Two-meson elastic scattering amplitude T

T  =  V + VGV + VGVGV + ...   =  V + TGV

  EvB and GR, arXiv:hep-ph/0304105,
  Int. J. Theor. Phys. Group Theor. Nonlin. Opt. 11, 179 (2006).

Two-meson production sub-amplitude in hadronic decay P

P  =  1 + VG + VGVG + ...   =  1 + TG

  EvB and GR, arXiv:0706.4119 [hep-ph]
  DOI: 10.1016/j.aop.2007.11.012

Hence

PV  =  (1 + TG)V  =  V + TGV  =  T