Measurement Of D~* Electromagnetic Form Factors At Time-like Momentum Transfer Using Belle Data

Electromagnetic form factors,as a function of momentum transfer squared q²,re-fleet spatial distribution of electromagnetic quantities such as charge,magnetic moment and quadrupole moment.Measuring electromagnetic form factors provides information on internal structure of hadrons.For spin 1 bound states,perturbative quantum chromo-dynamics?QCD?predicted the charge,magnetic and quadrupole form factors to have the ratios Gc?q²?:GM?q²?:GQ?q²?=?1-2/3??:2:-1 at large space-like or time-like momentum transfer,where ?=-q²/4M2 with M the particle mass.We developed a method for experimentally determining the charge,magnetic and quadrupole form factors of the D^*meson at time-like momentum transfer.We calcu-lated the differential cross section of the e?e^-??*?D^*+D^*-process,and found that only magnitudes of the form factors are present.From the angular distribution and the total cross section we can only obtain | GM | and a linear combination of | GC|² and|GQ |².The phases of the form factors are contained in spin states of the D^*'s and exhibit in the angular distributions of subsequent decays.Therefore we calculated the differen-tial cross section of the process e+e^-??^*? D^*+*-,D^*+?D0?+,D^*-?D⁰?-.In the 5-dimensional angular distribution function,the magnitudes and phases of the form factors are reduced to 4 parameters,which can be extracted by observing 4 in-dependent 1-dimensional angular distributions.The best values of the parameters are found by an unbinned extended maximum likelihood fit.The method is verified with Monte Carlo simulations.Using 800 fb-1 data near???= 10.58 GeV accumulated by the Belle detector at the KEKB asymmetric-energy e+e-collider,we measure magnitudes and relative phase angles of the charge,magnetic and quadrupole form factors of the D^*meson at momentum transfer squared q² = 10.582 = 111.94?GeV/c?2 to be |Gc| = 5021 ±514 ± 427,|GM| = 5908 ± 118 ± 385,|GQ|=424 ± 153 ± 114,?C-?M =?23.0 ±17.0 ± 5.2?° and ?Q-?M =?-117 ± 18 ± 15??,where the first errors are statistical and the second errors systematic?the same below?.The results are not consistent with the perturbative QCD prediction.We also measure the cross section of the e+e-?D^*+D^*-process at???= 10.58 GeV to be ? =?0.42 ± 0.01 ± 0.05?pb,and the Born cross section ?0=?0.60 ± 0.02 ± 0.08?pb,which is roughly consistent with the theoretical prediction of 0.53 pb.The helicity decompositions of the cross section are ??e+e-? DL*?DL*-?= 27.8 ± 7.9 fb,??e?e-?DL*+DT*-?382 ± 11 fbAbstract and ?(e+e-?DT*+DT*-= 11.1 ± 7.7 fb.The DLL*+DT*-fraction?90.7 ± 4.0?%is not consistent with the theoretical prediction of 65%.In addition,we measure the branching fraction for ??4S?decaying to D^*?D^*-to be Br???4S?? D^*?D^*-?=?1.0 ± 1.3 ± 1.1?×10^-6,or Br???4S??D^*+D^*-?<4.4×10^-6 in terms of upper limit at the 90%confidence level.