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An Enquiry Concerning Charmless Semileptonic Decays of Bottom Mesons

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An Enquiry Concerning Charmless Semileptonic Decays of Bottom Mesons An Enquiry Concerning Charmless Semileptonic Decays of Bottom Mesons A dissertation presented by Kris Somboon Chaisanguanthum to The Department of Physics in partial fulfillment of the requirements for the degree of Doctor of Philosophy in the subject of Physics Harvard University Cambridge, Massachusetts May 2008 2008 - Kris Somboon Chaisanguanthum All rights reserved. Professor Masahiro Morii Kris Somboon Chaisanguanthum An Enquiry Concerning Charmless Semileptonic Decays of Bottom Mesons Abstract The branching fractions for the decays B → Pν, where P are the pseudoscalar charmless mesons π±, π0, η and η and is an electron or muon, are measured with B0 and B± mesons ∗ found in the recoil of a second B meson decaying as B → Dν or B → D ν.The − √ measurements are based on a data set of 348 fb 1 of e+e− collisions at s =10.58 GeV recorded with the BABAR detector. Assuming isospin symmetry, measured pionic branching fractions are combined into 0 − + −4 B(B → π ν)=(1.54 ± 0.17(stat) ± 0.09(syst)) × 10 . + + First evidence of the B → η ν decay is seen; its branching fraction is measured to be + + −4 B(B → η ν)=(0.64 ± 0.20(stat) ± 0.03(syst)) × 10 . It is determined that + + −4 B(B → η ν) < 0.47 × 10 to 90% confidence. Partial branching fractions for the pionic decays in ranges of the momentum transfer and various published calculations of the B → π hadronic form factor are used to obtain values of the magnitude of the Cabibbo-Kobayashi-Maskawa matrix element −3 Vub between 3.61 and 4.07 × 10 . iii Table of contents Abstract iii Table of contents vi Acknowledgements vii Dedication viii 1 On the importance of |Vub| 1 1.1 The violation of charge-parity symmetry . ...................... 3 1.2 The unitarity of VCKM ................................. 4 2 Phenomenological considerations 7 2.1 Inclusive charmless semileptonic decays . ...................... 7 2.2 Exclusive charmless semileptonic decays . ...................... 10 2.3Hadronicformfactors................................. 12 2.3.1 Lattice quantum chromodynamics ...................... 13 2.3.2 Light-cone sum rules .............................. 14 2.3.3 Constituent quark model ........................... 14 2.3.4 Form factors for B+ → η()ν ......................... 15 3 Experimental apparatus 16 3.1 PEP-II .......................................... 16 3.2 The BABAR detector.................................. 18 3.2.1 Silicon vertex tracker .............................. 19 3.2.2 Drift chamber .................................. 22 3.2.3 Detector of internally reflected Cerenkovˇ light ................ 24 iv 3.2.4 Electromagnetic calorimeter .......................... 27 3.2.5 Instrumented flux return ............................ 27 3.3 The BABAR trigger ................................... 30 4 Analysis method 33 4.1 Derivation of cos(BY ) ................................. 35 2 4.2 Derivation of cos φB .................................. 35 5Dataset 37 5.1 Event reconstruction .................................. 37 5.1.1 Charged tracks ................................. 37 5.1.2 Neutral clusters ................................. 38 5.1.3 Particle identification ............................. 38 5.1.4 Composite particles .............................. 39 5.2 Simulated data ..................................... 40 5.2.1 Physics simulation ............................... 40 5.2.2 Detector simulation .............................. 43 6 Event, candidate selection 44 6.1Skim........................................... 44 6.1.1 Extension to the skim ............................. 45 6.2 Preselection ....................................... 46 6.3 Main selection ..................................... 46 6.3.1 Tag side selection ................................ 47 6.3.2 Signal side selection .............................. 48 6.4 Optimization ...................................... 53 6.5 Validation ........................................ 60 7 Selection efficiency 71 7.1 Squared momentum transfer .............................. 71 7.2 Double tags ....................................... 78 8 Yield extraction 82 8.1 Exception for ην, q2 ≥ 16 GeV2/c2 ......................... 83 v 8.2 Validation ........................................ 84 8.3Fitresult........................................ 85 8.3.1 A note on B+ → η+ν ............................ 85 8.4 Determination of branching fractions . ...................... 89 9 Systematic uncertainties 96 9.1Modelingofphysicsprocesses............................. 96 9.1.1 Charmless semileptonic decay . ...................... 96 9.1.2 Background spectra .............................. 101 9.1.3 Charmed semileptonic decay . ...................... 