PHYSICAL REVIEW D VOLUME 48, NUMBER 1 Dalitz plot analysis of D = lt m. n. decays 1 JULY 1993 J. C. Anjos, ~ J. A. Appel, ~ A. Bean, S. B. Bracker, T. E. Browder, "' L. M. Cremaldi, " G. M. Danner, ' J. Duboscq, ' ' J. R. Elliott, "' C. O. Escobar, M. C. Gibney, " ' A. S. Gordon, "" G. F. Hartner, P. E. Karchin, " B. R. Kumar, M. J. Losty, G. J. Luste, P. M. Mantsch, ~ J. F. Martin, S. McHugh, S. R. Menary, ' ' R. J. Morrison, T. Nash, ~ P. Ong, J. Pinfold, ~ G. Punkar, ' ' M. V. Purohit, ' J. R. Raab, '"' W. R. Ross, I' A. F. S. Santoro ~ A. L. Shoup, ~"' J. S. Sidhu, ~'"' K. Sliwa, ~'"' M. D. Sokoloff, ~ M. H. G. Souza, ~ M. E. Streetman, & A. B. Stundzia, W. D. Volkmuth, ' and M. S. Witherell University of California, Santa Barbara, California 93106 ~Carleton University, Ottawa, Ontario, Canada K1S5B6 Centro Brasileiro de Pesquisas Fssicas, Rio de Janeiro, Brazil University of Cincinnati, Cincinnati, Ohio 45221 'University of Colorado, Boulder, Colorado 80309 Fermi National Accelerator Laboratory, Batavia, Illinois 60510 University of Mississippi, University, Mississippi 38677 National Research Council, Ottawa, Ontario, Canada KIA OR6 'Princeton University, Princeton, New Jersey 08544 'Universidade de Sao Paulo, Sao Paulo, Brazil "University of Toronto, Toronto, Ontario, Canada M5S 1A 7 "Yale University, New Haven, Connecticut 06511 (Received 2 December 1992) + Decays of the D meson to K ~+a. and K m+n. and of the D+ to K ~+a+ have been analyzed for resonant substructure. We present results on the amplitudes and phases of each decay mode and corn- pare the results with other measurements. We confirm the highly nonresonant nature of the D+ to K ~+a+ decays. There is general agreement with theoretical models for the branching ratios mea- sured. PACS number(s): 13. 25. + m, 14. 40.Ev, 14. 40. Jz I. INTRODUCTION Hadronic decays of charmed particles have been a sub- ject of much study in the past few years as new informa- tion from experiments has become available. Theorists have attempted to understand these data and have made predictions concerning hadronic decays [1, 2]. Since the charm quark is not very heavy, charm hadrons decay mainly into two, three, and four particles. Here we ex- amine three-body decays of the D meson to E and K m+m. and of the D+ to K ~+m+ to determine the fractions into two-body modes and the relative phases of the decay amplitudes. In this paper we implicitly in- clude decays of antiparticles. Now at Cornell University, Ithaca, NY. Now at CERN, Geneva, Switzerland. ' Now at Electro Magnetic Applications, Inc. , Denver, CO. ( ]Now at Nichols Research, Colorado Springs, CO. ~ Now at Harvard University, Cambridge, MA. "Now at the Univ. of California, Santa Barbara, CA. ~g Now at SLAC, Stanford, CA. " Now at Mainz University, Mainz, Germany. ' Now at the Univ. of California, Irvine, CA. ~]Deceased. "Now at Tufts University, Medford, MA. The data sample comes from the fixed-target photopro- duction experiment E691 done at Fermilab during 1985 and described elsewhere [3]. The experiment recorded 100X 10 events from which approximately 10, 000 charm particle decays were reconstructed. We first describe the reconstruction and analysis common to all three modes and then describe the event selection specific to individu- al modes. II. EVENT SELECTION Events were selected by requiring that the D meson de- cay tracks satisfy a vertex hypothesis with a y per de- grees of freedom (y /ND„) less than 3.5, that the recon- structed candidate D point back to within 80 pm of the primary vertex in the transverse plane, and that the pri- mary vertex itself have a y'/N»(6. We further re- quired that the separation of the primary and secondary vertices along the beam direction divided by the error on this quantity be larger than 6. In all three decay modes we required that the charged tracks go through at least one of our two analysis magnets and that each track have a particle identification probability based on Cerenkov in- formation of at least 50%. In the case of the D+ ~K m+m+ decays, we required that there be no other tracks within 100 pm of the secon- dary vertex in the transverse direction. A signal of 4149+79 events results (Fig. 1). In order to minimize backgrounds in both the D decay modes, we select only 0556-2821/93/48(1)/56(7)/$06. 00 56 1993 The American Physical Society