Application of the Uniformized Mittag-Leffler Expansion to $Λ(1405)$

Abstract

We study the pole properties of Λ(1405) in a model-independent manner by applying the Uniformized Mittag-Leffler expansion proposed in our previous paper. The resonant energy, width and residues are determined by expanding the observable as a sum of resonant-pole pairs under an appropriate parameterization which expresses the observable to be single-valued, and fitting it to experimental dataof the invariant-mass distribution of π + Σ − , π − Σ + , π 0 Σ 0 final states in the reaction, γp → K + πΣ, and the elastic and inelastic cross section, K − p → K − p, K0 n, π + Σ − , π − Σ + . As we gradually increase the number of pairs from one to three, the first pair converges while the second and third pairs emerge further and further away from the first pair, implying that the Uniformized Mittag-Leffler expansion with three pairs is almost convergent in the vicinity of the Λ(1405). The broad peak structure between the πΣ and KN thresholds regarded to be Λ( 1405) is explained by a single pair with a resonant energy of 1420 ± 1 MeV, and a half width of 48 ± 2 MeV, which is consistent with the single-pole picture of Λ(1405). We conclude that the Uniformized Mittag-Leffler expansion turns out to be a very powerful method to obtain resonance energy, width and residues from the near-threshold spectrum.

Is two-poles' $Λ(1405)$ one state or two?

“…Using a modelindependent of the Uniformized Mittag-Leffler expansion, Ref. [63] fitted the experimental data well and supported the single-pole picture of the Λ(1405). Recently, also with the full off-shell dependence for the effective potential, the two-pole structure was confirmed once again in Ref.…”