Transverse densities of the energy-momentum tensor and the gravitational form factors the pion
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arXiv
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| Natura: | Preprint |
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2024
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| author | Broniowski, Wojciech Arriola, Enrique Ruiz |
| author_facet | Broniowski, Wojciech Arriola, Enrique Ruiz |
| contents | We present general features of the transverse densities of the stress-energy-momentum tensor $Θ^{μν}$ in the pion. We show positivity of the transverse density of $Θ^{++}$ (analogous to the positivity of the transverse density of the electromagnetic current $J^+$) and discuss its consequences in conjunction with analyticity and quark-hadron duality, as well as the connection to $ππ$ scattering at low energies. Our analysis takes into account the perturbative QCD effects, dominating at high momenta (or low transverse coordinate $b$), the effects of Chiral Perturbation Theory, dominating at low momenta (high $b$), and meson dominance in the intermediate region. We incorporate constraints form analyticity, leading to sum rules for the spectral densities of the corresponding form factors, which {\em i.a.} are relevant for the high-momentum (or the low-$b$) asymptotics. With the obtained high- and low-$b$ behavior, we deduce that the scalar (trace-anomaly) gravitational transverse density $Θ^μ_μ(b)$ must change sign, unlike the case of the positive definite $J^+(b)$ or $Θ^{++}(b)$. We also discuss the transverse pressure in the pion, which is positive and singular at low $b$, and negative at high $b$, in harmony with the stability criterion. The results for the form factors for space-like momenta are compared to the recent lattice QCD data. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_00848 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Transverse densities of the energy-momentum tensor and the gravitational form factors the pion Broniowski, Wojciech Arriola, Enrique Ruiz High Energy Physics - Phenomenology High Energy Physics - Lattice We present general features of the transverse densities of the stress-energy-momentum tensor $Θ^{μν}$ in the pion. We show positivity of the transverse density of $Θ^{++}$ (analogous to the positivity of the transverse density of the electromagnetic current $J^+$) and discuss its consequences in conjunction with analyticity and quark-hadron duality, as well as the connection to $ππ$ scattering at low energies. Our analysis takes into account the perturbative QCD effects, dominating at high momenta (or low transverse coordinate $b$), the effects of Chiral Perturbation Theory, dominating at low momenta (high $b$), and meson dominance in the intermediate region. We incorporate constraints form analyticity, leading to sum rules for the spectral densities of the corresponding form factors, which {\em i.a.} are relevant for the high-momentum (or the low-$b$) asymptotics. With the obtained high- and low-$b$ behavior, we deduce that the scalar (trace-anomaly) gravitational transverse density $Θ^μ_μ(b)$ must change sign, unlike the case of the positive definite $J^+(b)$ or $Θ^{++}(b)$. We also discuss the transverse pressure in the pion, which is positive and singular at low $b$, and negative at high $b$, in harmony with the stability criterion. The results for the form factors for space-like momenta are compared to the recent lattice QCD data. |
| title | Transverse densities of the energy-momentum tensor and the gravitational form factors the pion |
| topic | High Energy Physics - Phenomenology High Energy Physics - Lattice |
| url | https://arxiv.org/abs/2412.00848 |