Di-Pion Decays of Heavy Quarkonium in the Field Correlator Method
Abstract
Description
Mechanism of di-pion transitions $nS\to n'Sππ(n=3,2; n'=2,1)$ in bottomonium and charmonium is studied with the use of the chiral string-breaking Lagrangian allowing for the emission of any number of $π(K,η),$ and not containing fitting parameters. The transition amplitude contains two terms, $M=a-b$, where first term (a) refers to subsequent one-pion emission: $Υ(nS)\toπB\bar B^*\toπΥ(n'S)π$ and second term (b) refers to two-pion emission: $Υ(nS)\toππB\bar B\toππΥ(n'S)$. The one-parameter formula for the di-pion mass distribution is derived, $\frac{dw}{dq}\sim$(phase space) $|η-x|^2$, where $x=\frac{q^2-4m^2_π}{q^2_{max}-4m^2_π},$ $q^2\equiv M^2_{ππ}$. The parameter $η$ dependent on the process is calculated, using SHO wave functions and imposing PCAC restrictions (Adler zero) on amplitudes a,b. The resulting di-pion mass distributions are in agreement with experimental data.
62 pages,8 tables,7 figures
62 pages,8 tables,7 figures