Study of $B_{(s)}^0 to K_{rm S}^0 h^{+} h^{prime -}$ decays with first observation of $B_{s}^0 to K_{rm S}^0 K^{pm} pi^{mp}$ and $B_{s}^0 to K_{rm S}^0 pi^{+} pi^{-}$

A search for charmless three-body decays of $B^0$ and $B_{s}^0$ mesons with a $K_{rm S}^0$ meson in the final state is performed using the $pp$ collision data, corresponding to an integrated luminosity of $1.0,mbox{fb}^{-1}$, collected at a centre-of-mass energy of $7mathrm{,Tekern -0.1em V}$ recorded by the LHCb experiment. Branching fractions of the $B_{(s)}^0 to K_{rm S}^0 h^{+} h^{prime -}$ decay modes ($h^{(prime)} = pi, K$), relative to the well measured $B^0 to K_{rm S}^0 pi^{+} pi^{-}$ decay, are obtained. First observation of the decay modes $B_s^0 to K_{rm S}^0 K^{pm} pi^{mp}$ and $B_s^0 to K_{rm S}^0 pi^{+} pi^{-}$ and confirmation of the decay $B^0 to K_{rm S}^0 K^{pm} pi^{mp}$ are reported. The following relative branching fraction measurements or limits are obtained begin{eqnarray*} onumber frac{{cal B}(B^0 to K_{rm S}^0 K^{pm} pi^{mp})}{{cal B}(B^0 to K_{rm S}^0 pi^{+} pi^{-})} &=& 0.128 pm 0.017 , ({rm stat.}) pm 0.009 , ({rm syst.}) ,, onumber frac{{cal B}(B^0 to K_{rm S}^0 K^{+} K^{-} )}{{cal B}(B^0 to K_{rm S}^0 pi^{+} pi^{-})} &=& 0.385 pm 0.031 , ({rm stat.}) pm 0.023 , ({rm syst.}) ,, onumber frac{{cal B}(B_s^0 to K_{rm S}^0 pi^{+} pi^{-} )}{{cal B}(B^0 to K_{rm S}^0 pi^{+} pi^{-})} &=& 0.29phantom{0} pm 0.06phantom{0} , ({rm stat.}) pm 0.03phantom{0} , ({rm syst.}) pm 0.02 , (f_s/f_d) ,, onumber frac{{cal B}(B_s^0 to K_{rm S}^0 K^{pm} pi^{mp})}{{cal B}(B^0 to K_{rm S}^0 pi^{+} pi^{-})} &=& 1.48phantom{0} pm 0.12phantom{0} , ({rm stat.}) pm 0.08phantom{0} , ({rm syst.}) pm 0.12 , (f_s/f_d) ,, onumber frac{{cal B}(B_s^0 to K_{rm S}^0 K^{+} K^{-} )}{{cal B}(B^0 to K_{rm S}^0 pi^{+} pi^{-})} &in& [0.004;0.068] ; {rm at ;; 90% ; CL} ,. end{eqnarray*}