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Uppsala University Department of Physics and Astronomy Master Thesis Search for the C-violating φ ! !γ decay and acceptance studies of the rare ! ! l+l−π0 decay with the KLOE experiment Author: Walter Andersson Ikegami Supervisor: Andrzej Kupsc Abstract This thesis is a groundwork for a search for the C-violating φ ! !γ decay and the rare ! ! l+l−π0 decay with the KLOE detector. A feasibility study of the detection acceptance for the ! ! π+π−π0 and ! ! l+l−π0 decays produced in + − + − 0 the e e ! !γISR and e e ! !π production channels. A study of the main + − background to the forbidden φ decay, the e e ! !γISR process, is performed −1 using a data sample with an integrated luminosityp of L = 1:6 fb collected by the KLOE detector at center of mass energy s = 1019 MeV. Table of contents 1 Popul¨arvetenskaplig sammanfattning 5 2 Summary 7 3 Theoretical Introduction 9 3.1 The Standard Model . .9 3.2 Form Factors . 11 3.3 Symmetries . 12 3.4 C-violating φ ! !γ decay . 12 3.5 Initial State Radiation . 13 3.6 Decay kinematics and differential decay rates . 14 3.7 The ! ! π+π−π0 decay . 15 3.8 The ! ! l+l−π0 conversion decay . 16 3.9 The π0 ! γγ decay . 18 4 The KLOE detector at DAΦNE and Software Tools 19 4.1 The DAΦNE Collider . 19 4.2 The KLOE Detector . 20 4.3 KLOE Monte Carlo program GEANFI . 21 4.4 Data Sample used in this Thesis . 22 4.5 ROOT . 23 4.6 Phokhara . 23 + − 5 Feasibility study of the e e ! !γISR reaction 24 5.1 Constructing the ISR event generator . 24 5.2 Acceptance . 25 5.3 Preselection criteria for a potential new data sample . 27 6 Monte Carlo analysis of the !γ final state in the KLOE detector 29 6.1 Reconstructing of four-momentum . 29 + − 6.2 Extraction of e e ! !γISR signal from MC . 29 6.3 Background rejection cut: 3 photons . 30 6.4 Photon pairing . 31 6.5 Background rejection cut: Monochromatic photon energy . 32 6.6 Background rejection cut: γ! angle difference . 32 6.7 Background rejection cut: Charged particle identification (CPI) . 33 6.8 Efficiencies . 34 + − 7 Results on Monte Carlo study of e e ! !γISR process 36 2 8 Feasibility studies of ! conversion decays 39 8.1 The event generators . 39 8.2 Acceptance . 39 8.3 Preselection criteria for a potential new data sample . 41 9 Outlook 42 9.1 New data sample . 42 9.2 Kinematic fit . 42 9.3 Simulation of a hypothetical φ ! !γ decay . 43 9.4 Fitting Monte Carlo sample to the data . 43 9.5 Energy scan . 44 10 Summary and Conclusion 45 3 Acknowledgement I would like to express my gratitude to my supervisor, Andrzej Kupsc, for his continued support throughout the making of this thesis. I would also like to thank Li Caldeira Balkest˚ahl,Lena Heijkenskj¨old, Joachim Pettersson for always being available for questions, assistance and discussions re- lating to my work. Finally, I would like to thank Karin Sch¨onning for proof-reading my thesis and providing valuable suggestions. 4 1 Popul¨arvetenskaplig sammanfattning Standardmodellen ¨ar en teorin som beskriver alla elementarpartiklar och hur de v¨axelverkar. I denna teori kan processer som till exempel partikels¨onderfall ber¨aknas. F¨or att testa Standardmodellen j¨amf¨or man dess f¨oruts¨agelser med experimentel- la resultat. Eftersom s˚am˚anga f¨oruts¨agelser st¨ammer v¨al ¨overens med experi- mentella m¨atningar med h¨og precision s˚aanses Standardmodellen vara den mest framg˚angsrika beskrivningen av universums minsta byggstenar. Experimentella m¨atningar utf¨ors oftast i partikelacceleratorer d¨ar partiklar ac- celereras till h¨oga energier och krockar med varandra. I dessa krockar skapas nya partiklar som m¨ats med toppmoderna detektorer. Detektorerna brukar