Topological transition in a parallel electromagnetic field
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866914792283832320 |
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| author | Cao, Gaoqing |
| author_facet | Cao, Gaoqing |
| contents | In this work, we attack the problem of "chiral phase instability" ($χ$PI) in a quantum chromodynamics (QCD) system under a parallel and constant electromagnetic field. The $χ$PI refers to that: When $I_2\equiv{\bf E\cdot B}$ is larger than the threshold $I_2^c$, no homogeneous solution can be found for $σ$ or $π^0$ condensate, and the chiral phase (or angle) $θ$ becomes unstable. Within the two-flavor chiral perturbation theory, we obtain an effective Lagrangian density for $θ(x)$ where the chiral anomalous Wess-Zumino-Witten term is found to play a role of "source" to the "potential field" $θ(x)$. The Euler-Lagrangian equation is applied to derive the equation of motion for $θ(x)$, and physical solutions are worked out for several shapes of system. In the case $I_2>I_2^c$, it is found that the $χ$PI actually implies an inhomogeneous QCD phase with $θ(x)$ spatially dependent. By its very nature, the homogeneous-inhomogeneous phase transition is of pure topological and second order at $I_2^c$. Finally, the work is extended to the three-flavor case, where an inhomogeneous $η$ condensation is also found to be developed for $I_2>I_2^c$. Correspondingly, there is a second critical point, $I_2^{c'}=24.3I_2^c$, across which the transition is also of topological and second order by its very nature. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2308_16448 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Topological transition in a parallel electromagnetic field Cao, Gaoqing Nuclear Theory Materials Science High Energy Physics - Theory In this work, we attack the problem of "chiral phase instability" ($χ$PI) in a quantum chromodynamics (QCD) system under a parallel and constant electromagnetic field. The $χ$PI refers to that: When $I_2\equiv{\bf E\cdot B}$ is larger than the threshold $I_2^c$, no homogeneous solution can be found for $σ$ or $π^0$ condensate, and the chiral phase (or angle) $θ$ becomes unstable. Within the two-flavor chiral perturbation theory, we obtain an effective Lagrangian density for $θ(x)$ where the chiral anomalous Wess-Zumino-Witten term is found to play a role of "source" to the "potential field" $θ(x)$. The Euler-Lagrangian equation is applied to derive the equation of motion for $θ(x)$, and physical solutions are worked out for several shapes of system. In the case $I_2>I_2^c$, it is found that the $χ$PI actually implies an inhomogeneous QCD phase with $θ(x)$ spatially dependent. By its very nature, the homogeneous-inhomogeneous phase transition is of pure topological and second order at $I_2^c$. Finally, the work is extended to the three-flavor case, where an inhomogeneous $η$ condensation is also found to be developed for $I_2>I_2^c$. Correspondingly, there is a second critical point, $I_2^{c'}=24.3I_2^c$, across which the transition is also of topological and second order by its very nature. |
| title | Topological transition in a parallel electromagnetic field |
| topic | Nuclear Theory Materials Science High Energy Physics - Theory |
| url | https://arxiv.org/abs/2308.16448 |