Charm Meson Molecules and the X(3872)
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Charm Meson Molecules and the X(3872) DISSERTATION Presented in Partial Fulfillment of the Requirements for the Degree Doctor of Philosophy in the Graduate School of The Ohio State University By Masaoki Kusunoki, B.S. ***** The Ohio State University 2005 Dissertation Committee: Approved by Professor Eric Braaten, Adviser Professor Richard J. Furnstahl Adviser Professor Junko Shigemitsu Graduate Program in Professor Brian L. Winer Physics Abstract The recently discovered resonance X(3872) is interpreted as a loosely-bound S- wave charm meson molecule whose constituents are a superposition of the charm mesons D0D¯ ¤0 and D¤0D¯ 0. The unnaturally small binding energy of the molecule implies that it has some universal properties that depend only on its binding energy and its width. The existence of such a small energy scale motivates the separation of scales that leads to factorization formulas for production rates and decay rates of the X(3872). Factorization formulas are applied to predict that the line shape of the X(3872) differs significantly from that of a Breit-Wigner resonance and that there should be a peak in the invariant mass distribution for B ! D0D¯ ¤0K near the D0D¯ ¤0 threshold. An analysis of data by the Babar collaboration on B ! D(¤)D¯ (¤)K is used to predict that the decay B0 ! XK0 should be suppressed compared to B+ ! XK+. The differential decay rates of the X(3872) into J=à and light hadrons are also calculated up to multiplicative constants. If the X(3872) is indeed an S-wave charm meson molecule, it will provide a beautiful example of the predictive power of universality. ii To my family iii ACKNOWLEDGMENTS My greatest thank goes to my advisor Eric Braaten. I am deeply grateful to his advice, encouragement, and the way he has supported me through everything. I have learned more from him than I can acknowledge here. It has been an honor and privilege to work with him. I would like to thank Hans-W. Hammer, Yu Jia, Tom Mehen, Shmuel Nussinov, and Dongqing Zhang for fruitful collaboration on various research projects. I have truly enjoyed working with them and have learned many things that I could not have gained just from textbooks. I would also like to thank all of my physics classmates and the past and previous occupants in room 4012 Smith Laboratory. In particular, thanks to Yaojun Du, Emel Gulez, Motomichi Harada, Jongjoo Kim, Youngmin Kim, Kohjiro Kobayashi, Ashish Saxena, Leslie Schradin, and Yuko Shiroyanagi for innumerable reasons that have made my life inside and outside physics enjoyable. My deepest gratitude goes to my parents Masami and Tomoko Kusunoki, and my brothers Masayoshi and Keizo for their support. Without them this work or my graduate career would not have been possible. Last but not the least, I want to give special thanks to my wife Ruriko for her love, encouragement, and believing in me. This research was supported in part by the Department of Energy under grant DE-FG02-91-ER4069. iv VITA July 16, 1975 . Born - Kamakura city, Japan 1999 . B.S. Applied Physics, Waseda Univer- sity, Tokyo, Japan 1999-present . .Graduate Teaching and Research Asso- ciate, The Ohio State University PUBLICATIONS Research Publications E. Braaten and M. Kusunoki, “Factorization in the Production and Decay of the X(3872),” Phys. Rev. D 72, 014012 (2005) [arXiv: hep-ph/0506087]. E. Braaten and M. Kusunoki, “Exclusive Production of the X(3872) in B Meson Decay,” Phys. Rev. D 71, 074005 (2005) [arXiv: hep-ph/0412268]. E. Braaten, M. Kusunoki and S. Nussinov, “Production of the X(3872) in B Meson Decay by the Coalescence of Charm Mesons”, Phys. Rev. Lett. 93 162001 (2004), [arXiv:hep-ph/0404161]. E. Braaten and M. Kusunoki, “Production of the X(3870) at the Υ(4S) by the Coales- cence of Charm Mesons”, Phys. Rev. D 69, 114012 (2004) [arXiv: hep-ph/0402177]. E. Braaten and M. Kusunoki, “Low-energy Universality and the New Charmonium Resonance at 3870 MeV”, Phys. Rev. D 69, 074005 (2004) [arXiv:hep-ph/0311147]. + ¡ E. Braaten, M. Kusunoki, Y. Jia and T. Mehen, “Λc =Λc Asymmetry in Hadroproduc- tion from Heavy-Quark Recombination”, Phys. Rev. D 70, 054021 (2004) [arXiv:hep- ph/0304280]. v E. Braaten, H.-W. Hammer and M. Kusunoki, “Efimov States in a BEC near a Feshbach Resonance”, Phys. Rev. Lett. 90, 170402 (2003) [arXiv:cond-mat/0206232]. E. Braaten, H.