econd and third row correpond to the generic and continuum MC ample. The bottom left how the ignificance of the ignal over background. The bottom right plot how the preciion of the ignal xvii

19 4.8 Optimization plot for the δm election criterion in the D + K + K π + mode uing pion-fitted track in the imulated ample. The top left plot i the ditribution of δm in the ignal Monte Carlo ample. The top right plot graph the number of ignal MC ample event accepted by the criterion a we increae the cut width plotted on the x-axi. The plot in the econd and third row correpond to the generic and continuum MC ample. The bottom left how the ignificance of the ignal over background. The bottom right plot how the preciion of the ignal Optimization plot for the d election criterion in the D + K + K π + mode uing pion-fitted track in the imulated ample. The top left plot i the ditribution of d between the e + e track in the ignal Monte Carlo ample. The top right plot graph the number of ignal MC ample event accepted by the criterion a we vary the cut on the x-axi. The plot in the econd and third row correpond to the generic and continuum MC ample. The bottom left how the ignificance of the ignal over background. The bottom right plot how the preciion of the ignal Optimization plot for the φ election criterion in the D + K + K π + mode uing pion-fitted track in the imulated ample. The top left plot i the ditribution of φ between the e + e track in the ignal Monte Carlo ample. The top right plot graph the number of ignal MC ample event accepted by the criterion a we vary the cut on the x-axi. The plot in the econd and third row correpond to the generic and continuum MC ample. The bottom left how the ignificance of the ignal over background. The bottom right plot how the preciion of the ignal Optimization plot for the m D + election criterion in the D + K + K π + mode uing electron-fitted track in the imulated ample. The top left plot i the ditribution of m D + in the ignal Monte Carlo ample. The top right plot graph the number of ignal MC ample event accepted by the criterion a we increae the cut width plotted on the x-axi. The plot in the econd, third and fourth row correpond to the D + D + γ, generic and continuum MC ample. The bottom left how the ignificance of the ignal over background. The bottom right plot how the preciion of the ignal xviii

20 4. Optimization plot for the election criterion in the D + K + K π + mode uing electron-fitted track in the imulated ample. The top left plot i the ditribution of in the ignal Monte Carlo ample. The top right plot graph the number of ignal MC ample event accepted by the criterion a we increae the cut width plotted on the x-axi. The plot in the econd, third and fourth row correpond to the D + D + γ, generic and continuum MC ample. The bottom left how the ignificance of the ignal over background. The bottom right plot how the preciion of the ignal Optimization plot for the δm election criterion in the D + K + K π + mode uing electron-fitted track in the imulated ample. The top left plot i the ditribution of δm in the ignal Monte Carlo ample. The top right plot graph the number of ignal MC ample event accepted by the criterion a we increae the cut width plotted on the x-axi. The plot in the econd, third and fourth row correpond to the D + D + γ, generic and continuum MC ample. The bottom left how the ignificance of the ignal over background. The bottom right plot how the preciion of the ignal Optimization plot for the d election criterion in the D + K + K π + mode uing electron-fitted track in the imulated ample. The top left plot i the ditribution of d between the e + e track in the ignal Monte Carlo ample. The top right plot graph the number of ignal MC ample event accepted by the criterion a we vary the cut on the x-axi. The plot in the econd, third and fourth row correpond to the D + D + γ, generic and continuum MC ample. The bottom left how the ignificance of the ignal over background. The bottom right plot how the preciion of the ignal Optimization plot for the φ election criterion in the D + K + K π + mode uing electron-fitted track in the imulated ample. The top left plot i the ditribution of φ between the e + e track in the ignal Monte Carlo ample. The top right plot graph the number of ignal MC ample event accepted by the criterion a we vary the cut on the x-axi. The plot in the econd, third and fourth row correpond to the D + D + γ, generic and continuum MC ample. The bottom left how the ignificance of the ignal over background. The bottom right plot how the preciion of the ignal Signal efficiency for recontructing D + D + e + e in D + K + K π + a repreented in the ditribution Signal efficiency for recontructing D + D + e + e in D + K S K + a repreented in the ditribution xix

