_First observation of Λπ+ and Λπ− signals near the KN(I=1) mass threshold inΛ+c → Λπ+π+π− decayY. Ma1), J. Yelton2), K. Tanida3), et. al. (Belle Collaboration)1): RIKEN 2): Univ. of Florida 3): Res. Gr. for Hadron Nuclear Physics, JAEA

Hyperon spectroscopy near thethreshold has been asource of excitement for more than half a century. A typicalexample is the Λ(1405)(I=0) state 1, which is interpreted as anorbitally excited state with uds quarks in the naïve quark model,
but an exotic interpretation as abound state is considered tobe more likely. On the other hand, the only known I=1 state inthis mass region is the Σ(1385), and the standard quark model
does not predict any more states. So, if a Σ* resonance isobserved, it must be exotic. Here, the(I=1) interaction is,most likely, not strong enough to produce a bound state, but avirtual state could exist [1] and could be observed as a thresholdcusp. The shape of such a cusp reflects the scattering length of(I=1) interaction, which is particularly interesting in
therelation with kaon condensation in neutron stars, where K-ninteraction plays most important role.
In the present work, we have studied Λπ+ and Λπ- invariant
mass distributions in the decay Λc+ → Λπ+π+π−, using the full
data sample of the Belle experiment at the KEKB asymmetricenergy e+e− collider [2].
The reconstructed Λπ± invariant mass spectrum is shown inFig. 1. Clear enhancements near themass thresholds areobserved in both of the Λπ+ and Λπ- invariant mass spectra for
the first time. We investigated the signals using two differentparametrizations of the signal shape: a standard Breit-Wigner
function which describes a Σ* resonance, and the Dalitz model[3] which describes acusp. For the background, we used aBreit-Wigner function for the Σ(1385) contribution and asecond-order Chebyshev polynomial function for the high-mass
background events.
With the fit to a Breit-Wigner function, we obtained the mass
and width to be 1434.3±0.6(stat)±0.9(syst) [1438.5±0.9(stat)± 2.5(syst)] MeV/c2 and 11.5 ± 2.8(stat) ± 5.3(syst) [33.0 ±7.5(stat) ± 23.6(syst)] MeV, respectively, for the Λπ+ (Λπ-)
mode with the χ2/NDF of 74.4/68 (92.3/68).
In the Dalitz model fit, we obtained the complex scatteringinteraction to be a=0.48 ±length (a+ib) of the0.32(stat) ± 0.38(syst) [1.24 ± 0.57(stat) ± 1.56(syst)] fm andb=1.22±0.83(stat)±2.54(syst) [0.18±0.13(stat)±0.20(syst)]
fm with the χ2/NDF of 68.9/68 (78.1/68). The scattering lengths
derived in our data analysis are larger than the previous results[4–6]. This difference may be due to the neglected decay form
factor of an order of 0.5 fm.
The significance for the observed signals is 7.5σ (6.2σ) forthe Λπ+ (Λπ-) mode. Limited by the statistics and the shape ofthe background, we cannot distinguish between Σ∗ resonancesandthreshold cusps, since both fits give similar χ2s. On thetheoretical side, both interpretations are discussed, but the cusp
interpretation may be more favored. Oller and Meißner
discussed the possibility of a resonance in the I=1 channel andreported a pole at (1444.0 − i69.4) MeV in the second Riemannsheet [1]. However, the imaginary part is too large to explain thepresent structure. Many theories [5-7] predicted a threshold cusp

� 𝟎 𝒑 mass threshold𝑲

𝑲− 𝒏 mass threshold

Fig. 1 Λπ+ (a) and Λπ- (b) invariant mass distributions fitted with theDalitz model [3] for the signal and a background function. The solid(dotted) green, red, and blue curves represent the (breakdown)
background, signal, and total fit function, respectively.

in the I=1 channel. In addition, Ref. [1] also reported another(virtual) pole in the third Riemann sheet below the threshold,which could produce a cusp at the threshold.
References[1] J. Oller and U.-G. Meißner, Phys. Lett. B 500, 263 (2001).
[2] S. Kurokawa and E. Kikutani, and other papers included inthis volume Nucl. Instrum. Methods Phys. Res., Sect. A 499,1 (2003); T. Abe et al., Prog. Theor. Exp. Phys. 2013,03A001 (2013); and references therein.
[3] R. H. Dalitz and A. Deloff, Czech. J. Phys. B 32, 1021
(1982).
[4] B. Borasoy, U. G. Meissner, and R. Nissler, Phys. Rev. C 74,055201 (2006).
[5] Y. Ikeda et al., Nucl. Phys. A881, 98 (2012).
[6] J. Yamagata-Sekihara et al., Prog. Theor. Exp. Phys. 2013,043D02 (2013).
[7] Y. Kamiya et al., Nucl. Phys. A954, 41 (2016).
1 For the notation of hadrons, please refer to textbooks orParticle Data Group webpage (https://pdg.lbl.gov/).