dorsal/arxiv
View Schema$\pi\pi$ scattering in the $\rho$-meson channel at finite temperature
| Authors | Y. B. He, J. Hüfner, S. P. Klevansky, P. Rehberg |
|---|---|
| Categories | |
| ArXiv ID | nucl-th/9712051 |
| URL | https://arxiv.org/abs/nucl-th/9712051 |
| DOI | 10.1016/S0375-9474(98)00807-0 |
| Journal | Nucl.Phys. A630 (1998) 719-742 |
Abstract
We study $\pi\pi$ scattering in the I=1, $J^P=1^-$ channel at finite temperature in the framework of the extended Nambu-Jona-Lasinio model that explicitly includes vector and axial-vector degrees of freedom in addition to the usual scalar and pseudoscalar sector. The S-matrix in the coupled channels $q\bar q$ and $\pi \pi$ is constructed via $\rho$-exchange in the $s$-channel. The self-energy of the $\rho$-meson contains both quark and pion loop contributions. The analytic structure of the S-matrix for $T\geq 0$ is investigated and the motion of the $\rho$-pole as a function of coupling constant and temperature is followed in the complex $\sqrt{s}$-plane. For numerical calculations, parameters are chosen in order that $m_\pi$, $f_\pi$ and the experimental $\pi\pi$ phase shifts $\delta_1^1$ at zero temperature are reproduced, and then the behavior of the $\rho$-pole as well as the $\pi\pi$ cross section is investigated as a function of the temperature. We find that the position of the $\rho$ mass stays practically constant for $0\leq T\leq 130$ MeV, and then moves down in energy by about 200 MeV for 130 MeV$\leq T\leq 230$ MeV.
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"abstract": "We study $\\pi\\pi$ scattering in the I=1, $J^P=1^-$ channel at finite\ntemperature in the framework of the extended Nambu-Jona-Lasinio model that\nexplicitly includes vector and axial-vector degrees of freedom in addition to\nthe usual scalar and pseudoscalar sector. The S-matrix in the coupled channels\n$q\\bar q$ and $\\pi \\pi$ is constructed via $\\rho$-exchange in the $s$-channel.\nThe self-energy of the $\\rho$-meson contains both quark and pion loop\ncontributions. The analytic structure of the S-matrix for $T\\geq 0$ is\ninvestigated and the motion of the $\\rho$-pole as a function of coupling\nconstant and temperature is followed in the complex $\\sqrt{s}$-plane. For\nnumerical calculations, parameters are chosen in order that $m_\\pi$, $f_\\pi$\nand the experimental $\\pi\\pi$ phase shifts $\\delta_1^1$ at zero temperature are\nreproduced, and then the behavior of the $\\rho$-pole as well as the $\\pi\\pi$\ncross section is investigated as a function of the temperature. We find that\nthe position of the $\\rho$ mass stays practically constant for $0\\leq T\\leq\n130$ MeV, and then moves down in energy by about 200 MeV for 130 MeV$\\leq T\\leq\n230$ MeV.",
"arxiv_id": "nucl-th/9712051",
"authors": [
"Y. B. He",
"J. H\u00fcfner",
"S. P. Klevansky",
"P. Rehberg"
],
"categories": [
"nucl-th",
"hep-ph"
],
"doi": "10.1016/S0375-9474(98)00807-0",
"journal_ref": "Nucl.Phys. A630 (1998) 719-742",
"title": "$\\pi\\pi$ scattering in the $\\rho$-meson channel at finite temperature",
"url": "https://arxiv.org/abs/nucl-th/9712051"
},
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