utformas med n˚agrahuvudsyften men kan anv¨andas f¨or att utf¨ora studier p˚aalla m¨ojliga re- aktioner, s˚avidadessa f¨oljer experimentets grundf¨oruts¨attningar. N¨ar man har en ny id´eom n˚agotman vill unders¨oka brukar man utf¨ora effektivitetsstudier. Dessa visar om en reaktion har tillr¨ackligt goda f¨oruts¨attningar f¨or att kunna m¨atas med detektorn. I den h¨ar rapporten har studier genomf¨orts p˚atv˚aspecifika s¨onderfall hos tv˚a partiklar; omega-mesonen (betecknas med grekiska bokstaven !) och fi-mesonen (betecknas φ). S¨onderfallet d¨ar en φ-meson s¨onderfaller till en !-meson och en foton bryter mot en fundamental symmetrilag inom Standardmodellen. Konsekvensen av detta symmetribrott ¨ar att sannolikheten f¨or att φ meson s¨onderfallet sker blir extremt litet. Sannolikheten f¨or detta s¨onderfall uppm¨attes senast ˚ar1966. Denna m¨atning baserades p˚aett litet stickprov med d˚aliguppl¨osning och d¨arf¨or ¨ar os¨akerheten i m¨atningen mycket stor. D¨arf¨or g˚ardet inte att dra slutsatsen om formuleringen av symmetrin ¨ar korrekt eller om fysik bortom Standardmodellen p˚averkar sanno- likheten f¨or att s¨onderfallet kan ske. φ-mesoner bildas i acceleratorn DAΦNE i Italien. Positroner och elektroner accelereras i DAΦNE till mycket h¨oga energier for att sedan krocka och bilda φ-mesoner. Genom MonteCarlosimuleringar har skillnaden mellan φ-s¨onderfallet och den s˚akallade ISR-processen studerats. ISR ¨ar ett specialfall d˚aelektronen eller positronen skickar ut en foton innan en meson bildas. N¨ar en !-meson bildas i ISR-processen s˚abildas samma partiklar som φ-meson s¨onderfallet. Experimentellt ¨ar dessa tv˚ah¨andelser mycket sv˚araatt skilja ˚atd˚ade ger liknande signaler i detektorn. Det f¨orv¨antade antalet ISR-h¨andelser i DAΦNE anses vara tillr¨ackligt h¨ogt f¨or att kunna studeras och ge en b¨attre f¨orst˚aelseav processen. Jag har ocks˚agjort f¨orstudier som kommer underl¨atta den f¨orest˚aendem¨atningen av φ-s¨onderfallet, d¨ar en b¨attre m¨atning p˚a φ-s¨onderfallets sannolikhet ska kunna g¨oras. En s˚adan m¨atning skulle kunna styrka Standardmodellens legitimitet om den ¨overensst¨ammer med Standardmodellens f¨oruts¨agelser. Om den inte g¨or det, tyder det p˚afysik bort- om Standardmodellen. 5 Uppskattningar av antalet !-s¨onderfall har ocks˚agenomf¨orts i denna rapport. I detta arbete s˚avisas att antalet ! meson s¨onderfall som man kan f¨orv¨anta sig i den datam¨angd som insamlades i DAΦNE experimentet ¨ar v¨aldigt f˚a.D¨aremot framkom att fler h¨andelser skulle kunna erh˚allas om man ¨andrar p˚avissa paramet- rar som anv¨ands f¨or att filtrera den reaktion man vill ˚at.Det antal ISR-processer som f¨orv¨antas i datam¨angden kan anv¨andas av andra forskare f¨or att utf¨ora en f¨orb¨attrad m¨atning av φ mesonens sannolikhet att s¨onderfalla. 6 2 Summary The Standard Model is the primary theory describing the elementary particles and their interactions via the electromagnetic, weak and strong forces. The discoveries of new elementary particles have given further credence to the Standard Model. While the Standard Model has been successful in predicting the electromagnetic, weak interactions and the strong interactions at high energies, it does not include the gravitational force. Moreover, there are some phenomena that the Standard Model leaves unexplained, such as dark matter. The generation of mass of particles held together by the strong interaction is also not explained in the Standard Model. Searches for suppressed and forbidden processes provide precision tests of the Standard Model predictions. In this thesis I have investigated one such process; namely φ ! !γ. The φ ! !