Determination of crossing-symmetric $ππ$ scattering amplitudes and the quark mass evolution of the $σ$ constrained by lattice QCD
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866929265296015360 |
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| author | Rodas, Arkaitz Dudek, Jozef J. Edwards, Robert G. |
| author_facet | Rodas, Arkaitz Dudek, Jozef J. Edwards, Robert G. |
| contents | Lattice QCD spectra can be used to constrain partial-wave scattering amplitudes that, while satisfying unitarity, do not have to respect crossing symmetry and analyticity. This becomes a particular problem when extrapolated far from real energies, e.g. in the case of broad resonances like the $σ$, leading to large systematic uncertainties in the pole position. In this manuscript, we will show how dispersion relations can implement the additional constraints, using as input lattice--determined $ππ$ partial-wave scattering amplitudes with isospin--0,1,2. We will show that only certain combinations of amplitude parameterizations satisfy all constraints, and that when we restrict to these, the $σ$ pole position is determined with minimal systematic uncertainty. The evolution of the now well-constrained $σ$ pole with varying light quark mass is presented, showing how it transitions from a bound-state to a broad resonance. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2304_03762 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Determination of crossing-symmetric $ππ$ scattering amplitudes and the quark mass evolution of the $σ$ constrained by lattice QCD Rodas, Arkaitz Dudek, Jozef J. Edwards, Robert G. High Energy Physics - Lattice High Energy Physics - Phenomenology Lattice QCD spectra can be used to constrain partial-wave scattering amplitudes that, while satisfying unitarity, do not have to respect crossing symmetry and analyticity. This becomes a particular problem when extrapolated far from real energies, e.g. in the case of broad resonances like the $σ$, leading to large systematic uncertainties in the pole position. In this manuscript, we will show how dispersion relations can implement the additional constraints, using as input lattice--determined $ππ$ partial-wave scattering amplitudes with isospin--0,1,2. We will show that only certain combinations of amplitude parameterizations satisfy all constraints, and that when we restrict to these, the $σ$ pole position is determined with minimal systematic uncertainty. The evolution of the now well-constrained $σ$ pole with varying light quark mass is presented, showing how it transitions from a bound-state to a broad resonance. |
| title | Determination of crossing-symmetric $ππ$ scattering amplitudes and the quark mass evolution of the $σ$ constrained by lattice QCD |
| topic | High Energy Physics - Lattice High Energy Physics - Phenomenology |
| url | https://arxiv.org/abs/2304.03762 |