Another look at<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>π</mml:mi><mml:mi>π</mml:mi></mml:math>scattering in the scalar channel

Igi, Keiji; Hikasa, K.

doi:10.1103/physrevd.59.034005

Cited by 68 publications

(54 citation statements)

References 48 publications

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“…The σ meson is a broad scalar resonance with strong coupling to I = 0 ππ S-wave scattering states. Its mass is not definite but around 400∼600 MeV [40][41][42]. We choose two limit cases, m σ = 400 MeV and 600 MeV.…”

Section: The S Wave Dd Systemmentioning

confidence: 99%

DD¯production and their interactions

Liu¹,

Oka²,

Takizawa³

et al. 2010

Phys. Rev. D

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S-and P-wave DD scatterings are studied in a meson exchange model with the coupling constants obtained in the heavy quark effective theory. With the extracted P-wave phase shifts and the separable potential approximation, we include the DD rescattering effect and investigate the production process e + e − → DD. We find that it is difficult to explain the anomalous line shape observed by the BES Collaboration with this mechanism. Combining our model calculation and the experimental measurement, we estimate the upper limit of the nearly universal cutoff parameter to be around 2 GeV. With this number, the upper limits of the binding energies of the S-wave DD and BB bound states are obtained. Assuming that the S-wave and P-wave interactions rely on the same cutoff, our study provides a way of extracting the information about S-wave molecular bound states from the P-wave meson pair production.

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Section: The S Wave Dd Systemmentioning

confidence: 99%

DD¯production and their interactions

Liu¹,

Oka²,

Takizawa³

et al. 2010

Phys. Rev. D

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“…At the same time, this condition guarantees that the present amplitude with schannel unitarity coincides with the crossed amplitude with u-channel unitarity at √ s = M T . This prescription was first introduced in the π-π scattering [31], and was applied to the meson-baryon scattering in Ref. [11].…”

Section: B Unitarization and Regularizationmentioning

confidence: 99%

Study of exotic hadrons inS-wave scatterings induced by chiral interaction in the flavor symmetric limit

Hyodo

Jido

Hosaka³

2007

Phys. Rev. D

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We study s-wave bound states of a hadron and a light pseudoscalar meson induced by the Weinberg-Tomozawa (WT) interaction in the flavor SU(3) symmetric limit. The WT interaction is a driving force to generate quasibound states dynamically in the chiral unitary approaches. The strength and sign of the WT interaction are determined only by the group theoretical structure of the target hadrons, and we present a general expression of the strengths for the flavor SU(3) case. We show that, for the channels which are more exotic than the target, the interaction is repulsive in most cases, and the strength of the attractive interaction is universal for any possible target states. We demonstrate that the attractive coupling is not strong enough to generate an exotic state from the physically known masses of target hadrons. In addition, we also find a nontrivial Nc dependence of the coupling strengths. We show that the channels which are attractive at Nc = 3 changes into repulsive ones for large Nc, and, therefore, no attractive interaction exists in exotic channels in the large-Nc limit.

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“…It should be emphasized that for obtaining this result, it is essential to respect chiral symmetry, analyticity and crossing symmetry even in an approximate way as in the N/D method [12].…”

Section: The Sigma Meson and The Soft Modesmentioning

confidence: 99%

Chiral transition and the scalar and vector correlations

Kunihiro¹

2001

AIP Conference Proceedings

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The properties of the scalar and vector correlations in the hot and/or dense hadronic matter close to chiral transition are discussed. Presuming that the linear realization of chiral symmetry will become appropriate at least near the critical point, we argue that the strength function in the I = J = 0 channel will soften near the critical point, and the sigma meson will accordingly become a clearer resonance in hot and/or dense medium than in the free space. It is shown that the steep rise of the baryon-number susceptibility χB around the critical point seen in the lattice simulations may suggest that the interactions between quarks in the vector channel become week near the critical point; this implies that the peculiar behavior of the χB does not necessarily imply a proliferation of baryons and antibaryons (Skyrmions) which is though a natural scenario of chiral transition in the non-linear realization of chiral symmetry. The sigma meson and the soft modesChiral transition is a phase transition of the QCD vacuum with qq being the order parameter. When exploring a phase transition in any physical system, the study of fluctuations of physical quantities, especially ones related to the order parameter is as important as that of the phase diagram for the system in equilibrium. The fluctuations of observables are also related with dynamical phenomena such as the transport properties of the system. If a phase transition is of 2nd order or weak 1st order, there exist soft modes, which are the fluctuations of the order parameter as is well known in condensed matter physics[1] and nuclear physics [2]. For the chiral transition, the fluctuation of the order parameter (qq) 2 is a scalar-isoscalar meson which one calls the σ-meson. The σ meson may become the soft mode of chiral transition at T = 0 and/or ρ B = 0 [3,4]. In fact, the existence of the sigma meson as the quantum fluctuation of the order parameter of the chiral transition is still controversial [5], though the recent active studies on the phase-shift analysis of the π-π scattering in the I = J = 0 channel, i.e., the sigma channel, have been confirming the existence of the pole deep in the second Riemann sheet with the real part ranging from 400 MeV to 800 MeV [6,7]. If this pole is identified with the quantum fluctuation of the amplitude of the chiral condensate, it may imply that the linear realization of chiral symmetry is appropriate in the resonance energy region, although the chiral perturbation theory based on the non-linear chiral Lagrangians [8] works well in the rather low-energy region.The first half of this report is concerned with the sigma meson and the precursory soft modes for chiral transition in nuclear medium, and is essentially a recapitulation of the talk presented at Tohoku university, a week before of the present workshop; the manuscript for the proceedings is now on the net [9]. Referring to the above proceedings for the detail of the content, here I only give a brief summary of the report and some comments:(1) The existence of t...

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Another look atππscattering in the scalar channel

Cited by 68 publications

References 48 publications

DD¯production and their interactions

DD¯production and their interactions

Study of exotic hadrons inS-wave scatterings induced by chiral interaction in the flavor symmetric limit

Chiral transition and the scalar and vector correlations

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