Model-Independent Approaches to QCD and B Decays Christian Arnesen

Model-Independent Approaches to QCD and B Decays by Christian Arnesen Submitted to the Department of Physics in partial fulfillment of the requirements for the degree of Doctorate of Philosophy at the MASSACHUSETTS INSTITUTE OF TECHNOLOGY May 2007 @ Christian Arnesen, MMVII. All rights reserved. The author hereby grants to MIT permission to reproduce and distribute publicly paper and electronic copies of this thesis document in whole or in part. A uthor ......... .. .................. Department of Physics May 30, 2007 Certified by.......... Iain W. Stewart Assistant Professor Thesis Supervisor Accepted by ........... whomaa eytak MASSACHLSEMI TMiTUTE• OF TECHNOLOGBY Associate Department Head foY Education OCT 0 9 2008 LIBRARIES ARCHIVES Model-Independent Approaches to QCD and B Decays by Christian Arnesen Submitted to the Department of Physics on May 30, 2007, in partial fulfillment of the requirements for the degree of Doctorate of Philosophy Abstract We investigate theoretical expectations for B-meson decay rates in the Standard Model. Strong-interaction effects described by quantum chromodynamics (QCD) make this a challenging endeavor. Exact solutions to QCD are not known, but an arsenal of approximation techniques have been developed. We apply effective field theory methods, in particular the sophisticated machinery of the soft-collinear effective theory (SCET), to B decays with energetic hadrons in the final state. SCET separates perturbative interactions at the scales mb and V/mbAQcD from hadronic physics at AQCD by expanding in ratios of these scales. After a review of SCET, we construct a complete reparametrization-invariant basis for heavy-to-light currents in SCET at next-to-next-to-leading order in the power-counting expansion. Next we classify AQCD/mb corrections to non-leptonic B -+ M M2 decays, where M1 ,2 are charmless mesons (flavor singlets excluded). The leading contributions to annihilation amplitudes as well as the leading "chirally enhanced" contributions are calculated and depend on twist-2 two-parton and twist-3 three-parton distributions. We demonstrate that non-perturbative strong phases in annihilation are suppressed. Using simple models, we find that the three-parton and two-parton terms have comparable magnitude, both consistent with the expected size of power corrections. Finally, we present a method for determining IVubl from B -- 7irv data that is competitive with inclusive methods. At large q2, the form factor is taken from unquenched lattice QCD. At q2 = 0, we impose a model-independent constraint obtained from B -+ r7 using SCET, and the form factor shape is constrained using QCD dispersion relations. Theory error is dominated by the input points, with negligible uncertainty from the dispersion relations. Thesis Supervisor: Iain W. Stewart Title: Assistant Professor Biographical Sketch The author was born Mark Christian Arnesen on August 9, 1979, to Mark Allen Arnesen and Patricia Marie Arnesen (nee Ahrens). He attended primary school at Wooddale Montessori Academy in Edina, Minnesota, followed by middle and high school at the International School of Minnesota, in Eden Prairie, where he graduated as valedictorian in 1997. He continued his education at the California Institute of Technology, in Pasadena, majoring in physics. Notable honors from that time include a Carnation Merit Scholarship for academic achievement (1/3rd tuition for his junior year), and a letter in varsity basketball in each of his four years. He received his Bachelor of Science degree with honors from Caltech in 2001. His graduate studies took place from 2002-2007 at the Massachusetts Institute of Technology in Cambridge, the first two years of which he was supported by the Karl Taylor Compton fellowship. This thesis is the culmination of those studies. Acknowledgments I would like to thank my collaborators in the research described in this thesis: Ben Grinstein, Joydip Kundu, Zoltan Ligeti, Ira Rothstein, and in particular, Iain Stewart for collaboration and supervision. In the course of my graduate studies, I have bene- fitted from discussions with numerous physicists including: Mauro Brigante, Qudsia Ejaz, Casey Huang, Ambar Jain, Alejandro Jenkins, Bjorn Lange, Keith Lee, Hong Liu, Sonny Mantry, Claudio Marcantonini, Vivek Mohta, Dan Pirjol, Krishna Ra- jagopal, Sean Robinson, Rishi Sharma, and Jessie Shelton. I deeply appreciate the support and encouragement that all my family and friends have given, none more than my parents, Mark and Pat, and the kind people I have lived with, Jessica Halverson, Sophie Hood, and Francis MacDonald. Finally, I acknowledge funding from the Karl Taylor Compton fellowship, the MIT physics department, and the Department of Energy under cooperative research agreement DOE-FC02-94ER40818. Contents 1 Introduction 9 1.1 The Standard Model ..... ... ... .. .