Effective degrees of freedom, trace anomaly and c-theorem like condition in the hadron resonance gas model
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866914410878992384 |
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| author | Kouno, Hiroaki Oshima, Riki Kashiwa, Kouji |
| author_facet | Kouno, Hiroaki Oshima, Riki Kashiwa, Kouji |
| contents | The relation between the effective degrees of freedom (EDOF) and the trace anomaly is studied in the hadron resonance gas (HRG) model. If we regard the thermodynamical relation as the evolution equation and define the EDOF as P/T^4, where P and T are the pressure and the temperature, respectively, we obtain the equation which relates to the trace anomaly. The structure of the equation resembles that of the so-called c-theorem, which asserts that the EDOF should not increase as the energy scale parameter decreases, in the two dimensional conformal field theory. There is a stationary point where the trace anomaly (modified trace anomaly) vanishes, and the scale symmetry is restored. To investigate the limiting temperature of the HRG model with the excluded volume effects, we consider two types of the c-theorem like conditions for the EDOF. The first condition requires that the EDOF should not decrease when T increases. This condition is equivalent to the condition that the trace anomaly (modified trace anomaly) should not be negative. The second condition requires that the EDOF should be convex downwards as a function of T. It is found that the first condition gives the limiting temperature of the HRG model with the excluded volume effect which is much higher than the crossover transition temperature obtained by the lattice QCD calculation and, at zero baryon number density, is close to the transition temperature in the pure gluonic theory, while the second one gives the limiting temperature which almost coincides with the one obtained by using the normalized baryon number fluctuation in the previous study and is consistent with the critical point predicted by the lattice QCD calculation. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2603_02085 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Effective degrees of freedom, trace anomaly and c-theorem like condition in the hadron resonance gas model Kouno, Hiroaki Oshima, Riki Kashiwa, Kouji High Energy Physics - Phenomenology High Energy Physics - Experiment High Energy Physics - Lattice Nuclear Experiment Nuclear Theory The relation between the effective degrees of freedom (EDOF) and the trace anomaly is studied in the hadron resonance gas (HRG) model. If we regard the thermodynamical relation as the evolution equation and define the EDOF as P/T^4, where P and T are the pressure and the temperature, respectively, we obtain the equation which relates to the trace anomaly. The structure of the equation resembles that of the so-called c-theorem, which asserts that the EDOF should not increase as the energy scale parameter decreases, in the two dimensional conformal field theory. There is a stationary point where the trace anomaly (modified trace anomaly) vanishes, and the scale symmetry is restored. To investigate the limiting temperature of the HRG model with the excluded volume effects, we consider two types of the c-theorem like conditions for the EDOF. The first condition requires that the EDOF should not decrease when T increases. This condition is equivalent to the condition that the trace anomaly (modified trace anomaly) should not be negative. The second condition requires that the EDOF should be convex downwards as a function of T. It is found that the first condition gives the limiting temperature of the HRG model with the excluded volume effect which is much higher than the crossover transition temperature obtained by the lattice QCD calculation and, at zero baryon number density, is close to the transition temperature in the pure gluonic theory, while the second one gives the limiting temperature which almost coincides with the one obtained by using the normalized baryon number fluctuation in the previous study and is consistent with the critical point predicted by the lattice QCD calculation. |
| title | Effective degrees of freedom, trace anomaly and c-theorem like condition in the hadron resonance gas model |
| topic | High Energy Physics - Phenomenology High Energy Physics - Experiment High Energy Physics - Lattice Nuclear Experiment Nuclear Theory |
| url | https://arxiv.org/abs/2603.02085 |