Improved method for CKM constraints in charmless three-body B and B_s decays

Recently Ciuchini, Pierini and Silvestrini proposed a method for constraining CKM parameters in B->K pi pi and B_s-> K pi pi through phase measurements of amplitudes involving I=3/2 K*pi final states. We show that complementary information on CKM parameters may be obtained by studying the phases of Delta I=1 B->(K*pi)_{I=1/2}, B_s->(K*\bar K)_{I=1} and B_s->(\bar K* K)_{I=1} amplitudes. Hadronic uncertainties in these constraints from electroweak penguin operators O_9 and O_10, studied using flavor SU(3), are shown to be very small in B->K pi pi and B_s->K pi pi and somewhat larger in B_s-> K\bar K pi. The first processes imply a precise linear relation between \bar rho and \bar eta, with a measurable slope and an intercept at \bar eta=0 involving a theoretical error of 0.03. The decays B_s-> K pi pi permit a measurement of gamma involving a theoretical error below a degree. We note that while time-dependence is required when studying B^0 decays at the Upsilon(4S), it may not be needed when studying B_s decays at hadronic colliders.