Dipion decays of heavy quarkonium in the field correlator method

The mechanism of dipion transitions nS → 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, ν), 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, Υ (nS) → π B B^ * → π Υ (n'S)π , and the second term (b) refers to two-pion emission, Υ (nS) → π π B B → π π Υ (n'S) . The one parameter formula for the dipion mass distribution is derived, dw/dq∼ (phase space) × | η − x|2, where x = (q 2 − 4m π 2 )/(q max 2 − 4m π 2 ), q 2 m= M ππ 2 . The parameter ν 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.