105 9.1.4 Continuum background ............................ 106 9.1.5 Final state radiation .............................. 109 9.1.6 Branching fractions of η, η mesons......................109 9.2Modelingofdetectorresponse............................. 110 9.3Doubletaganalysis...................................111 9.3.1 Neutral veto .................................. 111 9.3.2 Factorizability of tags ............................. 111 9.4Bremsstrahlungmodeling............................... 112 9.5 Other uncertainties ................................... 115 10 Results 116 10.1 Correlation of statistical uncertainties . ...................... 116 10.2 Combined B → πν branching fraction . ...................... 118 10.3 Upper limits for B(B+ → ην) ............................ 119 10.4 Extraction of |Vub| ................................... 120 11 Cross-checks 122 12 Discussion 128 13 Conclusions 131 Bibliography 133 vi Acknowledgements Thank you, ...Masahiro Morii, without whose guidance and infinite patience this would not be possible. I am as surprised as you are that I’ve made it this far. ...Alan Weinstein, George Brandenburg, Michael Schmitt and Melissa Franklin, for whose tutelage and generosity over the years I will forever be indebted. ...all I’ve intersected in the Harvard BABAR group: Stephen, Eunil, Kevin, Jinwei, Corry. ...Maria, Caolionn, Ayana and Michael, for acknowledging me in their respective dissertations [1, 2, 3, 4] and for a plethora of other reasons into which I cannot go now. ...Tae Min, for letting me win (at graduating). ...the political dynasty of Jesse and Adam. ...Nathaniel and Wesley, my graduate school chums. ...my East Coast shorties, Victoria and Leah. ...Christie, my favorite lesbian, and Megan,1 who comes in a respectable second. ...Millie and Rhiju, for, among other things, your hospitality in Seattle; I had a splendid time. ...Seth (Pants), for breaking all of my theories, and, also, Adele. ...Jared, my BFF; KIT, TCCIC, etc. ...Greg—hell yeah! ...Abigail, Cassandra, Barbara, Ryan and Jack, who have been like a family to me. ...Roslyn (and Paul), Mom, Michael2 (and Marsha) and Dad, who have also been like a family to me. 1Megan Toby is my girlfriend. 2Thank you especially, Michael, for your insights on heavy quark effective theory, which proved instrumental in the development of 2.1. vii in memoriam Daniel Satchyu Weiss (1979 - 2007) The world is a better place for having known you. viii Chapter 1 On the importance of |Vub| In the Standard Model of particle physics, the weak and electromagnetic interactions are described by a manifestly chiral SU(2) × U(1) gauge symmetry which is broken by a scalar Higgs field φ with a nonzero vacuum expectation value. Where the fields W a and B and coupling constants g and g correspond to the SU(2) and U(1) components of the gauge group respectively, the covariant derivative Dμ of a fermion field with U(1) charge y is given by a a Dμ = ∂μ − igWμ T − ig yBμ; (1.1) T a are SU(2) generators1 [5]. In this framework, left-handed quark fields are paired in doublets QLi in the spinor representation of SU(2): ⎛ ⎞ ⎛ ⎞ ⎛ ⎞ ⎜ uL ⎟ ⎜ cL ⎟ ⎜ tL ⎟ ⎝ ⎠ , ⎝ ⎠ and ⎝ ⎠ (1.2) dL sL bL with U(1) charge y =1/6. Right-handed quark fields uR, dR,etc.areSU(2) singlets and do 01 1We use the convention that, in the spinor representation, T 1 = 1 , 2 10 0 −i 10 T 2 = 1 and T 3 = 1 . 2 i 0 2 0 −1 1 not couple to W a. The covariant derivative leads to kinetic terms in the Lagrangian density: μ ΔLkinetic = QLi(iγ Dμ)QLi μ a a = ···+ gγ QLiWμ T QLi + ···. (1.3) Charged weak fields take the form W ± = √1 (W 1 ∓ iW 2); the terms in Equation 1.3 describing 2 the coupling of quarks to these fields, where uLi = uL,cL,tL and so forth, are g + μ − μ ΔLcharged = √ Wμ (uLiγ dLi)+Wμ (dLiγ uLi) , (1.4) 2 i.e., charged weak currents couple left-handed up-type and down-type quarks within the same doublet. Electromagnetic and neutral weak interactions, mediated by (linear combinations of) W 3 and B, do not change quark flavor. The Cabbibo-Kobayashi-Maskawa matrix VCKM arises from Yukawa coupling of quark fields to the Higgs field [6]; these interactions take the general form d u ∗ ΔLYukawa = −YijQLiφdRj − Yij QLi φ uRj + [Hermitian conjugate], (1.5) with the (SU(2) spinor) antisymmetric tensor; Y u,d descibe the strength of the Yukawa couplings. The Higgs field takes a vacuum expectation value, written canonically, in the same √ representation, as the SU(2) spinor φ =(0,v/ 2); Equation 1.5 becomes v d u ΔLYukawa = √ −YijdLidRj − Yij uLiuRj + [Hermitian conjugate], (1.6) 2 √ giving rise to quark mass matrices M u,d = vY u,d/ 2, which can be diagonalized to M˜ u,d via the transformation u,d u,d u,d u,d† M˜ = VL M VR , (1.7) u,d u where VL,R are unitary matrices relating quark mass eigenstates uLi ≡ (VL )ij uLj,etc.tothe natural weak flavor eigenstates as defined by the SU(2) doublets described above. With
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