-W. Hammer and M. Kusunoki, “Universal Equation for Efimov States”, Phys. Rev. A 67, 022505 (2003) [arXiv:cond-mat/0201281]. FIELDS OF STUDY Major Field: Physics vi TABLE OF CONTENTS Page Abstract . ii Dedication . iii Acknowledgments . iv Vita......................................... v List of Tables . x List of Figures . xii Chapters: 1. Introduction . 1 1.1 From quarks to hadrons . 1 1.2 Discovery of the X(3872) . 8 1.3 Quantum numbers and width of the X(3872) . 9 1.4 Interpretations of the X(3872) . 11 1.4.1 Charmonium . 11 1.4.2 Charm meson molecules . 15 1.4.3 Other options . 17 1.5 Thesis structure . 19 2. Experimental Results . 21 2.1 Observed decay modes . 21 2.2 Upper limits on other decay modes . 25 2.3 Inclusive production at the Tevatron . 29 vii 3. Universality for Large Scattering Length . 32 3.1 Universal properties of the DD¤ molecule . 32 3.2 Complex scattering length . 35 3.3 Hadronic states with nearby thresholds . 37 3.4 Discussion . 39 4. Scattering Models . 42 4.1 Zero-range model . 42 4.2 Resonance model . 45 4.3 Two-channel model . 50 4.3.1 Two-body amplitudes . 51 4.3.2 Large scattering length . 54 4.3.3 Unstable particle in the second channel . 55 4.3.4 Factorization . 57 5. Factorization in the Production and Decay of the X(3872) . 60 5.1 Short-distance decays of X ...................... 60 5.2 Production of X ............................ 65 5.3 Production of D0D¯ ¤0 near threshold . 70 5.4 The X line shape . 74 6. Production of the X(3872) via B ! XK . 81 6.1 The decay B ! XK .......................... 81 6.2 Analysis of B ! D¯ (¤)D(¤)K branching fractions . 83 6.3 Predictions for B ! XK decays . 92 7. Decays of the X(3872) into J=à and Light Hadrons . 97 7.1 Swanson’s model . 97 7.2 Decays of X into J=à h . 101 7.2.1 Vector meson decay amplitudes . 101 7.2.2 Decay into J=à ¼+¼¡ . 104 7.2.3 Decay into J=à ¼+¼¡¼0 . 105 7.2.4 Decay into J=à ¼0γ . 107 7.2.5 Decay into J=à γ . 108 7.3 Factorization of short-distance decay rates . 109 7.4 Partial width for X ! J=à ¼+¼¡¼0 . 111 viii 8. Conclusion . 114 Appendices: A. Absence of Efimov States . 120 B. Vector Meson Decays . 123 Bibliography . 128 ix LIST OF TABLES Table Page 1.1 Mesons that appear in this thesis, together with their quark contents, masses, and J P or J PC quantum numbers. The list includes only three charmonium states. Several other charmonium states are mentioned briefly in Section 1.4.1. 7 1.2 Standard nomenclature for charmonia. In the notation nL, n = 1; 2; 3; ¢ ¢ ¢ is the radial excitation quantum number and L = S; P; D; ¢ ¢ ¢ speci- fies the orbital angular momentum quantum number 0; 1; 2 ¢ ¢ ¢ . The PC ¡¡ Ã1(nD) with J = 1 is often referred to as Ã(nD) without its subscript. 12 1.3 Potential model predictions for masses of 1D and 2P states. In the 3 ELQ potential model, the value of the 1 D1 state is an input. 14 1.4 Possible weakly-bound states of charm mesons due to the one-pion- exchange potential [38]. 16 2.1 Measured mass of the X(3872). In each measurement, the first error is statistical error and the second is systematic error. Babar’s result includes both statistical and systematic errors. 23 2.2 Upper limits on the ratio of the branching fractions for various decay mode of the X into final states h discussed in text. 29 6.1 Branching fractions (in %) for B+ ! D¯ (¤)D(¤)K: measurements from Ref. [73], our 3-parameter fit, and our 7-parameter fit. 85 6.2 Branching fractions (in %) for B0 ! D¯ (¤)D(¤)K: measurements from Ref. [73], our 3-parameter fit, and our 7-parameter fit. 86 x B.1 Inputs that are used to determine the coupling constants in the vector meson decay amplitudes. The partial widths are taken from Ref. [56]. 124 xi LIST OF FIGURES Figure Page 2.1 M(J=à ¼+¼¡) ¡ M(J=Ã) for B§ ! K§J=à ¼+¼¡ seen in the Belle ex- periment. The large peak at 0.59 GeV corresponds to B§ ! K§Ã(2S) followed by Ã(2S) ! J=ü+¼¡. The small peak at 0.776 GeV is the signal for X(3872) ! J=à ¼+¼¡. Figure is taken from Ref. [16]. 22 2.2 The dipion invariant mass M(¼+¼¡) distribution for events in the X(3872) signal peak. The shaded histogram is the sideband-determined background; the curve is the result of a fit with a ½ ! ¼+¼¡ line shape. Figure is taken from Ref. [58]. 24 2.3 The mass distributions of J=à ¼+¼¡ candidates with M(¼+¼¡) > 0:5 GeV (points) and M(¼+¼¡) < 0:5 GeV (open circles). The curve is a fit with two Gaussians and a quadratic background. The inset shows an enlargement of the high dipion-mass data and fit [6]. 30 4.1 The geometric series of Feynman diagrams whose sum is the universal amplitude A(E). ............................. 43 + ¡ ¡1=2 5.1 Feynman diagram for X ! J=à ¼ ¼ that scale like (am¼) .