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This feature of the SDMEs and the information present in there is encoded in the √−t |λN −λ∆| behavior of the half-angle factor in the amplitude. Continuing to the polarised SDMEs, the diagonal el- ements of theρ 1 add up to the BSA shown in Fig. 3. The interpretation of the BSA is straight forward in the reflectivity basis. Using the definition of theρ 1 λ∆λ′ ∆ given in Eq. (D6), we see that the BSA, Σ = P σ(|Nσ|2 − |Uσ|2)P σ(|Nσ|2 +|U σ|2) (27) Thus, the sign of the BSA represents the dominance of the respective reflectivity amplitudes which in turn implies the dominance of the respective naturality ex- changes [15]. Comparing with Fig. 3 we see that the unnatural parity exchange dominate in the small-tregion and the natural parity exchanges dominate for larger val- ues of|t|. This behavior is consistent with the predictions from the Stichel theorem [37, 38]. Finally, we note that the off-diagonal elements ofρ (0,1) 31 andρ 2 λ∆λ′ ∆ are negligibly small in the large-tregion. As we can see from Eq. (D1), this behavior stems from the approximate cos(2ϕ) dependence of the distribution of the decay products of the ∆(1232) in the large-tregion. Consequently, sinceρ 2 λ∆λ′ ∆ is given by the interference between the amplitudes of different reflectivities, this im- plies that one reflectivity dominates over the other. B. Amplitudes We now discuss the amplitudes. We show the plots of some of the amplitudes in Fig. 5. A few observations on the helicity amplitudes are in order. We see
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