21 4.8 Signal efficiency for recontructing D + D + e + e in D + ηπ + a repreented in the ditribution Signal efficiency for recontructing D + D + e+ e in D + η π + ; η π + π η; η γγ a repreented in the ditribution Signal efficiency for recontructing D + D + e+ e in D + K + K π + π a repreented in the ditribution Signal efficiency for recontructing D + D + e+ e in D + π + π π + a repreented in the ditribution Signal efficiency for recontructing D + D + e + e in D + K + K a repreented in the ditribution Signal efficiency for recontructing D + D + e+ e in D + ηρ + ; η γγ; ρ + π + π a repreented in the ditribution Signal efficiency for recontructing D + D + e+ e in D + η π + ; η ρ γ a repreented in the ditribution Ditribution of in Monte Carlo and data. The blue region i ditribution of in Continuum MC. On top of that, in green, i tacked the Generic MC with Converion type event excluded. The Converion MC i tacked on top of that in red. The black curve i fitted to the um of the aforementioned background ditribution. The Signal MC i tacked on top of the background MC to how roughly what expect to ee when we unblind data. Data point, blinded in the ignal region, are overlaid in magenta. The magenta curve i fitted to the data in the ideband region, a decribed in the text Ditribution of δm in Monte Carlo and data. The blue region i ditribution of δm in Continuum MC. On top of that, in green, i tacked the Generic MC with Converion type event excluded. The Converion MC i tacked on top of that in red. The black curve i fitted to the um of the aforementioned background ditribution. The Signal MC i tacked on top of the background MC to how roughly what expect to ee when we unblind data. Data point, blinded in the ignal region, are overlaid in magenta. The magenta curve i fitted to the data in the ideband region, a decribed in the text The variou background and ignal MC expected in the vicinity of the ignal region in ditribution of the D + K + K π + mode. The data, blinded in the ignal region, i overlaid in magenta point. The black and magenta curve are MC and data hape caled by maximum likelihood to the point of data in the ideband region xx

22 4.8 The variou background and ignal MC expected in the vicinity of the ignal region in δm ditribution of the D + K + K π + mode. The data, blinded in the ignal region, i overlaid in magenta point. The black and magenta curve are MC and data hape caled by maximum likelihood to the point of data in the ideband region The variou background and ignal MC expected in the vicinity of the ignal region in ditribution of the D + K S K + mode. The data, blinded in the ignal region, i overlaid in magenta point. The black and magenta curve are MC and data hape caled by maximum likelihood to the point of data in the ideband region The variou background and ignal MC expected in the vicinity of the ignal region in δm ditribution of the D + K S K + mode. The data, blinded in the ignal region, i overlaid in magenta point. The black and magenta curve are MC and data hape caled by maximum likelihood to the point of data in the ideband region The variou background and ignal MC expected in the vicinity of the ignal region in ditribution of the D + ηπ + ; η γγ mode. The data, blinded in the ignal region, i overlaid in magenta point. The black and magenta curve are MC and data hape caled by maximum likelihood to the point of data in the ideband region The variou background and ignal MC expected in the vicinity of the ignal region in δm ditribution of the D + ηπ + ; η γγ mode. The data, blinded in the ignal region, i overlaid in magenta point. The black and magenta curve are MC and data hape caled by maximum likelihood to the point of data in the ideband region The variou background and ignal MC expected in the vicinity of the ignal region in ditribution of the D + η π + ; η π + π η; η γγ mode. The data, blinded in the ignal region, i overlaid in magenta point. The black and magenta curve are MC and data hape caled by maximum likelihood to the point of data in the ideband region The variou background and ignal MC expected in the vicinity of the ignal region in δm ditribution of the D + η π + ; η π + π η; η γγ mode. The data, blinded in the ignal region, i overlaid in magenta point. The black and magenta curve are MC and data hape caled by maximum likelihood to the point of data in the ideband region xxi

