RIKEN Accel. Prog. Rep. 48 (2015)

Ⅱ-5. Hadron Physics (Theory)

Theoretical analysis of Λ(1405) → (Σπ)0 mass spectra
produced in p + p → p + Λ(1405) + K + reactions
M. Hassanvand,∗1,∗2 S. Z. Kalantari,∗2 Y. Akaishi,∗1,∗3 and T. Yamazaki ∗1,∗40.12(b)(d)

0.08(a)(c)Σ+π- + Σ-π+

0.06

20.04

M=1405 MeV/c

2dσ/dM [µbb/(MeV/c )]0.10

p+Λ∗ +K + reactions, in which both the incident channel for a quasi-bound K − p state and its decay processto (Σπ)0 were taken into account realistically1) . We
calculated M (Σπ) spectral shapes for various theoretical models for Λ∗ . They are asymmetric and skewed,and were compared with recent experimental data ofHADES2) . The nearly isotropic proton distribution
observed in DISTO3) and HADES is ascribed to a shortcollision length in the production of Λ∗ , which justiﬁes
the high sticking mechanism of Λ∗ and the participating proton into K − pp4) .
In the present work we formulate the spectral shapeof the (Σπ)0 mass to provide theoretical guides to analyze experimental data of (Σπ)0 mass spectra fromthe above reaction. We take into account both the formation and the decay processes of Λ∗ in pp reactions
realistically, following our K̄N − Σπ coupled-channel
formalism5) . In this way, we derive the general formof the spectral function, which is not symmetric, butskewed with respect to the pole position. Then, we analyzed (Σ+− π −+ )0 spectra from HADES at Tp = 3.50
2GeV2) , and obtained: M (Λ∗ ) = 1405+11−9 MeV/c andΓ = 62 ± 10 MeV, where the interference eﬀects of theK̄N -Σπ resonance with I= 0 and 1 Σπ continuum areconsidered. Whereas the HADES spectrum shows avery broad peak centered around 1385 MeV/c2 , significantly lower lying than 1405 MeV/c2 , we have clariﬁedthat it is due to kinematical distortion. The present result on M and Γ is in good agreement with the PDG12and PDG14 values6) . The Hyodo-Weise (HW) spectra7) , shown as the curves (c) and (d) in the ﬁgure, do
not account for the experimental spectrum.

HKAY (1405), χ2 =9PDG (1405.1), χ2=14HW, T 21 , χ2 = 111
HW, T22 , χ2 = 39

0.02
0.00-0.02
13001350

14001450+21500

MM(pK ) [MeV/c ]

PDG

PDG

Fig. 1. (Color online) (Upper) Comparison of HADES data
(Σ+ π − + Σ− π + , closed squares) at Tp = 3.50 GeV?)
with best-ﬁt theoretical spectral functions S(x). a)
Best-ﬁt HKAY curves (with χ2 = 9.5, M = 1405+11−9
MeV/c2 and Γ = 62 ± 10 MeV). b) AY model with
the PDG parameters (with χ2 = 14, M = 1405.1+1.3−1.0
MeV/c2 and Γ = 50 MeV6) ). The Chiral model using
HW’s T21 (with χ2 = 111, c)) and T22 (with χ2 = 40,d)). (Lower) Conﬁdence level contours from χ2 ﬁttingof the HADES data of Σ+ π − +Σ− π + at Tp = 3.50 GeV.
The PDG12 values are also shown.

We formulated the Λ(1405) (abbreviated as Λ∗ )→ (Σπ)0 invariant-mass spectra produced in p + p →∗1∗2∗3∗4RIKEN Nishina Center
Department of Physics, Isfahan University of Technology
College of Science and Technology, Nihon University
Department of Physics, University of Tokyo

References
1) M. Hassanvand, S.Z. Kalantari, Y. Akaishi and T. Yamazaki, Phys. Rev. C 87, 055202 (2013); Phys. Rev. C88, 019905(E) (2013).
2) G. Agakishiev et al. (HADES collaboration), Phys. Rev.
C 87, 025201 (2013).
3) T. Yamazaki et al., Phys. Rev. Lett. 104 (2010) 132502;
P. Kienle et al., Eur. Phys. J. A 48 (2012) 183.
4) T. Yamazaki and Y. Akaishi, Phys. Rev. C 76 (2007)
045201.
5) Y. Akaishi, Khin Swe Myint and T. Yamazaki, Proc.
Jpn. Acad. B 84, (2008) 264.
6) Particle Data Group 2012, J. Beringer et al., Phys. Rev.
D 86 (2012) 010001; Particle Data Group 2014, K.A.
Olive et al., Chin. Phys. C 38, 090001 (2014).
7) T. Hyodo and W. Weise, Phys. Rev. C 77, 035204(2008).

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