Spectra of the transitions Υ(nS)→Υ(mS)π+π−

The spectra of the transitions Υ(nS)→Υ(mS)${\pi }^{+}$ ${\pi }^{\mathrm{-}}$ are discussed, taking account of multipole-expansion corrections as well as of final-state ${\pi }^{+}$ ${\pi }^{\mathrm{-}}$ and Υπ interactions. The inclusion of a four-quark resonance in the Υπ channel, as suggested by Voloshin, together with ${\pi }^{+}$ ${\pi }^{\mathrm{-}}$ final-state interactions, may explain the presence of two peaks in the Υ(3S)→Υ(1S)${\pi }^{+}$ ${\pi }^{\mathrm{-}}$ spectrum. Further tests of this model are proposed.