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We analyse the width of the $theta(frac12^+)$ pentaquark assuming that it is a bound state of two extended spin-zero $ud$-diquarks and the $bar s$ antiquark (the Jaffe-Wilczek scenario). The width obtained when the size parameters of the pentaquark wave function are taken to be close to the parameters of the nucleon is found to be $simeq 150$ MeV, i.e. it has a normal value for a $P$-wave hadron decay with the corresponding energy release.However, we found a strong dynamical suppression of the decay width if the pentaquark has an asymmetric peanut structure with the strange antiquark in the center and the two diquarks rotating around. In this case a decay width of $simeq$ 1 MeV is a natural possibility.
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If Jaffe and Wilczeks diquark picture for $Theta_5$ pentaquark is correct, there should also exist a $SU_F$(3) pentaquark octet and singlet with no orbital excitation between the diquark pair, hence $J^P={1/2}^-$. These states are lighter than the $Theta_5$ anti-decuplet and lie close to the orbitally excited (L=1) three-quark states in the conventional quark model. We calculate their masses and magnetic moments and discuss their possible strong decays using the chiral Lagrangian formalism. Among them two pentaquarks with nucleon quantum numbers may be narrow. Selection rules of strong decays are derived. We propose the experimental search of these nine additional $J^P={1/2}^-$ baryon states. Especially there are two additional $J^P={1/2}^-$ $Lambda$ baryons around $Lambda (1405)$. We also discuss the interesting possibility of interpreting $Lambda (1405)$ as a pentaquark. The presence of these additional states will provide strong support of the diquark picture for the pentaquarks. If future experimental searches fail, one has to re-evaluate the relevance of this picture for the pentaquarks.
$QQ^prime qqbar q$ pentaquarks are studied in a potential model, under the hypothesis that they are composite objects of two diquarks and one antiquark. The interaction between two colored objects includes two contributions, one based on the $qbar q$ potential in QCD, computed in the gauge/string duality approach, and another describing the spin-spin interaction. The model has been extended to investigate pentaquarks with different quark content, as $Qqqqbar q$ and $Qqqqbar Q$, the latter including the states observed by LHCb, $P_c(4380)^+$ and $P_c(4450)^+$, later updated, with a new data sample, to $P_c(4312)^+$, $P_c(4440)^+$, and $P_c(4457)^+$.
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.
Within the Quark-Gluon String Model A.B. Kaidalov found a behaviour of quark and diquark fragmentation functions for $zrightarrow 0$ and $zrightarrow 1$, and proposed interpolation formulae for the functions in the whole region of $z$. These functions must be a solution of the well-known system of the integral equations. A simplified Monte Carlo estimation of the functions, based on usage of the fragmentation functions at $zrightarrow 1$ as the kernel functions of the system, does not reproduce Kaidalovs results. An improvement of the Monte Carlo simulations is proposed in this paper. It can be implemented in Monte Carlo event generators such as Los Alamos QGSM, QGSJet-II and the Geant4 QGS model. It will improve a description of experimental data in the models, especially, the description of the latest NA61/SHINE Collaboration data on $pi{rm C}$ interactions. Description of the data is a problem in DPMJet, QGSJet, EPOS and Sibyll models.
We study the photoproduction of the $Lambda(1405)$ and $Sigma(1400)$ hyperon resonances, the latter of which is not a well established state. We evaluate the $s$-, $t$- and $u$-channel diagrams in the Born approximation by employing the effective Lagrangians. A new ingredient is the inclusion of a nucleon resonance $N^*(1895)$ that is dynamically generated with predictions for its coupling to the $KLambda(1405)$ and $KSigma(1400)$ channels. To extend the applicability of the model to energies beyond the threshold region, we consider a Regge model for the $t$-channel $K$- and $K^*$-exchanges. Our results are in good agreement with the CLAS data available on $Lambda(1405)$, while for $Sigma(1400)$ we predict observables for its production. We also provide polarization observables for both hyperon productions, which can be useful in future experimental investigations. The present study provides new information on the nucleon resonance $N^*(1895)$ which can be an alternative source for generating the hyperon resonances $Lambda(1405)$ and $Sigma(1400)$.
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