Measurement of the Dipion Mass Spectrum in X(3872) ->J/Psi Pi+ Pi- Decays

We measure the dipion mass spectrum in X (3872) → J/ψ π + π − decays using 360 pb − 1 of ¯ pp collisions at √ s = 1 . 96 TeV collected with the CDF II detector. The spectrum is fit with predictions for odd C -parity ( 3 S 1 , 1 P 1 , and 3 D J ) charmonia decaying to J/ψ π + π − , as well as even C -parity states in which the pions are from ρ 0 decay. The latter case also encompasses exotic interpretations, such as a D 0 D ∗ 0 molecule. Only the 3 S 1 and J/ψ ρ hypotheses are compatible with our data. Since 3 S 1 is untenable on other grounds, decay via J/ψ ρ is favored, which implies C = +1 for the X (3872). Models for different J/ψ - ρ angular momenta L are considered. Flexibility in the models, especially the introduction of ρ - ω interference, enable good descriptions of our data for both L = 0 and 1.