γ decay violates charge conjugation C-parity and is therefore forbidden in strong and electromagnetic interactions. Consequently, its branching ratio is expected to be very small. Currently, an experimental upper limit for the decay branching ratio is < 5% with a 84% confidence level which, for a theoretically forbidden reaction, is a very weak constraint. It is based on an experiment with a hydrogen bubble chamber exposed to a K− beam carried out at Brookhaven National Laboratory in 1966 [1]. The DAΦNE electron-positron collider which is designed to operate at the cen- ter of mass energy corresponding to the φ meson mass is an excellent facility which could significantly improve this upper limit. The DAΦNE collider is located at La- boratori Nazionale di Frascati (LNF)) Italy. During data taking runs, DAΦNE has reached luminosities up to 1:3 · 1032 cm−2s−1 and between 1999 and 2005 KLOE, the general purpose detector located in DAΦNE, recorded an integrated luminosity of ∼ 2:5 fb−1 [2]. −1 For this study, a data samplep of L = 1:6 fb integrated luminosity collected at the center of mass energy s = 1019 MeV by the KLOE detector is used. The data sample was originally prepared for φ ! ηγ ! π+π−π0γ measurements by removing unwanted events. This was done by requiring two charged tracks and at least three neutral clusters where one of the clusters has energy greater than 250 MeV in every event. The most important source of background to the forbidden φ ! !γ decay is the + − initial state radiation process (ISR) e e ! !γISR which has the same final state particles but, in contrast to the φ ! !γ decay, conserves C-parity. Understanding this process in the data sample is the first step towards constraining the branching ratio of the φ ! !γ decay, which can be done in multiple ways. + − Prior to the analysis of the data sample, a feasibility study for the e e ! !γISR process was done as a prestudy to determine whether a sufficient number of events were collected for the improvement of the upper bound for the branching ratio of the φ ! !γ decay.
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  • Space-Time Symmetries

    Space-Time Symmetries

    Space-Time Symmetries • Outline – Translation and rotation – Parity – Charge Conjugation – Positronium – T violation J. Brau Physics 661, Space-Time Symmetries 1 Conservation Rules Interaction Conserved quantity strong EM weak energy-momentum charge yes yes yes baryon number lepton number CPT yes yes yes P (parity) yes yes no C (charge conjugation parity) yes yes no CP (or T) yes yes 10-3 violation I (isospin) yes no no J. Brau Physics 661, Space-Time Symmetries 2 Discrete and Continuous Symmtries • Continuous Symmetries – Space-time symmetries – Lorentz transformations – Poincare transformations • combined space-time translation and Lorentz Trans. • Discrete symmetries – cannot be built from succession of infinitesimally small transformations –eg. Time reversal, Spatial Inversion • Other types of symmetries – Dynamical symmetries – of the equations of motion – Internal symmetries – such as spin, charge, color, or isospin J. Brau Physics 661, Space-Time Symmetries 3 Conservation Laws • Continuous symmetries lead to additive conservation laws: – energy, momentum • Discrete symmetries lead to multiplicative conservation laws – parity, charge conjugation J. Brau Physics 661, Space-Time Symmetries 4 Translation and Rotation • Invariance of the energy of an isolated physical system under space translations leads to conservation of linear momentum • Invariance of the energy of an isolated physical system under spatial rotations leads to conservation of angular momentum • Noether’s Theorem (Emmy Noether, 1915) E. Noether, "Invariante Varlationsprobleme",