Precision Measurement of the $X(3872)$ Mass in $J/\psi \pi^+ \pi^-$ Decays

We thank E. Braaten for useful discussions. We thank the Fermilabstaff and the technical staffs of the participating institutions for their vital contributions. This work was supported by the U.S. Department of Energy and National Science Foundation; the Italian Istituto Nazionale di Fisica Nucleare; the Ministry of Education, Culture, Sports, Scienceand Technology of Japan; the Natural Sciences and Engineering ResearchCouncil of Canada; the National Science Council of the Republic of China; the Swiss National Science Foundation; the A.P. Sloan Foundation; the Bundesministerium fur Bildung und Forschung, Germany; the Korean Science and Engineering Foundation and the Korean Research Foundation; the Science and Technology Facilities Council and the Royal Society, UK; the Institut National de Physique Nucleaire et Physique des Particules/CNRS; the Russian Foundation for Basic Research; the Ministerio de Ciencia e Innovacion, and Programa Consolider-Ingenio 2010, Spain; the SlovakRD and the Academy of Finland.