23 4.5 The variou background and ignal MC expected in the vicinity of the ignal region in ditribution of the D + K + K π + π mode. The data, blinded in the ignal region, i overlaid in magenta point. The black and magenta curve are MC and data hape caled by maximum likelihood to the point of data in the ideband region The variou background and ignal MC expected in the vicinity of the ignal region in δm ditribution of the D + K+ K π + π mode. The data, blinded in the ignal region, i overlaid in magenta point. The black and magenta curve are MC and data hape caled by maximum likelihood to the point of data in the ideband region The variou background and ignal MC expected in the vicinity of the ignal region in ditribution of the D + π + π π + mode. The data, blinded in the ignal region, i overlaid in magenta point. The black and magenta curve are MC and data hape caled by maximum likelihood to the point of data in the ideband region The variou background and ignal MC expected in the vicinity of the ignal region in δm ditribution of the D + π + π π + mode. The data, blinded in the ignal region, i overlaid in magenta point. The black and magenta curve are MC and data hape caled by maximum likelihood to the point of data in the ideband region The variou background and ignal MC expected in the vicinity of the ignal region in ditribution of the D + K + K mode. The data, blinded in the ignal region, i overlaid in magenta point. The black and magenta curve are MC and data hape caled by maximum likelihood to the point of data in the ideband region The variou background and ignal MC expected in the vicinity of the ignal region in δm ditribution of the D + K + K mode. The data, blinded in the ignal region, i overlaid in magenta point. The black and magenta curve are MC and data hape caled by maximum likelihood to the point of data in the ideband region The variou background and ignal MC expected in the vicinity of the ignal region in ditribution of the D + ηρ + ; η γγ; ρ + π + π mode. The data, blinded in the ignal region, i overlaid in magenta point. The black and magenta curve are MC and data hape caled by maximum likelihood to the point of data in the ideband region xxii

24 4.4 The variou background and ignal MC expected in the vicinity of the ignal region in δm ditribution of the D + ηρ + ; η γγ; ρ + π + π mode. The data, blinded in the ignal region, i overlaid in magenta point. The black and magenta curve are MC and data hape caled by maximum likelihood to the point of data in the ideband region The variou background and ignal MC expected in the vicinity of the ignal region in ditribution of the D + η π + ; η ρ γ mode. The data, blinded in the ignal region, i overlaid in magenta point. The black and magenta curve are MC and data hape caled by maximum likelihood to the point of data in the ideband region The variou background and ignal MC expected in the vicinity of the ignal region in δm ditribution of the D + η π + ; η ρ γ mode. The data, blinded in the ignal region, i overlaid in magenta point. The black and magenta curve are MC and data hape caled by maximum likelihood to the point of data in the ideband region Ditribution of δm in the ignal Monte Carlo ample of D + D + γ event where D + K + K π +. The plot i normalized o a to directly read out the efficiency of the δm election criterion Ditribution of in the ignal Monte Carlo ample of D + D + γ event where D+ K+ K π +. The plot i normalized o a to directly read out the efficiency of the election criterion Ditribution of in the ignal Monte Carlo ample of D + D + γ event where D+ K+ K π Combinatorial background tructured in the ditribution coniting of event where the D + ha been recontructed out of the D and the γ, and where both the D and the γ have been matched to their generated counterpart in the Monte Carlo imulation. Thi ditribution ha been fitted to a hape decribed by Eq Combinatorial background tructured in the ditribution coniting of event where the D + ha been recontructed out of the D and the γ, and the D ha been matched to it generated counterpart but the γ ha failed to match the photon from the D + decay at the generator level of the Monte Carlo imulation. Thi ditribution ha been fitted to a hape decribed by Eq Ditribution of of D + D + γ event where D + K + K π + in 586 pb of Generic Monte Carlo Ditribution of of D + D + γ event where D+ K+ K π + in 586 pb of data xxiii

25 4.5 Ditribution of δm in the ignal Monte Carlo ample of D + D + γ event where D+ K S K +. The plot i normalized o a to directly read out the efficiency of the δm election criterion Ditribution of in the ignal Monte Carlo ample of D + D + γ event where D+ K S K +. The plot i normalized o a to directly read out the efficiency of the election criterion Ditribution of in the ignal Monte Carlo ample of D + D + γ event where D+ K S K Combinatorial background in the ditribution coniting of event where the D + ha been recontructed out of the D and the γ, and where both the D and the γ have been matched to their generated counterpart in the Monte Carlo imulation. Thi ditribution ha been fitted to a hape decribed by Eq Combinatorial background tructured in the ditribution coniting of event where the D + ha been recontructed out of the D and the γ, and the D ha been matched to it generated counterpart but the γ ha failed to match the photon from the D + decay at the generator level of the Monte Carlo imulation. Thi ditribution ha been fitted to a hape decribed by Eq Ditribution of of D + D + γ event where D+ K S K + in 586 pb of Generic Monte Carlo Ditribution of of D + D + γ event where D+ K S K + in 586 pb of data Ditribution of δm in the ignal Monte Carlo ample of D + D + γ event where D+ ηπ + ; η γγ. The plot i normalized o a to directly read out the efficiency of the δm election criterion Ditribution of in the ignal Monte Carlo ample of D + D + γ event where D+ ηπ + ; η γγ. The plot i normalized o a to directly read out the efficiency of the election criterion from the area under the fit within the ignal region Ditribution of in the ignal Monte Carlo ample of D + D + γ event where D + ηπ + ; η γγ Combinatorial background in the ditribution coniting of 7 event where the D + ha been recontructed out of the D and the γ, and where both the D and the γ have been matched to their generated counterpart in the Monte Carlo imulation. Thi ditribution ha been fitted to a hape decribed by Eq xxiv

