Meson scattering and tetraquarks in two-dimensional QCD
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866918143971033088 |
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| author | Sazdjian, Hagop |
| author_facet | Sazdjian, Hagop |
| contents | Two-quark--two-antiquark systems with four different quark flavors are considered in the framework of two-dimensional QCD, in the light-cone gauge, at leading orders of the $1/N_c^{}$ expansion. Introducing basis functions with color-singlet mesonic clusters, integral equations are established for the Green's functions and the related scattering amplitudes involved in the sectors of the direct and quark-exchange channels. The problem of infrared divergences is dealt with via a systematic use of an infrared regulator cutoff introduced in the gluon propagator. It is shown that the on-mass shell scattering amplitudes are free of infrared divergences up to order $1/N_c^2$. In the limit of vanishing of the infrared cutoff, they can be represented by effective four-meson contact-type interaction terms with unitarity loops, calculable in terms of the meson wave functions and propagators. The results, obtained at order $1/N_c^2$, are summed with the constraint of unitarization. The unitarized scattering amplitudes are continued in the total mass-squared variable below the two-meson thresholds, leading to a tetraquark bound state equation, which generally has one solution. Spectroscopic applications of the above results are sketched and discussed. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_19809 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Meson scattering and tetraquarks in two-dimensional QCD Sazdjian, Hagop High Energy Physics - Phenomenology Two-quark--two-antiquark systems with four different quark flavors are considered in the framework of two-dimensional QCD, in the light-cone gauge, at leading orders of the $1/N_c^{}$ expansion. Introducing basis functions with color-singlet mesonic clusters, integral equations are established for the Green's functions and the related scattering amplitudes involved in the sectors of the direct and quark-exchange channels. The problem of infrared divergences is dealt with via a systematic use of an infrared regulator cutoff introduced in the gluon propagator. It is shown that the on-mass shell scattering amplitudes are free of infrared divergences up to order $1/N_c^2$. In the limit of vanishing of the infrared cutoff, they can be represented by effective four-meson contact-type interaction terms with unitarity loops, calculable in terms of the meson wave functions and propagators. The results, obtained at order $1/N_c^2$, are summed with the constraint of unitarization. The unitarized scattering amplitudes are continued in the total mass-squared variable below the two-meson thresholds, leading to a tetraquark bound state equation, which generally has one solution. Spectroscopic applications of the above results are sketched and discussed. |
| title | Meson scattering and tetraquarks in two-dimensional QCD |
| topic | High Energy Physics - Phenomenology |
| url | https://arxiv.org/abs/2504.19809 |