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）=（1-2/3η）:2:-1 at large space-like or time-like momentum transfer,where η=-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^-→γ*→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^-→γ^*→ D^*+*-,D^*+→D0π+,D^*-→D⁰π-.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,δC-δM =（23.0 ±17.0 ± 5.2）° and δQ-δM =（-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 σ =（0.42 ± 0.01 ± 0.05）pb,and the Born cross section σ0=（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 σ（e+e-→ DL*＋DL*-）= 27.8 ± 7.9 fb,σ（e＋e-→DL*+DT*-）382 ± 11 fbAbstract and σ(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 γ（4S）decaying to D^*＋D^*-to be Br（γ（4S）→ D^*＋D^*-）=（1.0 ± 1.3 ± 1.1）×10^-6,or Br（γ（4S）→D^*+D^*-）<4.4×10^-6 in terms of upper limit at the 90%confidence level.