26 4.6 Combinatorial background tructured in the ditribution coniting of event where the D + ha been recontructed out of the D and the γ, and the D ha been matched to it generated counterpart but the γ ha failed to match the photon from the D + decay at the generator level of the Monte Carlo imulation. Thi ditribution ha been fitted to a hape decribed by Eq Ditribution of of D + D + γ event where D+ ηπ+ ; η γγ in 586 pb of Generic Monte Carlo Ditribution of of D + D + γ event where D+ ηπ+ ; η γγ in 586 pb of data Ditribution of δm in the ignal Monte Carlo ample of D + D + γ event where D+ η π + ; η π + π η; η γγ. The plot i normalized o a to directly read out the efficiency of the δm election criterion Ditribution of in the ignal Monte Carlo ample of D + D + γ event where D + η π + ; η π + π η; η γγ. The plot i normalized o a to directly read out the efficiency of the election criterion from the area under the fit within the ignal region Ditribution of in the ignal Monte Carlo ample of D + D + γ event where D + η π + ; η π + π η; η γγ Combinatorial background in the ditribution coniting of 4 event where the D + ha been recontructed out of the D and the γ, and where both the D and the γ have been matched to their generated counterpart in the Monte Carlo imulation. Thi ditribution ha been fitted to a hape decribed by Eq Combinatorial background tructured in the ditribution coniting of event where the D + ha been recontructed out of the D and the γ, and the D ha been matched to it generated counterpart but the γ ha failed to match the photon from the D + decay at the generator level of the Monte Carlo imulation. Thi ditribution ha been fitted to a hape decribed by Eq Ditribution of of D + D + γ event where D + η π + ; η π + π η; η γγ in 586 pb of Generic Monte Carlo Ditribution of of D + D + γ event where D+ η π + ; η π + π η; η γγ in 586 pb of data Ditribution of δm in the ignal Monte Carlo ample of D + D + γ event where D + K + K π + π. The plot i normalized o a to directly read out the efficiency of the δm election criterion xxv

27 4.74 Ditribution of in the ignal Monte Carlo ample of D + D + γ event where D+ K+ K π + π. The plot i normalized o a to directly read out the efficiency of the election criterion from the area under the fit within the ignal region Ditribution of in the ignal Monte Carlo ample of D + D + γ event where D + K + K π + π Combinatorial background in the ditribution coniting of 49 event where the D + ha been recontructed out of the D and the γ, and where both the D and the γ have been matched to their generated counterpart in the Monte Carlo imulation. Thi ditribution ha been fitted to a hape decribed by Eq Combinatorial background tructured in the ditribution coniting of event where the D + ha been recontructed out of the D and the γ, and the D ha been matched to it generated counterpart but the γ ha failed to match the photon from the D + decay at the generator level of the Monte Carlo imulation. Thi ditribution ha been fitted to a hape decribed by Eq Ditribution of of D + D + γ event where D+ K+ K π + π in 586 pb of Generic Monte Carlo Ditribution of of D + D + γ event where D+ K+ K π + π in 586 pb of data Ditribution of δm in the ignal Monte Carlo ample of D + D + γ event where D+ π+ π π +. The plot i normalized o a to directly read out the efficiency of the δm election criterion Ditribution of in the ignal Monte Carlo ample of D + D + γ event where D + π + π π +. The plot i normalized o a to directly read out the efficiency of the election criterion from the area under the fit within the ignal region Ditribution of in the ignal Monte Carlo ample of D + D + γ event where D+ π+ π π Combinatorial background in the ditribution coniting of 55 event where the D + ha been recontructed out of the D and the γ, and where both the D and the γ have been matched to their generated counterpart in the Monte Carlo imulation. Thi ditribution ha been fitted to a hape decribed by Eq Combinatorial background tructured in the ditribution coniting of event where the D + ha been recontructed out of the D and the γ, and the D ha been matched to it generated counterpart but the γ ha failed to match the photon from the D + decay at the generator level of the Monte Carlo imulation. Thi ditribution ha been fitted to a hape decribed by Eq xxvi