No Arabic abstract
In the present work, we investigate the hidden-strangeness production process in the $S=+1$ channel via $K^+pto K^+phi,p$, focussing on the exotic textit{pentaquark} molecular $K^*Sigma$ bound state, assigned by $P^+_s(2071,3/2^-)$. For this purpose, we employ the effective Lagrangian approach in the tree-level Born approximation. Using the experimental and theoretical inputs for the exotic state and for the ground-state hadron interactions, the numerical results show a small but obvious peak structure from $P^+_s$ with the signal-to-background ratio $approx1.7,%$, and it is enhanced in the backward-scattering region of the outgoing $K^+$ in the center-of-mass frame. We also find that the contribution from the $K^*(1680,1^-)$ meson plays an important role to reproduce the data. The proton-spin polarizations are taken into account to find a way to reduce the background. The effects of the possible $27$-plet pentaquark $Theta^{++}_{27}$ is discussed as well.
In this talk, we investigate $Xi(1690)^-$ production from the $K^-pto K^+K^-Lambda$ reaction wit the effective Lagrangian method and consider the $s$- and $u$-channel $Sigma/Lambda$ ground states and resonances for the $Xi$-pole contributions, in addition to the $s$-channel $Lambda$, $u$-channel nucleon pole, and $t$-channel $K^-$-exchange for the $phi$-pole contributions. The $Xi$-pole includes $Xi(1320)$, $Xi(1535)$, $Xi(1690)(J^p=1/2^-)$, and $Xi(1820)(J^p=3/2^-)$. We compute the Dalitz plot density of $(d^2sigma/dM_{K^+K^-}dM_{K^-Lambda}$ at 4.2 GeV$/c$) and the total cross sections for the $K^-pto K^+K^-Lambda$. Employing the parameters from the fit, we present the cross sections for the two-body $K^-pto K^+Xi(1690)^-$ reaction near the threshold. We also demonstrate that the Dalitz plot analysis for $p_{K^-}=1.915 sim2.065$ GeV/c makes us to explore direct information for $Xi(1690)^-$ production, which can be done by future $K^-$ beam experiments.
We study the $bar K p to Y Kbar K pi$ reactions with $bar K = bar K^0, K^-$ and $Y=Sigma^0, Sigma^+, Lambda$, in the region of $Kbar K pi$ invariant masses of $1200-1550$ MeV. The strong coupling of the $f_1(1285)$ resonance to $K^* bar K$ makes the mechanism based on $K^*$ exchange very efficient to produce this resonance observed in the $Kbar K pi$ invariant mass distribution. In addition, in all the reactions one observes an associated peak at $1420$ MeV which comes from the $K^* bar K$ decay mode of the $f_1(1285)$ when the $K^*$ is placed off shell at higher invariant masses. We claim this to be the reason for the peak of the $K^* bar K$ distribution seen in the experiments which has been associated to the $f_1(1420)$ resonance.
We investigate $S=-2$ production from the $Lambda pto K^+X$ reactions within the effective Lagrangian approach. The $Lambda pto K^+LambdaLambda$ and $Lambda pto K^+Xi^-p$ reactions are considered to find the lightest $S=-2$ system, which is $H$-dibaryon. We assume that the $H(2250)toLambdaLambda$, and $H(2270)toXi^-p$ decays with the intrinsic decay width of 1 MeV. According to our calculations, the total cross-sections for $Lambda pto K^+LambdaLambda$ and $Lambda pto K^+Xi^-p$ reactions were found to be of the order of a few $mu$b in the $Lambda$ beam momentum range of up to 5 GeV$/c$. Furthermore, the direct access of information regarding the interference patterns between the $H$-dibaryon and non-resonant contributions was demonstrated.
We show that for some $kle 3570$ and all $k$ with $442720643463713815200|k$, the equation $phi(n)=phi(n+k)$ has infinitely many solutions $n$, where $phi$ is Eulers totient function. We also show that for a positive proportion of all $k$, the equation $sigma(n)=sigma(n+k)$ has infinitely many solutions $n$. The proofs rely on recent progress on the prime $k$-tuples conjecture by Zhang, Maynard, Tao and PolyMath.
We perform a theoretical study of the $chi_{cJ} to phi K^* bar K to phi Kpi bar K$ reaction taking into account the $K^* bar K$ final state interaction, which in the chiral unitary approach is responsible, together with its coupled channels, for the formation of the low lying axial vector mesons, in this case the $h_1(1380)$ given the selection of quantum numbers. Based on this picture we can easily explain why in the $chi_{c0}$ decay the $h_1(1380)$ resonance is not produced, and, in the case of $chi_{c1}$ and $chi_{c2}$ decay, why a dip in the $K^+ pi^0 K^-$ mass distribution appears in the 1550-1600 MeV region, that in our picture comes from a destructive interference between the tree level mechanism and the rescattering that generates the $h_1(1380)$ state. Such a dip is not reproduced in pictures where the nominal $h_1(1380)$ signal is added incoherently to a background, which provides support to the picture where the resonance appears from rescattering of vector-pseudoscalar components.