Faddeev calculation of pentaquark Θ+\Theta^+ in the Nambu-Jona-Lasinio model-based diquark picture

A Bethe-Salpeter-Faddeev (BSF) calculation is performed for the pentaquark $\Theta^+$ in the diquark picture of Jaffe and Wilczek in which $\Theta^+$ is a diquark-diquark-${\bar s}$ three-body system. Nambu-Jona-Lasinio (NJL) model is used to calculate the lowest order diagrams in the two-body scatterings of ${\bar s}D$ and $D D$. With the use of coupling constants determined from the meson sector, we find that ${\bar s}D$ interaction is attractive in s-wave while $DD$ interaction is repulsive in p-wave. With only the lowest three-body channel considered, we do not find a bound $\frac 12^+$ pentaquark state. Instead, a bound pentaquark $\Theta^+$ with $\frac 12^-$ is obtained with a unphysically strong vector mesonic coupling constants.Comment: 22 pages, 11 figures, accepted version in Phys. Rev. C. Summary of main changes/corrections: 1. "which only holds at tree level" below the eq. (23) is added. 2. In the last paragraph of p.23 we added a remark that the coupling constant obtained from Lambda mass is different from the estimate as obtained from the meson spectru

A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram

An important concern in the application of gamma-ray bursts (GRBs) to cosmology is that the calibration of GRB luminosity/energy relations depends on the cosmological model, due to the lack of a sufficient low-redshift GRB sample. In this paper, we present a new method to calibrate GRB relations in a cosmology-independent way. Since objects at the same redshift should have the same luminosity distance and since the distance moduli of Type Ia supernovae (SNe Ia) obtained directly from observations are completely cosmology independent, we obtain the distance modulus of a GRB at a given redshift by interpolating from the Hubble diagram of SNe Ia. Then we calibrate seven GRB relations without assuming a particular cosmological model and construct a GRB Hubble diagram to constrain cosmological parameters. From the 42 GRBs at $1.4<z\le6.6$, we obtain $\Omega_{\rm M}=0.25_{-0.05}^{+0.04}$, $\Omega_{\Lambda}=0.75_{-0.04}^{+0.05}$ for the flat $\Lambda$CDM model, and for the dark energy model with a constant equation of state $w_0=-1.05_{-0.40}^{+0.27}$, which is consistent with the concordance model in a 1-$\sigma$ confidence region.Comment: 7 pages, 3 figures, 1 table, now matches the editorially revised version; accepted for publication in ApJ (vol 685)