°.. 9 1.2 B physics ............ .. .... .... ... 10 1.3 Quantum chromodynamics . ........ .... 12 1.4 Effective field theory ..... .... .... .... 14 1.5 Plan of the Thesis ....... ... ..... ..... 18 2 Theory 21 2.1 The Standard Model ................. ..... 21 2.2 Weak effective Hamiltonian . ......... ... .. ... 26 2.3 Heavy-quark effective theory ............. .. .. 30 2.4 Soft-collinear effective theory I . ........... ... .. 33 2.4.1 Degrees of freedom and Lagrangian .. ... ..... 34 2.4.2 Gauge invariance ............... ..... 42 2.4.3 Reduction in spin structures ......... .. .. 46 2.4.4 Reparameterization invariance .... .... .. .. 47 2.4.5 Comments on boundary conditions for Y(x) . .. .. 53 2.5 Soft-collinear effective theory II ......... .. .. .. 59 2.5.1 Degrees of freedom and Lagrangian ... .. .. .. 60 3 Heavy-to-light currents in SCET 65 3.1 Introduction ............ .. ......... ....... 65 3.2 Heavy-to-light currents to O(A2) . 67 3.2.1 Current field structures at O(A2) .............. 67 3.2.2 Constraint equations from reparameterization invariance . .. 71 3.2.3 Solutions to the constraint equations . ............. 75 3.2.4 Absence of supplementary projected operators at O(A2) .... 85 3.3 Change of Basis and Comparison with Tree Level Results ...... 87 3.3.1 Conversion ............................. 88 3.3.2 Wilson coefficients at tree level . ................ 90 3.3.3 One-Loop Results ......................... 92 4 B decays to two light mesons in SCET 97 4.1 Introduction ................................ 97 4.2 Annihilation Contributions in SCET . ................. 100 4.3 Local six-quark operators in SCETII . ................. 108 4.4 Three-body annihilation ......................... 118 4.5 Chirally Enhanced Local Annihilation Contributions . ........ 128 4.6 Generating Strong Phases ........................ 135 4.7 Applications ........... ............. .. .. 139 4.7.1 Phenomenological Implications . ............ .139 4.7.2 Annihilation with simple models for 0M, q 3M and ;M ..... 144 5 IVub from B -- x7r£ 151 5.1 Introduction ................................ 151 5.2 Analyticity Bounds ........................... 153 5.3 Input Points ................. ............. .. 155 5.4 Determining f+ .............................. 158 5.5 IVubI from total Br fraction ....................... 159 5.6 IVub from q2 spectra ........... ............... 160 5.7 Improving the determination . .................. .... 162 6 Conclusions 165 A Zero-bin subtractions for a 2D distribution 167 Chapter 1 Introduction 1.1 The Standard Model In the 20th century, it became clear that the sub-atomic world required a radical departure from the classical physics of daily life. Special relativity, important for large velocities, redefined the relationship between space and time. Quantum mechanics, important for short distances, had particles acting like waves and energy coming only in discrete nuggets, or quanta. Quantum field theory (QFT) incorporated both of these advances into a single mathematical framework. In such a theory, fields replace particles as the basic building block, and particles emerge as quantized excitations of those fields. This representation formalizes in a natural way the wave-particle duality and indisinguishability of elementary particles that had puzzled physicists for decades. By the end of the 1970s, a coherent theoretical picture had emerged. The Standard Model (SM) of particle physics, a QFT, built all matter from a relatively small number of elementary particles: six "flavors" of quark (up, down, charm, strange, top, bottom) which can interact via the strong force, and six leptons (e, /, 7, v~, vy, v, ) which feel only electromagnetic and weak forces. Interactions' derive from a symmetry principle, local gauge invariance, a simple mathematical statement with far-reaching consequences. By the 1990s, predictions of the Standard Model had been verified by a 1Gravity, negligible for the processes described in this thesis, is not included in the SM. multitude of experiments probing energies over many orders of magnitude. The sector of the theory governing quark flavor transitions through weak interactions, however, was still poorly constrained, and theoretical tools for understanding the influence of strong interactions were still being developed. 1.2 B physics Quark flavor transitions can be studied by observing weak decays of hadrons. Since the late 1980's, the CLEO collaboration at the Cornell Electron Storage Ring has been measuring decay rates of D mesons, cq bound states, and B mesons, bq bound states, where q is a light quark. As the lightest charmed and bottomed hadrons, respectively, these mesons can only decay

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