New Elementary Operator for Kaon Photoproduction on the Nucleon and Nuclei

TL;DR

The paper develops a comprehensive elementary operator for kaon photoproduction on the nucleon and nuclei within a Feynman-diagrammatic framework, fitting electromagnetic and hadronic couplings across the six isospin channels. It includes $K\Lambda$-channel nucleon resonances and $K\Sigma$-channel $\Delta$ resonances, and reforms the operator in Pauli space with multiple frame-independent representations to facilitate nuclear applications and nonrelativistic approximations. The formalism restores gauge invariance and employs a consistent interaction for high-spin states, yielding improved agreement with extensive experimental data compared to Kaon-Maid, and providing reliable outputs up to several GeV in $W$ depending on the channel. The operator is designed for integration into various nuclear frameworks (impulse approximation, covariant, few-body) and is complemented by a clear path to extend to electroproduction in future work, underscoring its practical impact for hypernuclear physics and related nuclear reactions.

Abstract

A new elementary operator for kaon photoproduction on the nucleon and nuclei has been developed within a Feynman diagrammatic framework. By fitting the unknown coupling strengths at the electromagnetic and hadronic vertices of the baryon resonances to all available experimental data across the six isospin channels, the model achieves excellent agreement with the data. The operator includes 26 nucleon resonances in the $KΛ$ channels and 17 additional $Δ$ resonances in the $KΣ$ channels. For applications to nuclear reactions, such as hypernuclear photoproduction, the operator is formulated in Pauli space, allowing a straightforward implementation of the nonrelativistic approximation. Several alternative forms for expressing the operator output are proposed. In one of them, the spin operators and photon polarization vectors are separated from the operator, since both are frame dependent, thereby enhancing its versatility in nuclear applications.

Figures (9)

• Figure 1: Feynman diagrams for kaon photoproduction on the nucleon, showing the contributions from (a) $s$-channel intermediate nucleon and nucleon-resonance states, (b) $u$-channel intermediate hyperon and hyperon-resonance states, and (c) $t$-channel intermediate kaon and kaon-resonance states.
• Figure 2: Differential cross section for the $\gamma p \to K^+ \Lambda$ reaction as a function of the c.m. energy for three different kaon angles. The solid and dashed curves correspond to Model A and Model B of Ref. Luthfiyah:2021yqe, respectively, while the dotted curves represent the results of Kaon-Maid Mart:1999edBennhold:1999mt, which is valid only up to $W=2.2$ GeV. Experimental data are taken from the Crystal Ball 2014 (open circles) CrystalBallatMAMI:2013iig, CLAS 2010 (solid circles) CLAS:2009rdi, CLAS 2006 (open squares) CLAS:2005lui, and LEPS 2006 (solid triangles) LEPS:2005hji.
• Figure 3: Same as Fig. \ref{['fig:dif_kpl']}, but for the $\gamma n \to K^0 \Lambda$ reaction. Experimental data are taken from the CLAS g10 and g13 Collaborations (open circles and open squares, respectively) CLAS:2017gsu, and from the MAMI 2018 Collaboration (solid circles) A2:2018doh. Note that the Kaon-Maid prediction has been multiplied by a factor of 0.5 to fit the scale.
• Figure 4: Differential cross section for for the $\gamma p \to K^+ \Sigma^0$ channel as a function of the c.m. energy for three different kaon angles. The solid and dashed curves correspond to Model C and Model D of Ref. Luthfiyah:2021yqe, respectively, while the dotted curves represent the results of Kaon-Maid Mart:2000jv. Experimental data are taken from the CLAS 2006 (solid diamonds) CLAS:2005lui, CLAS 2010 (solid circles) CLAS:2010aen, and Crystal Ball 2014 (open circles) CrystalBallatMAMI:2013iig Collaborations.
• Figure 5: As in Fig. \ref{['fig:dif_kps0']}, but for the $\gamma+p\to K^0+\Sigma^+$ channel. Experimental data are taken from the SAPHIR 2005 (open circles) Lawall:2005np, CBELSA 2008 (solid circles) CBELSATAPS:2007oqn, MAMI A2 2013 (solid squares) A2:2013cqk, MAMI A2 2019 (open squares) A2:2018doh.