Study of quasi-two-body $$B_{(s)}\rightarrow \phi (f_0(980)/f_2(1270)\rightarrow )\pi \pi $$ decays in perturbative QCD approach

Abstract In 2017, LHCb collaboration reported their first observation of the rare decays $$B_s \rightarrow \phi (f_0(980)$$ Bs→ϕ(f0(980) $$/f_2(1270) ) \pi ^+\pi ^-$$ xmlns:mml="http://www.w3.org/1998/Math/MathML">/f2(1270)→)π+π- and evidence $$B^0 (f_0(980)/f_2(1270)\rightarrow )\pi xmlns:mml="http://www.w3.org/1998/Math/MathML">B0→ϕ(f0(980)/f2(1270)→)π+π- . Motivated by this, we study these quasi-two-body in perturbative QCD approach. The branching fractions, CP asymmetries polarization fractions are calculated. We find that within appropriate two-meson wave functions, calculated agreement with measurements LHCb. Based on narrow-width approximation, also calculate $$B_{d,s}\rightarrow ^0\pi ^0$$ xmlns:mml="http://www.w3.org/1998/Math/MathML">Bd,s→ϕ(f0(980)/f2(1270)→)π0π0 (f_2(1270)\rightarrow K^+K^-$$ xmlns:mml="http://www.w3.org/1998/Math/MathML">Bd,s→ϕ(f2(1270)→)K+K- , hope predictions to be tested ongoing Belle II experiments. Moreover, processes f_2(1270)$$ xmlns:mml="http://www.w3.org/1998/Math/MathML">Bd,s→ϕf2(1270) analyzed under approximation. note very small, because either penguin dominant or pure processes.