Dipion decays of heavy quarkonium in the field correlator method

The mechanism of dipion transitions nS -> n ' S pi pi (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 pi(K,eta), and not containing fitting parameters. The transition amplitude contains two terms: M = a-b, where the first term (a) refers to subsequent one-pion emission, Gamma(nS) -> pi B (B) over bar* -> pi Gamma(n ' S)pi, and the second term (b) refers to two-pion emission, Gamma(nS) ->pi pi B (B) over bar -> pi pi Gamma(n ' S). The one-parameter formula for the dipion mass distribution is derived, dw/dq similar to (phase space) x |eta-x|(2), where x = (q(2)-4m(pi)(2))/(q(max)(2)-4m(pi)(2)), q(2) = M-pi pi(2). The parameter eta dependent on the process is calculated, using SHO wave functions and imposing PCAC restrictions (Adler zero) on amplitudes a and b. The resulting dipion mass distributions are in agreement with experimental data.